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Essays in asset demand: dividends, institutions, and price

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Content ESSAYS IN ASSET DEMAND:
DIVIDENDS, INSTITUTIONS, AND PRICE
by
Reed Douglas
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BUSINESS ADMINISTRATION)
May 2023
Copyright (©) 2023 Reed Douglas
This work is dedicated to those who helped me most; my wife,
my parents,
Phoebe,
Jessie.
ii
I am forever indebted to my superb advisors;
Wayne Ferson and Lukas Schmid.
Thank you both.
I would also like to thank
Chris Jones, Ricardo De la O, Kenneth Ahern,
Larry Harris, Vincenzo Quadrini, and Zhao Zhang
for always lending their support.
iii
TABLE OF CONTENTS
DEDICATION................................................................... ii
ACKNOWLEDGEMENTS ....................................................... iii
LIST OF TABLES ............................................................... vi
LIST OF FIGURES.............................................................. vii
ABSTRACT..................................................................... viii
1 Who Cares About Dividends? ................................................. 1
1.1 Introduction............................................................. 1
1.2 Empirical Study ......................................................... 9
1.2.1 Identifying Elasticities............................................. 12
1.2.2 Data ............................................................. 13
1.2.3 Empirical Results ................................................. 18
1.2.4 Delays in Response to Dividend Changes ........................... 27
1.2.5 Variation in Elasticity Through Time............................... 30
1.2.6 Counterfactual Exercises........................................... 33
1.3 Dividend-Demand Model ................................................. 40
1.3.1 Firms ............................................................ 41
1.3.2 Investors ......................................................... 42
1.3.3 Intermediaries .................................................... 43
1.3.4 Equilibrium and Prices ............................................ 47
1.3.5 Data ............................................................. 48
1.3.6 Results and Performance .......................................... 49
1.3.7 Counterfactual Exercises........................................... 56
1.4 Conclusion .............................................................. 62
1.5 Appendix Tables......................................................... 65
1.5.1 2SLS Results ..................................................... 65
1.6 Appendix: Calendar-Time Analysis ....................................... 66
2 Return and Dividend Expectations in the Cross-Section of Prices................. 71
2.1 Introduction............................................................. 71
2.2 Models and Methods ..................................................... 78
2.2.1 General Panel Regression .......................................... 79
2.2.2 Cross-Sectional Regressions ........................................ 79
iv
2.2.3 Price-to-Dividend Ratio Decomposition ............................. 80
2.3 Data .................................................................... 84
2.3.1 Individual Firms .................................................. 84
2.3.2 Portfolios......................................................... 85
2.4 Empirical Results ........................................................ 87
2.4.1 In-Sample, Individual Firms ....................................... 87
2.4.2 In Sample, Portfolios .............................................. 99
2.4.3 Out-of-Sample .................................................... 101
2.4.4 Out-of-Sample, Portfolios .......................................... 112
2.5 The Campbell and Shiller Model in the Cross-Section....................... 119
2.6 Conclusion .............................................................. 119
2.7 Appendix: Variable Discussion............................................ 122
2.7.1 Characteristics and Factors ........................................ 122
REFERENCES .................................................................. 127
v
LIST OF TABLES
Table Page
1.1 AUM Percentage Breakdown by Type (Excludes Other) .................... 17
1.2 GMM Results, Aggregate, Payments and Yields............................ 19
1.3 GMM Results, Dividend Payments ........................................ 21
1.4 GMM Results, Dividend Yield with MC ................................... 24
1.5 GMM Results, Net-Payout ............................................... 26
1.6 GMM Results, Net-Payout Yield with MC ................................. 27
1.7 Coefficients on Additional Lags of Percentage Change ...................... 29
1.8 Mean Characteristics of Winners versus Losers ............................. 35
1.9 Predicting Price Changes Assuming Mutual Fund η →0 .................... 37
1.10 Predicting Price Changes Assuming Immediate Rebalancing ................ 39
1.11 Model Parameters ....................................................... 50
1.12 Model Comparisons ...................................................... 54
1.13 Total Net Payout (Modeled) .............................................. 59
1.14 Regression of P − P
cf
on Recession Indicators ............................. 61
1.15 GMM Results, Dividend Yield ............................................ 65
1.16 GMM Regression Results, Aggregate, Payments ............................ 66
1.17 Regression Results with Dividend Characteristics........................... 66
1.18 Three-Way Fixed Effects with Control for Price Volatility................... 68
2.1 Analysis of Cross-Sectional and Time-Series Variance ....................... 74
2.2 Analysis of Cross-Sectional and Time-Series Variance ....................... 88
2.3 Cross-Sectional Regressions of Price on Matched r
∗ i,t
, d
∗ i,t
, K
prev.
1
, K
prev.
2
× V .. 89
2.4 Cross-Sectional Regressions of ∆ P/D and ∆ P/E on r
∗ i,t
, d
∗ i,t
, K
prev.
1
, K
prev.
2
× V 94
2.5 Analysis of Cross-Sectional and Time-Series Variance ....................... 96
2.6 Decomposing K
prev.
1,i,t
on X
i,t
............................................... 97
2.7 Decomposing K
prev.
2,i,t
× V
prev.
on X
i,t
....................................... 98
2.8 Cross-Sectional Regressions of Price on Matched r
∗ i,t
, d
∗ i,t
, K
prev.
1
, K
prev.
2
× V .. 100
2.9 Out-of-Sample Model Comparison, One-Month Lag......................... 104
2.10 Out-of-Sample Model Comparison, One-Month Lag......................... 105
2.11 Regression of Out-of-Sample MSPE on X
i,t
................................ 109
2.12 Regression of Out-of-Sample MSPE on X
i,t
with lagged δ i
.................. 110
2.13 Out-of-Sample Model Comparison, 5x5 Portfolios .......................... 113
2.14 Regression of Out-of-Sample MSPE on X
i,t
................................ 116
2.15 Regression of Out-of-Sample MSPE on X
i,t
................................ 117
vi
LIST OF FIGURES
Figure Page
1.1 Elasticities Through Time ................................................ 31
1.2 Comparison of Dividend Demand and Adjustment Cost..................... 52
1.3 Actual Payouts vs. Modeled Frictionless Payouts ........................... 57
1.4 Calendar Time Response to Dividends..................................... 67
vii
Abstract
The asset-pricing literature has long focused on rate of returns. In fact, Cochrane (2011)
goes so far as to ask when the field of “asset pricing” became “asset expected-returning.” In
the following two chapters, I provide alternative asset pricing studies which put the price-
setting mechanism in full focus. The first study uses a Koijen and Yogo (2019) demand
system to analyze how investors demand assets as dividend policies change. The second
study uses a Campbell and Shiller (1988) decomposition to examine the cross-section of
individual stock price-ratios. Together, these studies re-evaluate classic questions in a new
light, and provide substantially different insights.
In Chapter 1, I use institutional portfolio positions to estimate dividend elasticities. I
find most financial intermediaries have a positive elasticity of demand for firm-level divi-
dends, but delayed short-term rebalancing. This delay can incentivize firm managers to keep
dividends stable and generates a 2% market-capitalization premium for sticky dividends. I
then propose an intermediary asset pricing model incorporating my empirically estimated
elasticities which matches aggregate payouts with a correlation of about 0.9; a marked im-
provement. Counterfactualsshowdividendsreflectasimpleinsurancecontractbetweenfirms
and investors that boosts payouts during recessions by 10pp, or about $14 billion in 2021,
and may explain why dividends exist at all.
In Chapter 2, I build a price-ratio model based on the Campbell and Shiller (1988)
decomposition to test which components of investor expectations best explain cross-sectional
price differences. I evaluate the in- and out-of-sample performance of my model, which uses
a higher-order expansion with an added variance term. In-sample, I find differences in price-
viii
ratios are attributable primarily to cash-flow expectations, not returns. Out-of-sample, the
Campbell and Shiller model struggles with individual firms but works well for characteristic-
sortedportfolioswhereinformationinthecross-sectioncanbeusedtogenerateout-of-sample
predictions. Finally, I decompose the model’s missed variation and find that firms with high
levels of institutional ownership or operating profitability are not well explained in this auto-
regressive framework.
Together, these studies advance our understanding of how investors allocate capital. In
particular, they highlight the importance of institutional ownership and dividend policies on
firm prices. The impact of both institutions and dividends appear long-lasting, helping us
understand persistent differences in firm valuations.
ix
Chapter 1
Who Cares About Dividends?
1.1 Introduction
“... [one company examined] had an
erratic set of dividend decisions which
reflected the capricious personality of a
dominating member of the management
far more than any other consideration.”
Lintner (1956, p. 106)
Price should equal discounted future dividends, but it is unclear which investors care
about dividends or even if they should. Instead, the existing literature appears to lack a
systematic way of measuring the elasticity of individual investors’ demand for dividends
or understanding how firms respond to those demands. On one hand, classic studies have
shown that dividend policy should be irrelevant (Miller and Modigliani, 1961), that dividend
volatilitycannotexplainpricevolatility(Shiller,1981), andthatinvestorsappeartoattribute
exceedinglylittleimportancetodividendchanges(CampbellandShiller,1988). Ontheother
hand, investors have documented preferences for dividends that appear to incentivize fund
managers to change allocations around payout dates (Baker, Nagel, and Wurgler, 2007;
1
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
Harris, Hartzmark, and Solomon, 2015; Hartzmark and Solomon, 2019, 2022), and clientele
oragencyproblemscancausevaryingdividendpreferencestoarise(BakerandWurgler,2004;
DeAngelo, DeAngelo, and Skinner, 2009). A broad understanding of investor preferences for
dividends seems likely to help us explain the demand-based incentives which exist between
investors and the firms they own.
In this paper, I use a demand-based asset pricing model to estimate market-wide elas-
ticities for dividend payments. I use the response of institutional portfolios to changes in
dividend policies to evaluate which market participants care about dividends. I find that
preferences in favor of dividend payments are more or less discernible among most investors
in my sample. This is surprising as much of the existing literature has assumed this prefer-
ence resides primarily among unsophisticated household investors. I then use these results
to discipline an intermediary asset-pricing model which shows that the structure of our mar-
ket, specifically the use of financial intermediaries like mutual funds, may help explain why
dividends exist, and why they remain stable or “sticky” through time.
The demand-based asset pricing model I build follows the methods used by Koijen and
Yogo (2019), and helps formalize the elasticities for dividends across investors. A demand
system allows me to express allocations within portfolios around the dividend payments of
individual firms while controlling for stock-specific average effects and information. I then
track how institutional investors respond when a position in their portfolio has a large or
uncharacteristic shock to its dividend policy, revealing an investor-level measure of dividend
elasticity.
I find that most investors increase allocations to firms following a new, higher dividend
policy but underreact in the short-run to these increasing dividend growth rates. Instead,
manyinstitutionalinvestorsallowtheirpositionstodeclineafterthefirmgrowstheirpayouts,
before eventually taking a higher position. I model these delays as costs which are around
50% of the change in dividend policy over the short-run. However, I argue that these results
are also consistent with the slow movement of institutional capital to trading opportunities
2
1.1. INTRODUCTION
discussed by Duffie (2010). Interestingly, investors do not show the same preferences or costs
for net payouts, allowing managers to use them as short-term variable sources of capital
distribution (a pattern Brav, Graham, Harvey, and Michaely, 2005, noted in their survey).
In equilibrium, costly rebalancing and the preferences of most investors for dividends
may explain a central puzzle in the dividend literature; sticky dividends. The reason for
sticky dividends has been well debated, including in instutional settings (Allen, Bernardo,
and Welch, 2000). These studies often argue that managers actively choose to issue sticky
dividends, eitherasasignal, apreference, orbecauseoffrictions. Inthispaper, Idemonstrate
that completely frictionless managers, with no incentive or ability to signal, may still choose
to pay sticky dividends because of these demand-side dynamics which I document. Costly
rebalancing and institutional preferences for dividends can replicate the sticky dividend
puzzle without any regard for managerial preferences as an equilibrium outcome. This
introduces an equilibrium outcome to the sticky dividends puzzle which I show exists even
with perfectly rational and frictionless managers.
My elasticity estimates form a hierarchy of investor sensitivities towards payouts. At
the aggregate level, investors have a positive demand elasticity for dividend payments and
yields. This is driven primarily by banks, households, small institutions, and potentially
investment advisors. Mutual funds, which generally pass dividends through to investors,
show a weaker but significant preference, while pensions have a significant negative elasticity.
From a positioning perspective, investors become more exposed to firms which recently
increased their dividend payments. These results contradict the literature that finds few
investors reinvest their dividend payments, suggesting that institutions may rebalance their
portfolios in other ways to shift their exposure towards dividend-increasing firms (Hartzmark
and Solomon, 2019). This preference in favor of dividend payments is almost universal and
suggests that many investors are willing to accept a higher price for a firm that has a higher
dividend payment.
In a set of empirically-based counterfactual exercises, I show that managers who match
3
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
dividend policy to the preferences of their investors stand to gain a price premium. Fur-
thermore, a manager who chooses to keep dividends stable can receive a premium on the
order of 2% of market capitalization, suggesting that the stable dividend premium is real
and statistically significant (as suggested by Lintner, 1965).
My empirical results coincide with existing studies which have shown that some investors
prefer dividend payments. However, my reliance on the change in firm-level dividend policy
provides new insights. Mutual funds, for example, must pass-through dividends to investors
for tax reasons. I would therefore expect them to have a negative or near-zero loading
on dividends if they did not liquidate other positions to offset the higher dividend payment.
However, I find that mutual funds demand more equity after an increase to dividends despite
these pass-through requirements. This suggests that they may liquidate other positions to
increase exposure to the stock that increased its dividend, despite effectively losing AUM in
the process.
I then use an intermediary asset pricing model to test the implications of my investor
elasticities on equilibrium payout policies. Specifically, I test if the rebalancing institutions
undertake in favor of stocks increasing dividends can plausibly explain aggregate payouts. A
significant literature has examined the incentives of firm managers to cater dividend policies
toinvestorpreferences, butItestiftheconnectionbetweeninvestorelasticitiesandmanagers’
decisions is strong enough to explain aggregate dividend policies. I show that the existence
and high autocorrelation or stickiness of dividends can be attributed to my observed investor
elasticities. In a model where firms are value-maximizing, managers freely choose to issue
dividends, and those dividends are highly autocorrelated, matching empirical data well.
To implement my intermediary model, I assume that investors purchase equity with an
expected payout per period and incorporate those expectations into their budget constraint.
Dividends can be used for reinvestment, or they can be used for consumption consistent with
Bakeretal.(2007)and Hartzmark andSolomon(2019). Ithenassumethatthe intermediary,
not stocks, incur a cost when dividend payments change relative to their previous value. This
4
1.1. INTRODUCTION
cost is rooted in both investor preferences to smooth consumption and in the preferences
of investment managers, who charge more fees on stock and bond positions, to keep capital
invested (i.e., retained earnings). My empirical data suggest that this cost is approximately
50%, which says that when a stocks changes dividends, investors respond by approximately
50% of what that change would imply relative to their elasticity for dividend payments in the
short-run. With this response dampening included, the model matches real-world dividend
data quite well with a correlation of about 0.87 and a near-perfect autocorrelation of 0.96; a
marked improvement over similar models, and particularly strong during recessions.
A model is important in this setting as it allows me to trace the mechanisms that give
rise to stable dividends, of which there are three forces at play. First, I allow intermediaries
modeled after mutual funds to select a (bounded) management fee on the stock and bond
portfolio but not on dividend payments, creating a small preference for dividends. Second, I
build in a rebalancing cost for the intermediary portfolio consistent with my empirical data,
whichdelaysrebalancinganddisincentivizesfirmsfromincreasingtheirdividendpaymentsin
the short run. Finally, stocks in the model can exert a small amount of pressure on the SDF
they face, since investors receiving dividends can use them to offset consumption (Baker
et al., 2007). The dynamics of these three pressures seem to explain aggregate dividend
policy well, including their stickiness.
In my second set of counterfactual exercises, I examine what these preferences imply for
investors. I focus on two aspects; the cost to investors of dividend smoothing and if these
preferences help us understand why payouts exist at all. Smoothing dividends seems to
require a bit of work on the part of a stock’s managers, and it does appear that they charge
for this service on the order of 68 basis points per quarter. However, managers also appear
to smooth dividends when market returns are low, leading to a (counterfactual) dividend
stimulus on the order of 10% of total quarterly payouts (approximately $14 billion in 2021)
at the start of a recession.
I also show that my model may provide insights as to why firms choose to pay dividends.
5
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
AbroadliteraturegoingbacktoMillerandModigliani(1961)andBlack(1976)hasaskedwhy
dividends exist at all. My calibrated model shows that, at least in extreme cases where there
are no frictions, the Miller and Modigliani predictions hold and firms have no net positive
payouts. Instead, any cash-flows to investors are met with offsetting equity issuances. As
soon as investor preferences for stable dividends are added to the model, positive payouts
are seen in equilibrium and are highly autocorrelated. This result suggests that it may be
the preference of investors for dividends and the cost of rebalancing around those dividend
payments which encourages firms to pay dividends at all, and pay them consistently.
Related Literature
This paper is certainly not the first to examine payout policy, but I take a different stance
on it than many. Lintner (1965) is one of the earliest examples asking how firms set dividend
policy. Many of the managers surveyed note the importance of prior dividend payments. It
is easy to see that this sentiment can almost mechanically create the high autocorrelation
that we observe in empirical data. In a related study, Daniel, Garlappi, and Xiao (2021)
examine investor demands for dividend payments using individual investors’ portfolios, and
link demand for dividend paying assets to the prevailing interest rate environment. I also
examine portfolio positions, but use a broad set of institutional portfolios and focus on
changes in individual firm dividend policy instead of aggregate interest rates. This allows
me to understand the dynamics between investors and the firms they own.
In the dividends-as-characteristics literature, Lucas Jr (1978) incorporates dividends as
an exogenous characteristic within an endowment economy. Koijen and Yogo cite this treat-
ment as motivation of using dividend payments as part of their characteristic set when
determining the relative weights of positions within institutional investors’ investment uni-
verse. Haddad, Huebner, and Loualiche (2022) also treat dividends as a characteristic of
price, even when including price on the left-hand side. In this paper, I examine the differ-
ence between dividends as characteristics and dividend-yields as the basis of investor prices.
I find that a subset of investors appears to use dividends as a deterministic measure of price,
6
1.1. INTRODUCTION
not as a firm characteristic.
Non demand-based studies have also followed the example of Lucas Jr (1978). Zhang
(2005) builds a neoclassical model in which there are no households, but the cost of adjusting
dividends through time – to account for their autocorrelation – is modeled as a direct cost to
the value of the firm, not to the end investor. Jermann and Quadrini (2012) build an RBC
model which does have households, and the decision of how dividends are paid is modeled
in a similar way to Zhang (2005) and hinted at in Lintner (1956); assuming firms pay an
adjustment cost. In both of these studies, the stickiness of dividends, and how dividend
policy is determined, is modeled as an adjustment cost paid by the firm. I transfer this
cost to investors and investment managers, calibrated using empirical responses to changing
dividend rates.
This study is related to Campbell and Shiller (1988). In that paper, the authors de-
compose price-dividend ratios and show that changing levels of dividend payments do not
explain as much variation as return expectations at the aggregate market level. Vuolteenaho
(2002) applies a similar method to individual firms and shows that cash-flow expectations
may play a larger role at the individual firm level. In this paper, I use a demand-based asset
pricing model to examine the elasticity of firm-level dividends and dividend growth rates
on investor allocations. Douglas (2022a,b) use the Campbell and Shiller (1988) model to
decompose the cross-section of stock prices. Douglas (2022a) shows that institutions play
a significant role in price differences between firms. Douglas (2022b) shows that change in
dividend payments plays a much more significant role in cross-sectional price variation than
do discount rates. This paper extends both of those studies by examining the preferences
for cash-flows by investor type.
There are many corporate finance studies which examine dividend payouts through the
lens of demand. Excellent surveys include DeAngelo et al. (2009) and Ben-David (2010),
both of which cover a broad array of perspectives. Many studies have asked why dividends
exist at all, a question which remains open (Black, 1976; Ben-David, 2010). Brav et al.
7
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
(2005) show that some managers make decisions based on their investor base’s preferences,
though Grinstein and Michaely (2005) do not find much support for these so-called “clientele”
theories. Thispapercontributesbyaddinganew, verygranularsetofdatatothisdiscussion,
and by proposing a feasible channel through which these preferences can be conveyed to
managers.
A recent resurgence in the dividend literature has often found that investors, often retail,
show a preference in favor of dividend payments. Baker et al. (2007) show that investors
may use dividends for consumption, while Hartzmark and Solomon (2019) show that many
investors view dividends as separate from the capital gains component of their underlying
investments. The authors argue that similar patterns exist for institutional investors. Hartz-
mark and Solomon (2022) demonstrate the biases that separate dividends from the capital
gains component of investments extend to analysts providing price targets. Kapons, Kelly,
Stoumbos, and Zambrana (2023) show that the level of dividend demand in a portfolio is
negatively related to the level of investor trust; investors with a lower level of trust seek out
firms with dividend payments. While I cannot argue whether dividend demand is related to
investor trust in my setting, I do not find significant cross-sectional variation in the level of
dividend demand.
Of course, the importance of dividends in the returns literature is not new. Cochrane
(2008) shows that price-dividend ratios, an important component of my demand system, are
long-run predictors of returns. In this paper, the dividend yield can also predict portfolio
holdings. Empirically, yield appears to help explain how investors position their portfolios
and how they rebalance those portfolios over time.
Stable dividends and the processes that create those stable dividends have also been
well studied (Jagannathan, Stephens, and Weisbach, 2000; Guay and Harford, 2000; Allen
and Michaely, 2003; Leary and Michaely, 2011). Brav et al. (2005) discuss the perceived
importance that managers place on keeping dividend payments stable over time and that
they treat share buybacks as a more flexible form of returning capital to shareholders. I
8
1.2. EMPIRICAL STUDY
generally find strong support for these claims at the firm level.
Thisstudyproceedsasfollows. Section1.2containsadiscussionofthedatausedthrough-
out my empirical exercise, my model of dividend demand, and the associated results. Section
1.3 outlines my intermediary asset-pricing model and resulting counterfactual exercises. Sec-
tion 1.4 summarizes and concludes.
1.2 Empirical Study
I start with a demand system similar to that used in Koijen and Yogo (2019) and Haddad
et al. (2022). I then modify the model to focus on dividend payments, yields, and character-
istics. This serves as the basis for examining investor elasticities for dividend characteristics.
Taken together, this model shows that there is likely a stable dividend premium as described
by Lintner, but my counterfactual exercises show that managers may not fully appreciate
the size of this premium.
I start with the following demand system for the quantity of equity demanded, Q
t
;
Q
t
=A
t
(P
t
)
− η (1.1)
where A
t
is the time t wealth of our investor, P
t
is a measure of price and η is the
elasticity of demand to price changes. Linearizing and taking the log of this results in the
following;
q
t
= ¯q− η (p
t
− ¯p) (1.2)
where I take lower-case variables to represent the natural log (i.e. q
t
= ln(Q
t
)), ¯q to be the
steady-state or baseline values for quantity and inter-period variation in wealth combined,
and ¯ptobethebaselinevalueofprice. Thisequationgivesthenatural-logquantitydemanded
as a function of the average/baseline value, wealth, and price.
I use two definitions of price, each with a different interpretation to the end investor.
9
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
I start by taking the price to be the market capitalization of individual firms. This is
consistent with the definition of price used in Koijen and Yogo (2019) and Haddad et al.
(2022). However, I also use two alternative definitions of price; the dividend-yield (“D/P”)
ratio, and the net-payout-yield (“NP/P”) ratio. Net-payout adds to cash dividend payments
the shares repurchased and subtracts shares issued. The dividend-yield ratio, which is the
inverse of the price-dividend ratio, tests if investors – potentially unsophisticated investors
as discussed by Harris et al. (2015) – use dividend-yield as a measure of value. I also use
net-payout-yield as a second form, allowing me to test if investors are sensitive to changes
in share float to the same degree that they are sensitive to changes in dividend payments.
Substituting in any of my price measures, MC, P/D, or P/NP
1
, yields a model where q
t
is decreasing in price, and when using P/D or P/NP, increasing in the payout of dividends
or net payouts; a seemingly reasonable demand function. I expand this model to include
multiple investments indexed by j. To do this I multiply A
t
by the weight invested into asset
j at time t, w
t,j
. This equation can be rewritten in terms of quantities relative to investment
in the risk-free asset by defining the quantity demanded as q
t,j
= ln

Atw
t,j
P
t,j

and including
an index for investor i,
ln

w
i,t,j
w
i,t,0

= ¯q− η (P
t,j
) (1.3)
where ¯q absorbs the average level of the left-hand side, including small variations in
wealth. I take w
i,t,j
to be the weight of investor i at time t in investment (stock) j, and w
i,t,0
is the weight of investor i’s time t investment in the risk-free asset. The ratio of w
i,t,j
to
w
i,t,0
was shown by Koijen and Yogo (2019) to be the quantity demanded when investors are
risk-return maximizing (see their Internet Appendix for more detail). Specifically, they show
that a logit regression holds if investors are mean-variance optimizing, if returns follow a
factor structure, and assets have characteristic-specific factor loadings. I define ¯q =q
0
+q
′
1
X
1
When using D/P or NP/P, the definition of price is the inverse of these ratios; P
t
= y
− 1
t
for y
t
=
{D/P,NP/P}.
10
1.2. EMPIRICAL STUDY
where X is information used to help identify the portion of demand not due to dividends or
price. For my purposes, I include characteristics of payout demand, such as recent changes,
the skew of the payout distribution, and the kurtosis of that distribution in X. I rewrite
these into a more standard regression specification which is given by the following;
w
i,t,j
w
i,t,0
=exp{η i,t
P
t,j
+γ i,t
X
t,j
+α i,t
+α j
}ϵ i,t,j
(1.4)
where P
t,j
∈{MC, P/D, P/NP}, η i,t
is the regression coefficient and estimated elasticity
to the price or yield, and γ i,t
are the coefficients on various controls including the percent
change in the last period’s dividend payment, market capitalization, dividend skew, and
kurtosis. α i,t
and α j
are investor-time and stock fixed-effects, respectively, and ϵ i,t,j
is the
error term or latent demand which exists outside of the characteristics I include in Equation
1.4. I do not include these fixed-effects in all specifications, and will clarify when they are
excluded. I discuss the selection of fixed-effects below.
The specification is run using generalized methods of moments (“GMM”), with the fol-
lowing moment conditions;
g
i,t,j
=

w
i,t,j
w
i,t,0
− exp{f(P
t,j
,X
t,j
)}ϵ i,t,j

⊗ z
t− 1,j
(1.5)
where f(P
t,j
,X
t,j
)=η i,t
P
t,j
+γ i,t
X
t,j
+α i,t
+α j
. The term z
t− 1,j
is a GMM instrument
which is multiplied using a Kronecker product to each of the moment conditions.
My estimation of this GMM system generally uses investor-date, and/or stock fixed-
effects,
2
heteroskedasticityadjusted(two-stage)GMMstandarderrors,andIclusterstandard
errors whenever possible at the investor, date, and stock levels. My selection of fixed-effects
allows me to examine the way investors choose to allocate capital in their portfolio (investor-
date) cross-sectionally, relative to the dividend payments of firms. Using stock fixed-effects
in several of my regression specifications allows me to understand how investors change their
2
Fixed-effects are estimated to a high degree of accuracy (third-degree cross-terms) following the method-
ology outlined in Rios-Avila (2015) and confirmed with the methodology used in Bergé et al. (2018).
11
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
allocations as firms’ dividend payments change. In all regressions, the starting value of
GMM minimization is the univariate coefficients from an OLS projection. I also include an
instrument to help in identifying the coefficient on MC which is discussed below.
I use GMM for three reasons. First, to follow a similar procedure used in the original
demand-system model proposed by Koijen and Yogo (2019), which is estimated using GMM.
Second, and as noted by Koijen and Yogo, I find that GMM provides a more conservative
elasticity estimate than (two-stage) least-squares. And third, GMM’s use of instruments,
z
t− 1,j
, as trading information available at time t works well in the context of my model.
1.2.1 Identifying Elasticities
I use shifts in dividend policy to identify my dividend elasticities. Specifically, I measure
the rebalancing response of investors after a firm has an unmodeled change in dividend
payments. Equations 1.4 and 1.5 demonstrate how this is done. To control for average stock
characteristics, I rely on the stock fixed-effect. I combine this with information in z
t− 1,j
which estimates dividend elasticities above variation in profits, investment, and book-equity.
As discussed and shown in the appendix, dividends at the aggregate level seem closely tied
to profits, averaging approximately 20% of annual firm profitability. Including operating
profits in my estimation helps to ensure that variations in dividend policies are not those
which are in response to (known) variation in operating profits.
I choose to use this definition of a “shock” for two reasons. As discussed by Duffie
(2010), capital is often slow-moving, and a large portion of my data set is likely subject to
this critique. As a result, measuring shocks to dividend policies in the cross-section would
likely lead to the conclusion that investor have lower elasticities in the period following a
growth in dividends. Since stocks should see a lower price after going ex-dividend, this could
include many positions which (mechanically) see a lower allocation. I hope to avoid these
measurement issues by relying on the allocation over time at the individual stock level after
shocks to dividend policy.
12
1.2. EMPIRICAL STUDY
Second, Baker et al. (2007) show that the largest response to changes in dividend policy
are not autocorrelated between periods. In their paper, this seems to indicate that the
response is largely to the unexpected portion of dividend changes, not the expected. In my
setting, I try as best as possible to eliminate the expected portion of change in dividends.
1.2.2 Data
Institutional ownership information is taken from the SEC Form 13f reporting information,
whichrequiresinstitutionswithover$100millioninmarketablesecuritiestoreportownership
information on their long positions. These data are collected from the Refinitiv s34 Holdings
Database, available on a quarterly basis (hence stock information data is calculated as of
quarter end). This data is then merged with a mapping of each institution’s type (by
managernumber), whichbreaksthisownershipinformationintosixgroups: banks, insurance
companies, investment advisors, mutual funds, pension funds, as well as other institutions
and households. Other institutions are all those institutions required to file, but which do
not fall into other categories, or smaller firms and households with less than $100 million in
assets.
3
I source the mapping for investors from Koijen and Yogo (2019), which includes their
corrections for errors which occurred in the database after December 1998. The Refinitiv s34
database provides type codes which generally align with their mapping. Banks, insurance
companies, andpensionfunds, aregenerallyclearintheirtypemapping. Investmentadvisors
includehedge fundsamongothernon-hedge fundadvisoryandmanagementservices. Several
large banks report both to the bank type and as investment advisors, though on separate
pools of assets. Other institutions are largely comprised of households, endowments, foun-
dations, and other non-corporate entities. This category has the most variability because of
the household portion. Households and small institutions include all non-measured entities
with less than $100 million in long AUM, so variation around this threshold primarily affects
3
This data set matching is not available to all institutions on WRDS; mappings between manager number
and type provided by Ralph Koijen and Motohiro Yogo.
13
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
the other category.
From this holding information, I calculate the total long holdings of each institution,
as well as the total holdings in each equity, which gives me the weight of each institution
invested in that equity, w
i,t,j
. This information is merged with stock-level information on
dividends, share repurchases, operating profitability, book equity, investments, and several
other characteristics used in this paper. All stock characteristics are sourced from CRSP
and Compustat, and are collected at the highest frequency available starting in 1980 and
running through 2017. Data following 2017 was unavailable due to limited manager mapping
data. The data on investment, operating profitability, and book equity is updated in June
of each year following Fama and French (1993, 2015). I include these values in my GMM
information set.
Dividend information is collected as the sum of dividends paid over a full quarter, and
then summed over four quarters. Stock level information is taken on the close of the last
trading day of the quarter. All information from dividends should be incorporated as of
quarter end for two reasons. First, I collect dividend information as of the date of payment,
so all firms should be ex-dividend in order to show up in my data set. Second, firms are
likely aware of changing dividend positions long before any changes to dividends are first
paid out. Dividend skew, kurtosis, and dividend-yield volatility are measured over a rolling
five years. I choose to include the percent change in dividends, (d
t− 1
− ¯ d)/
¯ d, instead of the
second moment because dividends are far more likely to increase in my data than they are
to decrease. For this reason, dividend skew and dividend volatility end up measuring very
similar information – the historical likelihood of a firm to increase their dividends.
One limitation of my data set is the imprecise gap between when dividends are paid
and when my quarter-end holdings data are observed. In my primary data set, dividend
payments are lagged between two and 90 days, depending on the day investors receive their
cash dividends. The next possible lag adds an additional quarter, taking that gap to between
92 and 180 days. With this gap, the results are very similar. However, after yet another one
14
1.2. EMPIRICAL STUDY
quarter lag, interpretation becomes difficult, and the coefficients often become insignificant.
I also include a measure of periodic change in dividend payments compared to a long-run
average. This value is calculated as the one-quarter lagged annualized dividend payment,
less the average long-run (20 quarter, five year) annual dividend payment, normalized by
that long-run dividend;

d
t− 1
− ¯ d

/
¯ d. The numerator of this term is partially motivated
by the difference between current period dividends ( d
1
) and an investor’s reference-point
(d
0
) in Baker, Mendel, and Wurgler (2016),
4
divided by
¯ d to make the terms comparable.
However, I am not able to fit this value differently for dividend increases and decreases given
restrictions in my theoretical model, and the rarity of dividend decreases in my dataset.
Empirically, this term measures the position response of institutions around very short term
changes to dividend policy. If institutions are aware of this term, but choose not rebalance
their portfolio to minimize costs, this term then captures the perceived ‘cost’ to institutions
for immediate rebalancing.
I use the instrument proposed in Koijen and Yogo (2019) and used again by Haddad
et al. (2022). This instrument is the equal-weighted (counterfactual) market capitalization
based on the available investment mandate for each investor. The investment mandate is
defined as the holdings of any particular investor over the prior three years, inclusive; the
same definition used by Koijen and Yogo. This definition of investment mandate allows for
variation in weights as investors remove positions for up to twelve quarters. The instrument
is calculated as;
ˆ p
j,t
=ln

X
i
A
i,t
1
j∈M
i
|M
i
|
!
(1.6)
where ˆ p
j,t
is the instrument for investment j at time t, which is calculated as the equal-
weighted wealth investment in a given stock, j, across all mandates, M
i
. Here, |M
i
| is the
“size” or number of available positions for investor i. This instrument is essentially the
counterfactual price of each investment if it were held in equal-weight for all investors who
have that asset in their mandate. It has been shown to be valid in demand-systems, and I
4
Who reference the prospect theory of Kahneman and Tversky (1979) when building their model.
15
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
find that it is also valid in my specifications.
The motivation behind this instrument lies in the ‘mandate effect.’ As more firms are
able to purchase a particular security (that is, the security is in their mandate), more money
will be chasing that security. This would mechanically raise prices and increase market
capitalization. However, this mandate effect seems unlikely to consistently influence that
stock’s loading on the model’s explanatory variables. This implies that the mandate effect
is unlikely to correlate with errors.
I employ this instrument because it has been shown to work well in demand-system
models, but also because it exploits important variation in two ways. First, it is a function
of the number of mandates that a given investment fits into. Second, it accounts for the
assets,A
i,t
, of a particular investor with access to the investment. All tests of this instrument
in my dataset indicate that it is strong.
Data Set Summary Statistics
My dataset has many clusters of variation. It is organized as type-by-investor-by-date-by-
investment. I have the weight of the investor’s investment within each observation. Within
eachinvestment-by-datesetofobservations, Ihavethedividendspershare, trailing12-month
dividend yield, signed dividend (yield) change, dividend percent change, dividend skew, and
dividend kurtosis.
Table 1.1 provides various summary statistics by entity type. The AUM is the average
over the entire sample studied per entity type, excluding the ‘Other’ category, which is a
plug of the remaining positions. The number of investors is calculated as the total number
of unique entities over the entire sample period for which I have portfolio information. The
average position weight is the average of the relative weight of a position divided by the
weight in the risk-free asset. A value of 1.0 implies that the average position is of the same
size in the portfolio as the investor’s holding of the risk-free asset. The average quarterly
positions are calculated as the average size of a portfolio in number of positions for a given
16
1.2. EMPIRICAL STUDY
Table 1.1: AUM Percentage Breakdown by Type (Excludes Other)
Banks Insurance Cos. Invest. Advisors Mutual Funds Pensions
Percent of Total AUM 17.6% 4.8% 26.4% 46.8% 4.4%
Number of Investors 671 168 5720 461 102
Avg. Position Weight 1.047 1.209 1.040 0.786 0.443
Avg. Quarterly Positions 251 266 94 236 436
Quantiles, Quarterly Positions
25th 70 41 23 55 80
50th 126 92 46 109 293
75th 259 266 88 246 605
100th 2634 2238 2786 3185 2521
This table contains summary statistics for the dataset used throughout this paper. The average quarterly
AUM percentage breakdown excludes the ‘Other’ category, which is a residual of positions not captured
by 13f filings. Number of investors includes the number of unique institutions in my dataset, captured
over all years. Average position weight is the average weight held by an institution, relative to that
institution’s holding of the risk-free asset. Average quarterly positions includes the average number of
holdings, and quantile of quarterly positions breaks those holdings down by quantile. Banks include
traditional money-center banks and direct holdings of medium and smaller institutions. Mutual funds
include those assets held by registered investment companies such as 1940’s-act funds and exchange-
traded funds. Data are calculated quarterly from 1980 through 2017.
type at any given point in time. This information is also broken down by quantile.
It is important to consider these summary statistics because they are highly dispersed
within and between groups. Many of the insights provided in this study should be considered
on an asset-weighted basis. For example, insurance companies and pension funds make up
a dramatically smaller proportion of my sample than mutual funds, investment advisors,
or banks. With nearly 47% of my sample, the effects of mutual funds shifting demand
would likely hide the effects of most other categories combined, so examining each of these
separately should help in understanding the source of equity payout demands.
This table also demonstrates the dispersion within groups. In particular, investment
advisors have an average portfolio size of only 88 positions below the 75th percentile, but
betweenthe75thand100thpercentile, thenumberofpositionsincreasebynearly2,700. This
is, however, consistent with the very high number of investment advisors in this category.
Some of the largest investors in the world, such as BlackRock and Goldman Sachs, report
positions within this category, but non-corporate and non-profit entities do as well.
17
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
1.2.3 Empirical Results
This section contains my primary empirical results regarding investor preferences for divi-
dends and payouts. The premise of my model is that investors may use dividend payments,
and their expectations for those payments, to set prices through their demand for equity. I
include results for both the aggregate equity market and broken down by investor type, and
for cash-dividend payments and net-payouts. This allows me to check for similarities across
groups, which would presumably apply to the aggregate market, as well as for differences
between investor types which may be illustrative of incentives.
The coefficients on dividend payments tell us how investors respond to dividends. If
investors receiving dividend payments did not reinvest, the coefficient on dividends should
be negative. If investors reinvested the amount of the dividend payment into the stock, then
the position should remain unchanged, and the coefficient would be near-zero. However,
if investors receiving a new, higher dividend purchased more of the security (more than
the dividend amount), the coefficient should be positive and significant. In general, I find
many investors end up owning more of the security than they did originally, after dividends
increase.
Aggregate Elasticities
Table 1.2 contains the estimated aggregate elasticities across all investors in my data set.
The table is broken into two sections based on the measure of price. The first two columns
use market-capitalization (“MC”) as the definition of price, and dividends and net-payouts
represent firm characteristics. The last four columns use either dividend-yield or net-payout-
yield as the measure of price, with or without an MC control.
I include fixed-effects for each investor on each date (“Investor-Date”) as well as a single
fixed-effect for each stock. The investor-date fixed effect allows me to examine the variation
across holdings within portfolios, while also controlling for similarities in positions based on
single-names. The stock fixed-effect allows me to examine the within-investment variation
18
1.2. EMPIRICAL STUDY
Table 1.2: GMM Results, Aggregate, Payments and Yields
Price: P
t,j
=MC P
t,j
=P/D or P/NP
(1) (2) (3) (4) (5) (6)
Dividends Net Payout P/D P/NP P/D P/NP
Payments or Yields 0.991 0.096 1.532 1.611 0.210 0.022
(6.621) (4.688) (57.033) (13.631) (5.333) (0.5449)
(d
t− 1
− ¯ d)/
¯ d -0.474 0.018 -0.114 -1.672 0.083 0.084
(-2.679) (0.491) (-0.606) (-3.815) (1.203) (1.208)
Skew 0.131 0.048 0.171 -1.136 0.144 0.143
(2.529) (1.029) (2.677) (-2.240) (2.910) (2.902)
Kurtosis -0.044 0.003 -0.028 0.063 0.001 0.000
(-1.638) (0.194) (-0.729) (0.557) (0.021) (0.015)
MC -0.326 -0.368 -0.282 -0.282
(-33.900) (-16.521) (-14.168) (-14.165)
Fixed-effects
Investor-Date Yes Yes Yes Yes Yes Yes
Stock Yes Yes Yes Yes Yes Yes
S.E. Cluster 3-Way 3-Way 3-Way 3-Way 3-Way 3-Way
GMM ⊗ z
t− 1,j
EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt)
INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE
Observations 14,255,850 12,694,451 14,255,850 12,694,451 14,255,850 12,694,451
ThistablecontainstheGMMcoefficients( t-stats.) fortheregressionmodelln

w
i,t,j
w
i,t,0

=η i,t
P
t,j
+γ i,t
X
t,j
+α i,t
+α j
+ϵ i,t,j
where P
t,j
∈ {MC, P/D, P/NP} and X
t,j
contains firm-level control characteristics, including dividend or net-payout
percentage change relative to long-run average, (d
t− 1
− ¯ d)/
¯ d, skew, kurtosis. The additional characteristics are generally
calculated on a rolling five year basis, except for d
t− 1
which is the previous quarter’s annualized dividend payment. α i,t
,
andα j
are intercepts representing investor-date and firm fixed-effects, respectively. The model is run using a BFGS-Newton
search algorithm with linear-regression coefficients serving as starting points. The GMM specification reports standard
errors clustered at investor, date, and stock level. Data are from January 1980 through December 2017.
through time. Standard errors are clustered at the investor, date, and investment levels, and
I include the equal-weight counterfactual price instrument (“EqME”) (described in Section
1.2.2), price-volatility, investment (“INV”), operating profitability (“OP”), and book equity
(“BE”) in my information set, which is denoted ‘GMM⊗ z
t− 1,j
.’
The first two columns use MC as the price measure. Both the payment of dividends and
net-payouts are positive and statistically significant. This implies that per-share (or per-
percentage of market capitalization) demand for equity within these portfolios increases as
thesepaymentsincrease. Thechangeinpayoutsrelativetothelong-runaverage, (d
t− 1
− ¯ d)/
¯ d,
is negative for dividend payments and insignificant for net-payouts. This term measures the
percentage change in dividends or net-payouts as of last-quarter, relative to the 20 previous
quarters’ average (
¯ d). The negative coefficient is surprising; as the rate of last-quarter’s
dividend payments increases relative to the average, investors’ positions decline. However,
there is no effect for net-payouts.
Investors do not appear to have strong preferences towards skew or kurtosis. The coef-
19
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
ficients on skew and kurtosis in the first two columns are generally insignificant. The only
exception is the coefficient on skew for dividend payments. In this model, as a given firm’s
historyofdividendskewincreases, investorstakeaslightlyhigherpositionintheequity. This
is despite ensuring the coefficients are orthogonal to operating profitability, book-equity, and
investment in the GMM specification.
The results in Table 1.2 suggest that investors care about dividend payments, but portfo-
lio allocations drop after a recent change to dividends. The coefficient on the percent change
in dividend is likely mechanically related to the price drop after the stock goes ex-dividend.
Investors appear to ignore this price drop and do not immediately rebalance their portfo-
lio. Investors could rebalance in this time as the lag in d
t− 1
implies a minimum of 92 days
between when the new dividends were paid and (d
t− 1
− ¯ d)/
¯ d is calculated.
5
Either through
inattention or cost minimization, they do not immediately rebalance.
The null results on (d
t− 1
− ¯ d)/
¯ d in Table 1.2 when d is equal to net-payouts (model
(2)) lends support to the idea that investors are not quick to rebalance their portfolios.
Net-payouts include adjustments to float which also impact price. A significant amount of
the net-payout component is attributable to share repurchases which increase price. Since
the growth rate of net-payouts does not appear to impact positions at all, despite having
dividend payments included, these results may signal that investors are not selling shares,
they just do not respond.
Although MC may be a more natural measure of price for most, certain investors may
use dividend yield as their measure of value, particularly if they are sensitive to dividend
payments. The results for dividend-yield and net-payout-yield as my measure of price in
models (3) and (4) have positive and significant impacts on investor positions. This is not
completely surprising since the divisor is price which has a negative and significant coefficient
in the first two columns (MC). In light of the positive coefficients on payments in the first two
5
There is a full quarter, or 90 day lag, built into my dataset. Cash-based dividend payments are recorded
as of the payment date, which means that there is at least a two day gap between when the firm goes
ex-dividend and when the dividend payment is seen in my dataset. This is a minimum delay between when
a new, higher dividend is paid, and when it shows up in this term of 92 days.
20
1.2. EMPIRICAL STUDY
columns, it appears that at least some investors use yield as their measure of price. Dividend
change, (d
t− 1
− ¯ d)/
¯ d, is insignificant for D/P, but negative and significant for NP/P (-1.672).
It appears that the patterns discussed above for dividend payments are not observable in
aggregate data when using dividend-yields as the sole price measure. Skew is positive and
significant for D/P as it was for dividend payments, and kurtosis is again insignificant.
Finally, models (5) and (6) include a control for firm size (MC). Even at an aggregate
level, it appears that a significant portion of investors make investment decisions based on
dividend yield, which is positive and significant in model (5), but there is no such significance
for net-payout yield in model (6). Cash-based dividend payments appear to generate more
response from investors than do share-based transactions.
Elasticities By Type
Table 1.3: GMM Results, Dividend Payments
Banks Insurance Invest. Advisors Mutual Funds Pensions Other
Dividends 1.228 1.032 1.682 0.572 0.321 1.333
(7.746) (7.817) (4.964) (4.705) (4.848) (3.854)
(d
t− 1
− ¯ d)/
¯ d -0.576 -0.909 -4.407 -0.460 -0.337 -1.823
(-2.651) (-3.655) (-5.046) (-3.245) (-3.633) (-4.415)
Skew -0.151 -0.047 0.452 -0.098 0.036 0.250
(-1.897) (-0.801) (3.630) (-1.657) (0.955) (3.201)
Kurtosis 0.038 -0.008 -0.051 0.056 -0.023 0.002
(1.094) (-0.373) (-0.801) (2.050) (-1.402) (0.065)
MC -0.351 -0.360 -0.298 -0.339 -0.309 -0.355
(-28.577) (-35.998) (-15.965) (-36.567) (-47.264) (-15.923)
Fixed-effects
Investor-Date Yes Yes Yes Yes Yes Yes
Stock Yes Yes Yes Yes Yes Yes
S.E. Cluster 3-Way 3-Way 3-Way 3-Way 3-Way 3-Way
GMM ⊗ z
i,t,j
EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt)
INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE
Observations 2,478,551 812,422 6,654,935 3,065,066 878,157 452,913
ThistablecontainstheGMMcoefficients( t-stats.) fortheregressionmodelln

w
i,t,j
w
i,t,0

=η i,t
P
t,j
+γ i,t
X
t,j
+α i,t
+α j
+ϵ i,t,j
whereP
t,j
= MC and X
t,j
contains firm-level control characteristics, including dividend or net-payout percentage change
relative to long-run average, (d
t− 1
− ¯ d)/
¯ d, skew, kurtosis. The additional characteristics are generally calculated on a rolling
five year basis, except for d
t− 1
which is the previous quarter’s annualized dividend payment. α i,t
and α j
are intercepts
representing investor-date and firm fixed-effects, respectively. The model is run using a BFGS-Newton search algorithm
with linear-regression coefficients serving as starting points. The GMM specification reports standard errors clustered at
investor, date, and stock level. Data are from January 1980 through December 2017.
Tables 1.3 and 1.4 contain results for dividend payments broken down by investor type.
I start with Table 1.3, which decomposes the first column of Table 1.2 by type. Here, MC
21
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
is my measure of price which has a negative coefficient as expected, signifying that demand
is downward sloping. The coefficient on dividends is positive and significant in all columns,
and ranges from a low of 0.321 for pension funds, to a high of 1.682 for investment advisors.
Across all investor types in my sample, there is a positive demand for firms based on the
dividend payments those investors receive. With a stock fixed-effect included, this implies
that a higher dividend payment is associated with an increase in position weights within
investor-type portfolios. Most investors seem to like dividends.
The coefficient on the percent change in dividend payments, (d
t− 1
− ¯ d)/
¯ d, is similarly
consistent, and negative, across all investor types. Investors prefer higher dividend pay-
ments, but their weight in stocks which have an increasing rate of dividend growth declines.
This does not appear to be type-specific, but the effect is dramatic for investment advisors
(coefficient of -4.407) and the other category (coefficient of -1.823).
Interpretation of the coefficients are relative to the cash holdings. The same firm should
expect mutual funds to allocate 0.57% more and banks to allocate 1.23% more to the firm if
dividends were 1% higher. Meanwhile, when last quarter’s dividend grows by 1% compared
to the rolling historic average of the firm, the allocation is lower by 0.46% for mutual funds,
and 0.58% for banks. The coefficients across all investors are positive, suggesting that a
firm increasing their dividends may achieve higher allocations at the cost of other portfolio
positions.
Consider what these results imply for mutual funds, which are usually required to pass-
through dividends to their investors. They say that, despite the pass-through, mutual funds
allocate half a percent more to this position in the long-run. That is half a percent more
than they need to allocate in order to get the position back to the pre-dividend level, which
is equal to the price drop after going ex-dividend. So, presumably, mutual funds not only
liquidate positions to get the higher dividend paying stock back to even, but they then
allocate even more.
The coefficients on skew and kurtosis are mixed in Table 1.3, as they were in Table
22
1.2. EMPIRICAL STUDY
1.2. It does not appear that the historical propensity to increase dividend payments or
the peakedness of the dividend distribution have consistent effects on investors. Investment
advisors and the other category are the exception for skew, and appear to increase their
relative holdings of firms which have a history of increasing their rate of dividend payments,
while mutual funds seek out stocks which have more peaked dividend payment histories.
In asking the question ‘Who Cares About Dividends,’ the answer appears to be; almost
all investor types. Within each type of investor category that I have, a significant number
of investors appear to hold strong preferences towards dividend payments above and beyond
the effect of price, and allocate more capital towards a firm as its dividend increases.
I include Appendix Table 1.15, which decomposes the third column of Table 1.2 by type.
I use P/D as my measure of price, excluding MC. This allows me to test if certain investors
view the yield on equity as their measure of value. Such a view would imply that investors
may treat equities in a way similar to bonds – as a source of “coupon”-like income instead
of a capital appreciating asset. I relegate this table to the appendix because it is difficult to
interpret. P/D is everywhere positive and significant – unsurprising given that price makes
up the denominator of this ratio. However, the negative response to increasing dividend
growth rates remains for investment advisors and other, suggesting that those investors,
which make up a significant portion of the market, even fail to respond to fluctuations in
yields.
In order to try and disentangle the effects of price (MC) from the effects of equity yield,
I use my equal-weight instrument, EqME, to orthogonalize all of my moment conditions,
g
i,t,j
, when interacted (using a kronecker product) with the other data in z
t− 1,j
. This allows
me to instrument the model with the pair-wise multiplied terms in z
t− 1,j
. This procedure
should allow us to understand how much the ‘yield’ component contributes to the demand
for equity while helping to removing the effects for price.
These results are contained in Table 1.4. We can see that banks, other, and to a lesser
extentinvestmentadvisors, aresensitivetotheyieldofequityevenwhencontrollingforprice.
23
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
Table 1.4: GMM Results, Dividend Yield with MC
Banks Insurance Invest. Managers Mutual Funds Pensions Other
Yield 0.438 -0.151 0.187 -0.078 -0.232 3.119
(2.644) (-0.810) (1.624) (-0.618) (-1.880) (5.659)
(d
t− 1
− ¯ d)/
¯ d -0.806 -0.987 -0.290 -0.493 -0.445 -2.092
(-4.095) (-4.367) (-2.250) (-3.302) (-4.085) (-3.968)
Skew 0.156 0.091 0.126 0.124 0.165 0.466
(2.853) (2.185) (2.355) (2.472) (3.966) (3.168)
Kurtosis 0.037 -0.053 0.009 0.081 0.044 0.030
(1.304) (-2.015) (0.374) (2.714) (2.192) (0.430)
MC -0.202 -0.337 -0.208 -0.325 -0.333 0.277
(-6.922) (-9.353) (-10.350) (-13.495) (-13.397) (2.799)
Fixed-effects
Stock Yes Yes Yes Yes Yes Yes
Investor-Date Yes Yes Yes Yes Yes Yes
S.E. Cluster 3-Way 3-Way 3-Way 3-Way 3-Way 3-Way
GMM ⊗ z
i,t,j
EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt)
INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE
Observations 2,478,551 812,422 6,654,935 3,065,066 878,157 452,913
ThistablecontainstheGMMcoefficients( t-stats.) fortheregressionmodelln

w
i,t,j
w
i,t,0

=η i,t
P
t,j
+γ i,t
X
t,j
+α i,t
+α j
+ϵ i,t,j
whereP
t,j
=P/D and X
t,j
contains firm-level control characteristics, including dividend or net-payout percentage change
relative to long-run average, (d
t− 1
− ¯ d)/
¯ d, skew, kurtosis. The additional characteristics are generally calculated on a rolling
five year basis, except for d
t− 1
which is the previous quarter’s annualized dividend payment. α i,t
and α j
are intercepts
representing investor-date and firm fixed-effects, respectively. The model is run using a BFGS-Newton search algorithm
with linear-regression coefficients serving as starting points. The GMM specification reports standard errors clustered at
investor, date, and stock level. Data are from January 1980 through December 2017.
The coefficient on (d
t− 1
− ¯ d)/
¯ d is once again significant and negative across all investors,
consistent with a decline in relative holdings as dividend growth rates increase. Skew is
everywhere positive when significant, indicating that investors prefer firms which have a
history of increasing their dividend payments, but the results for kurtosis are mixed between
significant and insignificant.
These results suggest that equity yield is a significant positive predictor of the allocation
decisions for banks, investment advisors, households, and small institutions. Further, this
shows that once centered around MC, dividend growth rate seems to negatively predict
almost all investors’ portfolio allocations. One notable exception to this finding can be seen
in the other category, which actively seek out investments with higher price. In the same
setting skew is generally statistically significant and positive, indicating that investors are
sensitive to the five-year growth rate of dividends, but perhaps not to the fourth moment,
kurtosis.
In this section, I have examined the impact of dividend payments on investor portfolio
24
1.2. EMPIRICAL STUDY
allocations. I do this through two different regimes: one in which dividends are a per-
share characteristic which investors include into their decision process along with price, and
a second in which dividend-yields are the definition of price. The results suggest that a
significant percentage of the market is sensitive to the dividend payments of equities, but
have lower positions as dividend growth rates increase.
Net-Payouts
Net-payouts are a natural extension of cash dividend payments. A wide literature has dis-
cussed the potential importance of using net-payouts as an alternative to cash dividend
payments (Boudoukh, Michaely, Richardson, and Roberts, 2007; De la O and Myers, 2020;
Douglas, 2022a, among others). However, in the context of my model it is unclear if net-
payouts will, or should, have the same bite as dividend payments. Net-payouts include
dividends and share repurchases as distributions to investors and subtract from that share
issuances. The results in Table 1.2 suggest that the average investor likely does not have the
same strong preference towards net-payouts as they do towards dividend payments.
If investors have a preference for cash-flows – that is, traditional dividend payments –
then I would not expect to see a strong impact when net-payouts are used. Investors who like
to receive dividend payments likely either prefer receiving them as cash for consumption, or
do not understand that they can make equivalent adjustments by selling a portion of equity.
If investors really care about cash, then I would not expect to see a dramatic response to
changes in total net-payouts.
Tables 1.5 and 1.6 examine the effects of net-payouts instead of dividend payments. I
do not find strong evidence in support of investors basing their investment decisions on net-
payout-yields, and may even lower their holdings when net-payouts increase in level. In this
table, the elasticity of demand for this measure is statistically insignificant for all investors.
Investors also do not appear to respond much to the change in these payouts, (d
t− 1
− ¯ d)/
¯ d.
There appears to be surprisingly little response in terms of portfolio rebalancing.
25
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
Table 1.5: GMM Results, Net-Payout
Banks Insurance Invest. Advisors Mutual Funds Pensions Other
Net Payout -0.049 -0.158 -0.155 -0.171 -0.135 0.082
(-0.755) (-2.512) (-2.657) (-2.860) (-2.826) (1.296)
(d
t− 1
− ¯ d)/
¯ d 0.003 0.040 0.206 0.101 0.067 -0.014
(0.032) (0.575) (2.387) (2.023) (1.450) (-0.249)
Skew -0.145 -0.127 -0.095 -0.286 -0.179 0.014
(-2.078) (-2.048) (-1.250) (-2.886) (-3.271) (0.202)
Kurtosis 0.041 0.030 -0.020 0.083 0.052 -0.010
(1.960) (1.654) (-0.735) (3.199) (3.452) (-0.533)
MC -0.283 -0.302 -0.226 -0.298 -0.280 -0.328
(-25.021) (-26.757) (-23.031) (-28.718) (-30.235) (-20.861)
Fixed-effects
Investor-Date Yes Yes Yes Yes Yes Yes
Stock Yes Yes Yes Yes Yes Yes
S.E. Cluster 3-Way 3-Way 3-Way 3-Way 3-Way 3-Way
GMM ⊗ z
i,t,j
EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt)
INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE
Observations 2,478,551 812,422 6,654,935 3,065,066 878,157 452,913
ThistablecontainstheGMMcoefficients( t-stats.) fortheregressionmodelln

w
i,t,j
w
i,t,0

=η i,t
P
t,j
+γ i,t
X
t,j
+α i,t
+α j
+ϵ i,t,j
whereP
t,j
= MC and X
t,j
contains firm-level control characteristics, including net-payouts, net-payout percentage change
relative to long-run average, (d
t− 1
− ¯ d)/
¯ d, skew, kurtosis. The additional characteristics are generally calculated on a rolling
five year basis, except for d
t− 1
which is the previous quarter’s annualized dividend payment. α i,t
, and α j
are intercepts
representing investor-date and firm fixed-effects, respectively. The model is run using a BFGS-Newton search algorithm
with linear-regression coefficients serving as starting points. The GMM specification reports standard errors clustered at
investor, date, and stock level. Data are from January 1980 through December 2017.
While it is surprising to see how little investors respond to changes in net-payouts, these
results do support a widely held view of managers. The survey literature has generally
found that managers perceive dividend payments as a sticky process but believe that share
repurchases can be adjusted more frequently with little impact (Brav et al., 2005). Whether
that claim have been justified from the investors’ perspectives is less clear.
However, the evidence above suggests that managers’ perceptions are largely correct.
Investors do not respond to stock-based (net-payout) transactions, but they do respond
when managers change their dividend payments. The response of managers in surveys seems
to suggest that they are picking up on an actual preference of investors for high, stable
dividend payments, but that the stability of net-payouts is relatively less important. The
results for skew are negative and run the opposite direction as those for dividends, and the
results for kurtosis are mixed.
As a measure of price, net-payouts do not appear to work. Investors do not necessarily
plan their portfolio allocations on net-payouts. However, as a test of the strength of dividend
26
1.2. EMPIRICAL STUDY
Table 1.6: GMM Results, Net-Payout Yield with MC
Banks Insurance Invest. Advisors Mutual Funds Pensions Other
Net Payout Yield -0.001 -0.001 -0.000 -0.002 -0.001 0.000
(-0.660) (-0.932) (-0.244) (-1.285) (-0.866) ( 0.075)
(d
t− 1
− ¯ d)/
¯ d 0.017 0.037 0.024 0.024 0.046 0.042
(0.213) (0.512) (0.774) (0.452) (1.004) (1.073)
Skew -0.222 -0.242 -0.128 -0.179 -0.188 -0.159
(-2.523) (-2.971) (-1.354) (-2.467) (-3.232) (-1.465)
Kurtosis 0.017 0.028 0.018 0.016 0.025 0.028
(0.616) (1.117) (0.886) (0.801) (1.546) (1.169)
MC -0.280 -0.311 -0.241 -0.314 -0.291 -0.300
(-16.328) (-17.984) (-25.564) (-20.388) (-20.795) (-14.664)
Fixed-effects
Investor-Date Yes Yes Yes Yes Yes Yes
Stock Yes Yes Yes Yes Yes Yes
S.E. Cluster 3-Way 3-Way 3-Way 3-Way 3-Way 3-Way
GMM ⊗ z
i,t,j
EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt)
INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE
Observations 2,478,551 812,422 6,654,935 3,065,066 878,157 452,913
ThistablecontainstheGMMcoefficients( t-stats.) fortheregressionmodelln

w
i,t,j
w
i,t,0

=η i,t
P
t,j
+γ i,t
X
t,j
+α i,t
+α j
+ϵ i,t,j
whereP
t,j
= NP/P and X
t,j
contains firm-level control characteristics, including dividend or net-payout percentage change
relative to long-run average, (d
t− 1
− ¯ d)/
¯ d, skew, kurtosis. The additional characteristics are generally calculated on a rolling
five year basis, except for d
t− 1
which is the previous quarter’s annualized dividend payment. α i,t
, and α j
are intercepts
representing investor-date and firm fixed-effects, respectively. The model is run using a BFGS-Newton search algorithm
with linear-regression coefficients serving as starting points. The GMM specification reports standard errors clustered at
investor, date, and stock level. Data are from January 1980 through December 2017.
payments, these results suggest that investors do use cash payments as a basis of their
investment decisions and not adjustments to shares outstanding. Finally, as a test of the
perception of managers deciding on the split between dividends and share adjustments, it
does appear that the survey results are broadly correct: investors may not perceive share
repurchases as a critical part of their capital allocation decisions, as they do dividends.
I include Appendix Table 1.16 for net-payout yield without MC. In general the results
are similar to 1.15, but given the use of price in the net-payout-yield ratio, it seems unlikely
that this is due to the effect of price in the denominator, not to payout-yield.
1.2.4 Delays in Response to Dividend Changes
I now explore the delay between a firm increasing their dividend payout rates and their
investors’ response. The results in the previous sections suggest that after a one-quarter
delay, investors who like dividend payments allow their position to decline (negative coeffi-
27
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
cient) when firms increase the payout rate (measured here by (d
t− 1
− ¯ d)/
¯ d). This negative
coefficient can be seen in Appendix Figure 1.4 which breaks the response down by type. In
these graphs, time zero on the x-axis represents the quarter in which a dividend increase
occurred. Negative dates are quarters before the dividend increase, and positive dates are
quarters after. Mutual funds, banks, other, and to a lesser extent insurance companies show
a pattern in which positions fall for at least a few quarters following an increase in the rate
of dividend growth. Eventually, these positions seem to recover to their original level. This
pattern can also be seen in Tables 1.2, 1.3, 1.4 and 1.17 in the estimated coefficient for
(d
t− 1
− ¯ d)/
¯ d which is negative in these tables.
The delay appears to last for a few quarters for those investors with a “V” shape calendar-
time response. Mutual funds, for example, allow their position to fall abruptly in the quarter
of a dividend increase. This decline takes about two quarters to recover, and then by the
fifth quarter or so, the position has actually increased slightly above the prior level (this
increase is statistically significant, p-value of 0.001). I now turn to test how long this delay
in rebalancing lasts.
To do this, I regress the portfolio weight on lagged (d
t− j
− ¯ d)/
¯ d for lags j of up to two
years (8 quarters) in Table 1.7. I include the same investor-date two-way fixed effects as
well as stock fixed effects in these results, and I separate the regression by institutional only
(excluding other), and then the full data set. The results in Table 1.7 demonstrate that lags
of up to five quarters are either negative and significant or insignificant. The two-quarter
lag, (d
t− 2
− ¯ d)/
¯ d, is the only time in the first year and a quarter that the coefficient is not
significant but is also not positive. It seems that the largest positive increase occurs around
seven lagged quarters, which is where the coefficient becomes positive and significant in both
columns. I can confirm that beyond two years, the coefficients are generally all positive up
to four years (16 quarters) of lags.
The delay between when firms increase their dividend payments and when investors
respond is significantly longer than the one-quarter delay in the previous tables. Visually,
28
1.2. EMPIRICAL STUDY
Table 1.7: Coefficients on Additional Lags of Percentage Change
All Types Inst. Only (Excl. Other)
Variables
(d
t− 1
− ¯ d)/
¯ d -0.1664
∗∗∗ -0.1658
∗∗∗ (-5.994) (-5.971)
(d
t− 2
− ¯ d)/
¯ d -0.0025 -0.0025
(-0.1890) (-0.1937)
(d
t− 3
− ¯ d)/
¯ d -0.0270
∗∗ -0.0267
∗∗ (-2.455) (-2.418)
(d
t− 4
− ¯ d)/
¯ d -0.0295
∗∗ -0.0301
∗∗ (-2.203) (-2.255)
(d
t− 5
− ¯ d)/
¯ d -0.0251
∗∗ -0.0248
∗∗ (-2.147) (-2.108)
(d
t− 6
− ¯ d)/
¯ d -0.000 0.000
(-0.0378) (0.0056)
(d
t− 7
− ¯ d)/
¯ d 0.0197
∗∗ 0.0201
∗∗ (2.076) (2.152)
(d
t− 8
− ¯ d)/
¯ d 0.0470
∗ 0.0457
(1.674) (1.607)
Fixed-effects
Investor-Date Yes Yes
Stock Yes Yes
Fit statistics
Observations 5,221,329 5,103,250
R
2
0.711 0.707
Signif. Codes: ***: 0.01, **: 0.05, *: 0.1
This table contains the OLS coefficients ( t-stats.) for the regression model ln

wi,t,j
wi,t,0

= (d
t− j
− ¯ d)/
¯ d+
α i,t
+α j
+ϵ i,t,j
for values of j between 1 and 8, and where P
t,j
= P/D and X
t,j
contains firm-level
control characteristics, including dividend or net-payout percentage change relative to long-run average,
(d
t− 1
− ¯ d)/
¯ d, skew, kurtosis. The additional characteristics are generally calculated on a rolling five
year basis, except for d
t− 1
which is the previous quarter’s annualized dividend payment. α i,t
, and α j
are intercepts representing investor-date and firm fixed-effects, respectively. The model is run using a
BFGS-Newton search algorithm with linear-regression coefficients serving as starting points. The OLS
specification reports standard errors clustered at investor, date, and stock level. Data are from January
1980 through December 2017.
Appendix Figure 1.4 suggests that it is on the order of 6 to 12 months. Statistically, Table
1.7 shows this delay may be slightly longer with either a two- or five- quarter delay until
that effect has equalized out.
These results demonstrate that the growth rates of dividend payments are not imme-
diately incorporated into investors’ positions. Instead, as the rate of dividend payments
changes, investors seem to delay rebalancing their portfolios relative to their preferences for
dividend payments possibly because of attention or cost.
29
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
This pattern is not completely unexpected. The definition of (d
t− j
− ¯ d)/
¯ d is a modified
version of the anchoring mechanism used in Baker et al. (2016). I choose to observe how
investors respond to changes around a reference point (
¯ d) instead of making assumptions
about their utility functions. Eventually, investor positions are not penalized for dividend
growth, but that takes time. Investors appear to anchor in their belief that the long-run
average dividend payout will return, creating the negative coefficient on this variable.
Adelayinresponseshouldbeexpectedwiththisdata, composedprimarilyofinstitutional
portfolios. Duffie (2010) discusses the slow movement of largely institutional capital toward
trading opportunities. I argue that this could result from costs that make rebalancing a
single stock after a dividend change impractical. Such delays could be the result of search
costs and other ‘impediments to immediate trade.’ While the effects appear dramatic from
a statistical perspective, the fluctuations are generally much less than 20 basis points of a
position, and the benefits of rebalancing may not outweigh the costs.
1.2.5 Variation in Elasticity Through Time
Equity prices vary over time, and so the demand for equities likely changes as investors
receive new information and modify their portfolio weights. These changes may be the
result of changes in characteristics, such as the information contained in my X
t,j
matrix, the
price (MC), the latent demand ϵ i,t,j
, or captured by stock fixed-effects.
The results in the prior section characterize the demand for equities based on dividends,
but they are focused on panel GMM estimates which give a single estimated elasticity either
in the aggregate or by type. In this section, I estimate a time series of asset-weighted
elasticity coefficients, stratified by investor type. I estimate these time series by running
cross-sectional regressions of each investor’s portfolio weights on my set of characteristics,
separately, for each time t. This creates a single elasticity estimate in each period based on
the observable portfolios of investors at time t. I then weight the resulting coefficients by
investor AUM within that investor’s respective type category, calculated separately in every
30
1.2. EMPIRICAL STUDY
time period.
Figure 1.1: Elasticities Through Time
(a) Dividend-Yield (b) Market Cap
(c) Dividend Skew (d) Dividend Kurtosis
This figure contains the time-series of asset-weighted GMM coefficients on various char-
acteristics in Equation 1.4. The GMM model is estimated at every date and for every
investor separately. The coefficients are then asset-weighted and separated by type.
Figure 1.1 plots these time series of asset-weighted average elasticities by investor type.
I include the coefficients from my primary regression specification including dividend-yield,
market cap, dividend skew, and dividend kurtosis. Two patterns can be seen immediately
across all graphs: all institutional investors (banks, insurance companies, investment advi-
sors, mutual funds, and pension funds) tend to follow very closely to one another in their
elasticity estimates, but households and small institutions (the other category) tend to vary
significantly, seemingly at random. This may be indication that households and small in-
vestors do not consistently rely on dividends (or other signals) when making their investment
decisions; they are very noisy investors. Alternatively the volatility in the other type’s elas-
31
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
ticities could be due to a threshold affect; since only institutions with over $100 million in
AUM are required to report in 13f filings, long-lasting bull and bear markets may cause a
significant number of institutions to enter or exit my data set all at once. This is a limitation
of this data set, but should largely be confined to the other category.
Elasticities for dividend-yield (Figure A) vary significantly through time. The average
investor’s elasticity of demand appears to change with economic conditions. Elasticity for
dividend-yield spikes around the dot-com bubble and the 2008 recession. Most institutional
investors appear more sensitive to dividend payments going into recessions, consistent with
the idea of matching liabilities or perceiving dividend payers as safer.
Also important to note, mutual funds (Red) appear to have flipped sometime around
the early 2000’s, potentially with the growth of index funds, moving from near the highest
elasticity to consistently one of the lowest in the following ten years. And finally households
and small institutions (Brown) have large swings in their elasticities, seemingly at random.
There is little response in their elasticities over the dot-com bubble or the 2008 recession,
despite massive fluctuations in the course of just a few years at the start of my sample period.
Dividend-yield volatility follows much the same pattern, though it is worth noting that prior
to 2000, institutions appear to be extremely sensitive to dividend volatility, while post 2000
this elasticity seems to decrease substantially.
Dividend skew and kurtosis again show similar patterns and are very similar between
institutions, though the other category has a volatile coefficient for dividend skew. The
remaining types’ coefficients on skew vary through time by small amounts, and appear to
respond slowly to changes in the economy. Kurtosis elasticity, however, drops at the start of
recessions, with investors accepting higher variation during downturns. This latter point is
surprising, and runs against what I had expected. During recessions – right when investors
would presumably value income from equity investments most – is when investors seem
willing (or are forced) to accept adjustments to their dividend process. This may signify
significant relative effects for dividend payments, which I explore more in my counterfactual
32
1.2. EMPIRICAL STUDY
exercises.
Figure 1.1 demonstrates that the elasticity of demand for dividends has increased in
the last decade. Since 2016, all institutional investors have had the highest elasticity of
demand since the start of my sample period. Despite the recent interest in understanding
share repurchases (among many others, Boudoukh et al., 2007; De la O, 2022), it appears
that the search for dividend-yield has become even more important in recent years, and
the demand between investor types is very similar. Dividends do not appear irrelevant
(Miller and Modigliani, 1961), at least to capital allocation, and if anything the above figures
demonstrate the elasticity of demand for dividend-yields may even be increasing.
1.2.6 Counterfactual Exercises
The previous sections outline the demand for equity dividend payments. I show that most
investors demand dividend payments, some demand dividend-yield, and in most cases there
is a delay between when firms increase dividends and investors rebalance, as captured by the
term (d
t− 1
− ¯ d)/
¯ d.
Now, I evaluate a selection of counterfactual stock price equilibria. The demand system
defined in Equations 1.1 and 1.4 combined with the market clearing condition allows me to
recalculate prices and dividend yields under alternative characteristics and loadings. The
model presented assumes that equity demand and prices are fully explained by the supply of
shares,s
t
, the characteristics of these equity shares, x
t
, the total periodic wealth of investors,
A
t
=
P
i
A
i,t
, along with the estimated coefficients, [η i,t
,γ i,t
], and the latent demand, ϵ i,t,j
;
p
t
=G(s
t
,x
t
,A
t
,[η i,t
,γ i,t
],ϵ i,t,j
) (1.7)
Manipulatingvaluesin[η i,t
,γ i,t
]isaconvenientwaytomeasurethepotentialpricechanges
when investor preferences change or firms modify their dividend-based characteristics. I rely
on the algorithm proposed in Koijen and Yogo (2019) which calculates counterfactual prices
33
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
for individual firms efficiently given the diagonal of the model’s Jacobian.
6
I find that their
method works well with my data and converges in about the same time as for their model.
Sensitivity to Increasing Dividends
In this section, I examine what may happen to equilibrium prices if all firms double their div-
idend payments. This exercise tests two aspects of dividends. First, this is meant to test the
trade-off between higher dividends and other firm or dividend characteristics. Before scal-
ing dividends, investors look at characteristics and make allocation decisions. After scaling,
investors could choose to keep their same portfolio, which now has the same characteristics
but yields twice as much, or they could instead rebalance. Second, this test provides some
insight as to the mechanisms that may allow us to predict returns using dividend yields. If
investors systematically rebalance after a shock to firm-level dividend policy, then we may
see a higher dividend yield predicts returns through systematic rebalancing.
The scaling of all firms’ dividends should not on its own affect the contemporaneous
incentives of investors to change their positioning; they just have a portfolio which now
yields twice as much as it did previously. Instead, it should be yields relative to other
characteristics or a threshold which causes them to rebalance. I keep other characteristics
unchanged so investors do not see any difference between firm characteristics, just the yield
per dollar invested they receive from their portfolios. If prices change dramatically in the
aggregate, this could indicate significant incentives for managers to cater their marginal
dividend policies to investor preferences. If prices do not change significantly, it indicates
thatinvestorsrelymoreonlatentdemand(containedinϵ )topriceequitiesthannewdividend
information.
The results are rather dramatic. Instead of positions remaining unchanged, the results in
Table 1.8 show a noticeable separation between those firms with price increases (“Winners”)
and those with price decreases (“Losers”). Approximately 19% of firms see an average price
6
See Koijen and Yogo’s Internet Appendix for full discussion and derivation.
34
1.2. EMPIRICAL STUDY
Table 1.8: Mean Characteristics of Winners versus Losers
Mean Characteristics Winners Losers
D/P 2.36% 3.25%
MC 12.43 13.75
Skew -0.11 0.00
Kurtosis -1.13 -0.99
Percentage of Firms 19% 81%
Average Gain 29% -16%
This table contains the average characteristics of firms which have a price increase (“Win-
ners”)andforthosewhichhaveapricedecrease(“Losers”)followingadoublingofallfirm’s
dividend payments. MC is expressed in logs of millions. Skew and kurtosis are measured
on a rolling five year basis. Data are from January 1980 through December 2017.
increase of 29% due to portfolio rebalancing, and 81% of firms see a modest decline of 16%.
The average winning firm had a dividend-yield of 2.36% before dividends were doubled, and
the average losing firm had a higher yield of 3.25%. This suggests that there is a practical
threshold for investors around which they demand dividend payments of a certain yield
outside their characteristic loading or latent demand. Doubling dividends helps the lower-
yielding firms more than the higher yielding firms, suggesting that investors had previously
chosen their portfolios with a yield constraint. However, after dividends and yields double,
investors are now willing to purchase those previously lower-yielding equities. Winning firms
also have a lower MC, suggesting again that prior to doubling yields, investors were willing
to accept higher price stocks if they came with a higher yield. Skew is slightly lower for the
winning firms, as is kurtosis, though the difference appears minimal.
The above results suggest that dividends and yields do not appear to be irrelevant.
Instead, dividends play an important role in the decisions investors make when purchasing
equities. Thisalsosuggeststhattheobservableinvestorelasticitiesuncoveredinmyempirical
analysis, changing dividend policies do predict relative returns (Cochrane, 2008).
35
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
Mutual Fund Transition to Passive
A central component of the model used in Haddad et al. (2022) is the effect of the transition
to passive management. As the market share of passive indexing increases, which is con-
tained primarily within my mutual fund category, we would expect the aggregate elasticity
of demand for dividend payments to decline. Since mutual funds represent an average quar-
terly AUM of 47% of my institutional sample, this represents a large part of the market that
could see a significant change in preferences towards dividends. My dividend-based elastic-
ity model gives me a direct way to test this prediction and examine the resulting impact on
stock prices.
I start by assuming the case where all mutual funds have η = 0. This may seem like
a relatively extreme assumption, but it is already the case that the average mutual fund
has a statistically insignificant elasticity for yield (Tables 1.4 and 1.5), and usually a low
elasticity for dividend level. However, the empirical data on this point is noisy; a significant
number of funds have positive elasticities, many have negative, and according to the ICI
fact-book, approximately 50% are passive. All I do here is assume that the transition of
investors towards passive strategies is full and complete.
This assumption allows me to test two important questions. First, the price effects of
this transition on the average stock. With the broad equity ownership mutual funds have,
the transition to a zero dividend elasticity could have a significant impact on price. Second,
the importance of dividend yields after a transition to passive indexing is also difficult to
predict. Since mutual funds make up such a significant percentage of the market, it is unclear
whether enough funds with η < 0 are driving the low importance of dividend yields for the
entire asset class.
When taking η = 0, the average price change is a statistically significant − 5.81% (H
0
=
0 p-value of 0.013, untabulated). The majority of firms are predicted to have a ± 25%
adjustment to price, which would seem reasonable given the size of the asset class. In Table
1.9, I regress these price changes on D/P and the characteristics in X
t,j
to see what firm
36
1.2. EMPIRICAL STUDY
Table 1.9: Predicting Price Changes Assuming Mutual Fund η →0
Parameter Std. Err. T-stat
D/P 0.1960 0.0135 14.552
(d
t− 1
− ¯ d)/
¯ d -0.1400 0.0127 -11.009
Skew 0.0012 0.0026 0.4393
Kurtosis -0.0001 0.0009 -0.1603
MC 0.2291 0.0955 2.4005
Fixed-effects
Date Yes
Stock Yes
S.E. Cluster 2-Way
R
2
0.47
R
2
Between 0.11
This table contains the OLS coefficients and statistics for the regression model
ln(AltPrice)− ln(Price) = η i,t
P
t,j
+ γ i,t
X
t,j
+ α i,t
+ α j
+ ϵ i,t,j
where ln(AltPrice) is
the calculated counterfactual price, P
t,j
= D/P, and X
t,j
contains firm-level control
characteristics, including dividend or net-payout percentage change relative to long-run
average, (d
t− 1
− ¯ d)/
¯ d, skew, kurtosis. The additional characteristics are generally calcu-
lated on a rollingfive year basis, except for d
t− 1
which is thepreviousquarter’s annualized
dividend payment. α i,t
, and α j
are intercepts representing investor-date and firm fixed-
effects, respectively. The model is run using a BFGS-Newton search algorithm with
linear-regression coefficients serving as starting points. The GMM specification reports
standard errors clustered at investor, date, and stock level. Data are from January 1980
through December 2017.
37
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
characteristics fair best when mutual funds lose their elasticity. The results show that high
D/P firms see a net increase in their price, indicating that mutual funds with η < 0 currently
have a significant impact on the pricing of high-yielding firms. However, firms which have
recently increased their dividend payments would see a net decline in price by a statistically
significant value. This is consistent with the implied positive elasticity many mutual funds
havearounddividend increases, andsimilarto theideaof juicingthedividendyielddiscussed
by Harris et al. (2015) (see also Appendix Section 1.6).
Mutual funds are the largest single investor type in my sample, and as a result, their
shift towards inelastic demand with the growth of indexing can already be seen in my Table
1.4 with low aggregate elasticities. However, my dividend model suggests that the further
transition towards inelastic index funds will be met with lower average prices, but higher
importance placed on dividend yields. These results suggest that funds with η < 0 are
prevalent in the market and do impact prices.
Immediate Rebalancing
The negative coefficient on (d
t− 1
− ¯ d)/
¯ d can be seen consistently in Tables 1.2, 1.3, and 1.4.
This coefficient implies that investors may not rebalance their portfolio to increase their
position when dividends increase relative to their otherwise estimated dividend elasticities.
In this counterfactual exercise, I force the coefficient in γ i,t
on (d
t− 1
− ¯ d)/
¯ d towards zero.
This allows me to examine how immediate rebalancing affects equilibrium prices. Despite
havinganegativecoefficientonthisterm, marketcapitalizationalsohasanegativecoefficient
(demand is downward sloping in price). If investors began immediately purchasing equity
after a dividend increase, it is not clear if this would have a net positive or negative impact
on stock prices.
I find that dividend-paying stocks in this scenario see an average price decrease, but the
average cumulative effect is rather small at roughly -2.21%. Despite the seemingly small
decline, this is statistically significant ( p-value of 0.001, H
0
= 0). Preferences for stable
38
1.2. EMPIRICAL STUDY
Table 1.10: Predicting Price Changes Assuming Immediate Rebalancing
Parameter Std. Err. T-stat
D/P 0.062 0.011 5.526
(d
t− 1
− ¯ d)/
¯ d 0.0057 0.026 0.219
Skew -0.020 0.004 -5.401
Kurtosis -0.001 0.002 -0.543
Fixed-effects
Date Yes
Stock Yes
S.E. Cluster 2-Way
R
2
0.49
R
2
Between 0.11
This table contains the OLS coefficients and statistics for the regression model
ln(AltPrice)− ln(Price) = η i,t
P
t,j
+ γ i,t
X
t,j
+ α i,t
+ α j
+ ϵ i,t,j
where ln(AltPrice) is
the calculated counterfactual price, P
t,j
= D/P, and X
t,j
contains firm-level control
characteristics, including dividend or net-payout percentage change relative to long-run
average, (d
t− 1
− ¯ d)/
¯ d, skew, kurtosis. The additional characteristics are generally calcu-
lated on a rollingfive year basis, except for d
t− 1
which is thepreviousquarter’s annualized
dividend payment. α i,t
, and α j
are intercepts representing investor-date and firm fixed-
effects, respectively. The model is run using a BFGS-Newton search algorithm with
linear-regression coefficients serving as starting points. The GMM specification reports
standard errors clustered at investor, date, and stock level. Data are from January 1980
through December 2017.
dividends generally keep average stock price higher and dividend-yields lower. Investors’
preferences for stable payouts, discussed in Section 1.2.4 above, actually appear to keep
stock prices higher in the aggregate than if investors responded immediately, if firms are
willing to issue stable dividends. Of course, on an asset-weighted basis, these values should
be approximately equal.
I decompose the change in prices in Table 1.10. The results show that price changes
are mainly explained by dividend yield and skew. Firms with higher yields perform better
in this scenario, consistent with a trade-off between dividend level and dividend stability.
These results show that the stability of dividends can increase the aggregate values of the
firm. Firms which are most hurt by this premium are those which have low yields or which
39
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
have a recent history of increasing their payments (skew).
1.3 Dividend-Demand Model
I now develop an intermediary asset pricing model to provide one application of the empirical
results presented above. My findings suggest a link between managers and investors. The
payout decisions of firms tend to be stable over time, and investors appear to prefer highly
stable dividend payments. However, it is difficult to identify the direction of this link and
understand whether investors can effectively convey their preferences to managers. On the
one hand, investors may purchase securities because of their payout structure, which is
generally what I have assumed above. On the other hand, managers can respond to some
aggregate perception in the market, which would be consistent with the results in Baker and
Wurgler (2004). Understanding whether dividends exist and are stable because of aggregate
preferences of investors is difficult to conclusively answer empirically simply because firms
have been paying high stable dividends longer than we have a clean record of data. I now
examine this dynamic more closely.
I integrate findings from my empirical exercise into a model that includes investor pref-
erences for dividend-yield and dividend stability, as well as an intermediary. I start with a
model similar to that used by Jermann and Quadrini (2012). The model starts as a general
equilibrium, real-business-cycle model with both a productivity and financial shock. I then
augment it with an intermediary and adjustment costs to slow the response of portfolios
(aligning with the negative coefficient on (d
t− 1
− ¯ d)/
¯ d). I find that this model explains the
payout policy well and captures a significant amount of aggregate market payout variation.
In reality, this model serves to show that the elasticities uncovered in my empirical
exercises can explain equilibrium payouts. Instead of relying on supply-side frictions (that
is, dividend issuing stocks) to explain dividend policies, I show that my elasticity estimates
(on the demand-side) can explain equilibrium policy well even assuming firms are frictionless
40
1.3. DIVIDEND-DEMAND MODEL
and value maximizing. Firms in my setting respond without frictions to produce a dividend
stream that looks very similar to empirically observed firms.
1.3.1 Firms
I assume that there is a continuum of firms in which investors can purchase equity and from
which investors purchase goods and services (consumption). With economy-wide productiv-
ity z
t
, capital k
t
, and labor n
t
, a representative firm faces the revenue function,
7
F (z
t
,k
t
,n
t
)=z
t
k
θ t
n
1− θ t
(1.8)
Capital is determined through a standard process in which managers select capital of
time t+1 by solving equation k
t+1
= (1− δ )k
t
+i
t
, which accounts for depreciation δ and
investment i
t
. I take r
t
to be the interest rate, and the effective gross interest rate adjusted
for the tax benefit τ to be R
t
= 1+r
t
(1− τ ). I assume that firms pay an interest rate r
t
between periods on all forms of net debt.
Firms finance with equity and offsetting net debt, though my focus is on the equity
payout and, therefore, equity funding. Offsetting net debt is the net difference between debt
and saved cash. An important dynamic of this model is that firms are no longer required to
pay all remaining profits to equity holders in the form of dividends. Firms face the following
budget constraint,
w
t
n
t
+k
t+1
+b
t
+ϕ (d
t
)=(1− δ )k
t
+
b
t+1
1+R
+F (z
t
,k
t
,n
t
) (1.9)
Where w
t
n
t
is labor expense, b
t
is offsetting net debt (increasing in debt, decreasing in
savings), and ϕ (d
t
) is a function that determines the dividend payments at time t.
Jermann and Quadrini (2012) assume that ϕ (d
t
) = d
t
+ κ f

d
t
− d

2
, where d
t
is the
actual cash flow paid out to investors, κ f
is a scaling parameter for the adjustment cost of
7
Note that for convention, I keep z
t
here in the production function. This is not the same z
i,t,j
used in
the GMM specification, which will no longer be referenced.
41
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
cash flows,

d
t
− d

2
. This solution helps to increase the autocorrelation of equity payouts.
If a given firm were to adjust their dividends more frequently, they would have to accept this
dividend adjustment cost. I keep ϕ (d
t
) as defined by Jermann and Quadrini, but eventually
I collapse κ f
to zero, allowing these costs to instead be made through the SDF and paid by
investors. I include first-order conditions for the firm’s problem in the appendix.
F(z
t
,k
t
,n
t
) produces a perfectly liquid asset, l
t
. In the event of liquidation, the lender
can recover the value of capital with probability ξ t
that leads to the enforcement constraint,
ξ t

k
t+1
− b
t+1
1+r
t

=l
t
(1.10)
As discussed by Jermann and Quadrini, there is a computationally more rigorous model in
which the enforcement constraint is not binding, but it produces similar results. For this
reason, I keep this constraint binding throughout this paper.
1.3.2 Investors
In most intermediary models, the owners of the equity and consumers in the model are
generally called households. I abstract away from this slightly and label the capital-owning
entities investors to better align with the results of my empirical model above. This is only
an adjustment to the naming convention, not to the functionality of the model. I assume
that there is a continuum of homogeneous investors who face the following utility function
defined on their consumption, c
t
, and their labor, n
t
,
U(c
t
,n
t
)=ln(c
t
)+ln(1− n
t
) (1.11)
Investorsmaximizeexpectedlifetimeutilitysubjecttoanexogenousinter-perioddiscount
factor β ,
42
1.3. DIVIDEND-DEMAND MODEL
U =E
"
∞
X
t=1
β t
U(c
t
,n
t
)
#
(1.12)
and face the following budget constraint based on income, consumption, and their allo-
cation to capital investments and savings decisions D
t
,
w
t
n
t
+D
t
=D
t+1
+c
t
(1.13)
Here, w
t
n
t
is the wage rate and the hours worked, respectively, and D
t
is the income
earned from previous period investment. The investor uses income in two ways; to transfer
wealth into the next period, D
t+1
, and to consume, c
t
. D
t+1
is used to fund the investor’s
positions in debt, equity, and savings. I assume the investor holds shares through an interme-
diary such as a broker or investment vehicle (mutual fund, ETF, etc.). These intermediaries
follow the portfolio allocation requests of their end investors. The driving force behind this
assumption is that either competition or government regulation forces the intermediaries to
follow their investors’ preferences exactly. These intermediaries execute trades according to
the preferences of the end investors (capital owners), and the resulting portfolio is completely
exposed to the end investor.
1.3.3 Intermediaries
I model intermediaries to mimic real-world institutions as best I can, focusing on mutual
funds and ETFs. Mutual funds and ETFs make up the largest portion of my dataset and
of the aggregate market, so following their structure seems the most reasonable way to
model investment intermediaries. These intermediaries maximize their management fee, µ t
,
collected as a proportion of assets under management, s
t
p
t
+b
t
for time t shares s
t
of equity
at price p
t
and debt repayment of b
t
. Fees are not collected on deposits, s
t+1
p
t
+
b
t+1
(1+rt)
,
where (1+r
t
) is the discount applied to the bonds purchased at time t for redemption at
t+1. Under US securities law, mutual funds generally must pass capital distributions such
43
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
as dividends through to the end investor or face taxation at the fund level (see Harris et al.
(2015) for a discussion). To simplify this mechanism, I assume d
t
is passed through directly
to the end investor.
My intermediaries can manipulate revenues in two ways; by setting periodic management
fees and tilting the portfolio towards or away from dividend payments which do not yield
the same level of management fees as equity or debt. Management fees are determined
endogenously, but against a baseline of the average asset-weighted management fee of 0.6%.
8
This adjustment is necessary since the model does not incorporate the competition and
substitution between funds which has driven management fees down substantially.
Investors provide the funds, D
t+1
, which the intermediary uses to purchase debt and
equity. This does not incur management fees since investors pay their fees in the current
period on the value of their capital portfolio. The funds used to purchase next period’s
portfolio are given by,
D
t+1
=
b
t+1
1+r
t
+s
t+1
p
t
(1.14)
Intermediaries use these investments to generate D
t
,
D
t
=s
t
d
t
+s
t
κ i

d
t
− d
d

+(1− µ )(b
t
+s
t
p
t
) (1.15)
Here, ω = (1− µ ) is taken to be the proportion of the portfolio that remains after the
intermediaries charge management fees. For example, if the management fee is 1%, then
investors retain ω = (1− 0.01) = 0.99 of the portfolio value between periods. Since the
intermediary must distribute dividend payments to the end investor, I assume that they
face an expense and preference parameter when dividends deviate from steady state. In this
equilibriummodel, thisparametertakestheforms
t
κ i

dt− d
d

whichissimilartomyempirical
exercise, and captures delayed rebalancing. Here, κ i
controls the sensitivity towards or away
8
ICI Factbook: https://www.ici.org/system/files/2021-05/2021_factbook.pdf
44
1.3. DIVIDEND-DEMAND MODEL
from changes in dividend payments relative to the long-run expectations.
This term captures their preference towards firms which do not pay dividends and is
estimated in my empirical data. Given that µ is charged on equity and debt, but not on
dividend distributions, intermediaries would prefer if they could charge management fees,
and therefore have a preference towards firms which pay lower dividend payments.
The term s
t
κ i

dt− ¯ d
¯ d

adjusts the dividends received by investors at time t, s
t
d
t
, by the
relative distance of d
t
from the steady-state expectation,
¯ d. In addition to preferences for
retainedearningsasopposedtodividendpayments, thistermalsohelpscaptureimpediments
to immediate rebalancing, as discussed by Duffie (2010). These include practical costs in
adjusting consumption bundles and portfolios and missed revenue for intermediaries.
For firms, κ d
represents the firm’s sensitivity to the quadratic adjustment cost. For
investors, κ i
represents something similar; costs to rebalancing portfolios or consumption
bundles as dividend payments change, and missed intermediary revenue. In this way, I do
not view κ d
and κ i
as completely distinct. One scales the quadratic form assumed for firms,
while the other scales the linear normalized form for intermediaries and investors.
When κ i
and µ t
are equal to zero, the budget constraint is identical to the one used by
Jermann and Quadrini (2012). When κ i
> 0, this budget constraint implies that a change
in dividends is magnified in the same direction; d
t
− ¯ d > 0 increases consumption by more
than d
t
− ¯ d, and the opposite for d
t
− ¯ d < 0. If κ i
< 0, then any difference from long-run
expectations is moderated; d
t
− ¯ d > 0 leads to an increase in consumption of less than
d
t
− ¯ d, and d
t
− ¯ d < 0 leads to a drop in consumption of less than d
t
− ¯ d, all else equal.
It is not immediately clear if κ i
has a “correct” sign, and I am not aware of studies that
examine investor-specific dividend adjustment costs. However, the empirical results in Table
1.2 suggest that the coefficient should be negative.
Given D
t
and D
t+1
, intermediaries maximize their periodic profits π i
t
,
π i
t
=µ t
(b
t
+s
t
p
t
)− ζ [(µ t
− ¯µ )(b
t
+s
t
p
t
)]
2
(1.16)
45
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
Where µ t
(b
t
+s
t
p
t
) is their periodic revenue, and ζ [(µ t
− ¯µ t
)(b
t
+s
t
p
t
)]
2
is an adjustment
cost that penalizes the theoretical model when management fees, µ t
, deviate dramatically
from the average management fees observed in empirical data, ¯µ =0.6%. Here, ζ is a scalar
which I calibrate so that the deviations in µ t
approximate those observed in empirical data.
A value of ζ =29 does this well, matching a periodic autocorrelation at just over 0.90.
Discussion and Motivation
Three real-world constraints motivate how my intermediaries operate. First, their manage-
ment fees are nearly fixed or decreasing and generally do not fluctuate much between periods.
Management fees have slowly decreased over the last four decades, primarily benefitting the
capital owners as the number of competing funds has ballooned.
9
Second, and for simplicity,
I assume that investors can directly observe the underlying portfolio built by intermediaries.
This is true for most mutual funds and ETFs, and certainly all brokers. And third, the array
of available funds means that investors can pick one that exactly fits their preferences. This
last assumption simplifies the process through which intermediaries build portfolios. I as-
sume that investors have their preferences exactly reflected in the positions of the underlying
funds.
This last assumption is rooted in the very high number of funds available. At Vanguard
there are over 380 funds available to retail investors, while Fidelity is a close 371.
10
Consider-
ing that portfolios can easily be composed of any combination of these funds, I do not think
it is out of the question that intermediaries should be able to exactly match their investors’
preferences.
11
The assumption that intermediaries can extract information necessary to match their
client’spreferencesisalsoreasonable. TheFinancialIndustryRegulatoryAuthority(“FINRA”)
9
ICI Factbook, Chapter 6
10
From the respective companies’ websites, November 3, 2022.
11
We can also find motivation behind this type of intermediary in modern services such as Fidelity Go,
Fidelity FidFolios, Schwab Intelligent Portfolios, among many other ‘robo-advisors.’ Such advisory firms
build bespoke portfolios usually composed of ETFs to suit their client’s preferences (ideally), and they do so
in exchange for a small management fee.
46
1.3. DIVIDEND-DEMAND MODEL
requires money managers perform reasonable due diligence on the “opening and maintenance
of every account” to ensure that essential facts are recorded. This information often consti-
tutes the risk tolerance and preferences of their client investors across various asset classes
(debt, equity, derivatives, etc.) and must be updated continuously. This requirement helps
ensure that, even with minimal competition, intermediaries are required to know and main-
tain a record of their clients’ preferences.
1.3.4 Equilibrium and Prices
In practice, the intermediaries in my setting provide an open-book portfolio in exchange for
a fee which investors can use in their own optimization problem. This seems to be the most
relevant way to optimize the simple outsourced investment strategies that make up most
of my empirical data set. The costs associated with µ t
and s
t
κ i

dt− d
d

could be avoided if
investors directly managed their portfolios, but this is a relatively rare occurrence with a
small portion of the overall capital allocation in the US. For this reason, it appears that,
observationally, these two costs together are on average less than the cost to the average
investor of managing their own portfolio. Other investor types such as hedge funds may
have other incentives, which I do not cover in this paper.
The solution to this model is as simple as incorporating D
t
and D
t+1
into the investor’s
budget constraint. Taking the first-order condition for s
t+1
gives the following definition of
price,
p
t
=E
t

U
c
(c
t
,n
t
)
U
c
′ (c
t+1
,n
t+1
)

d
t+1
+κ i

d
t+1
− d
d

+
∞
X
j=1

β j
ω
j− 1
U
c
(c
t
,n
t
)
U
c
′ (c
t+j+1
,n
t+j+1
)

d
t+1
+κ i

d
t+j +1
− d
d

(1.17)
The SDF takes a very standard form and is split across two terms due to the exponents
on ω. The dividend term, however, is significantly different from what is generally used.
47
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
Investors form their discount rates based on consumption trade-offs, but a change in divi-
dends has an ‘adjustment’ based on the steady-state value of
¯ d and the value of κ i
. When
negative, even if investors have the right expectation for d
t+j
, they do not fully incorporate
that expectation into their price.
Part of my goal is to better understand the channel through which investors communicate
their preferences or beliefs for stable dividends to managers. This is seen in Equation 1.17
above. Here, investors use dividend payments in their consumption decisions, and are penal-
ized when they are unable to forecast what dividend payments will be. They communicate
this by adjusting their consumption, which adjusts the firm’s SDF and therefore affects the
price attributed to each firm’s dividend stream.
Equation 1.17 demonstrates how important the term κ i
is in my setting. The sign and
magnitude of κ i
determine how much a change in the dividend process affects investor con-
sumption and reinvestment, and therefore likely affects the SDF faced by the firm. If κ i
>0,
a positive change is magnified, and the firm faces a higher SDF when dividends increase and
a lower one when dividends decrease, all else equal. When κ i
< 0 the effect is moderated.
Increasing consumption through dividends implies that the firm is faced with a higher SDF,
but not by as much as κ i
≥ 0. Firms in this situation can increase their dividends, but
the SDF still keeps a higher emphasis on long-term dividend payments; that is investors
do not reward the firm by changing the SDF. The opposite is true for dividend declines; a
single-period decline in the dividend does not have as strong of an effect. A κ i
< 0 implies
that it is relatively more costly for the firm to induce a change in its price.
1.3.5 Data
I follow the dataset used by Jermann and Quadrini (2012), updated through 2021 for my pri-
mary empirical analysis. All data are sourced from either the National Income and Product
Accounts (‘NIPA’), the Flow of Funds Accounts from the Federal Reserve, or, for labor data,
the Current Employment Statistics (‘CES’) survey. Most series come from non-financial data
48
1.3. DIVIDEND-DEMAND MODEL
sets, but I clarify the exact sources below.
12
Equity payout is defined as net dividend payments less net increase in corporate equities,
less proprietors net investment of non-financial business. Debt repurchases represent the net
decrease in credit market instruments. However, in my model, this term makes up only a
portion of the total debt from the firm and is offset with retained cash. Equity and debt
values are expressed as ratios of business value added from NIPA. Depreciation is the sum
of fixed capital in non-financial corporate and non-financial non-corporate businesses, and
investment is measured as capital expenditure. As with Jerman and Quadrini’s data, all
variables are deflated by the price index for business value added as calculated in NIPA (a
table which had a significant relabeling and classification in recent data). Labor is the total
aggregated private weekly hours from the CES national survey.
1.3.6 Results and Performance
I now discuss the results of my dividend-demand model, which assumes that investors or the
intermediaries they use face a cost associated with dividend adjustment, not stocks.
Solving the Model
To start, I replicate the original Jermann and Quadrini (2012) model using their parameters,
including κ f
= 0.146 and κ i
= 0, and assume no management fees are charged by the
intermediary. I follow their calibration, and include Table 1.11 which shows the parameter
values I use. I am able to replicate their original findings very well. I then switch off the
dividend adjustment cost, taking κ f
=0, and test the model with an estimated value for κ i
.
I include Jermann and Quadrini’s productivity and financial shock. The productivity
residual, ˆ z
t
, is defined as the residual of productivity ˆ y
t
(GDP from the national account),
capital, labor, and production parameter θ ; ˆ z
t
= ˆ y
t
− θ ˆ
k
t
− (1− θ )ˆ n
t
. The financial residual
12
Relative table numbers have changed in recent surveys since the data were collected by Jermann and
Quadrini, so I have tried to match with the tables which are as close as possible to those they used. Not all
variables are perfect matches, and the replication code and data make clear the exact NIPA table numbers
used from the 2021 collection codes.
49
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
Table 1.11: Model Parameters
Discount Factor β = 0.9825
Tax advantage τ = 0.3500
Utility parameter α = 1.8834
Production technology θ = 0.3600
Depreciation rate δ = 0.0250
Enforcement parameter ξ = 0.1634
Management fee penalty parameter ζ =29
Firm payout cost parameter κ f
= 0.1460 or κ f
=0
Investor payout cost parameter κ i
= 0 or κ i
=− 0.5
Standard deviation productivity shock δ z
= 0.0045
Standard deviation financial shock δ ξ = 0.0098
Covariance Matrix for shocks A =

0.9457 − 0.0091
0.0321 0.9703

This table contains the parameters used in my model. The majority of parameters follow
those from the original calibration of Jermann and Quadrini (2012). κ i
is the investor’s
coefficient on their dividend-adjustment cost, and κ f
is the firm’s coefficient on their
dividend-adjustment cost. Note that when κ f
= 0.146, κ i
= 0, and when κ f
= 0, then
κ i
=− 0.5.
ˆ
ξ is estimated directly from Equation 1.10 where y
t
is the aggregate value of l
t
. After these
two series are estimated, I use a vector-autoregression to estimate the two shocks which are
then i.i.d. I include a full discussion of this process in the Internet Appendix.
I select a value for κ i
from the calendar-time data in my empirical section used to gen-
erate Figure 1.4. Across all firms in my sample, I select those firms which saw a dividend
increase. The average dividend increase was just under $2.00 per share, annualized. Using
the calendar-time data, I find that the asset-weighted response relative to long-run demand
is approximately 60%. That is, in the second quarter after a dividend increase, the firms’
portfolio weights recover to only 60% of the gap between their eventual future weight and
the trough after the dividend increase. Solving for the right-hand side of Equation 1.17,

d
t+j
+
κ i
¯ d
(d
t+j
− ¯ d)

, and keeping the SDF constant, I find a value of κ i
of -0.472. I take
d
t+j
to be the one-period increase in dividends, j = 1, and
¯ d to be the prior dividend level,
when making this estimate. I confirm this by taking the asset-weighted average elasticity of
demand in my data for (d
t− 1
− ¯ d)/
¯ d (see Tables 1.2 and 1.4). Using this data, I come up
50
1.3. DIVIDEND-DEMAND MODEL
with a slightly lower estimate, right around -0.602, but this varies substantially depending
on the date of the AUM data I use (and, importantly, the AUM of Mutual Funds). For this
reason I select the value of -0.50 to be between the two values.
13
The value of κ i
is less than zero, implying that investor sensitivity to dividend payouts is
moderated; investors do not adjust consumption and investment one-to-one with a change
in dividend payouts, all else equal, as seen in the empirical data. From the perspective of
the supply-side of dividends (stocks), increasing dividend payments has only a muted effect
on the price of the firm. As I discuss below, this likely has the effect of encouraging firms
to retain a portion of the would-be payouts since investors appear to remain focused on the
longer-run.
14
One concern is that this effect goes in the same direction as taxes. For taxable U.S.
investors, every additional dollar of dividend payout is less than a dollar of marginal con-
sumption and investment, since a significant portion of payout must be paid as tax. This
seems unlikely to explain this effect. First, the tax rate in most cases is less than the 50%
implied effect of κ i
. Second, this measure also includes adjustments to equity issuance and
repurchases, which would avoid many of these taxes and have become increasingly popular
in recent times, relative to dividend payout. And third, the effective tax rate on total pay-
outs should be much lower than the marginal dividend tax rate since the asset-weighted tax
rate includes non-taxable investors. Further, I do account for taxes in transactions wherever
possible, such as in the value of R. This makes the effect of taxes likely significantly lower
than the size of κ i
.
13
Values around -0.50 were checked in increments of 0.01 and did not yield a significant difference. Slightly
higher correlation with empirical data was found with a value of -0.45 than -0.5, but I stay with -0.5 to align
better with my estimated elasticities.
14
This can be seen directly in Equation 1.17. If firms increase dividends by $1, investor utility increases by
less than a $1 increase to consumption. Therefore, the numerator in Equation 1.17 remains smaller than it
would with κ i
= 0. This leads to a lower discount rate, keeping the emphasis on long-run dividend payouts.
51
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
Equity Payout Matching
Thissectioncomparestheperformanceoftheequitypayoutcomponent,d
t
, toempiricaldata.
I follow the equity payout definition and procedure used in Jermann and Quadrini (2012)
with my added intermediary. I start with the original specification in which κ f
=0.146 and
take the investors payout-adjustment scalar to be κ i
=0. I then compare this to an extreme
case where firms are free to payout dividends as a residual resulting in no cost ( κ f
=0), but
investors convey their demand for stable cash flow through the SDF. This is done by setting
κ i
=− 0.5, as discussed above. The results are compared in Figure 1.2.
Figure 1.2: Comparison of Dividend Demand and Adjustment Cost
The left graph compares the quarterly net-payout data as computed from the NIPA
tables, as discussed in Section 1.2.2. It shows the time-series net-payout for the empirical
data (green), the dividend-demand model proposed in this paper (blue) which uses κ i
=
− 0.5 and κ f
= 0, and the original Jermann and Quadrini specification (orange) which
takes κ i
=0 and κ f
=0.146. The right graph compares the cumulative gap between the
empirical data and each model’s respective estimate, expressed as a percentage of each
quarter’s payout.
Starting with the original specification, Figure 1.2 shows the original (adjustment-cost)
model does not fit the empirical data as well as it could. Throughout much of the data,
the blue and orange lines do have periods of divergence, particularly during recessions.
Startingaroundthe2008recession, wecanseethatthemodeledvalues(blue)aresignificantly
differentfromtheempiricalvalues(orange). Thedividend-demandmodel, inwhichinvestors’
52
1.3. DIVIDEND-DEMAND MODEL
adjustments to consumption are muted if dividend payments change, tends to fit the data
far better. It is still not a perfect match, but we can see that particularly around the 2008
recession, the model predicts a much more realistic decline in equity payout.
The comparatively strong performance of the proposed model in which investors are
sensitive to stable payouts is surprising. This is a relatively extreme case where I assume
there are no adjustment costs for firms when changing payout – that is, taking κ f
=0. Even
in this extreme case, the demand for dividend stability on the part of investors is enough to
generate high autocorrelation, such as that seen in empirical data.
The channel through which these preferences are relayed back to the firms can only be
through the SDF. In the model with κ f
= 0, the firm is free to adjust payout as though it
were an economic residual, similar to the model used in Zhang (2005). However, investors
who receive dividend payments different from their expectation,
¯ d, do not react immediately
to the firm’s adjustments. This is rather surprising; the model suggests that the impetus
for stable dividends is not a negative response from investors when dividends change, but a
lack of response. These muted reactions do not incentivize the firm to increase dividends,
which appears to encourage the high autocorrelation seen in the data, and (mechanically)
keeps investors focused on long-run dividend payouts. It seems likely, though I explore this
further below, that firms are therefore encouraged to retain dividends.
Table 1.12 compares the empirical data, my proposed dividend-demand model, and the
adjustment-cost model from Jermann and Quadrini (2012). I include the correlation of the
modeled equity-payout series with the empirical data, the autocorrelation of all three models,
the mean, median, and regression coefficients with t-stats. The regression coefficients are
from the centered regression of empirical equity payouts on modeled equity payout data.
I report all of these moment comparisons using all the data in my sample (through June
2021), as well as the data in the original study (through June 2010), and then new data only
(between June 2010 and June 2021).
Starting with all data, it is immediately clear that my proposed dividend-demand model
53
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
Table 1.12: Model Comparisons
1985-2021 1985-2010 2010-2021
Emp Dividend Demand Adj. Cost Emp Dividend Demand Adj. Cost Emp Dividend Demand Adj. Cost
Corr w. Emp - 0.81 0.35 - 0.87 0.36 - 0.40 0.16
Auto Corr 0.95 0.95 0.91 0.96 0.96 0.95 0.85 0.88 0.35
Mean -0.01 0.30 -0.57 0.03 0.62 -0.34 -0.11 -0.47 -1.13
Median -0.32 0.31 -0.37 -0.38 0.81 0.49 -0.27 -0.11 -1.00
Reg Coeff -0.01 0.66 0.29 0.03 0.74 0.30 -0.11 0.30 0.16
(T-Stat) 0.95 16.53 4.48 0.15 17.97 3.96 -0.66 2.83 1.04
This table compares the dividend-demand model and the standard RBC model with adjustment costs relative to the empirically observed data
(‘Emp’). Correlation with the empirical data (‘Corr w. Emp’) measures the sample correlation coefficient of the observed empirical data with
the dividend-demand or adjustment-cost models. Autocorrelation is calculated by regressing all observations on a one-period (one-quarter) shift
in those variables. Finally, the regression coefficient is calculated by regressing the adjustment cost or dividend-demand model’s predicted equity
payouts with the contemporaneous empirical model. All data includes all observations 1985 through June 2021.
54
1.3. DIVIDEND-DEMAND MODEL
hasacomparativelyhighcorrelationwiththetrueequitypayout; 0.81versustheadjustment-
cost model’s 0.35. The autocorrelation of all three are very close, but again the dividend-
demand model performs better. The use of a dividend adjustment cost appears well suited to
explaining the high autocorrelation of equity payouts, but it misses a significant amount of
the empirical data’s variation. Using adjustment costs excludes the (apparently significant)
effects of the demand side of payouts, and therefore the interaction with the SDF. Interest-
ingly, both the mean and the median for the dividend-demand model are not as close as with
the adjustment cost model, but this is likely due to some outliers as the actual regression
coefficient, 0.66, is much closer to one than the adjustment-cost model’s coefficient of 0.29
(though both are statistically different from 1.0).
The data from Jermann and Quadrini (2012) show very similar patterns, with the
dividend-demandmodelgeneratingveryhighcorrelationof0.87, whichisdramaticallyhigher
than the original model’s 0.36, and matching the high autocorrelation of the empirical data
(0.96). It is surprising to see just how well the dividend-demand model does in matching
the empirical data. The payout from the original specification correlates quite poorly with
the empirical data, a problem which is resolved by introducing a simple intermediary to the
model.
The data following 2010 through 2021 is noticeably harder to price, including the high-
growth period following the 2008 recession and the start of the COVID-19 pandemic. We
can see that the correlation of the standard adjustment-cost model and the empirical data
is quite low at 0.16. The dividend-demand model struggles as well in this period, but
still more than doubles the adjustment-cost model’s correlation coefficient with a value of
0.40. Rather surprisingly, the dividend-demand model gets very close to matching the high
autocorrelation of the empirical data, even during this tumultuous period. The model’s
autocorrelation is 0.88 compared to the empirical data’s 0.85. The adjustment-cost model
struggles substantially, generating an autocorrelation of only 0.35. The linear-regression
coefficientsarenoticeablylower,butthedividend-demandmodelstillcapturesmorevariation
55
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
in the empirical data than the adjustment-cost model. Table 1.12 demonstrates that the
dividend-demand model appears to be well suited to explaining dividend payout procedures
of firms in a steady-state equilibrium. In particular, the correlation with the empirical data
and the autocorrelation measures are very close.
My primary channel of interest works well when describing dividend payments. In my
setting, investors formbeliefsabout dividends, buildingportfoliosaround along-runassump-
tion of that payout. If firms were to deviate from this long-run expectation, investors do not
respond one-to-one, all else equal. Instead, their response is muted. This incentivizes firms
to maintain the status-quo, keeping dividends the same when they could afford to increase
them, and also maintaining them for longer when going into an economic downturn.
The model appears to produce reasonable predictions compared to models which assume
firms pay a cost associated with changing payouts. To some extent, dividend-adjustment
costs are meant to capture investor preferences for stable payouts, among other expenses.
I find that attributing these costs to investors who communicate their preferences through
the SDF works significantly better than assuming firms pay the full cost.
Highdividendautocorrelationcomesfrominvestorexpectationscenteredaround
¯ d. When
firms choose to increase (decrease) their payouts, investors do not increase (decrease) their
consumption one-to-one with the new, higher (lower) payout. Instead, only 50% of the
new payout is incorporated into their decisions. In my model, this keeps consumption in
the current period lower (higher), keeping investors focused on the long-run. This likely
encourages firms to retain otherwise would-be dividend payouts simply because investors
care relatively more about the long-run payout of the firm.
1.3.7 Counterfactual Exercises
In this section, I propose and examine counterfactual exercises around payout policies. The
dividend-demandmodelthatIuseinthispapermatchesempiricaldatawellwiththeinvestor
adjustment factor κ i
=− 0.5. Given this relatively strong match with real-world empirical
56
1.3. DIVIDEND-DEMAND MODEL
data, I adjust this term to test what would happen if investors more immediately adjusted
their consumption.
Figure 1.3: Actual Payouts vs. Modeled Frictionless Payouts
Date
Payout (% of Agg./GDP)
Thisfigurecomparesactualempiricalpayouts(Green)andthemodeledpayoutsassuming
a completely frictionless model (Blue). Vertical gray bars highlight NBER recession
periods. The y-axis is the payout of the aggregate U.S. equity market as a percentage of
that period’s annualized GDP.
I start by establishing a baseline and removing all adjustment costs from the model. I do
this by setting κ f
= κ i
= 0. This allows me to explore the ‘perfect markets’ scenario where
firms can freely issue equity and debt, investors show no preferences towards how dividends
are paid and can liquidate their equity costlessly, and dividends can be a residual of profit
less investments. The results of this simulation are shown in Figure 1.3. Here, we can see
that the equity payouts of the costless adjustment model follow with the empirical data, but
they are significantly more volatile. This pattern makes sense given the ability of firms to
costlessly adjust their dividend payments.
It is also evident that firms quickly decrease their dividend payments near the start of
recessions. In-fact, this costless adjustment model shows that dividend declines seem to be
leading indicators of coming recessions. This does not appear to be the case in the empirical
57
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
data, nor in the dividend-demand model. Instead, firm dividend payments remain high at
the start of a given recession, and even remain relatively high through the first few months
of that recession.
The relative cost of adjusting equity, and/or the preference of investors for stable equity
payouts, incentivizes management to keep dividends stable at the start of a recession. This
provides a potentially valuable payout right when economic activity is declining. Realizing
that investors prefer stable payouts, firms can retain a portion of earnings to use in the
future as a buffer to help smooth dividends, or because investors do not fully value increases
to dividend payments.
Positive Dividends
As discussed in the introduction, a broad literature has tried to understand why firms pay
dividends at all (Miller and Modigliani, 1961; Black, 1976; Ben-David, 2010). It is often
an argument that revolves around the inefficiencies which arise when the owners of a firm
(shareholders) take money out of the firm they own, and distribute it to themselves. This
distribution is often taxable, and nets out with a decline in their own equity’s valuation.
In this section, I test if the dividend-demand model I use in this paper can help us
understand why firms pay dividends. A negative total payout of the costless adjustment
model would be consistent with Miller and Modigliani (1961) – firms would choose, on net,
to issue only equity (a negative value) and not pay out additional funds. However, if the
dividend-demand model or the original Jermann and Quadrini specification were to provide
positive total payouts, it could be that a friction presented in one of these models creates
the incentive to pay dividends.
Table 1.13 contains the total payouts generated by firms in my theoretical model. Under
the standard model proposed by Jermann and Quadrini (2012), total payouts are about
-$85.29 billion. Over the life of the economy, firms issue more equity than they pay out
dividends. By removing all adjustment costs, both for the firms issuing dividends and
58
1.3. DIVIDEND-DEMAND MODEL
Table 1.13: Total Net Payout (Modeled)
Model Total Payout (Billions)
Standard Model (Adjustment-Cost) -$85.29
Dividend-Demand Model $45.19
Costless Adjustment -$69.52
This table compares the total payouts of firms over the period between 1984 and 2021.
This is the simple summation of all payouts in all quarters over that period, with negative
values representing share issuances paired with dividend declines, and positive values
representing positive payouts to shareholders. The ‘Costless Adjustment’ model takes
κ f
= κ i
= 0. The ‘Dividend-Demand’ model is the model studied in this paper with
κ i
=− 0.5, and κ f
=0. The ‘Standard Model (Adjustment-Cost)’ is the model proposed
by Jermann and Quadrini, which takes κ i
=0, and κ f
=0.146.
assuming investors have no preferences towards dividend payouts, the total payout is a
relatively similar -$69.52 billion. When managers face a dividend adjustment cost, it lowers
the likelihood that, over the period studied, they pay out any dividends.
Wheninvestorsdemonstratepreferencesforhighandstabledividendpayments, butthere
are no other adjustment costs in the model, investors receive a positive $45.19 billion. In-
vestors communicating their preferences to managers for high, stable dividend payments
through the SDF gain just shy of $115 billion in payouts over the life of the synthetic econ-
omy when calibrated to U.S. total equity payout. This finding is somewhat counterintuitive.
We assume that rational investors profit maximize, and in the absence of adjustment costs,
they end up paying out $69.519 billion more capital than they receive. However, by com-
municating their preferences to managers through the SDF, they stand to gain significantly
more.
The reason for these results likely resides in the capital gains component of returns.
This model cannot directly answer what the total investor capital gains are over the life of
the investment, and how much of that is currently retained, or what future dividends are
expected to be in the last period in time. However, it is illustrative of the difference between
the world in which we live, and the world of Miller and Modigliani (1961) without frictions.
My model is able to generate the non-dividend conditions in their setting, and seems to
59
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
provide a potential answer the question posed by Black (1976). With no frictions, firms
would not consistently pay net-positive dividends. With dividend adjustment costs, firms
would also choose to pay no net dividends. However, I am able to generate positive total
net payouts from firms by incorporating a simple assumption on how investors like their
dividend payments – namely consistent and smooth, with a positive elasticity of demand for
dividends, and a negative coefficient on firm-specific dividend growth, (d
t
− ¯ d)/
¯ d.
The “Savings Rule” for Dividend Payments, and the Implicit Insurance Contract
The above results motivate a simple adjustment to many neoclassical frameworks. It serves
to reason that most firms achieve dividend smoothing by retaining a certain portion of profits
or would-be dividends for future use (see Internet Appendix for additional discussion). In
doing so, firms create a reserve of future payments which are assets to the firm but could be
used to smooth future payouts to shareholders.
I explore this idea further in this counterfactual exercise. I have already examined above
how these preferences affect the total payout over the examined period, but I now look to
how these preferences affect payouts before and during recessions. I start with the model
which has no payout frictions; that is κ i
= κ f
= 0 and ω = 0. I then take the difference
in the counterfactual equity payout between the frictionless model, P
cf
, and the calibrated
payout from my model, P. This gives a stream of payouts, P− P
cf
, equal to the difference
between payouts in my intermediary asset pricing model (which closely mimic those of the
real-world), and the completely frictionless RBC model. I then regress these differences on
an indicator variable that is 1 in months during a recession, and 0 in months when there
is no recession. I include leading recession indicator variables which are 1 in the 6 months
prior to the start of a recession, and another which is 1 in months 12 to 6 prior to the start
of a recession. All recession data are sourced from NBER.
The goal of this analysis is to understand how investor preferences for stable equity pay-
outs affect the payouts of equity markets during expansion and contraction. If, as discussed
60
1.3. DIVIDEND-DEMAND MODEL
Table 1.14: Regression of P − P
cf
on Recession Indicators
Coefficient
Intercept -0.682
(-1.899)
Recession Indicator 10.278
(9.887)
I(6 Months Before Recession) 4.261
(2.989)
I(6 to 12 Months Before Recession) 2.309
(1.619)
R
2
0.413
Observations 150
This table contains the regression coefficients (t-stats.) of the gap between P, the price
withinvestoradjustmentcost,κ i
=− 0.5,whichmatchesempiricaldatawithacorrelation
of 0.87, and the costless adjustment model, P
cf
. Regression coefficients are adjusted for
time-series autocorrelation, data is quarterly between 1984 and 2021.
above, non-zero κ i
incentivizes firms to keep dividend payouts stable, then it is important
to understand how that affects payouts in normal times and in recessions. Keeping payout
stable during expansion likely implies that firms are retaining a portion of payouts, while
keeping them stable during a contraction could imply that firms are using those retained
payments to maintain their payout level. I examine this with the following regression speci-
fication;
P
t
− P
cf
t
=α +β 1
I(recession)+β 2
I(0 to 6 months before)+β 3
I(6 to 12 months before)+ϵ t
(1.18)
The result in Table 1.14 describes what appears to be a very simple insurance contract
between investors and managers. During normal periods (all recession indicators = 0), the
average payout of the model I explore is 0.68% less than the costless adjustment model. This
difference is marginally statistically significant, and is consistent with a small, but frequent,
premium paid to firms for issuing stable dividends. During a recession, the dividend-demand
model has an equity payout 10.28% higher than the costless adjustment model. Over those
61
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
periods, firms which have investors with a non-zero κ i
start to payout higher dividends
relative to the baseline model, presumably by using the reserves which they had been accu-
mulating. We can even start to see this in the 6 months before a recession begins, where the
dividend-demand model generates a 4.26% higher payout. This pattern is not seen between
6 to 12 months, where the coefficient is insignificant.
Thesepatternsdemonstratethatfirmsdosmoothdividends, andfordoingso, theycharge
approximately 68 bps per period as a premium. However, they also pay out higher dividends
in times of financial distress, and even do so in the months leading up to a recession. This
last point is particularly interesting; the frictionless RBC model, and the model used by
Jermann and Quadrini (2012), shows that equity payouts decline right before the start of
a recession, almost as if payout declines preempt recessions. Empirically, this is not the
case, and this pattern may have to do with the insurance-like contract built-in to equity
payouts, which is itself a result of investors’ elasticity of demand for dividends and their
intermediary’s delayed rebalancing. Given the results in Table 1.13, it does appear that in
the long-run, and excluding the capital gains component, this leads to higher total payouts
to shareholders.
1.4 Conclusion
Dividends remain a bit of a puzzle despite their deep theoretical importance in determin-
ing stock prices. On one hand, firms appear perfectly capable of returning more cash to
shareholders, but instead, are building large cash reserves while keeping dividends extremely
stable. On the other, the fact that firms pay dividends at all remains a bit of an anomaly
when taxes and even semi-efficient markets are considered. To account for the patterns we
see in dividends, many studies rely on adjustment costs or other frictions paid by firms to
induce the high autocorrelation that we observe in empirical data. These costs are generally
used to represent preferences of managers to keep dividend payments stable. But in the end,
62
1.4. CONCLUSION
it is the shareholders who own the firm, so should it not be their preferences we consider
when modeling equity payouts?
In this paper, I estimate the elasticities of demand for dividend payments and dividend
characteristics and show that these elasticities can help us model dividend flows without as-
sumptions on adjustment costs or managerial preferences. A natural empirical methodology
to use when examining these puzzles is one centered on equity demand, such as the model
used by Koijen and Yogo (2019). Using a demand-based equity pricing model, I find that
most investors in most cases show preferences towards higher, more stable payouts. This
finding is surprising given the prevalent stance in the literature that dividend preferences
may be reserved for unsophisticated investors or specific clienteles.
I also show that the elasticities of investors form a hierarchy. At the top are banks, who
show the most sensitivity to changes in dividend payments. After these are households, small
institutions, and investment advisors, who still prefer cash payments but do not appear to
make significant decisions on yield alone. Finally, at the bottom are pensions which do not
appear to have preferences towards dividend payments.
Then, I integrate these elasticities into an equilibrium intermediary asset price model.
I use this model to try and explain the sticky dividend puzzle using the elasticities that
I uncover in my empirical exercise. I find that investor dividend elasticities can generate
stable or sticky dividend payments even when firms are able to pick any dividend policy they
want, costlessly. Instead, investors communicate their preferences in favor of stable dividend
payments to the firm through the SDF to which value-maximizing managers appear to pay
close attention. The costly rebalancing to which intermediaries are subject acts to delay
responses to changing dividends, encouraging firms to provide smooth dividend payments.
I examine several counterfactual exercises using the models that I propose in this paper.
First, I show that intermediary preferences in the dividend-demand model meaningfully
impactequilibriumfirmpayouts. Inthelong-run(thelengthofstudy), removingtheinvestor
preference component leads to a negative total payout, meaning that firms take more from
63
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
investors than they pay out. Adding investors’ empirically estimated preferences increases
the total payout, making it net positive. Second, I show that the smoothing of dividends
in the real world may take the form of a simple insurance contract between firms and their
investors. During most periods, firms collect a small, per-period premium of approximately
68 bps. However, during recessions and economic turmoil, this insurance contract pays out,
increasing dividend yields by 10% above the frictionless model estimates, or about $14 billion
based on 2021 data.
The equilibrium conditions under which firms pay dividends should likely include the
preferences of investors. Investors face a menu of available dividend payout policies from
which they can choose, and value-maximizing managers should respond accordingly. How-
ever,dividendexpectationsalsoformthebasisofprice,andforthisreason,treatingdividends
as characteristics alone does not fully capture their complexity. Instead, we should try to
understand why investors and their intermediaries demand dividend-paying stocks and the
choices they make when faced with a variety of investment options.
64
1.5. APPENDIX TABLES
1.5 Appendix Tables
Table 1.15: GMM Results, Dividend Yield
Banks Insurance Invest. Advisors Mutual Funds Pensions Other
Yield 1.634 1.706 1.349 1.688 1.594 1.621
(33.194) (26.568) (40.565) (26.811) (27.874) (28.932)
(d
t− 1
− ¯ d)/
¯ d 0.145 0.199 -0.936 0.210 0.202 -1.477
(0.664) (0.763) (-4.161) (0.922) (1.132) (-5.162)
Skew 0.149 0.173 0.157 0.125 0.135 0.322
(2.442) (2.669) (2.200) (1.928) (2.181) (4.373)
Kurtosis -0.039 -0.027 0.001 -0.060 -0.067 -0.034
(-1.134) (-0.774) (0.044) (-1.804) (-2.300) (-0.853)
Fixed-effects
Investor-Date Yes Yes Yes Yes Yes Yes
Stock Yes Yes Yes Yes Yes Yes
S.E. Cluster 3-Way 3-Way 3-Way 3-Way 3-Way 3-Way
GMM ⊗ z
i,t,j
σ (pt) σ (pt) σ (pt) σ (pt) σ (pt) σ (pt)
INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE
Observations 2,478,551 812,422 6,654,935 3,065,066 878,157 452,913
ThistablecontainstheGMMcoefficients( t-stats.) fortheregressionmodelln

w
i,t,j
w
i,t,0

=η i,t
P
t,j
+γ i,t
X
t,j
+α i,t
+α j
+ϵ i,t,j
whereP
t,j
=P/D and X
t,j
contains firm-level control characteristics, including dividend or net-payout percentage change
relative to long-run average, (d
t− 1
− ¯ d)/
¯ d, skew, kurtosis. The additional characteristics are generally calculated on a rolling
five year basis, except for d
t− 1
which is the previous quarter’s annualized dividend payment. α i,t
and α j
are intercepts
representing investor-date and firm fixed-effects, respectively. The model is run using a BFGS-Newton search algorithm
with linear-regression coefficients serving as starting points. The GMM specification reports standard errors clustered at
investor, date, and stock level. Data are from January 1980 through December 2017.
1.5.1 2SLS Results
65
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
Table 1.16: GMM Regression Results, Aggregate, Payments
Banks Insurance Invest. Managers Mutual Funds Pensions Other
NP/P 1.491 1.596 1.010 1.556 1.584 1.242
18.427 20.420 7.371 21.505 20.610 6.658
(d
t− 1
− ¯ d)/
¯ d -0.813 -1.018 -0.736 -1.312 -1.884 -0.616
-2.701 -2.839 -1.428 -3.881 -4.753 -1.065
Skew -2.326 -2.277 -3.960 -2.424 -1.888 -4.885
-2.605 -2.593 -3.571 -2.588 -2.781 -3.341
Kurtosis 0.626 0.565 0.988 0.599 0.434 1.205
2.672 2.447 3.372 2.494 2.553 3.071
Fixed-effects
Investor-Date Yes Yes Yes Yes Yes Yes
Stock Yes Yes Yes Yes Yes Yes
S.E. Cluster 3-Way 3-Way 3-Way 3-Way 3-Way 3-Way
GMM ⊗ z
i,t,j
EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt)
INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE INV, OP, BE
Observations 2,478,551 812,422 6,654,935 3,065,066 878,157 452,913
Table 1.17: Regression Results with Dividend Characteristics
Banks Insurance Invest. Managers Mutual Funds Pensions Other
σ (D/P) -32.981 -26.457 -16.296 -27.778 -26.135 -18.331
(-6.792) (-4.872) (-4.038) (-6.365) (-9.180) (-4.731)
MC -0.225 -0.255 -0.210 -0.254 -0.228 -0.258
(-33.877) (-30.834) (-33.190) (-35.117) (-43.302) (-24.945)
Skew 0.383 0.456 0.208 0.468 0.483 0.195
(5.069) (5.162) (2.252) (5.259) (5.949) (2.029)
Kurtosis -0.123 -0.145 0.087 -0.109 -0.141 0.096
(-3.242) (-3.686) (2.132) (-3.523) (-4.907) (2.151)
(d
t− 1
− ¯ d)/
¯ d -2.607 -2.515 -0.725 -2.317 -2.264 -1.070
(-7.226) (-5.786) (-3.231) (-6.341) (-8.963) (-4.060)
Fixed-effects
Investor Yes Yes Yes Yes Yes Yes
Date Yes Yes Yes Yes Yes Yes
Investment No No No No No No
S.E. Cluster 2-Way 2-Way 2-Way 2-Way 2-Way 2-Way
GMM ⊗ z
i,t,j
EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt) EqME, σ (pt)
INV,OP,BE INV,OP,BE INV,OP,BE INV,OP,BE INV,OP,BE INV,OP,BE
Observations 2,478,551 812,422 6,654,935 3,065,066 878,157 452,913
ThistablecontainstheGMMcoefficients( t-stats.) fortheregressionmodelln

w
i,t,j
w
i,t,0

=γ i,t
X
t,j
+α i
+α t+ϵ i,t,j
whereX
t,j
contains firm-level control characteristics, including dividend or net-payout percentage change relative to long-run average,
(d
t− 1
− ¯ d)/
¯ d, skew, kurtosis. The additional characteristics are generally calculated on a rolling five year basis, except
for d
t− 1
which is the previous quarter’s annualized dividend payment. α i
and α t are intercepts representing investor and
date fixed-effects, respectively. The model is run using a BFGS-Newton search algorithm with linear-regression coefficients
serving as starting points. The GMM specification reports standard errors clustered at investor and date levels. Data are
from January 1980 through December 2017.
1.6 Appendix: Calendar-Time Analysis
In this section I explore how those variations affect investors by type and over what period
those investors respond to changes in an investment’s dividend policy.
66
1.6. APPENDIX: CALENDAR-TIME ANALYSIS
Figure 1.4: Calendar Time Response to Dividends
67
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
Table 1.18: Three-Way Fixed Effects with Control for Price Volatility
Banks Insurance Investment Mutual Funds Pensions Other
D/P 76.14
∗∗ 73.50
∗∗ 24.83
∗∗∗ 38.59
∗ 93.09
∗∗∗ 56.92
∗∗ (2.245) (2.260) (2.708) (1.961) (2.714) (2.223)
σ (D/P) -57.47
∗∗ -51.51
∗∗ -17.82
∗∗∗ -29.92
∗∗ -65.01
∗∗∗ -38.84
∗∗ (-2.433) (-2.389) (-2.998) (-2.278) (-2.735) (-2.280)
Skew 0.4197
∗∗ 0.3713
∗∗ 0.1391
∗∗∗ 0.2033
∗∗ 0.4927
∗∗∗ 0.3017
∗∗ (2.464) (2.417) (3.006) (2.303) (2.846) (2.157)
Kurt -0.1055
∗∗ -0.1004
∗∗ -0.0303
∗∗ -0.0575
∗∗ -0.1272
∗∗∗ -0.0614
∗ (-2.410) (-2.417) (-2.198) (-2.367) (-2.646) (-1.755)
σ (P) -0.0027 -0.0012 -0.0045 0.0022 -0.0087 -0.0128
(-0.2590) (-0.1338) (-0.9209) (0.4222) (-0.8256) (-1.312)
Fixed-effects
Investor Yes Yes Yes Yes Yes Yes
Date Yes Yes Yes Yes Yes Yes
Investment Yes Yes Yes Yes Yes Yes
Observations 2,478,551 812,422 6,654,935 3,065,066 878,157 452,913
Signif. Codes: ***: 0.01, **: 0.05, *: 0.1
This table contains the Panel OLS coefficients and t-statistics for the regression model ln

wi,t,j
w0,t,j

=
ϵ i,t
pt,j
dt,j
+γ i,t
X
i,t,j
+α t
+α j
+ϵ i,t,j
where X
i,t,j
contains the standard deviations of dividend-yield. These
standard deviations are calculated on a rolling 20 quarter (5 year) basis. α i
, α t
and α j
are intercepts
representing investor, date, and investment fixed-effects, respectively. D/P is instrumented against the
Equal Weighted Market Cap. Data are clustered at the investor, date, investment levels. Data are from
1980 through 2017.
Figure 1.4 plots the average weight around an increase to dividends at time t = 0 by
investor type. Negative values on the x-axis represent quarters before an increase to divi-
dends, and positive values represent quarters after the dividend increase. The left hand axis
represents the average weight of those securities for that investor type. Time t=0 is the ac-
tual quarter in which dividends are paid to the investors. Assuming even marginally efficient
markets, all investor types should be able to adjust their positions as necessary within the
time frame examined. I do not use dividend decreases because they are comparatively rare
and generally occur near recession events. All data are based on the annual total dividend
rate paid by firms.
The two largest investor types in the U.S., mutual funds and investment advisors, which
together account for nearly two-thirds of the institutional market by AUM, have completely
68
1.6. APPENDIX: CALENDAR-TIME ANALYSIS
opposite patterns. The largest group, mutual funds, appear to allow their position to decline
in weight leading up to a dividend increase, but eventually take a slightly higher position
in those equities within three to four months following the increase in payout. Investment
advisors are much the opposite; continually increasing their position in those firms which
are increasing their dividends up until the payout is made, and then reversing course and
returning weights to their previous value. The remaining categories show similarly varied
patterns, but they are significantly smaller in AUM (excluding ‘Other’). We can see banks,
insurance companies, and to a lesser extent the other types look relatively similar to mutual
funds, while pensions look much more similar to investment advisors.
These graphs demonstrate that the composition of an investor base likely has significant
impact on the discount rate applied to firms around a change to payout policy. Firms with
large mutual fund or insurance company ownership must optimize knowing that they will not
see an immediate increase to their ownership, but given time, will generally recover slightly
higher. Given how large these investors are, this is almost uniformally true. The opposite
is roughly true of firms heavily owned by pension funds. Firm with significant investment
advisor ownership likely benefit in the very short-run from their increased payout ratios,
but this boon reverts in a few months, returning back to nearly the same level. They
also demonstrate a primary motivation for my theoretical model discussed below: there are
significant gaps between when dividend policies change and when investors respond.
The results above show that the elasticity estimates for investment advisors may be
underestimated. Investment advisors allow their positions to nearly double over the two
quarterspriortoadividendincrease,onlytohaveitcompletelyreverseafterthenewdividend
is paid. This could have to do with the particular investments that they are holding, or it
could be indicative of managers trying to capture those cash-flows without taking an outsized
position in the firm.
69
CHAPTER 1. WHO CARES ABOUT DIVIDENDS?
70
Chapter 2
Return and Dividend Expectations in
the Cross-Section of Prices
2.1 Introduction
Classic finance theory shows that price-dividend (“P/D”) ratios should be fully explained by
the forward-looking return and cash-flow expectations of investors (Campbell and Shiller,
1988). However, the asset pricing literature’s heavy reliance on rates of return has left
our understanding of what drives prices comparatively limited. Cochrane (2011) notes this
reliance on returns, asking when “asset pricing” became “asset expected returning,” but
the literature remains heavily focused on returns. One gap in our understanding resulting
from this attention difference is how investor expectations contribute to differences in prices
betweenfirms. Answeringthisrequiresthatwedecomposepricesdirectlyinsteadofassuming
the results for returns will carry over. In the short-run, two firms can have identical return
processes, but still support different valuations or prices.
In this paper, I decompose the cross-sectional differences of individual firm prices across
investor return and cash-flows expectations following Campbell and Shiller (1988). In most
of my tests, I find that investor cash-flow expectations contribute significantly more to dif-
71
CHAPTER 2. THE CROSS-SECTION OF PRICES
ference in valuation than do return expectations. This result is opposite to much of the
returns literature, and the differences are not close; between two and ten times more cross-
sectional price-ratio variation is attributable to expected change in cash-flow than to returns.
This result suggests that the primary driver of differences in firm valuations comes down to
cash-flows that investors expect to receive. This seems to run against so-called cash-flow
irrelevance theories (Miller and Modigliani, 1961), suggesting that dividend payments do
contribute to (long-run, long-lasting) valuation differences.
I focus on price ratios at the firm level; in particular, Price-to-Dividend measured with
net-payout(“P/D”)andPrice-to-Earnings(“P/E”)measuredwiththe12-monthaverageearn-
ings per share. P/D is the standard ratio used in price decompositions, and I use P/E as
an alternative measure with earnings acting as a cash-flow proxy. There is support for using
alternative measures in lieu of cash-flows; Miller and Modigliani (1961) provide conditions
under which dividend policy is irrelevant for firm value, and Sadka (2007) argues that div-
idends are financial choices of the firm while earnings and profitability are not. Instead,
earnings and profitability may signal the ability of a firm to distribute dividends in the fu-
ture. I include P/E to help capture this idea, particularly in recent data where payments of
cash dividends have diminished. I show that some conclusions which can be drawn from the
different measures are similar, and I examine additional price-ratios in a robustness section.
Imodelthecross-sectionofpricesusingaCampbellandShiller(1988)decompositionwith
added precision. I estimate this model with a second-order Taylor expansion which adds a
new time-series variance term. I find that the higher-order expansion is generally statistically
significant when used with prices, indicating that investors are sensitive to historic price
volatility. These results hold even when standard measures of market risk are included in
the VAR, and industry controls are removed from the cross-section. When used with prices,
this model does seem to benefit from a higher-order expansion.
The Campbell and Shiller model is more frequently used in the time-series, and often as
a way to explain returns. The returns literature often finds that among the two components
72
2.1. INTRODUCTION
of the decomposition – expected returns and expected change in dividends – expected return
explains the larger portion. I instead use this model to examine price-ratios in the cross-
section which may provide insights as to where that dividend component has gone.
Examining the cross-sectional differences between price-ratios is actually a very natural
avenue of exploration. Consider a generic price-ratio, P
i,t
. The total variance is given by
1
NT
P
i
P
t

P
i,t
− P

2
forN firms over T time periods, whereP
i,t
is firm i’s timet price ratio,
and P is the grand mean. I add and subtract P
t
, the mean price ratio across firms at each
time t, which gives the following;
1
NT
X
i
X
t

P
i,t
− P

2
=
1
NT
X
i
X
t

P
i,t
− P
t

2
| {z }
TS Mean of XS Variance
+
1
NT
X
i
X
t

P
t
− P

2
| {z }
TS Variance of XS Mean
(2.1)
Thetworesultingtermssumtothetotalvariance. Thefirstisthetime-series(“TS”)mean
of the cross-sectional (“XS”) variance and the second is the time-series variance of the cross-
sectional mean. I calculate this decomposition with the data used throughout this paper
which includes individual firm-level price-to-dividend and price-to-earnings ratios of CRSP
stocks with positive dividends or positive earnings. I report the percentage contribution of
each term in Table 2.1 Panel A.
Table 2.1 shows that as much as 94% of the variation in my sample comes from the time-
series mean of the cross-sectional variance with the remaining 6% to 7% due to the time-
series variance of the cross-sectional mean. Taking the cross-sectional mean as an aggregate
market return implies that time-series analyses of price ratios examine only a small part of
the total variance. Many previous studies have used dividend-yields in the time-series, such
as Campbell and Shiller (1988) and Shiller (1981) among many others, but my analysis of
the cross-section adds new insights and examines a much larger part of the overall variation.
This decomposition demonstrates that price ratio variation lies primarily in the Fama and
MacBeth (1973)-style cross-section, and, for this reason, I use cross-sectional regressions
throughout this paper.
73
CHAPTER 2. THE CROSS-SECTION OF PRICES
Table 2.1: Analysis of Cross-Sectional and Time-Series Variance
Panel A P/D P/E
TS Mean of XS Var 94% 93%
TS Var of XS Mean 6% 7%
Total 100% 100%
Panel B P/D P/E
XS Mean of TS Var 61% 65%
XS Var of TS Mean 39% 35%
Total 100% 100%
Total Variance 0.32 0.134
This table provides a decomposition of the price-to-dividend (“P/D”) ratio and the price-to-earnings
(“P/D”) ratio for data used in this paper. The individual firms used in this calculation are a sample of
all firms listed on CRSP. Data is collected from 1985 through 2018. Observations are removed if a firm
is missing characteristics listed in Section 2.3.
I can decompose total variance in a second way by adding and subtracting P
i
, the time-
series means of the price ratios;
1
NT
X
i
X
t

P
i,t
− P

2
=
1
NT
X
i
X
t

P
i,t
− P
i

2
| {z }
XS Mean of TS Variance
+
1
NT
X
i
X
t

P
i
− P

2
| {z }
XS Variance of TS Mean
(2.2)
The resulting terms are the cross-sectional mean of the time-series variance and the
cross-sectional variance of the time-series means. Table 2.1 Panel B includes the results of
this decomposition, again expressed as a percentage of the total variance. Approximately
2/3
rds
of total variation comes from the cross-sectional mean of the time-series variance.
This is approximately the residual variance when a price-ratio regression includes only firm
fixed-effects that control for each firm’s average price-ratio, P
i
. Therefore, a regression
with only firm fixed-effects should explain approximately 1/3
rd
of the total variance of my
price-ratios. The remaining variation is attributable to the cross-sectional variance of the
time-series mean, which is approximately equal to a cross-sectional regression ran on prices
net of time-series average prices.
1
1
To see this connection more directly, recall in the first decomposition that P can be well approximated
(94% of the variation) byP
t
. Making this substitution into the decomposition yields the Fama and MacBeth
74
2.1. INTRODUCTION
These decompositions show that studying the cross-section of price-ratios is actually a
verynaturalplacetolookforvariation. ThefactthattheCampbellandShillermodeldecom-
poses price-ratios provides an ideal way to explore the components of cross-firm differences.
The decompositions even provide how much variation we should expect to capture in a panel
regression which I also explore in this paper, and indicate that studying the time-series of
price-ratios is not of much value.
Firmprice-ratiosare, understandably, noisydependingonwhichfirmsareincluded. Some
firms pay no dividends, or have highly volatile earnings, which can make estimation difficult.
I focus on results at the individual firm level, but I also combine stocks into portfolios
of characteristic-sorted assets into portfolios with aggregate price-ratios. With firms, highly
persistent price-ratios may be the result of a data limitation; namely, the need to smooth the
denominator between periods. Since dividends are often paid by many firms on a quarterly
basis, many months throughout the year have no cash-flows, thereby forcing some form
of smoothing or aggregation. Previous studies have instead relied on a market portfolio
(Campbell and Shiller, 1988; De la O and Myers, 2020), but my emphasis on the cross-
section necessitates multiple portfolios, each with price-ratio estimates.
To form these portfolios, I aggregate market capitalization and dividends across firms
within either 18 or 75 portfolios. This procedure allows me to form aggregated portfolios
that pay dividends in nearly every month and require no smoothing. By forming portfolios
with sorts similar to Fama and French (1992, 2015, 2019), and Douglas (2020), I am able to
capture broad coverage of equities while still generating cross-sectional price-ratio variation
between portfolios. This data produces significantly higher R
2
with large coefficients and
t-statistics, but tends to reconfirm many of the patterns seen at the firm level. The heavy
reliance in the cross-section on the dividend component remains. Return expectations do
appear stronger with portfolios than individual firms, but the cash-flow component remains
stronger still. It appears that the reliance of returns on the expected returns component
(1973)-style cross-sectional regression, but with a single cross-section using a time-series average price ratio.
This time-series average,P
i
, should capture about 2/3
rd
of total price ratio variation.
75
CHAPTER 2. THE CROSS-SECTION OF PRICES
does not coincide with a high reliance of price-ratios on that same component. In-fact, I
show that in some cases, the expected return component can be removed from the model
with very little impact.
I also show that investor expectations appear stable enough to provide a small amount of
out-of-sample predictability. I use cross-sectional regression coefficients paired with lagged
expectations to make predictions about relative valuations. Return and dividend expecta-
tions appear to predict price-ratios, but the ability to do so rely heavily upon the smoothness
of dividend payments. These results appear to suggest that expectations may respond faster
than price-ratios, and there is a delay between when these expectations can be calculated
and when they are incorporated into the gap between stock prices.
Related Literature
The emphasis of the existing asset-pricing literature on returns is somewhat surprising
considering the potential low power of returns-based models to reject the efficient market
hypothesis (Shiller, 1984; Summers, 1986). However, the disparity in attention between
price- and returns-based models is likely rooted in the non-stationarity of prices which makes
returns easier to use. In this paper, I address the issue of non-stationarity with the goal of
understanding what explains the cross-sectional variation in stock prices. Specifically, I
decompose the cross-sectional variation in individual stock price ratios, addressing the issue
of non-stationarity by forming price-ratios with either net-payouts or earnings in the divisor.
The decomposition of dividend-yields into expected returns and dividend growth rates
has been well studied. Campbell and Shiller (1988) show that the majority of dividend-
yield variation in the time-series is explained by expected future returns, and very little is
explained by expected dividend growth rates. Vuolteenaho (2002) uses the Campbell and
Shiller model with individual firms, and shows that cash-flow news is what explains most
of firm-level stock returns. De la O and Myers (2020) examine the split between expected
returns and dividend growth using a forward-looking definition of cash-flows and earnings,
and show that this shifts power away from expected returns. Many papers have worked
76
2.1. INTRODUCTION
with models similar to Campbell and Shiller (1988), providing a variety of breakdowns with
different LHS variables, though most of this work has focused on time-series variation.
Chen and Zhao (2009) examine, among other things, the relative sensitivity of the Camp-
bell and Shiller model’s vector auto-regression. They show that the statistical model used
to estimate the return and dividend decomposition are sensitive to omitted variables and
specification errors. They note that seemingly innocuous modifications, such as replacing the
10-year P/E with similar measures, can lead to opposite conclusions. Recent work by Pohl,
Schmedders, and Wilms (2018) demonstrates that in the long-run, the log-linearization tech-
niques used in these models may not be well suited to long-run risk, such as with Bansal and
Yaron (2004), among others. I attempt to address some of these concerns with a higher or-
der Taylor approximation. The resulting additional term, which represents estimation error
associated with the first-order Taylor approximation, does in fact prove to be an important
addition.
Several recent studies have noted the potential value in examining prices. Cho and
Polk (2019) develop a framework around price-based stochastic discount factors (“SDFs”)
and show that the CAPM explains prices in the cross-section better than it explains short-
horizon returns. Favero, Melone, and Tamoni (2020) study the information in prices, arguing
thatpricesarerelevantforlong-terminvestorsasopposedtoshort-termtraders. Theauthors
propose an equilibrium correction term derived from price which predicts portfolio returns.
Despitethisrecentinterest,thecritiqueofCochrane(2011)thatthefieldcanbecharacterized
as “asset expected returning” still holds essentially true give the disproportionately large
attention returns receive.
Cross-sectionalstudiesinfinancearerelativelymainstream, thoughmostexaminereturns
and not prices. Cohen, Polk, and Vuolteenaho (2003) study the cross-sectional structure of
book-to-market values using portfolios. The authors decompose book-to-market in terms of
expected returns, profitability, and persistence in valuation, and note that results for cross-
sectionsofportfolioscanlooksignificantlydifferentfromamarketportfolio. Theauthorsfind
77
CHAPTER 2. THE CROSS-SECTION OF PRICES
that expected returns explain about 20% to 25% of the cross-sectional variance of portfolios’
book-to-market ratios. Similarly, I find that the explanatory ability of expected returns is
substantially lower when applied to the cross-section of individual firms; generally less than
10%, though change in cash-flows is often more significant.
Much of my analysis relies on the methods of Fama and MacBeth (1973). In that paper,
the authors show that cross-sectional regression coefficients with returns on the LHS are
portfolio excess returns, each of which has loadings on a factor equal to one with all other
factor loadings equal to zero. Fama and MacBeth (1973), along with Fama (1976)
2
, use the
standard error of the mean from the time-series of the monthly cross-sectional regression
coefficients when calculating the t-statistic. This famous methodology has been used count-
less times, but I use it with prices which are heavily autocorrelated. To address this issue,
I adjust the standard-errors from the Fama-MacBeth regressions with an AR(1) model, and
consider robustness to alternatives.
This paper proceeds as follows. Section 2.2 reviews the models that I will use throughout
this paper. Section 2.3 discusses the datasets I use to assemble a collection of firm-specific
characteristics included in the vector auto-regressions when estimating return and dividend
expectations. Sections 2.4 and 2.5 discuss my empirical results, and Section 2.6 concludes.
2.2 Models and Methods
I employ two models through this paper; a panel regression which uses various fixed-effects
and a cross-sectional Fama-MacBeth regression specification adjusted for autocorrelation in
errors. Both of these models are motivated by the decomposition of price-ratios provided in
the introduction. Both models use price-ratios on the left-hand side (“LHS”) with predictors
and industry controls (when using firm-level data) on the right-hand side (“RHS”).
2
Chapter 9
78
2.2. MODELS AND METHODS
2.2.1 General Panel Regression
I start with a panel regression specification;
P
i,t+1
=X
i,t
β 1
+α i
+α t
+ϵ i,t+1
(2.3)
Which describes the price-ratio P
i,t+1
, either P/D
i,t+1
or P/E
i,t+1
at time t+1 for firm
or portfolio i as a function of predictors, X
i,t
, and firm and/or time fixed-effects, α i
, and
α t
. This model will be used to provide a general examination of how return and dividend
expectations (contained in X
i,t
) explain price-ratios in the panel.
The decomposition provided in the introduction suggests that a cross-sectional regression
should exploit the majority of variation. The panel regression will serve to provide insights,
though I use the cross-sectional regression in the following section as my basis for testing the
model between firms. The panel regression will allow me, however, to test how the results
from Vuolteenaho (2002) align with my data using price-ratio decompositions.
2.2.2 Cross-Sectional Regressions
I also explore a cross-sectional regression following Fama and MacBeth (1973). This model
allows me to directly consider the cross-section of price-ratios. Consider T cross-sectional
regressions stacked over time;
P
i,t+1
=λ 0,t
+X
i,t
λ 1,t+1
+I
i,t
λ 2,t+1
+ϵ i,t+1
;i=1,...,N(t),∀t (2.4)
In Equation 2.4, P
i,t+1
is the price ratio, either P/D
i,t+1
or P/E
i,t+1
at time t+1 for firm
or portfolio i. P
i,t+1
represents the price one month ahead of the RHS data. Here, λ 0,t
is
my intercept at time t, and I take X
i,t
to be a matrix of characteristics for firm or portfolio
i at time t (discussed below). I use this model under the assumption that observations
of characteristics, X
i,t
, at time t can influence the price ratio at time t+1, but that the
79
CHAPTER 2. THE CROSS-SECTION OF PRICES
information at time t is not available to investors until after prices are set in that period. I
i,t
is an Industry Membership control for firm i at time t, and is only used with firm-level data.
The primary coefficient of interest is λ 1,t+1
which contains the loadings of each characteristic
in X
i,t
.
I estimate these coefficients using OLS, though the results are generally robust to WLS.
Take B
t
as the matrix I am using for my projection; the column-wise union of a col-
umn of ones, X
i,t
, I
i,t
, and a constant at time t. I use the standard projection, λ t+1
=
(B
′
t
B
t
)
− 1
B
′
t
P
t+1
. Throughout, I use the AR(1)-adjusted t-statistics reported in Douglas
(2021) instead of the standard Fama MacBeth t-statistics. See Appendix for further details.
2.2.3 Price-to-Dividend Ratio Decomposition
I make use of the Campbell and Shiller (1988) decomposition rewritten in terms of P/D
and calculated at the individual firm or portfolio level. I leave the full derivation to the
Appendix. The Campbell and Shiller decomposition usually relies on a first-order Taylor
approximation, but I include a second-order term. This term is a function of the ex-post
variance of each firm or portfolio’s price-ratio.
Following Campbell and Shiller (1988), I start with the expression for continuously com-
pounded returns r
i,t
for firm i at time t, apply a Taylor expansion, then recursively solve
forward to get the following expression for pd=ln(P/D);
pd
i,t− 1
=− r
i,t
+k
1,i
+ρ i
pd
i,t
+∆ d
i,t
+k
2,i
(pd
i,t
− δ i
)
2
=− ∞
X
j=0
ρ j
i
r
i,t+j
+
∞
X
j=0
ρ j
i
∆ d
i,t+j
+
k
1,i
(1− ρ i
)
+k
2,i
∞
X
j=0
ρ j
i
(pd
i,t+j
− δ i
)
2
(2.5)
Whereρ i
≡
e
δ i

/

1+e
δ i

=

e
E(ln(P
i,t
/D
i,t
))

1+e
E(ln(P
i,t
/D
i,t
))

andk
1,i
=ln

1+e
δ i

− ρ i
δ i
for δ i
= E(ln(P
i,t
/D
i,t
)). The second-order volatility term on the RHS is a new
addition to this model, and is described in the Appendix. The primary component of
the term is the volatility of price-ratios, discounted and multiplied by a constant, k
2,i
=
80
2.2. MODELS AND METHODS

(1+e
− δ )(− δe
− δ )+δe
− 2δ
(1+e
− δ )
− 2
. Instead of using a fixed value for ρ , which is usually
around 0.97 or 0.98 in historical U.S. equity market data, I estimate ρ i
at the individual firm
or portfolio level which allows for additional cross-sectional variation.
Both k
1,i
and k
2,i
are functions of δ = E(ln(P
i,t
/D
i,t
)). The first-order intercept, k
1,i
, is
the same as the standard Campbell and Shiller (1988) k calculated at the firm level, but
the volatility multiplier, k
2,i
, arises only through the second-order Taylor expansion. In the
decomposition, r
i,t
is the return at time t, and ∆ d
i,t
is the log change in dividends between
time t and time t− 1. The equation decomposes the P/D ratio into an infinite sum of the
change in dividends, returns, and the new volatility term which I call V. With ρ < 1, this
should be well-behaved as the series eventually converges.
Partial motivation for the second-order term, k
2,i
∞
P
j=0
ρ j
i
(pd
i,t+j
− δ )
2
, comes from Table 2.1
which showed that the majority of price-ratio variation lies in the cross-section. When the
second-order Taylor-series is calculated, the resulting additional term is a function of price-
ratio variance, so including it in my cross-sectional analysis, where most of the price-ratio
variance lies, seems natural.
Equation 2.5 gives a convenient way to decompose the P/D ratio using a vector auto-
regression (“VAR”) following Campbell and Shiller (1988). I define the information set avail-
able to the VAR asy
i,t
=[
r
i,t
, ∆ d
i,t
, (pd
i,t
− δ )
2
, pd
i,t
x
′
i,t
]
′
. Takex
i,t
∈X
i
, which contains all other
variables I include to predict P/D ratios, discussed in Section 2.3, as well as the previous-
period price-ratio. That is, all the J variables I am testing in my cross-sectional regression
are also included in the VAR when computing expected returns and change in dividends.
The VAR(1) specification is given by y
i,t
=c
i
+ϕ i
y
i,t− 1
+ϵ i,t
where ϕ i
is a J× J coefficient
matrix describing the loading of various elements in the y
i,t− 1
vector, each of which is di-
mension J× 1. This approach gives the expectations of future returns and dividend growth
rates at time t conditional on information, y
i,t
.
I include the term (pd
i,t
− δ )
2
for all of my VAR regressions even though this term is not
strictly necessary to estimate the first-order terms, including expected returns and change
81
CHAPTER 2. THE CROSS-SECTION OF PRICES
in dividends. Including this term provides additional information to the VAR which would
not normally be available to a first-order approximation, but I find that including it makes
very little difference in the estimation of expected returns and change in dividends.
The infinite forward-looking sum of discounted expected returns is calculated as;
r
∗ i,t
=E

∞
X
j=1
ρ j
i
r
i,t+j

y
i,t
!
=
∞
X
j=1
ρ j
i
ϕ j
i
y
i,t
e
1
(2.6)
Wheree
1
selects the first element (i.e. e
1
= [1 0 0 ... 0]
′
). Similarly, the expected future
dividend growth rate is calculated as;
d
∗ i,t
=E

∞
X
j=1
ρ j
i
∆ d
i,t+j

y
i,t
!
=
∞
X
j=1
ρ j
i
ϕ j
i
y
i,t
e
2
(2.7)
Where e
2
selects the second element (i.e. e
2
= [0 1 0 ... 0]
′
). And finally, the expected
second-order term which is approximately the future variance of price-ratios is calculated as;
V
∗ i,t
=E

∞
X
j=1
ρ j
i
(pd
i,t+j
− δ )
2

y
i,t
!
=
∞
X
j=1
ρ j
i
ϕ j
i
y
i,t
e
3
(2.8)
Wheree
3
selects the third element (i.e. e
3
=[0 0 1 ... 0]
′
).
TheseexpressionsappearaspartofmysetofRHSvariablestohelpexplaincross-sectional
variation in prices. The Campbell and Shiller (1988) model has been interpreted to say that
the dividend-yield, D/P
t
, should be completely explained by r
∗ i,t
and d
∗ i,t
. However, applied
in the cross-section, K
2,i
× V
i
= k
2,i
∞
P
j=0
ρ j
i
(pd
i,t+j
− δ )
2
explains a small but statistically
significant amount of price variation, while
k
1,i
(1− ρ i
)
explains a very large and very significant
portion.
The expectations for r
∗ i,t
, d
∗ i,t
, and K
2,i
× V
i
formed using the above VAR are estimated
with error and they are used as predictors in my cross-sectional specification after being es-
timated. This opens up my cross-sectional specification to potential errors-in-variables bias.
To mitigate the estimation errors, I use a version of the Shanken (1992) adjustment when
82
2.2. MODELS AND METHODS
reporting the coefficients from my cross-sectional regressions. This exploits the fact that the
VAR provides estimates of the error variance for my Campbell and Shiller terms. I adjust
the cross-sectional regression estimator by the cross-sectional covariance of the estimation
errors of expected returns, change in dividends, and the second-order volatility term. This
adjustment does meaningfully impact the size of the coefficients in cross-sectional regressions
on expected returns, change in dividends, and volatility, but the impact on the t-statistics
is minimal.
Cross-Sectional k
1,i
and k
2,i
When the Campbell and Shiller (1988) decomposition is applied to the cross-section of in-
dividual stocks, important adjustments must be made. Consider the third and fourth terms
originating from Equation 2.5;
K
1,i
≡ k
1,i
(1− ρ i
)
=
ln

1+e
δ i

− ρ i
δ i
(1− ρ i
)
(2.9)
K
2,i
× V
i
≡ k
2,i
∞
X
j=0
ρ j
i
(pd
i,t+j
− δ i
)
2
(2.10)
Here, ρ i
=

e
δ i

/

1+e
δ i

is the weight of the log-price in the approximation, while 1− ρ i
is the weight of the log-dividend in the approximation. K
1,i
captures the price level of each
firm, discountedbyeachfirm’slog-dividendweight. Thistermistime-invariantandtherefore
usually ignored when applying the decomposition to the time-series, but it has reasonably
large cross-sectional variation. Similarly, K
2,i
× V
i
is generally ignored completely and only
results from the second-order estimation I include in Equation 2.5, but it is similarly time-
invariant.
I want to include these terms for their cross-sectional variation, but I do not want to
include future information at time t, so I calculate these each term at each time t using
only previous information, K
prev.
1,i,t
and K
prev.
2,i,t
× V
prev.
i,t
. These terms are the same as K
1,i
and K
2,i
× V
i
, but calculated at time t for firm or portfolio i using only backwards-looking
83
CHAPTER 2. THE CROSS-SECTION OF PRICES
information that is available at that time. For notational convenience, I will usually refer to
these terms as K
1,i
and K
2,i
× V
i
, noting that in all empirical results, these terms are fully
ex-post.
By calculating each of these terms at the individual firm or portfolio level using only
backward-looking information at each time t, I am able to examine them in the cross-
section through time. While this procedure adds significant computational complexity to
the datasets used in this paper, it enables me to better understand the dynamics of these
terms in relation to individual stock prices.
2.3 Data
2.3.1 Individual Firms
Campbell and Shiller (1988) rely on a “parsimonious” information set when building their
expectedreturnandchangeindividendestimates, whichincludesjustthelogofthedividend-
yield, returns, and change in dividends. I choose to supplement this selection because, as
noted by Campbell and Shiller (1988), doing so could only “strengthen a rejection of the
model.” The information set that I use, in addition to those used by Campbell and Shiller,
includes measures of firm-level risk and financial frictions. A complete discussion of these
variables is included in the Appendix.
I start with a set of variables meant to capture the variation explained by the FF5 model,
which I take to be my set of efficient market variables. Specifically, I include rolling market
beta, which is each firm’s backward-looking beta to the CRSP total market index, as well as
similarly defined SMB, HML, RMW, and CMA betas. I also include the standard deviation
of the error terms to help capture variation from missing terms in this efficient market
information set. I add to that set a standard measure of firm-leverage to capture potential
variation at the firm-level, which I primarily to provide information about the firm’s balance
sheet. While HML (formed on Book-to-Market ratios) may capture a measure of equity-
84
2.3. DATA
market leverage, this leverage here will provide the VAR information about non-market
leverage.
I add to that set of risk variables information about one-year forecasted earnings, includ-
ing the average estimate, number of analysts, and the standard deviation of those estimates.
I then add to the earnings information the standardized unexpected earnings of each firm,
(“SUE”), which should give a measure of how predictable the firm’s earnings have been.
So far, the information set includes what I would call “efficient-market variables.” These
terms are based on the FF5 with the addition of a term for firm leverage, as well as the
one-year forecasted earnings and information about the reliability of those forecasts. I now
move to additional variables which I call financial frictions. These frictions are terms which
would likely be of no use to investors in an efficient market, but have been shown to be of
value. I include measures of liquidity and the squared-liquidity value, share issuance and
repurchases, and institutional ownership as a percent of shares outstanding and the number
of institutional owners.
All the variables included are calculated at the individual firm level. Appendix 2.7
includes detailed information about these variables, their construction, and the reason for
including them.
2.3.2 Portfolios
I include in my analysis a total of 75 portfolios formed on a subset of the firm-level charac-
teristics. Of primary interest is the effect of smoothing dividends through time. Individual
firms have very lumpy dividends which require some smoothing between time periods if using
monthly data. The goal of using portfolios is examining what happens when I require little
to no averaging through time in my analysis by having at least one firm in each period which
pays a dividend.
These portfolios are composed of 75 “5x5” sorted portfolios, following the standard Fama
and French portfolio sorting methodologies (Fama and French, 1992, 1993, 2015, 2019).
85
CHAPTER 2. THE CROSS-SECTION OF PRICES
To form these portfolios, I collect firm-level information on market capitalization (MC),
operating profitability (OP), investment or change in total assets (INV), and book-to-market
ratio (BM). These LHS portfolios follow the 5x5 sort of MC
i,t
, the market capitalization of
the stocks in the portfolio at time t with BM
i,t
, OP
i,t
, or INV
i,t
. I form these portfolios and
update them at the end of June in each year.
Unlike the Fama and French research portfolios, my variable of interest is not returns.
Instead, I form each of these portfolios where the response variable is instead the ratio of
market-capitalization to total dividend payments within the portfolio. Using the simple
identity;
P
t
D
t
=
MCt
Shares Outstanding
t
Total Dividendst
Shares Outstanding
t
=
MC
t
Total Dividends
t
(2.11)
I aggregate firms into collections of price-ratios by summing up the total market capitaliza-
tion of all firms and dividing by the total dividend payments.
Extracting price-ratios of portfolios is relatively difficult. Unlike with returns, the asset-
weighted average of the underlying firms’ price-ratios is not necessarily the price-ratio of
the aggregate set of firms. Instead, the method I use here is approximately equal to each
portfolio acting as an acquirer which brings together each 5x5 portfolio’s firms under one
entity that has a size equal to the sum of market-capitalization and total cash-flows equal to
the sum total of all firms dividends. Forming portfolios in this way still allows me to examine
the cross-sectional variation of price-ratios but with the added benefits of using portfolios.
I do run into data limitations with this method. I need to split the equity market into 75
buckets with the goal of having as few months as possible with zero dividend payments in
each of those portfolios. Because of this, I exclude all characteristics which are not observed
at a monthly level or which force the removal of too many firms. The resulting dataset has
the same characteristics as the individual firms, except for the FF5. Instead of taking the
asset-weighted betas and error standard deviations of firms within each portfolios-month
observation, I instead include the asset-weighted characteristic used to generate SMB, HML,
RMW, and CMA; specifically MC, BM, OP, and INV. Using the firm-level betas forces the
86
2.4. EMPIRICAL RESULTS
elimination of too many observations.
I do not use this portfolio formulation as a primary result. Instead, I use this to see how
robust my individual firm-level results are to aggregation.
2.4 Empirical Results
I first examine individual firms and then move to portfolios. While I would prefer to use just
firm-level data, there are limitations to firm data such as the need to smooth dividends. As
I show, there may be ways to avoid this problem when using portfolios. My primary concern
is that smoothing the dividend process may inflate the overall importance of the dividend
component, so examining portfolios may lead to helpful insights.
2.4.1 In-Sample, Individual Firms
I start with panel regressions before decomposing the results further using the cross-sectional
Fama and MacBeth (1973) estimator. These results are meant to provide a high-level sum-
mary before estimating cross-sectional regressions. Table 2.2 contains these results. I include
firm and date fixed-effects and as a result, the variation captured ( R
2
) is closer to 50% than
one-third, as was estimated in the introduction. To keep notation simple, I take r
∗ =r
∗ i,t
and
d
∗ =d
∗ i,t
, which are themselves both expectations, and K
1
=K
prev.
1,i,t
, K
2
× V =K
prev.
2,i,t
× V
i,t
.
Note that my use of ‘in-sample’ here does not imply that everything is contemporaneous; I
still lag these terms, which can be seen in Equation 2.2.2.
For P/D (columns (1) - (3)), the coefficient on r
∗ is insignificant, but for d
∗ it is positive
and significant across all models. The addition of K
1
and K
2
× V does not change the
coefficientsforreturnordividendexpectationsbymuch, andbotharestatisticallysignificant.
For P/D, which is the firm-level predictor most similar to the original Campbell and Shiller
model’s response variable, it seems that expected returns do not appear to explain much
variation in the panel. Instead, the change in cash-flow component at the individual firm
87
CHAPTER 2. THE CROSS-SECTION OF PRICES
Table 2.2: Analysis of Cross-Sectional and Time-Series Variance
Dependent Variables: P/D P/E
Model: (1) (2) (3) (4) (5) (6)
Variables
r
∗ i,t
-0.0038 -0.0004 -0.0004 -0.0107 -0.0094 -0.0093
(-0.5164) (-0.0504) (-0.0502) (-3.796) (-3.084) (-3.074)
d
∗ i,t
0.0504 0.0512 0.0512 0.0288 0.0274 0.0274
(5.227) (4.685) (4.685) (7.379) (6.502) (6.478)
K
prev.
1
0.1076 0.1075 0.6641 0.6642
(7.843) (7.844) (35.82) (35.84)
K
prev.
2
× V
prev.
− 6.42 0.0001
(-19.93) (0.2845)
Fixed-effects
Firm Yes Yes Yes Yes Yes Yes
Date Yes Yes Yes Yes Yes Yes
Fit statistics
Observations 369,555 342,493 342,493 558,193 509,206 509,206
R
2
0.431 0.449 0.449 0.441 0.462 0.462
Within R
2
0.033 0.046 0.046 0.012 0.056 0.056
Clustered (NCUSIP & date) co-variance matrix, t-stats in parentheses
Signif. Codes: ***: 0.01, **: 0.05, *: 0.1
This table provides a decomposition of the price-to-dividend (“P/D”) ratio and the price-to-earnings
(“P/D”) ratio for data used in this paper. The individual firms used in this calculation are a sample of
all firms listed on CRSP. Data is collected from 1985 through 2018. Observations are removed if a firm
is missing characteristics listed in Section 2.3.
level seems more important.
For P/E (columns (4) - (6)), expected returns are negative and significant, while ex-
pected change in earnings is positive and significant. The coefficient on change in earnings
is generally about an order of magnitude larger than for expected returns. As with P/D, K
1
is positive and significant, but for this measure of price, K
2
× V is statistically insignificant.
These results show that while the coefficient signs are correct relative to the models predic-
tions, it seems that P/E is, like P/D, more sensitive to changes in earnings than to expected
returns.
The additional term resulting from the second-order Taylor approximation, K
2
× V, is
significant and negative for P/D which provides two insights as to how investors set P/D
ratios. First, the historic volatility of P/D does seem to impact a firms P/D ratio, but the
88
2.4. EMPIRICAL RESULTS
Table 2.3: Cross-Sectional Regressions of Price on Matched r
∗ i,t
, d
∗ i,t
, K
prev.
1
, K
prev.
2
× V
P/D P/E
(1) (2) (3) (4) (5) (6) (7) (8)
Intercept 5.108 5.108 5.108 5.108 2.956 2.956 2.956 2.956
(4.635) (4.635) (4.635) (4.635) (3.173) (3.173) (3.173) (3.173)
r
∗ i,t
-0.017 -0.016 -0.010 -0.001 -0.002 -0.027 -0.025 0.006
(-3.101) (-3.244) (-1.591) (-0.909) (-0.680) (-5.191) (-6.777) (5.633)
d
∗ i,t
0.130 0.122 0.121 0.001 0.056 0.070 0.064 -0.007
(8.315) (9.045) (9.330) (0.748) (8.145) (7.893) (9.647) (-4.878)
K
prev.
1
0.256 0.252 0.002 0.007 0.322 -0.003
(7.770) (7.922) (0.884) (2.922) (7.754) (-1.431)
K
prev.
2
× V
prev.
-0.028 0.002 0.051 0.007
(-1.933) (0.977) (7.242) (4.624)
Lagged LHS 1.031 0.613
(8.636) (11.404)
Industry YES YES YES YES YES YES YES YES
Avg. XS R
2
0.103 0.165 0.172 0.922 0.187 0.204 0.360 0.858
Sample Size 311,354 311,354 311,354 311,354 462,267 462,267 462,267 462,267
This table follows the method outlined in Fama and MacBeth (1973). I calculate the cross-sectional
OLS coefficient for r
∗ i,t
, d
∗ i,t
, K
prev.
1
, and K
prev.
2
× V. The LHS are the one-month-ahead natural log of
P/D and P/E which is Price divided by per-share Net-Payout and Earnings, respectively. I include an
Industry Control from the Fama-French 48 portfolios which are calculated using the primary SIC Code
listed on CRSP. The coefficients for r
∗ i,t
, d
∗ i,t
, K
2
× V include the Shanken (1992) adjustment, and change
in dividends matches the LHS divisor (see Section 2.2). Sample Size represents the data after missing
data are removed, and for which missing data and perfect 0 are removed from the Campbell and Shiller
approximations. Data is collected from 1985 through 2018. Observations are removed if a firm is missing
characteristics listed in Section 2.3.
same is not true of P/E. Second, as a term which is added onto the original Campbell and
Shiller specification, the significance of this terms shows that the second order model does
capture additional variation. The P/E ratio does not appear to be affected by the addition
of a second-order term.
The results in Table 2.2 provide a basis upon which the remaining results in this paper
build. These results seem to line up at least partially with the results in Vuolteenaho (2002),
suggesting that at the individual firm-level, the dividend (or as a proxy, earnings) component
is important. The analyses which follow use the differences between firm prices to further
examine this question.
I now turn to examining the cross-section specifically. Table 2.3 contains the cross-
sectional Fama-MacBeth results for the same data used in Table 2.2. I show the Fama
89
CHAPTER 2. THE CROSS-SECTION OF PRICES
and MacBeth (1973) coefficients with AR(1)-adjusted t-statistics for each of the four core
variables in the Campbell and Shiller (1988) decomposition in Section 2.2.3. The classic
version of this model includes just r
∗ and d
∗ , however I include terms for K
1
, K
2
× V, and
lagged price ratio.
Starting with columns (1) and (5) which include just r
∗ and d
∗ , expected returns, r
∗ ,
is negative, as expected from Equation 2.5, but is only significant for the P/D ratio with
a coefficient of -0.017. This is the opposite result found in the panel regressions, which
showed that r
∗ was only significant for P/E. Change in dividends, d
∗ , is significant for both
P/D and P/E with coefficients of 0.130 and 0.056, respectively, and t-statistics above 8.
The cross-sectional variation in price-ratios is at least partially explained by return and
dividend expectations, though the lack of significance for r
∗ with P/E is surprising given
the existing literature’s findings that expected returns are often more important. These two
terms together constitute the “classic” components of the Campbell and Shiller model, and
I find that in the cross-section of price-ratios, they capture between 10% and 19% of the
overall variation, generally more for price-to-earnings.
Next, I turn to K
1
in models (2) and (6). K
1
is generally ignored in time-series studies
since it is time-series invariant, but, as discussed in Section 2.2.3, it is a cross-sectionally
varying collection of terms resulting from the Taylor approximation. Adding K
1
in the
second column of each panel increases average XS R
2
to 0.165 and 0.204 for P/D and P/E,
respectively. K
1
has positive and significant coefficients for both P/D and P/E, and both r
∗ andd
∗ remain statistically significant with K
1
included. For P/E, the addition ofK
1
actually
makes r
∗ significant with a coefficient of -0.027 and a t-statistic of -5.191. This result is not
completely surprising given the discussion in Campbell and Shiller (1988), which shows that
the K
1
term is essentially the intercept of the model; excluding it could impact the other
terms. Overall, the K
1
term does increase the fit of both models, but it still leaves about
80% of variation in price-ratios unexplained.
3
3
In untabulated results, I calculate the models in columns (2) and (6) which excludes P/D and P/E from
the information-set that is available to the VAR when generating r
∗ and d
∗ . In this setting, the results favor
90
2.4. EMPIRICAL RESULTS
The decomposition provided in Campbell and Shiller (1988) relies on a first-order Taylor
approximation. Recent literature has shown that this procedure may miss important vari-
ation, particularly in long-run variables. To test for this, and potentially use this missed
variation to improve my model, I include this second-order term in the cross-sectional re-
gressions. The K
2
× V term is negative and significant for P/D with a coefficient of -0.028
and a t-statistic of -1.933, and positive and significant for P/E with a coefficient of 0.051
and a t-statistic of 7.242. For P/D, the first-order approximation appears to miss mean-
ingful variation, and including this second-order term lowers the cross-sectional variation in
P/D. For P/E, this also appears to be true, except the additional variance term increases
the cross-sectional variation in P/E. A first-order Taylor approximation does miss a signifi-
cant amount of variation for both price-ratios, though the direction and size of that effect is
dependent on the price-ratio used.
These results suggest that firms with a higher historical P/D variance tend to have lower
P/D ratios, equivalent to firms with high dividend-yield variation having higher dividend-
yields. However, firms with high P/E ratio variance tend to have higher P/E ratios. Perhaps
firmsthathavehighgrowthratesjustifyinghigherP/Eratios(abovetheirindustrycontrols).
The cross-sectional results for P/D line up with the panel regression results in Table 2.2, but
the cross-sectional results from P/E appear to be meaningfully different.
The last column of each panel in Table 2.3 contains all four of the derived terms in
Equation 2.5, as well as a lagged price-ratio. Since price-ratios are levels, they generally
have very high autocorrelation which would mean that the previous period’s price-ratio is
likely a very good indication of the current period’s price-ratio. Including a lagged price-ratio
in this regression tests the ability of my four term model to improve upon the estimate given
by the previous period’s price-ratio.
The results from this test show that lagged P/D and P/E (“Lagged LHS”) are both highly
K
1
significantly more, and the model which includes K
1
more than doubles the overall variation captured
by models (1) and (5) respectively. However, I include P/D in X
i,t
to better align with the model used in
Campbell and Shiller (1988)
91
CHAPTER 2. THE CROSS-SECTION OF PRICES
significant. For P/D in column (4), the coefficient on lagged P/D is about 1.0, and for P/E in
column (8) it is about 0.61, and both have t-statistics above 8. It is interesting to note that
P/E seems to have a lower autocorrelation than P/D with a coefficient that is noticeably
lower than one.
4
When the price-ratio is included, the loadings for r
∗ , d
∗ K
1
, and K
2
× V
become statistically insignificant and only lagged P/D is significant. For P/E, r
∗ and d
∗ are both much smaller than in previous columns, and their signs reverse, but they remain
statistically significant with lagged P/E included. For P/E, K
2
× V is statistically significant,
indicating that even with lagged P/E included, there is missed variation attributable to the
variance of P/E. Both price measures see a significant boost in overall fit with the average XS
R
2
is about 50% to 70% percentage points higher for both models when lagged price-ratios
are included.
Including lagged price-ratio in the regression demonstrates several important facts about
the Campbell and Shiller (1988) model when applied to the cross-section of returns. First,
a significant amount of variation seems to be missed by the model. The Campbell and
Shiller model decomposes price-ratios into three terms; r
∗ , d
∗ and K
1
. These terms still
appear to miss a significant amount of variation which can be captured by the lagged LHS,
despite including lagged P/D or P/E in the VAR specification that generates all three terms.
Second, the K
2
× V term is significant for P/E with a t-statistic of 4.624, implying that the
first-order linearization procedure which is most commonly used in these models appears to
miss meaningful variation (see Pohl et al., 2018). For P/E this shows that, even in a model
with an average cross-sectional R
2
of 0.858, some variation is missed if the historical P/E
variance term is excluded.
Lagged price-ratios are a great predictor for P/D which is unsurprising given its high
autocorrelation. In the cross-section of my data, the assumption that P/D is stationary in
Cochrane (2011) is not exactly correct in my data, but it is so close to true that no other term
in P/D can enter as significant. However, for P/E which has a lag coefficient ( t-statistic) of
4
Table 2.1 shows that the XS of P/E captures slightly less variation than P/D. The difference may come
down to the lower variance, allowing more variation to be captured by r
∗ , d
∗ , K
1
, and K
2
× V.
92
2.4. EMPIRICAL RESULTS
0.613 (11.404), the results admit far more variation in r
∗ , d
∗ , K
1
, and K
2
× V. So while the
high autocorrelation of P/D is not surprising in Table 2.3, this table does demonstrate that
the high autocorrelation in P/D ratios makes inference on return and dividend expectations
very difficult.
What explains the change in P/D and P/E?
P/D and P/E in my primary data set have autocorrelations greater than 0.90. These high
autocorrelationsmakeoneresultinTable2.3relativelyunsurprising; thebestsinglepredictor
price-ratios is the lagged price-ratio. However, the previous results show that in addition to
lagged price-ratio, K
1
and K
2
× V may retain some explanatory power. Further, while the
coefficient on lagged P/D is around 1.0, the coefficient for P/E it is only about 0.61. In order
to better understand the effects of this high autocorrelation, I now use r
∗ ,d
∗ ,K
1
, andK
2
× V
to explain the change in price-ratios between time periods; ∆ P/D =P/D
i,t+1
− P/D
i,t
and
∆ P/E = P/E
i,t+1
− P/E
i,t
. This is similar to forcing the regression coefficients on Lagged
LHS in Table 2.3 to be exactly 1.0, and a significant predictor is one which helps explain the
cross-sectional differences in the change in price-ratios between periods.
The results in Table 2.4 show that r
∗ is never significant for P/D (models (1)-(3)), and it
is always significant for P/E (models (4)-(6)). The coefficient on d
∗ is always negative, and
d
∗ is significant for all models in Table 2.4 regardless of LHS price-ratio used. This result is
rather surprising if we assume that investors should incorporate all available information into
prices at time t. Instead, firms with large changes in dividend payments or earnings tend to
have smaller changes in price-ratios between periods. While Equation 2.5 and Table 2.3 show
that firms which pay higher dividends will have higher price-ratios, this table demonstrates
that those same firms tend to have smaller adjustments to price-ratios.
I find the intercept of the first-order Taylor approximation, K
1
, is significant in the cross-
section of change in price-ratios even when using my ex-post definition. For P/D, K
1
has a
coefficient of -0.015 and a t-statistic of -3.739, while for P/E it has a coefficient of -0.020 and
93
CHAPTER 2. THE CROSS-SECTION OF PRICES
Table 2.4: Cross-Sectional Regressions of ∆ P/D and ∆ P/E on r
∗ i,t
, d
∗ i,t
, K
prev.
1
, K
prev.
2
× V
P/D P/E
(1) (2) (3) (4) (5) (6)
Intercept -0.001 -0.001 -0.001 0.007 0.007 0.007
(-0.374) (-0.374) (-0.374) (2.210) (2.210) (2.210)
r
∗ i,t
0.000 0.001 0.000 0.007 0.008 0.007
(0.260) (0.533) (0.148) (5.604) (6.178) (5.110)
d
∗ i,t
-0.004 -0.003 -0.002 -0.012 -0.011 -0.009
(-3.708) (-2.579) (-2.209) (-6.480) (-6.230) (-4.705)
K
prev.
1
-0.015 -0.014 -0.020 -0.020
(-3.739) (-3.668) (-8.854) (-8.841)
K
prev.
2
× V
prev.
0.001 0.007
(0.712) (4.215)
Industry YES YES YES YES YES YES
Avg. XS R
2
0.080 0.086 0.084 0.073 0.080 0.085
Sample Size 308,187 308,187 308,187 459,469 459,469 462,267
This table follows the method outlined in Fama and MacBeth (1973). I calculate the
cross-sectional OLS coefficient for r
∗ i,t
, d
∗ i,t
, K
prev.
1
, and K
prev.
2
× V. The LHS are the
changes in one-month-ahead natural log of P/D and P/E which is Price divided by per-
share Net-Payout and Earnings, respectively. ∆ P/D =P/D
i,t+1
− P/D
i,t
, and ∆ P/E =
P/E
i,t+1
− P/E
i,t
. I include an Industry Control from the Fama-French 48 portfolios
which are calculated using the primary SIC Code listed on CRSP. The coefficients for
r
∗ i,t
,d
∗ i,t
,K
2
× V include the Shanken (1992) adjustment, and change in dividends matches
the LHS divisor (see Section 2.2). Sample Size represents the data after missing data
are removed, and for which missing data and perfect 0 are removed from the Campbell
and Shiller approximations. Data is collected from 1985 through 2018. Observations are
removed if a firm is missing characteristics listed in Section 2.3.
94
2.4. EMPIRICAL RESULTS
a t-statistic of -8.854. This is surprising sinceK
1
is the intercept of the Taylor approximation
for P/D’s level, not change in P/D. It is clear that K
1
should explain a significant amount of
cross-sectional variation in price-levels, but I find that it also explains a significant amount
of variation in change in price-levels, even when studentized. Firms with a higher K
1
value
will have a smaller change in P/D between time-periods relative to other firms.
5
K
2
× V does capture a statistically significant amount of variation at the individual firm
level for P/E, but does not for P/D. The change in P/D, equivalent to controlling for lagged
P/D when the coefficient is forced to be 1.0, is fully explained by a two-term model, but
the cross-sectional dispersion in the change in P/E does rely on the second-order Taylor
approximation.
Decomposing K
1
and K
2
× V
So far, the newly added K
1
and K
2
× V terms appear to be meaningful predictors of cross-
sectional price variation. Time-series invariantK
1
is a large and significant component of the
variation captured by the Campbell and Shiller (1988) model. Similarly, the K
2
× V term,
which captures second-order variation missed by the traditional first-order decomposition,
appears to be significant for both P/D and P/E in levels, and for change in P/E. I now ask
if these terms capture information outside my information set X
i,t
, or if instead the VAR
used to generate these terms is missing information that is otherwise available.
To see why I want to decompose K
1
, I provide a percentage decomposition of the overall
variation captured by each term. Table 2.5 contains the univariate percentage decomposition
for each of r
∗ , d
∗ , K
1
and K
2
× V. To generate this table, I calculate the average XS R
2
for
each term, ran as a univariate regression, and express that a percentage of the total variance
captured by the four term Campbell and Shiller (1988) model. I do not orthogonalize these
terms for two reasons. First, they are already linear combinations of the predictors in X
i,t
,
so I do not want to over-penalize these terms since they are the results of an autoregressive
5
This may appear unsurprising since the coefficient on P/E in Table 2.3 was 0.613. However, what this
result shows is that the change through time to P/E increases when P/E is more volatile.
95
CHAPTER 2. THE CROSS-SECTION OF PRICES
Table 2.5: Analysis of Cross-Sectional and Time-Series Variance
Panel A P/D P/E
r
∗ i,t
1.42% 1.31%
d
∗ i,t
15.50% 2.93%
K
prev.
1
68.56% 93.09%
K
prev.
2
× V
prev.
14.53% 2.67%
This table contains the percentage decomposition of modeled cross-sectional R
2
at-
tributable to each term in the Campbell and Shiller (1988) model derived in Section
2.2.3. Data is collected from 1985 through 2018. Observations are removed if a firm is
missing characteristics listed in Section 2.3.
procedure. Second, I find that the actual amount of variation which is overlapping between
the terms is quite small; without orthogonalizing them, the total variation captured is almost
identical to that version when ran together.
The results in Table 2.5 are relatively surprising. Return expectations are almost neg-
ligible in the overall model, explaining less than 2% of variation for both P/D and P/E.
The change in dividend component is significantly stronger for P/D than it is for P/E (for
which this term represents change in earnings) at 15.50% compared to about 2.93%. The
largest predictor of cross-sectional price variation, by far, is the K
1
term which captures
about 68.56% of variation for P/D, and about 93.09% for P/E. The remainder is captured
by K
2
× V which is approximately the same explanatory power as the dividend component;
about 14.53% for P/D and 2.67% for P/E, and larger than the return component in both
cases.
Despite most papers finding that return expectations are the most significant predictor
in the Campbell and Shiller (1988) decomposition, I find that in the cross-section of price-
ratios, dividends play a much larger role than returns, explaining between three to ten times
more variation. The K
1
term is by far the largest contributor, and likely the key to using
this model at all in the cross-section of prices. However, K
2
× V also appears to be strong,
which is surprising given that the first-order decomposition is so commonly used. It appears
that the amount of variation missed by excluding the second-order term is approximately the
96
2.4. EMPIRICAL RESULTS
Table 2.6: Decomposing K
prev.
1,i,t
on X
i,t
P/D P/E
Coeff. T-Stat. Coeff. T-Stat.
Constant 6.762 65.175 3.603 166.919
Rolling Beta 0.135 3.370 0.008 1.038
Error Standard Deviation -1.824 -2.948 2.579 12.633
SMB Beta 0.015 0.557 0.020 3.856
HML Beta -0.094 -4.493 -0.075 -16.520
CMA Beta 0.006 0.465 0.016 5.160
RMW Beta 0.057 3.533 -0.049 -15.157
Leverage -0.025 -0.885 -0.000 -0.969
1-Year Forecasted EPS -0.027 -1.828 0.049 12.930
1-Year Analyst SD -0.022 -0.183 0.001 2.047
1-Year Num. Analysts 0.034 6.057 0.004 3.276
Standardized Unexpected Earnings 0.390 1.546 -0.727 -7.750
Illiquidity -0.167 -3.634 -0.103 -5.823
Illiquidity Squared 2.313 3.044 1.663 3.366
Shares Issued 0.000 0.540 -0.000 -1.615
Shares Repurchased -0.003 -0.395 0.001 0.402
Inst. Own. Percentage -0.001 -0.493 0.009 1.091
Number of Inst. Own. -0.001 -8.097 0.000 7.057
This table follows the method outlined in Fama and MacBeth (1973). I calculate the
cross-sectional OLS coefficient for all terms in my X
i,t
matrix. The LHS is the intercept
oftheTaylorapproximation,K
1
. Dataiscollectedfrom1985through2018. Observations
are removed if a firm is missing characteristics listed in Section 2.3.
same amount of variation missed by excluding cash-flow expectations, and significantly more
variation if excluding return expectations which are generally the most significant predictor.
I now explore what explains K
1
, the most important term in the model, by regressing
it on all the variables in X
i,t
. I include these results in Table 2.6. The K
1
term defined on
P/D loads significantly on market beta, error standard deviation, RMW beta, information
about 1-year EPS forecasted growth, and the number of institutional owners. For P/E,
the results are similar and the significant predictors include multiple beta measures, 1-year
EPS forecast information, unexpected earnings, and institutional ownership. All of this
information is included in the VAR when forming the expectations for returns and cash-
97
CHAPTER 2. THE CROSS-SECTION OF PRICES
Table 2.7: Decomposing K
prev.
2,i,t
× V
prev.
on X
i,t
P/D P/E
Coeff. T-Stat. Coeff. T-Stat.
Constant 1.441 1.989 0.014 0.477
Rolling Beta -0.186 -1.050 -0.022 -0.980
Error Standard Deviation -10.121 -1.332 0.953 3.657
SMB Beta -0.005 -0.078 0.010 1.241
HML Beta -0.004 -0.023 0.008 0.805
CMA Beta -0.117 -1.683 -0.019 -1.608
RMW Beta -0.098 -1.079 -0.021 -2.768
Leverage 0.029 0.430 -0.000 -0.040
1-Year Forecasted EPS -0.033 -0.790 -0.044 -2.270
1-Year Analyst SD -0.101 -0.457 0.000 1.919
1-Year Num. Analysts -0.006 -0.583 0.005 3.250
Standardized Unexpected Earnings 0.634 0.761 1.100 1.490
Illiquidity -0.102 -0.324 -0.033 -1.045
Illiquidity Squared 1.531 0.319 0.530 0.949
Shares Issued 0.001 0.842 -0.000 -0.574
Shares Repurchased -0.209 -0.781 0.004 1.455
Inst. Own. Percentage -0.000 -0.036 0.001 0.787
Number of Inst. Own. -0.000 -0.039 -0.000 -1.843
This table follows the method outlined in Fama and MacBeth (1973). I calculate the
cross-sectional OLS coefficient for all terms in my X
i,t
matrix. The LHS is the additional
termresultingfromasecond-orderTaylorapproximation,K
2
× V, andrepresentsthetime
t ex-post price-ratio variance. Data is collected from 1985 through 2018. Observations
are removed if a firm is missing characteristics listed in Section 2.3.
flows, but it appears the VAR still struggles to explain cross-sectional variation attributed
totheseterms. Sowhilethistermisveryimportant, andrepresentsthepersistentcomponent
of P/D, the variables in my model can capture a significant portion of price-ratio persistence.
I repeat this same exercise for K
2
× V in Table 2.7. For P/D this term is orthogonal to
almost all predictors, so it does not appear that the model has missed variation for P/D.
Instead, the variance term appears closer to an error term, orthogonal to all the data in my
information set. For P/E, however, K
2
× V loads significantly on several factors, including
many of those that were significant for K
1
. This includes information about the 1-year
forecasted EPS, RMW Beta, and error standard-deviation.
98
2.4. EMPIRICAL RESULTS
K
2
× V is both the added term resulting from a second-order Taylor approximation, and
when simplified, it also is a function of the underlying price-ratio’s variance. These results
have shown us that the variance of P/D is not well explained by any of the terms that I
already have included in my data set, while for P/E, it appears that variance increases in
analyst coverage, decreases in forecasted EPS growth, and decreases in loadings on RMW
Beta (operating profitability).
2.4.2 In Sample, Portfolios
The goal of this paper is to understand how return and cash-flow expectations differentially
affect firms’ price-ratios. It is most natural to examine this at the individual firm level since
that is where price-ratios vary. However, firm-level exploration requires a judgment calls to
be made in order to estimate the Campbell and Shiller model, such as aggregating dividends.
Firms pay dividends usually three or four times per year. These dividends vary throughout
the year, and leave about 75% of monthly observations with no cash-flows. For that reason,
I can either aggregate up to the annual level, or smooth by taking an annual average (which
is what I have done in the previous sections).
The smoothing of dividend payments is somewhat arbitrary. While it may be clear that
managers use a 12-month year as their basis of dividend payments, it is not clear that is the
right measurement for investors, who may use different windows for their measurement of
dividend-payment fluctuation. To check for the reliability of the above estimates, I combine
collections of firms into portfolios which are sorted on characteristics (see Section 2.3.2).
Theseportfoliosrequirenosmoothingandinsteadpaydividendsinsomeformatthemonthly
level.
Ofcoursethisdramaticallyincreasesthevariabilityofdividendpaymentsoverthisperiod,
but as a test of the aggregation methodology, this takes the most extreme possible view. I
assumethatinvestorsupdatetheirdefinitionofchangeindividendsatthemonthlyfrequency.
If the patterns found in the previous section can be observed with these high-variability
99
CHAPTER 2. THE CROSS-SECTION OF PRICES
Table 2.8: Cross-Sectional Regressions of Price on Matched r
∗ i,t
, d
∗ i,t
, K
prev.
1
, K
prev.
2
× V
5x5 with Asset-Weighted Chars.
(1) (2) (3) (4)
Intercept 6.707 6.707 6.707 6.707
(16.283) (16.283) (16.283) (16.283)
r
∗ i,t
-0.053 -0.006 -0.082 -0.001
(-10.904) (-1.546) (-0.001) (-0.113)
d
∗ i,t
0.194 0.032 0.026 0.027
(15.726) (5.733) (3.407) (3.596)
K
prev.
1
0.387 0.390 0.372
(16.617) (16.736) (17.819)
K
prev.
2
× V
prev.
-0.012 -0.011
(-1.872) (-1.706)
Lagged LHS 0.032
(4.517)
Avg. XS R
2
0.092 0.204 0.376 0.398
Sample Size 30,553 30,553 30,553 30,553
This table follows the method outlined in Fama and MacBeth (1973). I calculate the cross-sectional OLS
coefficient for r
∗ i,t
, d
∗ i,t
, K
prev.
1
, and K
prev.
2
× V using the 5x5 sorted portfolios. The 5x5 portfolios are
formed by interacting MC with OP, INV, and BM. The LHS are the one-month-ahead natural log of
P/D and P/E which is Price divided by per-share Net-Payout and Earnings, respectively. I include an
Industry Control from the Fama-French 48 portfolios which are calculated using the primary SIC Code
listed on CRSP. The coefficients for r
∗ i,t
, d
∗ i,t
, K
2
× V include the Shanken (1992) adjustment, and change
in dividends matches the LHS divisor (see Section 2.2). Sample Size represents the data after missing
data are removed, and for which missing data and perfect 0 are removed from the Campbell and Shiller
approximations. Data is collected from 1985 through 2018. Observations are removed if a firm is missing
characteristics listed in Section 2.3.
dividend payments then it would appear to confirm the strength of the dividend component
in determining cross-sectional price variation.
Table 2.8 contains the in-sample results for my 5x5 sorted portfolios. The results include
the sorted portfolios with their asset weighted characteristics (“5x5 with Asset-Weighted
Chars.”). Theseasset-weightedcharacteristicsareusedtoestimatetheVARfortheportfolio-
level return and cash-flow expectations ( r
∗ and d
∗ , respectively).
Table 2.8, model (1) includes r
∗ and d
∗ and has an R
2
of just under 10%, approximately
in line with the results in Table 2.3. Both terms are highly significant and with the expected
signs. The addition of K
1
in model (2) more than doubles the R
2
, but seems to absorb the
explanatory power of r
∗ while d
∗ remains positive and significant. The addition of K
2
× V in
model (3) again has a negative coefficient, but is only marginally significant with a t-statistic
100
2.4. EMPIRICAL RESULTS
of-1.872. However,K
2
× V doesincreaseR
2
from0.204to0.376, seeminglycontributingmore
to the model than K
1
. Finally, the addition of lagged price-ratio (model (4)) is significant,
but with a much smaller increase to R
2
than in Table 2.3.
Table 2.8 reconfirms many of the results found with individual firms, but applied to
portfolios that do not smooth the cash-flow process. This table suggests the Campbell and
Shiller model derived in Equation 2.5 does capture the cross-sectional variation in price-
ratios, and the results do not appear to be overly sensitive to smoothing dividends through
time. Aswiththeindividualfirmresults, theportfolioresultssuggestthatchangeinexpected
returns,r
∗ , doesnotappeartocontributemuchtothecross-sectionalvariationinprice-ratios.
Instead, the difference in firm ratios seem to rely most on the change in cash-flows received.
Eliminating the need to smooth cash-flows diminishes the relative strength of lagged price-
ratio, showing that the Campbell and Shiller model, with it’s K
1
term included, works as a
model of cross-sectional variation. Finally, the addition of K
2
× V is significant and positive
even with portfolios, suggesting that the first-order approximation leaves some variation
unexplained which can be captured with a more precise approximation.
2.4.3 Out-of-Sample
The in-sample results demonstrate that the Campbell and Shiller (1988) decomposition does
capture cross-sectional price variation, but an approximation more precise than a first-order
expansion may be warranted. Further, the level component, K
1
, and the variance term,
K
2
× V, both capture cross-sectional variation above what is captured by the previous-
period price-ratio. This suggests that there may be additional information contributed to
the models by these firm-specific terms which is otherwise missed if predicting prices with
the previous-period observations.
I now test how well the proposed model and its terms work out-of-sample in the cross-
sectionofprice-ratios. Inthecross-section, theconceptofout-of-sampleisabitmoredifficult
to pin down than in the time-series. Instead of asking how well I can predict price or returns
101
CHAPTER 2. THE CROSS-SECTION OF PRICES
in t+1, I am more interesting in understanding how well I can capture the cross-sectional
variation in price-ratios at t+1. Of course, a great time-series model should help in both
regards. However, rejecting a cross-sectional model because it fails to capture time-series
variation may lead to the wrong conclusions.
Asimpletime-seriespredictioncoulduseafixedloadingestimatedinthepreviousperiods
on lagged characteristics to form predictions. For example, if I were using price-ratios, such
a model may take the form P
i,t+1
=α 0,i
+β 1
r
∗ i,t
+β 2
d
∗ i,t
+ϵ i,t
where β 1
and β 2
are estimated
prior to the realization of information in X
i,t− 1
which is used to form r
∗ and d
∗ . However,
my emphasis on the cross-section requires a slightly different model where instead of using
time-series loadings, I use the cross-sectionally estimated λ t
values averaged over a time
period;
P
i,t+1
=
¯Λ r
∗ t− 1
r
∗ i,t
+
¯Λ d
∗ t− 1
d
∗ i,t
+
¯Λ K
1
t− 1
K
1,i,t
+
¯Λ K
2
× V
t− 1
(K
2,i,t
× V)+u
i,t
(2.12)
where
¯Λ c
∗ t
is a function which smooths or averages the cross-sectional regression coefficient
for characteristic c
∗ i,t
= r
∗ i,t
, d
∗ i,t
, K
1,i,t
, and K
2,i,t
× V. This generates a rolling window over
which I can create out-of-sample cross-sectional predictions. I use either a one-month or
twelve-month average of λ t
;
¯Λ x
t
=
P
t− 1
t− 1− N
λ x,t
N
for N = {1,12}. In my second set of out-of-
sample tests, I separate my data into two distinct test and train data sets, and average the
cross-sectional coefficients over the entire training data set.
I compare out-of-sample performance using the average mean-squared prediction error
(“MSPE”), squared bias, and variance, and two fit metrics. The first fit metric is the stan-
dard Campbell and Thompson (2007) measure of fit, which is essentially an out-of-sample
time-series test. For my second measure of out-of-sample R
2
, I include a measure of the pro-
portional reduction in out-of-sample cross-sectional price-ratio variation between firms. This
measure is more directly related to the goal of an out-of-sample model in that it measures
the reduction in the relative spread in price-ratios. The metric is as follows;
R
2
XSOS
=1− P
i
((P
i,t
− b
P
i,t
)− (
¯ P
t
− ¯b
P
t
))
2
P
i
(P
i,t
− ¯ P
t
)
2
(2.13)
102
2.4. EMPIRICAL RESULTS
where P
i,t
is the price-ratio,
b
P
i,t
is the predicted value of price-ratio,
¯ P
t
is the average price-
ratio at time t and
¯b
P
t
is the average predicted value at time t. This value maps directly into
the statistic used in Yufeng, He, Rapach, and Zhou (2021), but modified for price-ratios and
OLS.
6
Table2.9PanelAcontainstheone-monthlaggedout-of-sampletestfortheP/Dratio. For
this test, I run a cross-sectional regression following the model in Equation 2.4 with different
combinations of predictors. I then take the t− 2 cross-sectional regression coefficient and
pair those with the t− 1 characteristic (r
∗ , d
∗ , K
1
, or K
2
× V). I use the t− 2 cross-sectional
coefficient because using t− 1 would require that the time t price-ratio is realized.
Starting with the first three models in Panel A, MSPE, squared bias, and variance are
all lowest for model (2) which has r
∗ , d
∗ , and K
1
compared to models (1) (r
∗ and d
∗ ) and
(3) (r
∗ , d
∗ ,K
1
and K
2
× V). Compared to model (1) with just r
∗ and d
∗ , the addition of K
1
slightly lowers the prediction error, but the addition of K
2
× V in (3) appears to increase
MSPE through bias but with a lower variance. Between models (4)-(6) which add lagged
price-ratiotomodels(1)-(3), respectively, theadditionofK
1
actuallyincreasestheprediction
error compared to the model with just r
∗ , d
∗ , and lagged price-ratio. The addition of K
2
× V
in model (6) continues to underperform the predictions made in model (4) as well as the
baseline model that includes just P/D. In fact, none of the models that I explore in this
table outperform the baseline model which uses just one-month lagged price-dividend ratio.
In general, the addition of K
1
when lagged P/D is excluded brings the largest reduction in
MSPE and squared bias, with a slight increase to the average variance of the prediction. The
addition of K
2
× V seems to impede out-of-sample performance, increasing MSPE through
either the bias (without lagged P/D) or through variance (with lagged P/D).
The fit statistics in Panel A reveal that interpreting the cross-sectional fit is meaningfully
different from time-series fit. Here, even the lagged P/D ratio (which comes from time t− 2)
6
I do explore all tables here using WLS and find that there are very few differences between the OLS
and WLS estimator when using price-ratios. This is different from the findings in Yufeng et al. (2021) when
using returns.
103
CHAPTER 2. THE CROSS-SECTION OF PRICES
Table 2.9: Out-of-Sample Model Comparison, One-Month Lag
MSPE Decomposition, P/D Avg(MSPE) Avg(Bias
2
) Avg(Variance) CT R
2
XS R
2
Panel A: P/D 1-Month
(1) r
∗ , d
∗ 1.523 0.806 0.716 -7.608 0.015
(2) r
∗ , d
∗ , K
1
1.412 0.667 0.745 -7.220 0.074
(3) r
∗ , d
∗ , K
1
, K
2
× V 1.416 0.690 0.726 -7.251 0.063
(4) r
∗ , d
∗ , Lag(P/D) 0.246 0.021 0.225 -0.011 0.909
(5) r
∗ , d
∗ , K
1
, Lag(P/D) 0.249 0.022 0.227 -0.038 0.905
(6) r
∗ , d
∗ , K
1
, K
2
× V, Lag(P/D) 0.250 0.022 0.229 -0.048 0.904
(7) PD Lagged 1 Month 0.221 0.007 0.213 -0.030 0.905
Panel B: P/D 12-Months
(1) r
∗ , d
∗ 1.555 0.828 0.726 -7.699 0.015
(2) r
∗ , d
∗ , K
1
1.446 0.690 0.757 -7.312 0.072
(3) r
∗ , d
∗ , K
1
, K
2
× V 1.494 0.721 0.773 -7.641 0.017
(4) r
∗ , d
∗ , Lag(P/D) 0.243 0.022 0.221 0.004 0.884
(5) r
∗ , d
∗ , K
1
, Lag(P/D) 0.243 0.022 0.221 0.003 0.881
(6) r
∗ , d
∗ , K
1
, K
2
× V, Lag(P/D) 0.243 0.022 0.222 0.003 0.881
(7) PD Lagged 12 Month 0.886 0.323 0.563 -2.055 0.670
Panel C: Train/Test Split-Sample
(1) r
∗ , d
∗ 1.163 1.046 0.118 -7.414 0.005
(2) r
∗ , d
∗ , K
1
1.071 0.954 0.117 -6.775 0.094
(3) r
∗ , d
∗ , K
1
, K
2
× V 1.078 0.961 0.117 -6.834 0.086
(4) r
∗ , d
∗ , Lag(P/D) 0.067 0.012 0.055 0.555 0.948
(5) r
∗ , d
∗ , K
1
, Lag(P/D) 0.067 0.012 0.055 0.555 0.948
(6) r
∗ , d
∗ , K
1
, K
2
× V, Lag(P/D) 0.067 0.012 0.055 0.555 0.948
(7) PD 0.923 0.808 0.116 -5.923 NA
(8) λ (P/D) 0.067 0.012 0.055 0.055 0.949
This table reports the mean-squared prediction error (“MSPE”), squared-bias, and variance de-
composition for out-of-sample predictions of price-divided (“P/D”) ratios. The first column
includes the models which are used in each row. r
∗ is the expected returns, d
∗ is the expected
change in dividends, K
1
is the intercept of the first-order Taylor approximation, and K
2
× V is
the additional variance term resulting from a second-order Taylor approximation, all from the
Campbell and Shiller (1988) model. Lag(P/D) represents the lagged price-dividend ratio. CT
R
2
is the Campbell and Thompson (2007) R
2
measure, and XS R
2
is the cross-sectional R
2
model derived from Yufeng et al. (2021). In Panel A, these terms are used in a cross-sectional
regression following Fama and MacBeth (1973). The coefficients are then lagged one additional
period (t− 2), and multiplied by the t− 1 terms for that model. That generates the time t
prediction for P/D
t
. Panel B repeats Panel A, but uses the previous 12 averaged cross-sectional
regressioncoefficients( t− 13 :t− 2)interactedwiththet− 1termforthatmodel. PanelCrepeats
Panels A and B, but averages the coefficients over the full set of training data used throughout
this paper (January 1984 through June 2017), and keeps those coefficients the same over the
entire testing dataset (June 2017 through May 2018). Data is removed if missing characteristics
described in Section 2.3.
104
2.4. EMPIRICAL RESULTS
Table 2.10: Out-of-Sample Model Comparison, One-Month Lag
MSPE Decomposition, P/E Avg(MSPE) Avg(Bias
2
) Avg(Variance) CT R
2
XS R
2
Panel A: P/E 1-Month
(1) r
∗ , d
∗ 0.761 0.353 0.409 -3.269 0.006
(2) r
∗ , d
∗ , K
1
0.553 0.153 0.400 -2.211 0.275
(3) r
∗ , d
∗ , K
1
, K
2
× V 1.901 0.170 1.732 -4.442 -0.202
(4) r
∗ , d
∗ , Lag(P/E) 0.233 0.028 0.205 -0.020 0.840
(5) r
∗ , d
∗ , K
1
, Lag(P/E) 0.233 0.028 0.206 -0.022 0.837
(6) r
∗ , d
∗ , K
1
, K
2
× V, Lag(P/E) 0.248 0.028 0.220 -0.047 0.832
(7) PE Lagged 1 Month 0.216 0.007 0.209 0.000 0.907
Panel B: P/E 12-Months
(1) r
∗ , d
∗ 0.790 0.376 0.414 -3.285 0.004
(2) r
∗ , d
∗ , K
1
0.578 0.172 0.406 -2.274 0.266
(3) r
∗ , d
∗ , K
1
, K
2
× V 1.276 0.230 1.046 -3.419 0.024
(4) r
∗ , d
∗ , Lag(P/E) 0.235 0.032 0.203 0.001 0.815
(5) r
∗ , d
∗ , K
1
, Lag(P/E) 0.235 0.032 0.203 0.001 0.817
(6) r
∗ , d
∗ , K
1
, K
2
× V, Lag(P/E) 0.319 0.040 0.279 -0.139 0.785
(7) PE Lagged 12 Month 0.886 0.323 0.563 -2.055 0.670
Panel C: Train/Test Split-Sample
(1) r
∗ , d
∗ 0.678 0.608 0.069 -6.451 0.016
(2) r
∗ , d
∗ , K
1
0.435 0.366 0.069 -3.536 0.349
(3) r
∗ , d
∗ , K
1
, K
2
× V 0.440 0.372 0.068 -3.591 0.339
(4) r
∗ , d
∗ , Lag(P/E) 0.060 0.029 0.031 0.562 0.931
(5) r
∗ , d
∗ , K
1
, Lag(P/E) 0.060 0.030 0.031 0.562 0.931
(6) r
∗ , d
∗ , K
1
, K
2
× V, Lag(P/E) 0.060 0.030 0.030 0.561 0.930
(7) P/E 0.923 0.808 0.116 -5.923 NA
(8) λ (P/E) 0.067 0.012 0.055 0.055 0.949
This table reports the mean-squared prediction error (“MSPE”), squared-bias, and variance de-
composition for out-of-sample predictions of price-to-earnings (“P/E”) ratios. The first column
includes the models which are used in each row. r
∗ is the expected returns, d
∗ is the expected
change in dividends, K
1
is the intercept of the first-order Taylor approximation, and K
2
× V is
the additional variance term resulting from a second-order Taylor approximation, all from the
Campbell and Shiller (1988) model. Lag(P/E) represents the lagged price-to-earnings ratio. CT
R
2
is the Campbell and Thompson (2007) R
2
measure, and XS R
2
is the cross-sectional R
2
model derived from Yufeng et al. (2021). In Panel A, these terms are used in a cross-sectional
regression following Fama and MacBeth (1973). The coefficients are then lagged one additional
period (t− 2), and multiplied by the t− 1 terms for that model. That generates the time t
prediction for P/E
t
. Panel B repeats Panel A, but uses the previous 12 averaged cross-sectional
regressioncoefficients( t− 13 :t− 2)interactedwiththet− 1termforthatmodel. PanelCrepeats
Panels A and B, but averages the coefficients over the full set of training data used throughout
this paper (January 1984 through June 2017), and keeps those coefficients the same over the
entire testing dataset (June 2017 through May 2018). Data is removed if missing characteristics
described in Section 2.3.
105
CHAPTER 2. THE CROSS-SECTION OF PRICES
in model (7) generates a negative Campbell and Thompson (2007) R
2
(“CT R
2
”), despite
havinganautocorrelationofabout0.95. Thecross-sectionalR
2
statistic(“XSR
2
”, seeYufeng
et al., 2021) shows that the reduction in cross-sectional variation is actually highest for the
model which includes r
∗ , d
∗ , and lagged P/D, slightly outperforming the model which uses
just lagged price-ratio. Importantly, even the models without lagged price ratio, models (1)
- (3), have a positive cross-sectional R
2
, so they do capture some cross-sectional variation.
However, including lagged P/D increase the XS R
2
from less than 0.1 to about 0.9.
Table 2.9 Panel B contains the same analysis as in Panel A but with a twelve-month
average of the cross-sectional coefficients instead of a one-month lag, still predicting a one-
month ahead price-ratio. Between models (1)-(3) which exclude lagged price-ratio, it is again
clear that the addition of K
1
improves the model with just r
∗ and d
∗ while K
2
× V has a
substantially higher MSPE and variance. This table echoes the results in Panel A once
lagged price-ratios are added. Models (5) (r
∗ , d
∗ , K
1
, and lagged price) and (6) (r
∗ , d
∗ , K
1
,
K
2
× V, and lagged price) have very similar prediction errors, squared bias, and variance
compared to model (4) which has just r
∗ , d
∗ and lagged price as predictors. However, the
baseline model which uses the lagged 12 month price-ratio average is actually worse than
models (4) or (5) with a much higher prediction error coming from higher variance. Further,
both models (4) and (5) have small, but positive, out-of-sample Campbell and Thompson R
2
andseemcapturevariationmissedbythelaggedprice-ratio. Thecross-sectionalR
2
measures
demonstrates a significant reduction in cross-sectional variance for models (4) - (6), but not
as high as those in Panel A for those same models. The results from the XS R
2
measure in
Panel A are confirmed again, with model (4) having the highest reduction in cross-sectional
price variation.
Table2.9PanelCsplitsmydatasetintotwodistinctsetsinsteadofusingarollingwindow
measure. Here, I take the last 12 months of my dataset, June 2017 through May 2018, to
be the testing data and all remaining data prior to June 2017 as the training data. Taking
this snapshot in time over which I test my data set allows me to understand if differences
106
2.4. EMPIRICAL RESULTS
in model fit are consistent over a fixed sample. I find that the results are largely the same
with model (2) outperforming the models which do not include lagged P/D. However, the
performance of models (4)-(6) are so similar that they cannot clearly be differentiated.
7
For
this reason, I cannot say for certain if any one model which includes lagged P/D is better
than any other over this testing period. Model (7) which uses just lagged P/D underperforms
all models (4)-(6). Model (8) includes the training sample cross-sectional coefficient average
multiplied by lagged P/D, and I find that this model is exactly on par with models (4)-(6),
with a very slightly higher XS R
2
of 0.949, the best in this panel. This likely implies that
in models (4)-(6), almost all the predictive power is derived from the lagged P/D term and
not from the Campbell and Shiller decomposition terms.
Table 2.10 repeats these forecast exercise for the P/E ratio. The in-sample results above
showed that the P/E ratio can be meaningfully different from the P/D ratio. Here I test how
well r
∗ , d
∗ , K
1
, and K
2
× V work out-of-sample with P/E. Beyond slight deviations and the
smaller MSPE, the results for both P/D and P/E are surprisingly similar and follow the same
general pattern. As with P/D, P/E tends to be best approximated by lagged P/E, though
when lagged P/E is excluded, the model with r
∗ , d
∗ , and K
1
appears to be the strongest.
While the in-sample results found a clear connection for P/E with the second-order Taylor
term, the out-of-sample results show that this term really does not help and serves primarily
to inflate prediction errors and lower R
2
. This is seen regardless of which R
2
measure is
used. The information contained in the cross-section of the Campbell and Shiller model
does appear to be persistent, to some extent, through time with a positive cross-sectional
R
2
in almost every model, except Panel A model (3) which includes the K
2
× V term.
Panels A and B of both Tables 2.9 and 2.10 demonstrate that the lagged one-month price-
ratio is likely the best predictor of the next-period’s price-ratio. This is hardly surprising
given the high autocorrelation of individual firm price-ratios
8
. However, I also find that a
7
Differences are seen beyond 3 decimal places
8
A test for this was provided above, in-sample, in Table 2.4 which examined which factors explain the
change in price-ratios.
107
CHAPTER 2. THE CROSS-SECTION OF PRICES
twelve-month average of the lagged price-ratio effectively eliminates its competitive edge,
allowing the Campbell and Shiller model to improve the prediction (models (4) and (5) in
Panel B of both tables), providing a positive out-of-sample R
2
using both the time-series and
cross-sectional measures. Using the Campbell and Shiller model to predict the cross-section
of price-ratios does seem to work; in all cases, these model provides a positive out-of-sample
cross-sectional R
2
. However, these tests demonstrate that K
1
is not a perfect substitute for
lagged price, and the K
2
× V measure does not appear to provide meaningful out-of-sample
predictions.
Panel C in both tables demonstrates that the benefits from including the lagged price-
ratio are retained when we average the cross-sectional valuation-premium instead of the
price-ratio itself. In an out-of-sample test, models (4)-(6) appear to do an excellent job
compared to the models that include just lagged price-ratios (the baselines in rows (7) and
(8)). In these tables, the out-of-sample R
2
is right around 0.56, though it appears that the
addition of the K
2
× V term does not capture additional out-of-sample variation. In Table
2.9, the models benefit most from the cross-sectional coefficient on lagged-P/D, and these
results are about the same for P/E.
What Explains Prediction Errors?
I now check for systematic deviations in prediction errors explained by one of my factors or
firm characteristics. A characteristic which is significant in the cross-section of prediction
errors is one which is consistently missed by the forward-looking expectations formed in
the Campbell and Shiller model. Systematic errors may indicate that the Campbell and
Shiller models is failing to incorporate information or that there are systematic deviations
in price-ratios through time. I will now try to understand why price-ratios change based on
the predictions made between period from the Campbell and Shiller (1988) model.
The results of this exercise are contained in Tables 2.11 and 2.12. I focus only on the
results for P/D and include those for P/E in the Appendix. I examine the results without
108
2.4. EMPIRICAL RESULTS
Table 2.11: Regression of Out-of-Sample MSPE on X
i,t
Model Number (1) (2) (3) (4) (5) (6)
r
∗ , d
∗ , 1M r
∗ , d
∗ , 12M r
∗ , d
∗ , K
1
, 1M r
∗ , d
∗ , K
1
, 12M r
∗ , d
∗ , K
1
, K
2
× V, 1M r
∗ , d
∗ , K
1
, K
2
× V, 12M
Epsilon Squared Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats
Constant 1.529 16.610 1.555 16.423 1.397 16.437 1.418 16.362 1.432 16.164 1.503 14.214
Rolling Beta 0.097 3.001 0.105 3.142 0.086 2.512 0.090 2.536 0.072 1.671 0.022 0.319
Error Standard Deviation 0.137 5.515 0.137 5.315 0.128 5.410 0.129 5.275 0.111 4.263 0.035 0.461
SMB Beta -0.075 -2.704 -0.068 -2.393 -0.064 -2.317 -0.058 -2.036 -0.072 -2.459 -0.104 -2.515
HML Beta 0.015 0.569 0.006 0.243 0.004 0.113 -0.008 -0.221 0.030 0.702 -0.137 -0.981
CMA Beta 0.035 1.243 0.044 1.517 0.032 1.103 0.043 1.456 0.019 0.637 0.120 1.378
RMW Beta -0.027 -0.829 -0.030 -0.883 -0.027 -0.733 -0.031 -0.813 -0.056 -1.122 -0.127 -1.689
Leverage 0.107 5.158 0.109 5.045 0.105 5.321 0.109 5.260 0.128 5.041 0.262 2.682
1-Year Forecasted EPS -0.029 -1.464 -0.032 -1.552 -0.019 -0.944 -0.022 -1.055 -0.029 -1.410 -0.056 -1.949
1-Year Analyst SD 0.036 2.804 0.035 2.665 0.033 2.601 0.032 2.453 0.028 2.165 0.005 0.242
1-Year Num. Analysts 0.084 4.329 0.083 4.155 0.055 2.769 0.052 2.608 0.052 2.664 0.049 2.505
Standardized Unexpected Earnings 0.047 1.243 0.048 1.230 0.059 1.383 0.062 1.386 0.060 1.415 0.058 1.318
Illiquidity 0.161 3.339 0.155 3.032 0.110 2.541 0.099 2.176 0.096 1.835 0.516 1.513
Illiquidity
2
-0.149 -3.364 -0.143 -3.028 -0.120 -3.011 -0.111 -2.640 -0.105 -2.056 -0.459 -1.640
Shares Issued -0.020 -1.725 -0.025 -1.973 -0.027 -2.658 -0.031 -2.878 -0.028 -2.695 -0.036 -2.998
Shares Repurchased 0.065 2.833 0.075 2.935 0.024 1.090 0.033 1.429 0.029 1.243 0.005 0.136
Inst. Own. Percentage -0.075 -3.814 -0.067 -3.307 -0.045 -2.460 -0.039 -2.099 -0.072 -2.679 -0.151 -2.236
Number of Inst. Own. -0.002 -10.214 -0.002 -9.988 -0.002 -9.984 -0.002 -9.758 -0.002 -9.023 -0.002 -9.620
This table follows the method outlined in Fama and MacBeth (1973). I calculate the cross-sectional OLS coefficient for all variables in X
i,t
. The LHS are the 1-month ahead, out-of-sample predictions
errors when forecasting P/D in Table 2.9 without lagged P/D included. Sample Size represents the data after missing data are removed, and for which missing data and perfect 0 are removed from
the Campbell and Shiller approximations. Data is collected from 1985 through 2018. Observations are removed if a firm is missing characteristics listed in Section 2.3.
109
CHAPTER 2. THE CROSS-SECTION OF PRICES
Table 2.12: Regression of Out-of-Sample MSPE on X
i,t
with lagged δ i
Model Number (1) (2) (3) (4) (5) (6)
r
∗ , d
∗ , 1M r
∗ , d
∗ , 12M r
∗ , d
∗ , K
1
, 1M r
∗ , d
∗ , K
1
, 12M r
∗ , d
∗ , K
1
, K
2
× V, 1M r
∗ , d
∗ , K
1
, K
2
× V, 12M
Epsilon Squared Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats
Constant 0.177 7.033 0.175 6.800 0.177 6.552 0.174 6.392 0.181 6.658 0.177 6.455
Rolling Beta 0.012 0.440 0.012 0.428 0.013 0.418 0.013 0.394 0.012 0.393 0.011 0.359
Error Standard Deviation 0.014 0.783 0.014 0.757 0.011 0.558 0.011 0.546 0.011 0.595 0.011 0.564
SMB Beta -0.027 -1.162 -0.027 -1.120 -0.025 -0.999 -0.025 -0.968 -0.027 -1.086 -0.026 -1.034
HML Beta -0.007 -0.321 -0.007 -0.323 0.004 0.120 0.004 0.127 0.005 0.169 0.006 0.176
CMA Beta 0.017 0.667 0.017 0.656 0.015 0.547 0.015 0.533 0.015 0.546 0.014 0.523
RMW Beta -0.060 -2.376 -0.061 -2.365 -0.074 -2.245 -0.076 -2.230 -0.076 -2.254 -0.078 -2.250
Leverage 0.013 1.026 0.013 1.005 0.015 1.069 0.015 1.042 0.016 1.070 0.016 1.048
1-Year Forecasted EPS 0.003 0.182 0.003 0.166 0.001 0.069 0.001 0.036 -0.001 -0.027 -0.001 -0.043
1-Year Analyst SD -0.006 -0.646 -0.007 -0.696 -0.008 -0.873 -0.009 -0.904 -0.007 -0.803 -0.008 -0.840
1-Year Num. Analysts 0.001 0.075 0.001 0.089 0.003 0.153 0.002 0.137 0.004 0.245 0.004 0.207
Standardized Unexpected Earnings 0.056 1.474 0.058 1.481 0.064 1.400 0.066 1.412 0.064 1.420 0.066 1.431
Illiquidity -0.021 -0.624 -0.023 -0.643 -0.018 -0.472 -0.019 -0.482 -0.028 -0.771 -0.027 -0.739
illiq_sqd 0.019 0.583 0.020 0.607 0.014 0.395 0.015 0.409 0.023 0.712 0.023 0.695
Shares Issued -0.005 -0.734 -0.005 -0.750 -0.006 -0.886 -0.006 -0.892 -0.006 -0.852 -0.006 -0.829
Shares Repurchased -0.021 -1.689 -0.022 -1.693 -0.025 -1.833 -0.025 -1.792 -0.023 -1.715 -0.025 -1.802
Inst. Own. Percentage -0.027 -1.860 -0.027 -1.816 -0.030 -1.920 -0.030 -1.887 -0.032 -2.009 -0.031 -1.931
Number of Inst. Own. 0.000 -1.995 0.000 -2.010 0.000 -1.966 0.000 -1.969 0.000 -2.174 0.000 -2.126
Lagged Price 0.051 3.256 0.050 3.073 0.050 2.885 0.050 2.800 0.049 2.846 0.049 2.784
This table follows the method outlined in Fama and MacBeth (1973). I calculate the cross-sectional OLS coefficient for all variables in X
i,t
. The LHS are the 1-month ahead, out-of-sample predictions
errors when forecasting P/D in Table 2.9 with lagged P/D included. Sample Size represents the data after missing data are removed, and for which missing data and perfect 0 are removed from the
Campbell and Shiller approximations. Data is collected from 1985 through 2018. Observations are removed if a firm is missing characteristics listed in Section 2.3.
110
2.4. EMPIRICAL RESULTS
lagged price-ratio in Table 2.11, and then I test with lagged price-ratio in Table 2.12. For
all of these tests, I use Fama and MacBeth (1973) cross-sectional regressions where the LHS
consists of the MSPE from the results in Tables 2.9 and 2.10 on the factors included in my
X
i,t
matrix;
ϵ 2
i,t
=γ 0,t
+X
i,t
γ 1,t
+u (2.14)
Where ϵ 2
i,t
is the MSPE from the regressions in Table 2.9, and X
i,t
is the same set of data
included in Equation 2.4.
In Table 2.11, the results between models are surprisingly consistent, and for models (1)
through(4)thereappearstobeverylittlevariationinsignificance. TheCampbellandShiller
terms capture variation included in HML, CMA, RMW, analyst forecasts and unexpected
earningsrelativelywellastheMSPEbetweenperiodsdoesnotsystematicallyvarywiththese
factors. While even a model using only r
∗ and d
∗ seems to capture three of the four FF5
factors, it also consistently misses the size premium (SMB), market-beta, and firm-specific
leverage. Also seemingly missed by the model are measures institutional ownership. The
addition of K
1
does not appear to meaningfully change which factors explain prediction-
error. However, the results which include K
2
× V in columns (5) and (6) are different. A
factor in these columns which becomes insignificant would indicate that term is not well
captured by the first-order Taylor approximation used in the standard model. I find that
the addition of K
2
× V makes rolling market beta insignificant, and almost does the same
with illiquidity (which is marginally insignificant in column (5) and (6)). This says that the
standard Campbell and Shiller model fails to capture the variation within rolling-market
beta out-of-sample, but K
2
× V can.
Table 2.12 repeats this exercise, but includes the previous-period price ratio, P/D, in the
model. The lagged price-ratio brings down the significance of many terms. The character-
istics which remain significant are the measure of operating profitability (RMW Beta) as
well as institutional ownership. These terms remain significant throughout all columns of
Table 2.12, and indicate that prediction errors vary systematically in these characteristics.
111
CHAPTER 2. THE CROSS-SECTION OF PRICES
Despite giving the VAR all the same information (X
i,t
), these terms do not appear to be
well captured by a model of return and dividend expectations, K
1
or K
2
× V, even when
previous-period price-ratio is included.
The prediction errors which result from the predictive models in Table 2.9 vary systemat-
ically in at least three of my characteristics; operating profitability, institutional ownership,
and market beta, among a few others. This does not seem to change much between models
when previous-period P/D is excluded, except for when I addK
2
× V. This term is a measure
of the misspecification due to the first-order Taylor approximation, and rather surprisingly,
captures by market beta. Even when previous-period P/D is included in the regressions, a
few terms such as operating profitability (RMW Beta) and institutional ownership appear to
be missed by these models. Operating profitability and institutional ownership both appear
to have a meaningful impact on P/D, and remain unexplained by lagged P/D.
2.4.4 Out-of-Sample, Portfolios
Forecasting portfolio P/D ratios is not necessarily an easier task that forecasting those for
individual firms. While portfolios have smoother market capitalizations through time, the
dividend component of the portfolio P/D ratio varies significantly since it is the sum of each
month’s dividend payments for all firms in that cell.
Table 2.13 Panel A contains the MSPE decomposition for the 1-month lagged cross-
sectional regression coefficient in Equation 2.12 estimated using my 5x5 portfolios. The
results here are strikingly different than with individual firms, particularly since all models
generate positive out-of-sample R
2
values. Models (1) - (3) test the model in Equation 2.5
without lagged price. Despite the lower autocorrelation with the 5x5 portfolios, the addition
of K
1
in model (2) (r
∗ , d
∗ , and K
1
) to model (1) (r
∗ and d
∗ ) continues to improve overall
fit, lowering MSPE primarily through squared bias. Model (2) generates cross-section R
2
of 0.230 and a Campbell-Thompson R
2
of 0.303, seemingly high for a predictive R
2
with
a price-ratio that is now significantly less autocorrelated. The addition of K
2
× V again
112
2.4. EMPIRICAL RESULTS
Table 2.13: Out-of-Sample Model Comparison, 5x5 Portfolios
MSPE Decomposition, 5x5 Avg(MSPE) Avg(Bias
2
) Avg(Variance) CT R
2
XS R
2
Panel A: P/D 1-Month
(1) r
∗ , d
∗ 0.875 0.151 0.724 0.195 0.027
(2) r
∗ , d
∗ , K
1
0.753 0.005 0.748 0.303 0.230
(3) r
∗ , d
∗ , K
1
, K
2
× V 0.763 0.004 0.758 0.294 0.210
(4) r
∗ , d
∗ , Lag(P/D) 0.989 0.065 0.925 0.082 0.043
(5) r
∗ , d
∗ , K
1
, Lag(P/D) 0.795 0.003 0.792 0.262 0.190
(6) r
∗ , d
∗ , K
1
, K
2
× V, Lag(P/D) 0.805 0.003 0.802 0.253 0.168
(7) PD Lagged 1 Month 1.001 0.075 0.933 0.065 0.063
Panel B: P/D 12-Months
(1) r
∗ , d
∗ 0.663 0.159 0.504 0.395 0.061
(2) r
∗ , d
∗ , K
1
0.517 0.006 0.511 0.522 0.302
(3) r
∗ , d
∗ , K
1
, K
2
× V 0.517 0.006 0.512 0.522 0.302
(4) r
∗ , d
∗ , Lag(P/D) 0.642 0.073 0.569 0.407 0.141
(5) r
∗ , d
∗ , K
1
, Lag(P/D) 0.519 0.004 0.514 0.520 0.301
(6) r
∗ , d
∗ , K
1
, K
2
× V, Lag(P/D) 0.519 0.005 0.515 0.519 0.300
(7) PD Lagged 12 Month 0.672 0.074 0.598 0.137 0.369
Panel C: Train/Test Split-Sample
(1) r
∗ , d
∗ 0.848 0.320 0.528 0.007 -0.537
(2) r
∗ , d
∗ , K
1
0.774 0.248 0.526 0.309 -0.406
(3) r
∗ , d
∗ , K
1
, K
2
× V 0.777 0.251 0.526 0.310 -0.409
(4) r
∗ , d
∗ , Lag(P/D) 0.895 0.171 0.724 0.079 -0.627
(5) r
∗ , d
∗ , K
1
, Lag(P/D) 0.766 0.217 0.550 0.303 -0.393
(6) r
∗ , d
∗ , K
1
, K
2
× V, Lag(P/D) 0.769 0.220 0.549 0.303 -0.396
(7) PD Lagged 1 Month 0.933 0.173 0.759 -0.664 0.071
This table reports the mean-squared prediction error (“MSPE”), squared-bias, and variance de-
composition for out-of-sample predictions of price-dividend (“P/D”) ratios for the 5x5 sorted
portfolios. These portfolios are formed by interacting MC with OP, INV, and BM. The first
column includes the models which are used in each row. r
∗ is the expected returns, d
∗ is the
expected change in dividends, K
1
is the intercept of the first-order Taylor approximation, and
K
2
× V is the additional variance term resulting from a second-order Taylor approximation, all
from the Campbell and Shiller (1988) model. Lag(P/D) represents the lagged price-to-earnings
ratio. CT R
2
is the Campbell and Thompson (2007) R
2
measure, and XS R
2
is the cross-
sectional R
2
model derived from Yufeng et al. (2021). In Panel A, these terms are used in a
cross-sectional regression following Fama and MacBeth (1973). The coefficients are then lagged
one additional period (t− 2), and multiplied by the t− 1 terms for that model. That generates
the time t prediction for P/E
t
. Panel B repeats Panel A, but uses the previous 12 averaged
cross-sectional regression coefficients ( t− 13 :t− 2) interacted with thet− 1 term for that model.
Panel C repeats Panels A and B, but averages the coefficients over the full set of training data
used throughout this paper (January 1984 through June 2017), and keeps those coefficients the
same over the entire testing dataset (June 2017 through May 2018). Data is removed if missing
characteristics described in Section 2.3.
113
CHAPTER 2. THE CROSS-SECTION OF PRICES
increases MSPE relative to model (2) primarily through variance, similar to the firm-level
results in Table 2.9.
Models (4) - (6) in Panel A add lagged price-ratios to models (1) - (3), respectively.
Adding lagged price-ratio makes the performance of all models worse, increasing MSPE pri-
marily through variance. This striking result seems to say that increasing the frequency with
which dividends are measured allows us to better examine the underlying expectations of in-
vestors. Historicinformationcontainedinthoseexpectationsdoseemtogeneratemeaningful
out-of-sample predictions in a small win for rational expectations. This result is foreshad-
owed by model (7), the baseline model which uses just lagged P/D in the cross-sectional
model. Nearly all models are able to generate better predictions than this single-predictor
model. This is a substantial shift in comparison to Tables 2.9 and 2.10. Return and dividend
expectations do have meaningful out-of-sample predictive abilities in the cross-section.
Table 2.13 Panel B uses the 12-month average cross-sectional risk-premium to generate
predictions. The results here are a bit different than in the 1-month lagged case. The
addition of lagged price-dividend ratio does improve the model with r
∗ and d
∗ produces a
slightly smaller prediction error, a substantially smaller squared-bias, but a slightly higher
variance. However, the lowest prediction error is actually model (2) which uses r
∗ , d
∗ , and
K
1
. This model generates a Campbell-Thompson R
2
of 0.522 and a cross-sectional R
2
of
0.302, and outperforms lagged price-ratio across all criteria.
Finally, Panel C of Table 2.13 uses the same train/test split used in Panel C of Tables
2.9 and 2.10. In this table, none of the models or lagged price-ratio are able to generate
positive Campbell-Thompson R
2
, but all do generate positive cross-sectional R
2
. The lowest
prediction error belongs to model (5) with r
∗ , d
∗ , K
1
and lagged P/D as the predictors.
Compared to model (2), the addition of lagged price to model (5) slightly lowers prediction
error primarily through a significantly lower squared-bias, thought it does increase prediction
variance. However, all models in this table, except for the model using only r
∗ and d
∗ , are
able to meaningfully improve upon the baseline model with just lagged P/D.
114
2.4. EMPIRICAL RESULTS
Theout-of-sampletestsareawaytoseeifIcanelicitthereturnanddividendexpectations
of investors using historical information, and if those expectations can be used to generate
out-of-sample predictions. In this context, an out-of-sample prediction likely indicates that
thereiscontinuationinreturnexpectations, andthatportfolioswithhighreturnexpectations
in one month likely continue to have high return expectations the following month.
My results confirm that information contained in return and cash-flow expectations can
be used to generate out-of-sample predictions in the cross-section. Investor expectations
of portfolios do seem to continue through time, even when the contemporaneous or high-
frequency price-ratios do not. By updating the dividend component on a monthly basis, it
seems that not only do investors use return and dividend expectations (primarily the latter)
to price portfolios, but those expectations remain between periods.
What Explains Portfolio Prediction Errors?
The Campbell and Shiller model should explain the level price-dividend ratios, and it may
alsoexplainthechangethroughtimeofprice-dividendratiosifexpectationsremainconstant.
Ifindthatexpectedreturns, changeindividends, andtheintercept K
1
doappeartohaveout-
of-sample explanatory power. Once out-of-sample, however, they appear to systematically
miss variation in some variables.
Tables 2.14 and 2.15 decompose MSPE onto the characteristics included in the infor-
mation set for each portfolio. The results without price included are similar to those for
individual firms (Table 2.11) in that many terms appear to explain the Campbell and Shiller
model’s prediction errors. In Table 2.15 I add to this analysis lagged price-ratio, and the re-
sults are similar, and are surprisingly similar to the individual firm results in Tables 2.11 and
2.12. I focus on the regressors that remain significant between them; operating profitability,
analyst coverage, share issuance, and measures of institutional ownership.
I start with operating profitability and institutional ownership. Operating profitability
appears at both the individual firm and portfolio levels, and is generally negative. Perhaps
115
CHAPTER 2. THE CROSS-SECTION OF PRICES
Table 2.14: Regression of Out-of-Sample MSPE on X
i,t
Model Number (1) (2) (3) (4) (5) (6)
r
∗ , d
∗ , 1M r
∗ , d
∗ , 12M r
∗ , d
∗ , K
1
, 1M r
∗ , d
∗ , K
1
, 12M r
∗ , d
∗ , K
1
, K
2
× V, 1M r
∗ , d
∗ , K
1
, K
2
× V, 12M
Epsilon Squared Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats
Constant 0.861 18.783 0.646 20.253 0.745 17.236 0.510 19.020 0.754 17.245 0.510 19.029
ME 0.026 0.470 -0.018 -0.350 0.141 2.678 0.076 1.808 0.145 2.720 0.075 1.779
BM -0.068 -4.075 -0.054 -3.548 -0.046 -3.149 -0.003 -0.260 -0.046 -3.026 -0.009 -0.648
INV -0.016 -1.408 -0.019 -1.859 -0.012 -1.073 -0.015 -1.639 -0.016 -1.445 -0.016 -1.772
OP -0.107 -7.979 -0.075 -6.221 -0.082 -6.693 -0.043 -4.046 -0.085 -6.786 -0.044 -4.161
1-Year Forecasted EPS 2.700 1.698 3.766 1.913 1.052 1.319 2.063 1.846 0.877 1.098 1.871 1.784
1-Year Analyst SD -2.641 -1.335 -4.424 -1.661 -0.105 -0.077 -1.736 -0.828 0.204 0.160 -1.431 -0.722
1-Year Num. Analysts 0.181 3.376 0.177 3.388 0.157 3.060 0.167 3.551 0.154 2.956 0.167 3.555
Standardized Unexpected Earnings 0.561 0.481 1.492 1.006 -0.440 -0.399 0.403 0.261 -0.392 -0.355 0.398 0.266
Illiquidity -0.222 -3.462 -0.120 -1.960 -0.187 -3.124 -0.083 -1.467 -0.223 -3.264 -0.086 -1.581
Illiquidity Squared 0.193 2.513 0.114 1.618 0.183 2.561 0.110 1.642 0.200 2.616 0.107 1.672
Shares Issued 0.035 0.928 0.049 1.473 0.044 1.290 0.061 2.243 0.045 1.318 0.063 2.298
Shares Repurchased 0.039 1.285 0.024 0.797 0.040 1.377 0.026 0.882 0.044 1.556 0.026 0.882
Inst. Own. Percentage -0.150 -5.906 -0.143 -6.051 -0.076 -3.348 -0.051 -2.565 -0.087 -3.600 -0.056 -2.810
Number of Inst. Own. -0.156 -1.756 -0.149 -1.808 -0.300 -3.491 -0.276 -3.732 -0.316 -3.629 -0.275 -3.720
This table follows the method outlined in Fama and MacBeth (1973). I calculate the cross-sectional OLS coefficient for all variables in X
i,t
. The LHS are the 1-month ahead, out-of-sample predictions
errors when forecasting P/D in Table 2.9 without lagged P/D included. Sample Size represents the data after missing data are removed, and for which missing data and perfect 0 are removed from
the Campbell and Shiller approximations. Data is collected from 1985 through 2018. Observations are removed if a firm is missing characteristics listed in Section 2.3.
116
2.4. EMPIRICAL RESULTS
Table 2.15: Regression of Out-of-Sample MSPE on X
i,t
Model Number (1) (2) (3) (4) (5) (6)
r
∗ , d
∗ , 1M r
∗ , d
∗ , 12M r
∗ , d
∗ , K
1
, 1M r
∗ , d
∗ , K
1
, 12M r
∗ , d
∗ , K
1
, K
2
× V, 1M r
∗ , d
∗ , K
1
, K
2
× V, 12M
Epsilon Squared Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats Coeffs T-Stats
Constant 0.980 17.664 0.634 19.407 0.787 16.569 0.512 18.947 0.797 16.888 0.513 18.962
ME -0.001 -0.010 0.006 0.117 0.078 1.431 0.049 1.124 0.072 1.311 0.047 1.066
BM 0.009 0.473 0.016 1.132 -0.017 -1.055 0.018 1.316 -0.013 -0.781 0.014 1.070
INV -0.013 -1.063 -0.022 -2.229 -0.010 -0.866 -0.016 -1.691 -0.014 -1.172 -0.017 -1.786
OP -0.087 -6.237 -0.048 -4.335 -0.071 -5.599 -0.035 -3.376 -0.073 -5.646 -0.036 -3.454
1-Year Forecasted EPS -1.256 -0.574 1.033 0.666 -0.580 -0.455 0.942 0.836 -0.589 -0.451 0.866 0.781
1-Year Analyst SD 3.377 1.141 -0.111 -0.057 2.204 1.276 0.095 0.050 2.265 1.294 0.198 0.106
1-Year Num. Analysts 0.135 2.258 0.143 2.856 0.140 2.627 0.158 3.346 0.134 2.488 0.158 3.333
Standardized Unexpected Earnings -1.848 -1.735 -0.386 -0.389 -1.503 -1.714 -0.497 -0.377 -1.381 -1.469 -0.424 -0.323
Illiquidity -0.285 -4.605 -0.144 -2.783 -0.209 -3.581 -0.100 -1.847 -0.245 -3.923 -0.104 -1.984
Illiquidity Squared 0.257 3.550 0.146 2.512 0.199 2.972 0.112 1.928 0.217 3.094 0.112 2.001
Shares Issued -0.018 -0.396 0.041 1.222 0.018 0.478 0.048 1.621 0.016 0.421 0.049 1.652
Shares Repurchased 0.058 1.628 0.028 0.945 0.051 1.515 0.025 0.816 0.056 1.698 0.025 0.836
Inst. Own. Percentage -0.108 -4.196 -0.073 -3.428 -0.083 -3.580 -0.051 -2.498 -0.095 -3.978 -0.055 -2.705
Number of Inst. Own. 0.015 0.152 -0.108 -1.325 -0.169 -1.878 -0.216 -2.908 -0.167 -1.854 -0.213 -2.861
PD_lag 0.178 6.463 0.094 6.693 0.081 4.510 0.053 4.887 0.090 4.874 0.057 5.091
This table follows the method outlined in Fama and MacBeth (1973). I calculate the cross-sectional OLS coefficient for all variables in X
i,t
. The LHS are the 1-month ahead, out-of-sample predictions
errors when forecasting P/D in Table 2.9 without lagged P/D included. Sample Size represents the data after missing data are removed, and for which missing data and perfect 0 are removed from
the Campbell and Shiller approximations. Data is collected from 1985 through 2018. Observations are removed if a firm is missing characteristics listed in Section 2.3.
117
CHAPTER 2. THE CROSS-SECTION OF PRICES
unsurprisingly, firms with high operating profitability have price-dividend ratios which are
well captured by forward-looking return, cash-flow, and lagged price-dividend information
(through K
1
and lagged-P/D). What is surprising is that information about operating prof-
itability appears to be systematically missed by the Campbell and Shiller decomposition.
The same is true for institutional ownership. In model (6) of Table 2.14, operating prof-
itability has a coefficient ( t-statistic) of -0.044 (-4.161), while for institutional ownership
percentage it is -0.056 (-2.810) and for number of institutional owners it is -0.275 (-3.720).
A natural explanation for this would seem to be the effect of small firms. However,
the coefficients on market-equity (SMB), book-to-market (HML), and investments (CMA)
are statistically insignificant over the 12-month window (model 6) and when lagged price-
dividendisincluded. Further,thecoefficientsonprice-dividendratiotendtobepositivewhen
statistically significant. It seems unlikely, then, that the effect on institutional ownership and
operating profitability is somehow related to the size of the firms involved because several
other measures are included which should capture this variation.
The Campbell and Shiller model should capture change in price-dividend ratios if ex-
pectations between period remain the same or similar. I find that the model does capture
out-of-sample price variation when used with portfolios. However, it systematically misses
out-of-sample variation in several variables, depending on the combination of terms included
(r
∗ , d
∗ , K
1
, K
2
× V and/or lagged P/D). Across models and predictors, operating prof-
itability, institutional ownership, number of analysts covering a firm, and potentially share
issuance all appear to drive changes to investor expectations between periods. Operating
profitability and institutional ownership are two of the most consistent such influences on
investor expectations as they show up in individual firm data as well as portfolio data even
with lagged price-dividend included.
118
2.5. THE CAMPBELL AND SHILLER MODEL IN THE CROSS-SECTION
2.5 TheCampbellandShillerModelintheCross-Section
I have examined a second-order approximation of the Campbell and Shiller (1988) model in
thecross-sectionofindividualfirmsandaggregatedportfolioprice-ratios. Inthecross-section
ofprices,Ifindasurprisingresult–expectationsaroundchangesincash-flowsseemtoexplain
far more variation in the cross-section than expected returns. Between periods, though, I
find that the Campbell and Shiller model systematically misses variation in institutional
ownership and operating profitability despite including it in the VAR.
In terms of the cross-sectional variation of firm prices, this implies that institutional
ownership and extremes of operating profitability are not well-priced by (observable) investor
responses to returns and dividend payments. Instead, investors do not appear to respond in
proportion to these factors at an aggregate market level, even when controlling for industry-
level effects.
In addition, I also find that the model does appear to benefit from a more precise approx-
imation. The additional second-order term, K
2
× V is often statistically significant in the
cross-section, indicating that historic price-ratio volatility often implies a discount in relative
valuation.
2.6 Conclusion
Investors assign price-dividend ratios based on return and dividend expectations. If investors
have rational expectations, then these return and dividend expectations can be elicited from
historicalpricesanddividends. Thoseexpectationsarefrequentlyformedusingtheaggregate
equity-market portfolio, but they can also be formed from individual firms and portfolios.
In this paper, I use return and dividend expectations of individual firms and characteristic-
sorted portfolios to study the cross-sectional characteristics of valuation ratios.
At the firm-level, I find that investors appear to rely more heavily on changes in cash-flow
expectationswhendeterminingprice-dividendratiosthanexpectedreturns. Thepersistence-
119
CHAPTER 2. THE CROSS-SECTION OF PRICES
component δ i
captures the majority of variation, but cash-flows explain between two and
ten times the variation of return expectations. The majority of cross-sectional variation in
price-ratios, then, is due to cash-flow expectations, a very different conclusion than those for
returns. As part of my tests, I include a higher-order expansion of the Campbell and Shiller
(1988) model, and show my data likely benefits from a more precise decomposition.
I then test the Campbell and Shiller (1988) model on price-dividend portfolios sorted
on four characteristics. These portfolios serve to better understand two aspects of the in-
dividual firm results; the impact of high autocorrelations on the estimation procedure, and
to further test the misspecification of the first-order approximation. On both fronts, I find
that portfolios largely reaffirm the individual firm-level results, still loading primarily on
change in cash-flows, and demonstrating that a more precise second-order approximation is
warranted.
While other papers have examined the ability of characteristics to explain future re-
turn and cash-flow expectations (Cohen et al., 2003; Cochrane, 2011), I turn the estimation
around slightly and ask return and dividend expectations to explain out-of-sample price-
ratios. These predictions are formed from the cross-sectional regression coefficient and the
last-observed return or cash-flow expectation. If investors are rational, then historical in-
formation should elicit the importance of returns and change in cash-flows. However, if
the relationship between cross-sectional dispersion in price-ratios and expectations is stable
through time, then these tests may generate meaningful out-of-sample predictions.
For individual firms, the return and cash-flow expectations, which rely on 12-month
average dividends, provide mixed out-of-sample forecasts. They tend to improve the cross-
sectional predictions, but they are generally unable to improve upon the naive estimate
of previous-period price-ratio. For portfolios, however, which do not require smoothing of
dividends, this procedure can generate positive out-of-sample R
2
, both in the time-series
and the cross-section. Particularly for the more granular sorted portfolios, it appears that
cross-sectional information in return and cash-flow expectations not only can be elicited from
120
2.6. CONCLUSION
past information, but they seem likely to persist through time, generating better predictions
than lagged price-ratios.
121
CHAPTER 2. THE CROSS-SECTION OF PRICES
2.7 Appendix: Variable Discussion
2.7.1 Characteristics and Factors
To keep things organized, I group my predictors into seven categories; Risk, Future Growth,
Transaction Costs, Behavioral and Technical, Institutional Ownership, Supply Factors, and
Industry Membership. It is important to realize that the grouping is subjective – some
readers may feel that certain variables should be in different categories. I think that is
unavoidable, but grouping will become helpful when I provide a percentage decomposition
to characterize where cross-sectional price variation originates.
Risk
The Risk category contains the variables related to systematic risk. Since risk impacts
returns, it should also impact prices. Higher risk-premiums should mean lower prices.
Rolling Betas: For each time t, the rolling beta is the regression slope for the 36
months leading up to time t, but requiring only a minimum of 12 months of data. Defining
the window in this way minimizes the number of observations that are discarded when
filtering missing observations. I calculate betas for the FF5 factors; Market, HML, SMB,
RMW and CMA from Fama and French (2015) at the firm level. The market portfolio is
the value-weighted average of stocks on the NYSE, NASDAQ, and Amex. The data for this
requires only the monthly return and the factor values, which are available from Professor
Ken French’s website.
Error Standard Deviation: From the regression for the rolling market beta, I take
the regression error ϵ i,t:t− 36
, and calculate its standard-deviation, σ (ϵ i,t:t− 36
), as an additional
measure of risk for each firm. If the market beta was a complete measure of risk, then we
would expect this error term to be inconsequential in the cross-section. If beta does a poor
job of capturing risk, this standard deviation of the error term could capture exposure to
other missing factors.
122
2.7. APPENDIX: VARIABLE DISCUSSION
Firm Leverage: I use Long-Term Total Debt (item DLTTQ in Compustat) divided
by Total Assets (item ATQ in Compustat) for my measure of leverage. As with many of
the variables in this paper, I must adjust the periodicity of the data. Given that my price
observations are monthly, I fill the data with the most recently observed value. For both
variables, the highest frequency that I can get from Compustat is generally quarterly.
Future Growth
Analyst Median Estimates: I include the implied percent growth in earnings using me-
dian estimates of the one-year analyst forecast from I/B/E/S. This uses the most recently
available quarterly analyst data for each firm. I expect growth to have a positive relationship
with prices.
Standard Deviation of Analyst Estimates: Also included in the data set are the
cross-analyst standard deviations of one-year earnings estimates. Cross-analyst uncertainty
may capture opacity of the firm or uncertainty in how the market views their earnings
potential. Diether, Malloy, and Scherbina (2002) find that higher dispersion in analyst
forecasts is correlated with lower future returns. I find a negative coefficient in the cross-
section of prices consistent with a risk-premium but seemingly in contradiction to Diether
et al. (2002). This follows more of a risk argument in my data, lowering price to compensate
investors for holding stocks with a higher standard deviation.
Standardized Unexpected Earnings: I include Standardized Unexpected Earnings
(“SUE”). This is calculated as the most recent quarter’s one-year analyst forecast less actual
earnings release, divided by the quarter-end price. I would expect a lower SUE from the past
quarter-end to lead to a realization of value, and probably a higher price going forward.
Number of Analysts: I include the number of analyst supplying the estimates for each
period. While likely to correlate with the size of the firm, perhaps information about the
quality of the estimate can be had by considering the number of contributing analysts. I
find mixed results for this, though it is statistically significant and positive for three of four
123
CHAPTER 2. THE CROSS-SECTION OF PRICES
price measures.
Transaction Costs
My primary measure of transaction costs relies on the illiquidity measure of Amihud (2002).
I make one modification, and instead of using daily return and volume averaged to a yearly
frequency, I use daily values averaged to a monthly frequency.
Illiquidity: Illiquidity is expressed as the monthly average of the ratio of the absolute
value of daily returns divided by the trading volume of that day. Following Amihud (2002),
ILLIQ
i,m
=1/D
i,m
D
i,m
X
t=1
|R
i,m,d
|
VOLD
i,m,d
(2.15)
where D
i,m
is the number of days with observations in month m for stock i. VOLD
i,m,d
is
the daily volume for firm i in month m. I then take the average of the previous 12 months’
ILLIQ
i,m
values to serve as a given month’s measure of illiquidity.
To construct this variable using the daily stock file from CRSP, I calculate the above ratio
for each firm in my sample on a daily basis. Then, I aggregate it to the monthly level, take a
rolling 12-month average, and merge it with my monthly data set. If illiquidity is a risk that
investors are expecting compensation for, as was found in Amihud (2002), I would expect a
negative relationship between illiquidity and price, given the expectations of higher returns.
I also include the squared value of illiquidity, to capture potential non-linear relationships
between illiquidity and price (Amihud and Mendelson, 1986).
Institutional Ownership
This section includes variables that measure the amount of a firm owned by institutions.
These measures are included primarily to understand if institutional investors have the same
preferenceforinvestments,andrelatedly,iftheirpositioninafirmchangesthepricedynamics
going forward.
124
2.7. APPENDIX: VARIABLE DISCUSSION
Institutional Ownership Percentage: This is the total institutional ownership per-
centage as reported by the Thompson Reuter’s 13f Institutional Stock Holdings summary.
Values are reported quarterly, and the most recently available observations are used. Data
for this measure has a comparatively short history, starting around 1985. This is, however, a
valuable instrument in understanding how different market participants influence price. For
that reason, I include it and start my analysis set when this data becomes available.
Number of Institutional Owners: This measure also comes from the Thompson
Reuter’s 13f Institutional Stock Holdings, and is another example of institutional ownership.
Thismayberelatedtothesizeofthefirm,butmayalsoreflectpopularityamonginstitutional
investors. I find the number of institutional owners is only significant in two price measures,
but appears to have very low economic significance.
Supply
I want to capture the firm-level supply of shares available to the market. Weld, Michaely,
Thaler, andBenartzi(2009)discussanoddpattern; despitepricelevelsrisingroughlytenfold
since the Great Depression, nominal stock prices have been relatively stable at $35 per share.
This is no accident, the authors argue, and is instead the result of calculated adjustments
by firms. I include various measures of supply because they may be an important factor in
explaining the cross-sectional variation of prices and price setting. Pontiff and Woodgate
(2008) find that share issuance is a significant factor in future return, and find support
for the opportunistic view of managers; that is, insiders issuing when prices are high and
repurchasing when prices are low.
Common Shares Issued: This is the percentage of common shares issued over the
quarter, reported once per quarter. I take the average over the previous 12-months of the
available information as a monthly measure.
Common Shares Repurchased: A measure of the percentage of shares repurchased
over the quarter, reported once per quarter. I follow the same method as above, and average
125
CHAPTER 2. THE CROSS-SECTION OF PRICES
this using the available data over the previous 12-months. I find that shares repurchased
is significant for both price measures, and is correlated with lower price ratios. Despite
showing up in the denominator of P/D, I find this also statistically significant for P/CD and
P/E. This lends support to the opportunistic management view of Pontiff and Woodgate
(2008), though primarily with repurchases and less with issuances. Strangely, it seems that
any intervention in the shares outstanding by management corresponds to lower prices when
statistically significant.
Campbell and Shiller Variables
TheCampbellandShillermodel’sr
∗ ,d
∗ ,K
1
, andK
2
× V variablesaresignificantinthecross-
section but with small coefficients. P/E stands out because expected returns are significant,
but have a direction opposite from what theory would predict. However, in every case
expected change in cash-flows is positive and significant. This table cannot tell us how much
cross-sectional variation is explained by these factors, which will be examined later, but it
appears that with small coefficients the amount of variation they explain may be quite low.
In the following sections, I test these with multivariate regressions.
Industry Membership
Given similarities between firms within the same industry, a substantial amount of varia-
tion may be captured by an industry variable. I use dummy variables for the 48 Industry
Classifications following Fama and French (1997). Firms with common industries may have
common characteristics that can help explain price-ratio differences.
126
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Abstract (if available)

Abstract The asset-pricing literature has long focused on rate of returns. In fact, Cochrane (2011) goes so far as to ask when the field of ``asset pricing'' became ``asset expected-returning.'' In the following two chapters, I provide alternative asset pricing studies which put the price-setting mechanism in full focus. The first study uses a Koijen and Yogo (2019) demand system to analyze how investors demand assets as dividend policies change. The second study uses a Campbell and Shiller (1988) decomposition to examine the cross-section of individual stock price-ratios. Together, these studies re-evaluate classic questions in a new light, and provide substantially different insights.

In Chapter 1, I use institutional portfolio positions to estimate dividend elasticities. I find most financial intermediaries have a positive elasticity of demand for firm-level dividends, but delayed short-term rebalancing. This delay can incentivize firm managers to keep dividends stable and generates a 2% market-capitalization premium for sticky dividends. I then propose an intermediary asset pricing model incorporating my empirically estimated elasticities which matches aggregate payouts with a correlation of about 0.9; a marked improvement. Counterfactuals show dividends reflect a simple insurance contract between firms and investors that boosts payouts during recessions by 10pp, or about $14 billion in 2021, and may explain why dividends exist at all.

In Chapter 2, I build a price-ratio model based on the Campbell and Shiller (1988) decomposition to test which components of investor expectations best explain cross-sectional price differences. I evaluate the in- and out-of-sample performance of my model, which uses a higher-order expansion with an added variance term. In-sample, I find differences in price-ratios are attributable primarily to cash-flow expectations, not returns. Out-of-sample, the Campbell and Shiller model struggles with individual firms but works well for characteristic-sorted portfolios where information in the cross-section can be used to generate out-of-sample predictions. Finally, I decompose the model's missed variation and find that firms with high levels of institutional ownership or operating profitability are not well explained in this auto-regressive framework.

Together, these studies advance our understanding of how investors allocate capital. In particular, they highlight the importance of institutional ownership and dividend policies on firm prices. The impact of both institutions and dividends appear long-lasting, helping us understand persistent differences in firm valuations.

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Creator Douglas, Reed (author)

Core Title Essays in asset demand: dividends, institutions, and price

School Marshall School of Business

Degree Doctor of Philosophy

Degree Program Business Administration

Degree Conferral Date 2023-05

Publication Date 03/10/2025

Defense Date 03/02/2023

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

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