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Essays in behavioral and financial economics

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Essays in behavioral and financial economics

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Content ESSAYS IN BEHAVIORAL AND FINANCIAL ECONOMICS
by
Joshua Shemesh
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulllment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BUSINESS ADMINISTRATION)
May 2011
Copyright 2011 Joshua Shemesh
ii
Acknowledgements
I would like to thank my dissertation chair, Fernando Zapatero, for continuous guidance and
encouragement throughout my PhD. I deeply appreciate the time and patience you were
always willing to invest in me. I also thank my dissertation committee members: Richard
John, Christopher Jones and Oguzhan Ozbas, for oering valuable insights throughout
the entire process. Special thanks to Kevin Murphy for the data on incentives but, more
importantly, for reading several drafts of the manuscript and providing many insightful
comments.
I thank Ashwini Agrawal, Elias Albagli, Brad Barber, Irving Biederman, Juan Car-
rillo, Derek Horstmeyer, David Hirshliefer, Salvatore Miglietta, Udi Peleg, Francisco Perez-
Gonzalez, Breno Schmidt, Christopher Schwarz and seminar participants in the 2010 AFA
Annual Meeting, 2009 and 2010 FMA Annual Meeting, and BI Norwegian School of Man-
agement, Cal-State Fullerton, City University of Hong Kong, Claremont McKenna College,
UC Irvine, University of New South Wales, University of Missouri, University of Southern
California, University of Western Ontario and the University of Melbourne (which is my
new aliation!) for helpful comments. I thank Ulrike Malmendier and Georey Tate for
providing the list of award-winning CEOs.
I would also like to thank my classmates who have made my years at USC a tremendous
experience. I will especially miss my friend and colleague, Luis Goncalves-Pinto, whose
support and friendship helped me through the tough times.
I wouldn't be where I am today without my family. I thank my parents, Margalit and
Izak Shemesh, for always believing in me. I also express my deep appreciation to my wife
iii
Ronit, for allowing me to pursue my dream. I know that you have sacriced a lot, and
yet you supported me whole-heartedly to complete this doctoral dissertation. Last but not
least, I embrace my son Barak, for bringing me so much joy.
iv
Table of Contents
Acknowledgements ii
List of Tables vi
List of Figures viii
Abstract ix
Chapter 1: CEO Social Status and Risk Taking 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Data and empirical strategy . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.1 Measures for risk taking in rm-level decision variables . . . . . . 10
1.3.2 Measures for risk taking in rm-level outcomes . . . . . . . . . . 11
1.3.3 Empirical strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.1 Firm fundamentals and decision variables . . . . . . . . . . . . . 17
1.4.2 Firm-level outcomes and stock returns . . . . . . . . . . . . . . . 20
1.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.5.1 CEO awards and managerial risk taking . . . . . . . . . . . . . . 25
1.5.2 Individual-level decisions and risk aversion . . . . . . . . . . . . . 26
1.6 Direct and indirect eects on compensation . . . . . . . . . . . . . . . . 34
1.6.1 Empirical results for executive compensation . . . . . . . . . . . 36
1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Chapter 2: Thou Shalt not Covet Thy (suburban) Neighbor's Car 41
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2 Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.3.1 Descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.1 Counts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.4.2 Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.4.3 Logit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
v
Chapter 3: The Weekend Eect in Equity Option Returns 57
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Data and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3 Weekday patterns in option markets . . . . . . . . . . . . . . . . . . . . 67
3.3.1 Main ndings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.3.2 Weekday eects in other variables . . . . . . . . . . . . . . . . . 74
3.3.3 Midweek holidays, long weekends, and expiration weekends . . . 78
3.3.4 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.3.5 Subsample results . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.3.6 Nonparametric tests . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.4 Potential explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.4.1 Weekly patterns in liquidity . . . . . . . . . . . . . . . . . . . . . 93
3.4.2 Time decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.4.3 Weekly patterns in risk . . . . . . . . . . . . . . . . . . . . . . . 98
3.4.4 Market conditions and non-trading returns . . . . . . . . . . . . 104
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Bibliography 111
vi
List of Tables
Table 1.1: Logit regression results . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Table 1.2: Descriptive Statistics of award winners and predicted winners . . . . 16
Table 1.3: CEO turnover of award winners and predicted winners . . . . . . . . 17
Table 1.4: Capital expenditure, R&D expenditure, and total investment . . . . 19
Table 1.5: CEO awards and R&D expenditure . . . . . . . . . . . . . . . . . . . 20
Table 1.6: Decomposition of stock return volatility . . . . . . . . . . . . . . . . 23
Table 1.7: Share ownership of award-winning CEOs . . . . . . . . . . . . . . . . 31
Table 1.8: Vega elasticity and return variability . . . . . . . . . . . . . . . . . . 33
Table 1.9: Cash-weight-in-compensation of winners vs. predicted winners . . . . 38
Table 1.10: Cash-weight-in-compensation . . . . . . . . . . . . . . . . . . . . . . 38
Table 1.11: Cash-weight-in-compensation by corporate governance . . . . . . . . 40
Table 2.1: Descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Table 2.2: Car purchase counts, population density and income distribution . . 51
Table 2.3: Car purchase intervals, population density and income distribution . 54
Table 2.4: Logit model per make and block group, 3 months intervals, luxury cars 56
Table 3.1: Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Table 3.2: Unhedged excess returns, delta-sorted portfolios . . . . . . . . . . . . 68
Table 3.3: Delta-hedged excess returns, delta-sorted portfolios . . . . . . . . . . 69
Table 3.4: Delta-hedged excess returns, maturity-sorted portfolios . . . . . . . . 71
Table 3.5: First day of the week versus other days . . . . . . . . . . . . . . . . . 73
Table 3.6: Weekday eects in other variables . . . . . . . . . . . . . . . . . . . . 75
Table 3.7: Weekday eects in S&P 500 Index options . . . . . . . . . . . . . . . 76
vii
Table 3.8: Mid-week holidays, long weekends, and expiration weekends . . . . . 80
Table 3.9: Unhedged excess returns, delta-sorted portfolios, value-weighted . . . 83
Table 3.10: Delta-hedged excess returns, delta-sorted portfolios, value-weighted . 84
Table 3.11: Alternative sampling procedures . . . . . . . . . . . . . . . . . . . . . 86
Table 3.12: Average delta-hedged excess returns for each year of the sample . . . 87
Table 3.13: Frequencies of lowest and highest returns . . . . . . . . . . . . . . . . 92
Table 3.14: Relative bid-ask spreads, maturity-sorted portfolios . . . . . . . . . . 94
Table 3.15: Open interest and trading volume, maturity-sorted portfolios . . . . 96
Table 3.16: Stock return and VIX moments . . . . . . . . . . . . . . . . . . . . . 99
Table 3.17: Risk of portfolios of delta-hedged excess option returns . . . . . . . . 104
Table 3.18: Explaining delta-hedged excess option returns, equal weighted portfolios 106
Table 3.19: Explaining delta-hedged excess option returns, value weighted portfolios 107
viii
List of Figures
Figure 1.1: Decomposition of return variability for rms with award-winning CEOs 21
Figure 1.2: Dispersion of industry betas of rms with award-winning CEOs . . . 24
Figure 1.3: Median ownership of award-winning CEOs . . . . . . . . . . . . . . . 30
Figure 1.4: Total compensation and option compensation of award-winning CEOs 37
Figure 2.1: Household units per block group . . . . . . . . . . . . . . . . . . . . . 48
Figure 2.2: Population density per block group, by county . . . . . . . . . . . . . 49
Figure 2.3: Median family income per block group, by county . . . . . . . . . . . 50
Figure 2.4: Days between transactions of the same make, by density . . . . . . . 53
Figure 2.5: Days between transactions of any luxury make, by density . . . . . . 54
Figure 2.6: Days between transactions of dierent luxury make, by density . . . 55
Figure 3.1: Average Delta-Hedged Excess Return by Day of the Week . . . . . . 70
Figure 3.2: 3-Month Treasury Yield and TED Spread . . . . . . . . . . . . . . . 90
Figure 3.3: Frequency of Lowest Delta-Hedged Excess Returns by Day of the Week 91
ix
Abstract
This dissertation is comprised of three essays.
The rst essay, titled \CEO Social Status and Risk Taking," studies the implications of
relative concerns, or social comparisons, to risk taking of corporate ocers. The corporate
environment is a perfect setting to study such eects, as it seems plausible that high-ranking
corporate ocers value status to a signicant extent. There is little work, however, on the
interaction between social status concerns and managerial risk taking, which in turn aects
almost all corporate policy, ranging from investment choices to capital structure. I argue
that CEOs with higher reputation have an incentive to follow their peers and do what
other rms are doing, in order to lock-in their relative advantage. I use prestigious business
awards assigned by major media organizations (such as Business Week) to measure shocks
to CEO status. I then study how dierent measures of managerial risk taking change after
receiving an award. In line with the theoretical predictions of relative status concerns, I nd
that rms with award-winning CEOs monotonically decrease their idiosyncratic volatility
ratios and their industry betas converge to 1. R&D expenditure decreases by 20% while
investment in tangible assets increases relative to a matched sample of non-winning CEOs.
Finally, I nd that status may aect not merely observed risk taking but also underlying
risk preferences, as implied by individual-level asset allocation. I interpret the results as
evidence for the signicance of social status concerns in managerial risk taking.
The second essay is joint work with Fernando Zapatero. In this paper, titled \Thou
Shalt not Covet thy (Suburban) Neighbor's Car," we study the eect of population den-
sity on the intensity of \keeping up with the Joneses" behavior. Using a unique dataset
x
of car registrations from 2004 to 2006 in three counties of Southern California, we show
that neighbor eects are stronger in areas with lower population density. The decision to
buy a car is strongly in
uenced by previous car purchases of neighbors, and the eect is
substantially stronger in areas with lower population density. Such areas represent small
communities in which neighbors are likely to know each other, and can therefore manifest
their income or wealth through the public display of their consumption. The evidence is
consistent with two possible channels of in
uence: information and status concerns. We nd
evidence supporting both channels, as our results cannot be fully explained by information
exchange, or word of mouth. We argue that the stronger eect that we nd in areas with
lower population density is driven by status signaling reasons.
The third essay is joint work with Christopher Jones. In this paper, titled \The Weekend
Eect in Equity Option Returns," we revive one of the earliest and most studied pieces of
evidence against the Ecient Market Hypothesis - the weekend eect. During the weekend,
nancial markets are closed. For option writers, this means holding a position that exposes
them to unbounded losses, while not being able to trade. We nd that returns on options on
individual equities display markedly lower returns over weekends (Friday close to Monday
close) relative to any other day of the week. These patterns are observed both in unhedged
and delta-hedged positions, indicating that the eect is not the result of a weekend eect
in the underlying securities. We nd even stronger weekend eects in implied volatilities,
but only after an adjustment to quote implied volatilities in terms of trading days rather
than calendar days. Our results hold for puts and calls over a wide range of maturities and
strike prices, for both equally weighted portfolios and for portfolios weighted by the market
value of open interest, and also for samples that include only the most liquid options in the
market. We nd no evidence of a weekly seasonal in bid-ask spreads, trading volume, or
open interest that could drive the eect. We also nd little evidence that weekend returns
are driven by higher levels of risk over the weekend. The eect is particularly strong
over expiration weekends, and it is also present to a lesser degree over mid-week holidays.
Finally, the eect is stronger when the TED spread and market volatility are high, which
xi
we interpret as providing support for a limits to arbitrage explanation for the persistence of
the eect. Our interpretation is that the low Monday returns are driven by option writers,
who require compensation for holding open positions during the weekend. Our results are
consistent with the conjecture that investors are generally averse to holding positions with
unbounded losses when nancial markets are closed.
1
Chapter 1
CEO Social Status and Risk Taking
1.1 Introduction
Social status permeates the corporate environment, which in turn can aect corporate
choices. This paper tests the hypothesis that social status concerns aect managerial risk
taking. I assume that high-ranking corporate ocers obtain utility not only from their
wealth but also from their social status relative to others. If chief executive ocers (CEOs)
value social status to a substantial extent, then any eects that status concerns might have
on risk taking should be easier to identify in CEO behavior. By testing whether receiving a
prestigious business award aects subsequent risk-related business decisions and outcomes,
I show that changes in status aect managerial risk taking. CEO awards aect rm-level
decisions and outcomes in line with the theoretical predictions of a risk-taking tournament.
Managerial risk taking aects almost every corporate policy, ranging from investment
choices to capital structure. Excessive risk taking might lead to bankruptcy, while excessive
risk avoidance prevents growth and hurts shareholder value. The standard principal-agent
model highlights the tension between incentive alignment and managerial risk aversion.
Since managerial eort is unobservable, shareholders want to tie compensation to perfor-
mance. This compensation scheme, however, is also more expensive, as managers require
a risk premium for a random and uncertain wage. Understanding the factors that aect
managerial risk taking and preferences is thus an interesting and important question in
corporate nance. Individual managers are key factors in the determination of corporate
2
policy (Bertrand and Schoar [2003]). If managers have discretion inside their rm, they may
alter corporate decisions to advance their own objectives. This paper tests whether CEO's
social status concerns, as opposed to rm, industry, or market factors, aect managerial
risk taking.
So, how is status expected to aect risk taking? If CEOs value social status to a
signicant extent, one would expect them to act as if they were in a tournament. The basic
intuition of tournaments is that a trailing contestant has an incentive to choose a riskier
strategy, whereas a front runner should aim at the safe strategy. However, when the risky
strategies are correlated, the leading player has an incentive to imitate the risky strategy
of his opponent (Nieken and Sliwka [2010]). This is because imitating the risky strategy
becomes a means to protect the lead. If we allow the competitors to choose covariance, the
leader's best response is to \mimic" (increase the correlation with respect to) the laggard,
whereas the laggard's best response is to \dierentiate" from the leader (Cabral [2002]).
This is because when the risky strategy chosen by the competitor can be exactly replicated,
the relative position remains unchanged independent of the outcome. In a more complex
portfolio choice setting, Basak, Pavlova and Shapiro (2007) and Chen and Pennacchi (2009)
study the optimal asset allocation of a fund manager in the context of relative performance
evaluation. If managers can choose the degree of exposure to systematic versus idiosyncratic
risks, their optimal strategy manifests itself not in increasing or decreasing total volatility
but in deviating more or less from the benchmark index. Managers in the lead would want to
\lock in" their advantage by mimicking the benchmark, whereas underperforming managers
prefer to push the deviation of their portfolio away from the benchmark. Underperforming
managers can take on either more or less systematic risk than that of the benchmark,
as any strategy entailing a deviation from the benchmark is a gamble in the context of
relative performance evaluation. For example, by taking on less systematic risk than that
of the benchmark (reducing volatility), the underperforming manager bets on improving his
relative performance when the benchmark falls. The risk-taking tournament theory thus
3
predicts that winners will decrease company-specic risk and increase the correlation with
the industry they are in and with the entire economy.
While most models in nance assume that relative standing is dened by relative wealth
or consumption, I use awards as a proxy for social status, as they are widely visible and
draw a clear ranking order. I use prestigious business awards assigned by editorials of major
national publications (such as Business Week) to measure shocks to CEO status. The key
criterion for inclusion in the sample is that the award is national, so that it is prominent
enough to plausibly aect CEO status, and that the award is given to the CEO and not to
the rm as a whole. CEO Awards provide a signicant boost in terms of positive media
coverage and public appreciation (Francis et al. [2008]). I thus assume that awards represent
a tournament-like payo that is denominated in terms of social status. CEOs are generally
concerned that the market devalue their reputation based on poor industry-adjusted stock
price performance (Milbourn [2003]). Award-winning CEOs thus have more to lose, in
terms of their social status, if they make choices that result in poor rm performance. Such
CEOs would thus want to hold on to their advantage by making sure that they do not make
bad headlines, at least not in relative terms.
Media awards are exogenous in the sense that they are given by corporate outsiders who
can rely only on public information to assess CEO quality, and any CEO can potentially
win them. Nevertheless, it is possible that implicit incentives (i.e., pursuing awards to in-
crease compensation) play a role in CEO awards. I therefore explore alternative channels
though which awards may aect risk taking rationally, such as compensation or termina-
tion risk. Such alternative channels either predict the opposite outcome to that of social
status concerns, or have no signicant correlation with awards, consistently with the use
of awards as a proxy for social status. To the best of my knowledge, CEO award data
have not been used in the nance literature, except by Malmendier and Tate (2009). In
their paper, Malmendier and Tate (MT hereinafter) conjecture that awards increase CEO
power within their rms. Such managers become more entrenched, and so they put less
eort and extract more rents. The authors nd that award-winning CEOs subsequently
4
underperform, spending more time on public and private activities outside their companies,
such as assuming board seats, writing books and pursuing leisure activities such as golf. In
my paper, I explore a dierent aspect of awards, as they aect CEO social status outside
their rm, measured in relative terms with respect to other CEOs.
I employ a dierence-in-dierences approach to compare award winners to their most
similar non-winners. I rely mostly on a matching procedure, by which each award winner is
compared with his most similar non-winner. The dierence-in-dierences approach accounts
for the fact that awards are not random. Awards are likely granted based on outstanding
past performance which is likely to revert to the mean. It is also possible that risk-related
events before the award was granted are the cause of both the award and the adjustments
following it. For example, awards may be granted on successful innovation (such as FDA
approval), turnaround (such as reorganization and recovery from bankruptcy) or sheer luck.
Since awards are given by corporate outsiders who rely on public information to assess CEO
quality, any information they may consider should be manifested in stock returns leading
to the award. The matching is thus based on stock returns prior to the award, along with
additional rm and CEO characteristics that are correlated with the probability of receiving
an award. I construct a nearest-neighbor matching estimator to test whether award-winning
CEOs change their risk-taking behavior dierently than do their matched peers.
This paper nds that rms with award-winning CEOs increase their investment in tangi-
ble assets while decreasing their R&D expenditure by 20% from the pre-award expenditure
level. The decrease is R&D expenditure is signicant both relative to a matched sample
of non-winning CEOs, and after controlling for investment opportunities and cash
ow. In
line with the predictions of a risk-taking tournament, I nd that rms with winning CEOs
monotonically decrease their idiosyncratic volatility to total volatility ratios, as exposure
to systematic risks becomes a means to preserve their position. Correspondingly, their in-
dustry betas converge to 1, as average beta increases from 0.86 before the award to 0.97
four years after. I also nd that status may aect not merely observed risk taking but also
underlying risk aversion, as implied by individual-level asset allocation. Award-winning
5
CEOs decrease their share ownership by more than 20% from their pre-award ownership
level, as concentrated investment in the company they work for exposes them to company-
specic risk. In addition, rms with award-winning CEOs display a weaker relation between
option-based compensation and rm-level risk taking. More specically, Vega elasticity is
correlated with stock-return variability to a smaller extent following an award. I interpret
the results as evidence for the signicance of status and competition in CEO behavior, over
and above other factors that are commonly considered in the literature. CEO awards aect
rm-level decisions and outcomes, providing further evidence for the eect CEOs have over
rm policy.
The paper is structured as follows. In section 1.2 I describe the related literature on the
relation between social status and risk taking. Section 1.3 describes the empirical strategy
and the measures I use for risk taking, and section 1.4 presents the results. Section 1.5
discusses the dierent channels by which awards may aect managerial risk taking. In
section 1.6 I explore additional direct and indirect eects that CEO awards may have on
executive compensation, and section 1.7 concludes.
1.2 Literature review
CEOs matter to rm policy. Bertrand and Schoar (2003), for example, identify dierences
in \style" across managers by tracking top managers across dierent rms over time. They
nd that a signicant extent of the heterogeneity in investment, nancial, and organizational
practices of rms can be explained by the presence of manager xed eects. One concern
with this method is that turnover events and changes in policy may be driven by the same
forces. In my paper, I follow the same CEO at the same rm over time, and not across
dierent employers.
There is little work done thus far on how managerial risk taking is aected by social
status concerns. Adams, Almeida, and Ferreira (2005) show that stock returns are more
variable for rms run by powerful CEOs (identied by formal position and titles, status as a
6
founder, and status as the board's sole insider). Hirshleifer, Low and Teoh (2010) nd that
rms with overcondent CEOs (identied by press coverage or options exercise behavior)
have greater return volatility and invest more in innovation. In my paper, I focus only on
the time series, not on the cross section, and test whether shocks which aect the CEO on a
personal level result in corporate policy adjustments. The main contribution of this paper
is thus to test how shocks to CEO social status aect managerial risk taking.
If executives compete over their social status, one would expect them to act as if they
were in a tournament. I thus borrow from the tournament literature, with the added
assumption that CEOs obtain utility not only from their wealth but also from their social
status relative to others. The basic intuition of tournaments is that a trailing contestant
has an incentive to choose a riskier strategy, whereas a front runner should aim at the
safe strategy. Nieken and Sliwka (2010) study risk-taking behavior in a simple two-person
tournament, in a theoretical model as well as a laboratory experiment. The theoretical
model predicts that risk-taking behavior crucially depends on the correlation between the
outcomes of the risky strategies. Suppose that two agents play a winner-take-all type game.
The agents simultaneously decide between a risky and a safe strategy. The outcomes of
the risky strategies of the two players are normally distributed and may have dierent
correlations. If the outcome of the risky strategy is not correlated, then a Nash equilibria
in pure strategies exists, in which the trailing player chooses the risky strategy, and the
leading player chooses the safe strategy.
1
However, if the outcome of the risky strategy
is correlated across players, only a mixed-strategy equilibrium exists, in which the leading
player chooses the risky strategy with a higher probability than his opponent. The intuition
is that when the risky strategies are correlated, choosing the risky strategy becomes a means
to protect the lead. The leading player is now more likely to choose the risky strategy than
his opponent, as he imitates the risky strategy and can aord to gamble with a higher
1
A second Nash equilibrium in pure strategies exists, in which both players choose the risky strategy, if
the lead is suciently small relative to the expected performance of the risky strategy. Protecting a small
lead is not worthwhile when the risky strategy becomes more attractive in terms of expected performance.
7
probability due to his lead.
2
The Nieken-Sliwka model thus suggests that the optimal
strategy of the front runner depends on the correlation with the strategy of the trailing
contestant. However, it is unclear whether this result can be applied in a more complex
setting with multiple players in which the players can choose the correlation.
3
Cabral (2002) studies the strategic choice of covariance in races. In his model, two play-
ers face two alternative R&D paths. If players choose dierent paths then the probability
of success is independent across players. If both players choose the same path, however,
the outcome is perfectly correlated across players. In equilibrium, the leader is interested in
increasing the correlation with respect to the laggard. By doing so, the leader protects her
leadership by managing the risk that the laggard will earn a high return and overtake her.
The laggard, on the other hand, has an incentive to choose a dierent path from the leader.
The laggard is willing to trade o lower expected value for lower correlation with respect to
the leader. Cabral derives this result without assuming a convex payo function, that is, a
function with the properties that the leader has more to gain from extending his or her lead
than the laggard has to lose from falling farther behind. Instead, payos are determined
by the dierence between the two players. The crucial feature of the equilibrium is that
the leader has less to gain from moving farther ahead than he or she has to lose from being
caught up by the laggard, whereas the laggard has more to gain from moving closer to the
leader than he or she has to lose from falling farther behind.
Theoretical models in the mutual fund literature are more applied in the context of
this paper, as they consider multiple players who can choose the degree of exposure to
2
In this case, the higher expected payo of the risky strategy makes it more attractive to gamble and the
leading player can aord to gamble with a higher probability due to his lead. Taylor (2003) considers the
extreme case of perfect correlation in a mutual fund tournament. His model also predicts that the winning
manager is more likely to gamble.
3
The risk-taking tournament theory may predict cross-sectional dierences in the behavior of winners
depending on the heterogeneity of the industry they are in. Winners in industries with more heterogeneous
investment opportunities will decrease their total risk, while winners in industries with homogeneous in-
vestment opportunities will prefer the opposite course of action. In the context of capital budgeting, it is
plausible that rms generally face uncorrelated investment opportunities. This seems to hold in the data,
as I nd that idiosyncratic risk accounts for around 90% of total risk. If the uncorrelated case indeed holds,
one would expect award-winning CEOs - the leading players - to choose safer strategies then their peers.
8
systematic versus idiosyncratic risks. Similarly, in the context of capital budgeting, rms
face complex investment opportunities that may be company-specic, industry-specic or
economy-wide. In addition, implicit incentives in the mutual fund industry are comparable
to the highly skewed distribution of CEO public attention. Convexity can also originate
from managerial preferences, regardless of the incentive structure. CEOs value being in
\rst place" as an end in itself, in which case they act as if they were in a winner-take-all
tournament. In a portfolio choice setting, Basak, Pavlova and Shapiro (2007) study the
optimal asset allocation of a manager in the context of relative performance evaluation. In
the baseline model, a risk-averse manager faces convex incentives (in this case induced by
an increasing and convex relationship of fund
ows to relative performance). The authors
consider a setup in which managers can adjust their portfolio riskiness through taking on
idiosyncratic rather than systematic risk. If managers can choose the degree of exposure to
systematic versus idiosyncratic risks, their optimal strategy manifests itself not in increasing
or decreasing volatility but in deviating more or less from the benchmark index (tracking
error). While any strategy entailing a deviation from the benchmark is inherently risky
for managers in the lead, underperforming managers boost the deviation of their portfo-
lio from the benchmark, but do not necessarily increase the volatility of their portfolios.
Chen and Pennacchi (2009) replicate this result in a model with a smooth performance-
compensation function, rather than a piece-wise linear function. Their model predicts that
as the funds relative performance declines - the fund manager chooses to deviate more from
the benchmark portfolio, while not necessarily raising total volatility.
This result applies for this study, except that here I assume that CEOs obtain utility not
only from their wealth but also from their social status relative to others. In the tournament
over managerial social status, awards provide a signicant boost in terms of positive media
coverage and public appreciation (Francis et al. [2008]). If agents value status, one might
expect them to value winning the above game per-se, and not just as a means to receive
the monetary prize of winning. In this case, CEOs act as if they were in a winner-take-all
tournament, i.e. they value being in \rst place" as an end in itself. Winners would thus
9
want to hold on to their advantage by making sure that they do not make bad headlines, at
least not in relative terms. CEOs are concerned that the market devalue their reputation
based on poor industry-adjusted stock price performance (Milbourn [2003]). Award-winning
CEOs have more to lose, in terms of their social status, if they make choices that result
in poor rm performance. In this case, one would expect winners to decrease idiosyncratic
risk but increase systematic risk. Idiosyncratic risk here is the company-specic risk within
its industry. Managers compete within their industry (and less so within the economy), and
so the most appropriate comparison group for the decomposition of risk in this context is
the rm's industry.
In this paper I use awards as a social status measure because they are widely visible and
draw a clear ranking order. MT use prestigious business awards assigned by editorials of
major national publications to measure shocks to CEO status, and study the rst-moment
eects of an award on rm performance and managerial eort. They nd that award-
winning CEOs subsequently underperform, both relative to their prior performance and
relative to a matched sample of non-winning CEOs. They also spend more time on public
and private activities outside the companies, such as assuming board seats, writing books
and spending more time on leisure activities such as golf. That is, CEO awards have an
eect on the winner CEOs on a personal level, consistently with my use of awards as a
proxy for social status. I focus on the role CEO awards may have if CEOs care about their
social status relative to others.
MT also address the possibility that CEOs can aect the probability of receiving media
awards by self-promotion. They nd no signicant dierences between winners and their
matches in the number of TV interviews or in the number of mentions or interviews in
the printed press over the three years prior to awards. Awards, however, are positively
associated with press coverage during the year in which the award is granted. Francis et
al. (2008) observe a positive and highly signicant association between CEO awards and
10
the number of articles containing the CEOs name that appear in the major U.S. and global
business newspapers and business wire services.
4
1.3 Data and empirical strategy
I use CEO awards collected by Malmendier and Tate (2009), and I test whether the event
of receiving an award aects individual and rm-wide decisions and outcomes. The data
set covers 465 awards granted during the years 1992-2003, based on 13 dierent types
of awards. Business Week and Financial World are the two predominant publications
which conferred awards on CEOs during the sample period. Additional sources include
Chief Executive, Forbes, Industry Week, Morningstar.com, Time, Time/CNN, Electronic
Business Magazine, and Ernst & Young. The key criterion for inclusion in the sample is
that the award is national, so that it is prominent enough to plausibly aect CEO status.
I obtain CEO characteristics from the CompuStat ExecuComp database, and so I restrict
my analysis to CEOs in the ExecuComp universe. In addition, I use CRSP for stock return
variability and CompuStat for rm fundamentals. I next consider dierent measures for
managerial risk taking.
1.3.1 Measures for risk taking in rm-level decision variables
For CEO awards to aect rm-level decisions, CEOs should have at least some control over
rm policy. An eect on rm-level decisions thus also addresses important questions in cor-
porate nance, such as the level to which CEOs matter to rm policy, and the eectiveness
of governance mechanisms. Unfortunately, rm-level decision variables are the most prob-
lematic, as the mechanism through which managers aect rm risk might be unobservable.
For example, managers may engage in asset substitution, and so they do not necessarily
4
In panel B of Table 2, Francis et al. report logistic regressions of a Recognition dummy (equal to 1 if the
CEO is recognized in one or more lists of \top" CEOs in calendar year t, and 0 otherwise) on the number of
articles appearing in major U.S. newspapers that mention the CEOs name in calendar year t, the number of
articles appearing in major international newspapers that mention the CEOs name in calendar year t, and
the number of press releases that mention the CEOs name in calendar year t.
11
change investment levels, but instead choose safer or riskier projects. Thus, a change in
risk can be unrelated to investment levels. In addition, rm-level variables are based on the
managerial team as a whole and not just on the CEO. Since an award lowers the termination
risk that the CEO faces, it also lowers the probability of promotion of the VPs, and so they
may exert lower eort and have lower incentive to take risks. It is thus dicult to predict
how to aggregate the management team's eort and risk preferences.
1.3.2 Measures for risk taking in rm-level outcomes
I try to learn more about the type of decisions winners make following the award by look-
ing at the outcome of these decisions as it is manifested in stock returns. The risk-taking
tournament theory predicts that winners will decrease idiosyncratic risk but increase sys-
tematic risk, and so the decomposition of risk allows us to identify whether risk shifting
is rational/strategic in a tournament. It is also possible that the award increases investor
recognition in the CEO's rm and its securities (Merton [1987]). As investor attention
increases, one would expect stock-price informativeness to increase accordingly and thus
idiosyncratic volatility to go up as the stock price is tracking its fundamental value more
closely. One may consider an alternative model with incomplete information, in which an
award makes investors believe that they know more about the CEO's skills and will there-
fore update their beliefs to a lesser degree following rm-specic information; in this case,
the ratio of idiosyncratic volatility to total volatility after winning an award will decrease.
A consistent eect in both the decomposition of return variability and the decomposition
of investment may distinguish between the risk-taking tournament and alternative expla-
nations.
1.3.3 Empirical strategy
I rely mostly on an event-study method, by which for every award I select the years -1 to +3
relative to the year the award was made public. I then compare the last known information
prior to the award (year -1) to each of the four years following the award (years 0 to +3).
12
Since awards are given by corporate outsiders who rely on public information to assess CEO
quality, such variables may be used to control for cross-sectional dierences between award
winners and other rms. Due to the small sample size, as prestigious business awards are
granted to very few CEOs, I use a matching method to create a control group comparable
to award winners. According to this method, each rm with an award-winning CEO (the
treated rm) is matched with a control rm (the predicted winner). I follow MT in using
propensity-score matching which reduces the dimensionality of the matching process. MT
implement the matching using specic independent variables that are correlated with the
probability of receiving an award: Market value, book-to-market ratio, stock return during
the last three years prior to the award, CEO gender, age, and tenure. Johnson, Young
and Welker (1993) show that CEOs are more likely to win awards from the Financial
World magazine following outstanding rm performance, consistent with the notion that
accounting and capital market measures of rm performance convey information about CEO
productivity. Milbourn (2003) uses CEO tenure as a proxy for reputation. CEO tenure is
the result of past retention decisions, which depends on the board of directors assessments
of CEO ability.
The matching covariates are correlated not only with the independent variable (reputa-
tion), but also with the dependent variable (risk). In the context of managerial risk taking,
some of these control variables are very important. For example, executives may decrease
their risk exposure as they grow older and approach retirement age. In addition, awards
may be granted based on outstanding past performance, which is then likely to revert to the
population mean. It is also possible that risk-related events before the award was granted
are driving both the award and the adjustments following it. For example, the award could
be granted on luck (which is unsustainable by denition), successful innovation (such as
FDA approval) or turnaround (such as reorganization and recovery from bankruptcy). In
order to attend to such concerns, stock returns prior to the award are included as control
variables. Awards are given by corporate outsiders who rely on public information to assess
CEO quality, and so any information they may consider should be manifested in stock re-
13
turns leading to the award. By using propensity-score matching to study the eects of CEO
awards, I make sure that I only use relevant information and include the most comparable
rms in the control group. The control rms may thus be used as a proxy of what one can
expect to occur if the CEO had not received the award.
I thus use a nearest-neighbor matching estimator to test whether award-winning CEOs
change over time dierently than do their matched peers (predicted winners). More specif-
ically, for each variable of interest, I compare its change over time among award winners
to that of similar non-winners, a non-parametric dierence-in-dierences approach. This
method allows me to test how awards aect risk taking and risk preferences. Nevertheless,
matching is still not exact, i.e. there are dierence in covariates between matched units and
their matches. I follow Abadie and Imbens (2007) (AI hereinafter) in adjusting the results
using auxiliary regressions of each outcome variable of interest on the control variables used
in the matching process. This regression is preformed only on the control group (predicted
winners), and the coecients estimated are used to estimate the expected dierence be-
tween a treated rm and its match. As AI show, the simple matching estimator in nite
samples will have a bias corresponding to the matching discrepancies.
As an alternative method, I sometimes use panel regressions, in which I include all
rms common to CRSP, CompuStat and ExecuComp to control for time trends and cross-
sectional dierences. Each rm-year counts for one observation, and in each observation I
include award dummies indicating past winnings. The panel regression has some potential
problems: it might capture a general cross-sectional dierence in the characteristics of rms
that tend to have award-winning CEOs, which is not the question of interest in this paper.
The panel regression also makes strong assumptions on the distribution of the variables
of interest. In such a pooled model it is crucial to control for year and industry eects.
Campbell et al. (2001), for example, report a positive deterministic trend in idiosyncratic
rm-level volatility.
14
1.4 Results
Table 1.1 shows the logit results used to obtain the propensity scores. I include all rms
in each calendar month for which there was at least one award granted. The dependent
variable is a dummy variable equal to 1 if the CEO of the company won an award during
that month. Industry, year and award-type dummies are included to account for dierence
in the base probability of winning an award in the pooled regression. Consistent with
MT, CEOs of larger rms with lower book-to-market ratios and higher past returns are
signicantly more likely to win awards. CEOs with more tenure and younger CEOs are
more likely to win awards. Adding R&D intensity in the logit regression reveals that the
coecient is very insignicant, and is thus dropped as a covariate.
Table 1.1: Logit regression results
The dependent variable is a dummy variable equal to 1 if the CEO of the company won
an award during each month. Market value (CRSPlog(abs(PRC)SHROUT=1000))
is measured two months prior to the award month and is in log form. Book-to-Market
ratio (COMPUSTAT SEQ=(PRCC FCSHO)) is measured at the end of the last
scal year to end at least six months prior to the award month. Returns x y are the
total compound returns from the y
th
to the x
th
month prior to the award month.
Pseudo R-Square is the coecient of determination as in Cox and Snell (1989, pp.
208209)
Parameter Estimate Standard Error Wald Chi-Square Pr > ChiSq
Market value 0.8820

0.0454 377.4904 0.0001
Book-to-market -0.2575

0.0534 23.2588 0.0001
Returns 2 3 0.4447

0.1858 5.7304 0.0167
Returns 4 6 1.0504

0.2797 14.1008 0.0002
Returns 7 12 0.5945

0.1038 32.8067 0.0001
Returns 13 36 0.0376

0.0198 3.6203 0.0571
Female (dummy) 0.9895

0.5643 3.0745 0.0795
CEO age -0.1181

0.0091 166.8328 0.0001
CEO tenure 0.0298

0.0100 8.7963 0.0030
Industry dummies Yes
Year dummies Yes
Award-type dummies Yes
Pseudo R-Square 0.7392
Observations 55,941
15
Based on the propensity scores obtained using the logit model in table 1.1, I match
each award winner with the rm with the nearest score within the same month (minimum
absolute dierence), which has never won an award. The use of industry dummies allows
for matching to be made across industries, which is important for identication reasons.
Comparing the dierence between treated rms and the control group within the same
industry does not identify whether the tournament eect is driven by the leaders (the treated
rms), the laggers (the control group) or both. However, comparing winners to similar non-
winners across dierent industries suggests that the eect is indeed driven by the treated
rms. Table 1.2 shows descriptive statistics of award-winning CEOs and their control group
which was formed using the nearest-neighbor method as explain above. Predicted winners
are similar to winners, even in variables that are not used to match between the two. R&D
intensity, as are other variables that are known to be correlated with risk taking, are similar
for rms with award-winning CEOs and predicted winners. It seems that winners tend to
have lower idiosyncratic volatility ratios. Note that imposing a caliper on the matching
improves the similarity between winners and predicted winners, but since the sample is
small I prefer to keep all matches while adjusting for matching discrepancies.
In table 1.3 I look in more detail at dierences in CEO turnover between winners and
predicted winners. Termination risk may diminish managerial risk taking. If the board of
directors is reluctant to re superstars, such CEOs may thus engage in higher managerial
risk taking. I compute rates of post-award CEO turnover, due to either stepping down while
not leaving the rm, or leaving the rm following resignation/retirement. I nd that winners
tend to step down from the CEO position but remain in the rm more often, while more
non-winners tend to resign. Winners may face lower termination risk because the board of
directors will be reluctant to re a superstar. The wide recognition of award-winning CEOs
may thus protect them from termination following bad performance. This eect may also
induce higher managerial risk taking. The high frequency of CEOs who step down from the
CEO position and remain on the board is not surprising, given the high stock returns prior
to the award. Brickley, Linck and Coles (1999) report that CEO post-retirement board
16
Table 1.2: Descriptive Statistics of award winners and predicted winners
The sample includes winners and predicted-winners in all months in which a CEO award is conferred.
Predicted winners are matched by Market value, Book-to-market, returns 2 3, returns 4 6, Returns 7 12,
Returns 13 36, Female, Age and Tenure. Return standard deviation and Idiosyncratic volatility ratio are
based on daily stock returns for each scal year. Idiosyncratic volatility ratio is dened as the root-mean-
square error of rm return with respect to industry returns, divided by total return standard deviation.
Capital expenditure (CAPX), R&D expenditure (XRD), and total investment (CAPX+XRD) are nor-
malized by total assets (AT). Missing values of R&D expenditure are set to zero if capital expenditure is
positive. Share ownership is normalized by shares outstanding.
Winners Predicted winners Dierence in means
N Mean Median N Mean Median W-P Pr >jtj
Market value 270 9.796 9.8217 270 8.804 8.9494 0.9921

0.0001
Book-to-market 270 0.301 0.2579 270 0.2753 0.3252 0.0257 0.8292
Returns 2 3 270 0.0684 0.0509 270 0.2518 0.045 -0.1834

0.0368
Returns 4 6 270 0.0706 0.0658 270 0.0678 0.0544 0.00279 0.8843
Returns 7 12 270 0.2695 0.1641 270 0.3182 0.1538 -0.0487 0.3683
Returns 13 36 270 1.2188 0.5244 270 0.6545 0.3862 0.5643

0.0062
Female (dummy) 270 0.0148 0 270 0 0 0.0148

0.0448
CEO age 270 55.1556 56 270 49.2111 49 5.9444

0.0001
CEO tenure 270 7.2148 6 270 5.7444 4 1.4704

0.0164
Tobins Q 270 3.7764 2.0141 270 2.946 1.7533 0.8304

0.0721
Return standard deviation (%) 270 38.4247 31.6473 270 40.835 35.4063 -2.4103 0.1809
Idiosyncratic volatility ratio 270 0.8637 0.8833 270 0.8863 0.8907 -0.0226

0.0002
R&D expenditure 260 0.0453 0.0217 255 0.037 0.0068 0.00835 0.1659
Capital expenditure 260 0.066 0.0575 255 0.074 0.0589 -0.00793 0.1198
Investment 260 0.1114 0.0937 255 0.1109 0.0896 0.000419 0.9589
Share ownership (%) 248 3.3264 0.1971 265 3.7307 0.1301 -0.4043 0.5809
17
service is positively and strongly related with stock returns while CEO. Note that winners
tend to be older than predicted winners, as displayed in table 1.2, which may explain the
dierence in retirement rate.
Table 1.3: CEO turnover of award winners and predicted winners
Turnover is conditional on that the rm remains in the sample (i.e. was not
delisted or acquired). Turnover is imputed from ExecuComp data. If a CEO at
year t is reported as an executive but not as a CEO (CEOANN6= CEO) in year
t+1, he is assumed to step down. If a CEO in year t is no longer reported in
year t+1 he is assumed to either retire or resign, according to the `REASON'
provided by ExecuComp. Note that both resignations and retirements can be
voluntary (i.e. to take a better position elsewhere) so one should be careful when
interpreting \resigned" as \red"
Winners Predicted winners
Year Stepped down Resigned Retired Stepped down Resigned Retired
+1 7.1% 0.4% 2.6% 7.8% 1.5% 1.1%
+2 8.3% 0.4% 4.5% 4.6% 2.3% 2.7%
+3 6.2% 1.2% 3.1% 1.6% 2.0% 1.2%
+4 4.8% 0.4% 3.6% 5.0% 0.8% 2.9%
1.4.1 Firm fundamentals and decision variables
Risk taking in rm-level decisions is proxied by R&D expenditure. Firms often have to
choose between implementing a new technology or staying with the standard one. Ta-
ble 1.4 presents dierences and bias-adjusted dierences between winners and predicted
winners in several investment measures. More specically, I look at capital expenditure,
research & development expenditure and total investment (i.e. capital and R&D expen-
diture combined), with all measures normalized by total assets. Table 1.4 suggests that
rms with award-winning CEOs display a decrease in R&D expenditure and an increase
in capital expenditure relative to predicted winners. The decrease in R&D expenditure
is economically signicant, accounting for more than 20% from the pre-award expenditure
level. One interpretation is that award winners become myopic, and sacrice long-term
growth for short-term personal objectives (such as the preservation of their status). This
18
is because R&D expenditure usually represents long-term investments. In addition, R&D
investments come from the rm-specic investment opportunity set, i.e they expose the rm
to idiosyncratic risk.
Hirshleifer, Low and Teoh (2010) nd that rms with overcondent CEOs invest more
heavily in innovation. If award winners become more overcondent following an award,
one would expect them to invest more heavily in R&D. Furthermore, awards may provide a
positive reinforcement to the CEO, in the sense that he must have been doing the right thing.
Winners may thus become more extreme as they amplify current investments. On the other
hand, it is also possible that the award was granted following successful innovation (such
as FDA approval), which in turn may lead to a decrease in R&D expenditure afterwards.
I do not nd evidence for neither of these eects, as R&D expenditure of winners seems
to remain stable following the award (not reported). However, to further alleviate this
concern, I lter out 2 types of awards (which account for 4 awards) that may be correlated
with innovation, namely the Business Week Best Entrepreneur and the Ernst & Young
Entrepreneur of the Year awards. Results are similar whether I apply this lter or not.
Note however that the decrease in R&D expenditure could be driven by a decrease
in cash
ow following an award. In addition, since rms with award-winning CEOs un-
derperform the market (as reported by MT), it is unclear whether the decrease in R&D
expenditure can be explained by a decrease in investment opportunities following an award.
I thus test whether rms with award-winning CEOs display a decrease in R&D expenditure
following an award, controlling for investment opportunities and cash
ow. I use Tobin's
Q to proxy for investment opportunities, with the notion that managers of a rm with
poor investment opportunities (\low" Q) should invest less. Table 1.5 suggests that R&D
expenditure is lower for award winners-i.e., they invest less than other rms with similar
investment opportunities and cash
ows following the award. The panel includes all rms
with award-winning CEOs, as well as all other rms common to CRSP, CompuStat and
ExecuComp. Note that the coecients should be interpreted as in a dierence-in-dierences
19
Table 1.4: Capital expenditure, R&D expenditure, and total investment
The table tests whether rms with award-winning CEOs change their risk-taking behavior dierently than do
similar non-winners. More specically, for each variable of interest, I compare its change over time among award
winners to that of predicted-winners. I compare the last known information prior to the award (year -1) to each
of the four years following the award (years 0 to +3). Predicted winners are matched at year -1 by Market value,
Book-to-market, Returns 2 3, Returns 4 6, Returns 7 12, Returns 13 36, Female, Age and Tenure. Returns x y
are the total compound returns from the y
th
to the x
th
month prior to the award month. Capital expenditure
(CAPX), R&D expenditure (XRD), and total investment (CAPX+XRD) are normalized by total assets (AT).
Missing values of R&D expenditure are set to zero if capital expenditure is positive. Bias-adjusted dierence uses
an auxiliary regression of the outcome variable on the matching covariates following Abadie-Imbens.
Capital expenditure R&D expenditure Total investment
Bias-adjusted Bias-adjusted Bias-adjusted
N Dierence dierence Dierence dierence Dierence dierence
di[-1,+0] 205 -0.00083 -0.00315 -0.00438

-0.00471

-0.00521 -0.00787

(-0.24) (-0.83) (-1.94) (-2.07) (-1.21) (-1.71)
di[-1,+1] 160 0.0102

0.016

-0.00456

-0.00336 0.00569 0.0127

(2.28) (2.86) (-1.83) (-1.33) (1.06) (1.97)
di[-1,+2] 123 0.00694 0.00858 -0.00891

-0.00714

-0.00196 0.00144
(1.46) (1.43) (-2.76) (-2.17) (-0.33) (0.21)
di[-1,+3] 94 0.0102

0.0151

-0.00978

-0.00598 0.000373 0.00909
(1.71) (1.87) (-2.47) (-1.46) (0.05) (0.92)
20
model, since I control for rm xed eects and the post-award dummy is set to 1 only during
the 3 years following an award.
Table 1.5: CEO awards and R&D expenditure
Panel regression of R&D expenditure controlling for in-
vestment opportunities and cash
ow. Cash
ow is mea-
sured by Operating Income Before Depreciation (COM-
PUSTAT OIBDP), and investment opportunities are
measured by Tobins-Q (COMPUSTAT (ATSEQ +
(PRCC FCSHO))=AT ). The post-award dummy is
set to 1 only during the 3 years following an award.
Regression includes rm and year xed eects.
Parameter Estimate t Value Pr >jtj
Intercept 55.849 0.37 0.7078
Award (last 3 years) -79.928

-9.66 0.0001
Q -0.007 -0.32 0.7492
Cash
ow 0.068

72.47 0.0001
Firm xed eects Yes
Year xed eects Yes
R-Square 0.8892
Observations 46,730
R&D expenditure however is merely a rough measure for risk-taking, as it pools together
both innovative research projects and more reliable development investments. I thus try to
learn more about the type of decisions winners make following the award by looking at the
outcome of these decisions as it is manifested in stock returns.
1.4.2 Firm-level outcomes and stock returns
In line with the predictions of a risk-taking tournament, I study the decomposition of re-
turn variability. Recall that I expect winners to decrease idiosyncratic risk but increase
systematic risk. The most appropriate comparison group for the decomposition of risk in
this context is the rm's industry. I therefore regress daily stock returns on their respective
industry returns (Fama-French 48-industry classication) and compute the idiosyncratic
volatility ratio, dened as the resulting root-mean-square error divided by total return
standard deviation. I repeat the decomposition using the risk factors of Fama-French (mar-
21
0.75
0.8
0.85
0.9
0.95
-3 -2 -1 0 1 2 3
Idiosyncratic volatility ratio
Year
Idiosyncratic volatility WRT Industry (mean) Idiosyncratic volatility WRT Industry (median)
Idiosyncratic volatility WRT Fama-French (mean) Idiosyncratic volatility WRT Fama-French (median)
Figure 1.1: Decomposition of return variability for rms with award-winning CEOs
Graph plots the mean and median idiosyncratic volatility ratios of rms with award-winning CEOs.
Idiosyncratic volatility ratio is dened as the root-mean-square error of rm return with respect to
either industry returns or Fama-French factors, divided by total return standard deviation. Idiosyn-
cratic volatility ratios are based on daily stock returns for each scal year, relative to the scal year
during which the award was granted. For consistency, the graph includes only rms for which data
are available for the full window [-3:+3] (N=70).
ket excess return, small market capitalization minus big, high book-to-price ratio minus
low, and momentum).
The decrease in idiosyncratic volatility normalized by total volatility is shown in g-
ure 1.1. I plot both mean and median idiosyncratic volatility ratios, estimated using either
industry returns or the Fama-French four factors (mktrf, smb, hml, and umd).
Table 1.6 directly tests for signicance and for a cross-sectional dierence in the idiosyn-
cratic volatility ratio between rms with award-winning CEOs and predicted winners. In
22
Panel A, I decompose stock return volatility using industry returns, so that the decom-
position of risk is aligned with a potential risk-taking tournament within the industry. If
CEOs are measured relative to the industry, their safest approach is to increase the rm's
alignment with the industry. Results show that industry betas monotonically increase for
rms with winner CEOs (converging to 1 from an average beta of 0.86 in year -1 to 0.97 in
year +3). The convergence of industry betas to a beta of 1 is shown in gure 1.2, as the
range between the 5% and 95% percentiles decreases by around 25%. One interpretation is
that managers become more passive, increasing exposure to industry shocks and avoiding
idiosyncratic shocks. Note that beta is increasing despite the leverage eect driven by high
stock returns prior to the award.
Since winners and predicted winners are not exactly matched by their industry, compar-
ing their idiosyncratic volatility ratios with respect to industry is uninformative. In panel
B of table 1.6, I therefore use the risk factors of Fama-French (market excess return, small
market capitalization minus big, high book-to-price ratio minus low, and momentum) and
compute the idiosyncratic volatility ratio, dened as the resulting root-mean-square error
divided by total return standard deviation. Results show that idiosyncratic volatility ratios
go down to a larger extent for rms with award-winning CEOs relative to predicted win-
ners. Comparing winners to similar non-winners across dierent industries suggests that
the eect is indeed driven by the treated rms. These results are strengthened by the fact
that rms with award-winning CEOs tend to have lower idiosyncratic volatility ratio levels
on average, i.e. negative cross-sectional dierences are upward biased. Note that even if
managers reduce risk taking immediately following the award, this eect may take time to
manifest itself in rm-level performance. This is due to the fact that overlapping projects
take several years to manifest, so the projects from the previous several years still dominate
the risk exposure of the rm even after the award. I therefore look for a change in rm-level
risk measures over a longer period of ve years following an award.
The decrease in idiosyncratic volatility is consistent with the predictions of a risk-taking
tournament, as winners cling on to their industry. It is possible that winners engage in
23
Table 1.6: Decomposition of stock return volatility
Panel A: Decomposition of stock return volatility for winners
For each scal year relative to the award, I regress daily stock returns either
on their respective industry returns (Fama-French 48-industry classication) or
on the risk factors of Fama-French (market excess return, small market capital-
ization minus big, high book-to-price ratio minus low, and momentum). The
idiosyncratic volatility ratio is dened as the resulting root-mean-square error
divided by total return standard deviation.
Stock return Idiosyncratic volatility
N standard deviation Industry beta ratios WRT industry
di[-1,+0] 248 0.4489 0.0673

-0.0167

(0.6) (2.16) (-5.2)
di[-1,+1] 220 0.4905 0.0975

-0.0326

(0.47) (2.61) (-6.99)
di[-1,+2] 183 -0.5414 0.1059

-0.0427

(-0.34) (2.47) (-8.85)
di[-1,+3] 158 -0.9074 0.1095

-0.0511

(-0.47) (2.63) (-9.88)
Panel B: Idiosyncratic volatility ratios WRT Fama-French factors
Bias-adjusted dierence uses an auxiliary regression of the outcome variable on
the matching covariates following Abadie-Imbens.
Predicted Bias-adjusted
N Winners winners Dierence dierence
di[-1,+0] 224 -0.024

-0.00905

-0.015

-0.0157

(-5.02) (-1.85) (-2.19) (-2.28)
di[-1,+1] 178 -0.0467

-0.0227

-0.024

-0.0363

(-6.59) (-3.67) (-2.55) (-3.9)
di[-1,+2] 137 -0.0621

-0.0395

-0.0226

-0.0242

(-7.82) (-5.26) (-2.07) (-2.26)
di[-1,+3] 107 -0.0543

-0.045

-0.00934 -0.029

(-6.72) (-4.94) (-0.77) (-2.23)
earning smoothing which in turn may aect stock return variability. MT nd that award
winners are signicantly more likely to report negative earnings once ve years have passed
from their last award than other CEOs. While this kind of earnings management may
lower total volatility, it is unclear how it would aect the idiosyncratic volatility ratio. I
do not nd that total volatility (as measured by return standard deviation) signicantly
decreases following the award. Even if this kind of earnings management could aect the
idiosyncratic volatility ratio, its eect is most probably dominated by actual managerial
decisions. The eects reported here are consistent with the decomposition of investment
24
0
0.5
1
1.5
2
2.5
-3 -2 -1 0 1 2 3
Beta WRT Industry
Year
Mean 5% percentile 95% percentile
Figure 1.2: Dispersion of industry betas of rms with award-winning CEOs
Graph plots the mean and 5th and 95th percentiles of factor loadings on idustry returns of stock
returns of rms with award-winning CEOs. I regress daily stock returns on their respective industry
returns (Fama-French 48-industry classication). Industry betas are based on daily stock and indus-
try returns for each scal year, relative to the scal year during which the award was granted. For
consistency, the graph includes only rms for which data are available for the full window [-3:+3]
(N=70).
reported in table 1.4. A consistent eect in both the decomposition of return variability and
the decomposition of investment provides further support for the risk-taking tournament
explanation.
25
1.5 Discussion
1.5.1 CEO awards and managerial risk taking
There are additional channels though which awards may indirectly aect managerial risk
taking, even when there is no social tournament involved. It is plausible that awards provide
a positive reinforcement in the sense that the CEO must have been doing the right thing.
Winners may thus become more extreme as they amplify current investments. It is also
possible that award winners become more overcondent following an award and thus display
higher risk tolerance, as awards may cultivate CEO \hubris". MT suggest that CEOs who
become superstars increase their outside activities and thus exert less eort in their core
responsibilities. It is not clear whether and how such distractions aect managerial risk
taking. One may suggest that superstar CEOs become more passive in their investment
decisions,
In an agency model with incomplete information, winning an award may upgrade the
beliefs the board and shareholders hold regarding CEO skill. If the CEO then does badly, it
will not change their beliefs much, and so compensation will not decrease as much-i.e., pay
is less sensitive to performance. This eect may induce higher managerial risk taking. Note
that as documented by MT, award-winning CEOs subsequently underperform, but their
compensation is not negatively aected. This implies that pay-performance sensitivity of
award-winning CEOs indeed decreases signicantly following the award. Winners not only
face lower pay-performance sensitivity but they may also face lower termination risk because
the board of directors will be reluctant to re a superstar. The wide recognition of award-
winning CEOs may thus protect them from termination following bad performance. This
eect may also induce higher managerial risk taking.
In addition, higher status may mean higher CEO power in the decision-making process,
and thus more concentrated decision making. The other executives and the board members
may trust the superstar CEO and decide that they cannot stand up to him or her. If
decision making is more concentrated and made by one person and not by a group, one
26
might expect higher variability. Also, if award-winning CEOs experience an increase in
compensation, not shared by the next-highest paid executives in their rms, post-award
compensation increases intra-rm inequality, which may induce more group risk taking
at the management level (Kale, Reis, and Venkateswaran [2009]). There may be other
spillage eects within the management team; for example, if winning an award lowers the
termination risk that the CEO faces, it also lowers the probability of promotion of the VPs,
and so they may exert lower eort and have lower incentive to take risks. Alternatively, if a
rm with an awarded CEO faces a lower takeover risk, this aects the entire management
team, not just the CEO.
It is ex-ante unclear whether awards have a direct eect on risk taking. Since most
indirect eects presented above, as distinct from status concerns, suggest a positive relation
between winning an award and managerial risk taking, nding a negative relation suggests
that direct eects, driven by status concerns, dominate managerial risk taking. A negative
relation between winning an award and managerial risk taking would thus provide evidence
for the signicance of social status and competition in governing CEO behavior over and
above other factors that are commonly considered in the literature, such as compensation.
1.5.2 Individual-level decisions and risk aversion
In the tournament models described above, agents adjusted their risk exposure as an optimal
rational decision. Indeed, most of the literature that is focused on relative concerns and risk
taking assumes that agents value status as an end in itself and adjust their risk exposure to
maximize their status. Robson (1992) investigates the implications for risk-taking behavior
if individuals have identical utility functions, which are concave in wealth but convex in
relative wealth. The utility from relative wealth is dened by the wealth distribution-i.e.,
the number of individuals with wealth less than one's own wealth. The model provides a
\concave-convex-concave" curve, as the middle-class gambles in an attempt to jump up the
ladder. Roussanov (2010) uses a portfolio choice framework in which households choose
their level of exposure to idiosyncratic risk in order to \get ahead of the Joneses". In these
27
models agents value status as an end in itself, and adjust their risk exposure to maximize
their status.
Nevertheless, status may aect the underlying risk aversion, and not merely the observed
risk taking. Classical nance mostly assumes that risk aversion is constant, either in absolute
or in relative terms of wealth or consumption. Prospect theory, however, suggests that
preferences may be risk averse or risk tolerant, depending on the agent's reference point.
Several experimental and empirical papers document the house-money eect, by which
agents display increased risk taking following gains (Thaler and Johnson [1990]). It is thus
possible that status aects the underlying risk preferences and not merely the observed risk
taking.
While most of the overcondence literature is focused on cross-sectional dierences in
managerial characteristics, one may suggest that award winners become more overcondent
following an award and thus display higher risk tolerance. Williams and Wong Wee Voon
(1999) study how mood in
uences subsequent risk decisions among actual managers, based
on hypothetical business decisions with realistic outcomes. They nd that managers are
more likely to select riskier courses of action after they recall and describe a work-related
event they had experienced that made them feel really good. One possible explanation is
that the positive aect induced by these memories may be associated with optimism and
improved managerial expectations. If award winners indeed become more overcondent
following an award, one would expect them to invest more heavily in R&D (Hirshleifer,
Low and Teoh [2010]). An alternative behavioral theory could build on learning one's
ability: executives may not know their ability and skill levels, and they can only learn it
over time. Winning an award increases both their own subjective estimated ability and its
precision. Consequently, winning CEOs feel more condent and are more willing to make
risky choices.
There are alternative behavioral factors, however, which support the opposite view.
Psychologists such as Alice Isen show in a series of experiments that emotions aect risk
28
taking.
5
For example, Isen and Geva (1987) study the association between happiness and
risk aversion using a laboratory experiment. They nd that positive aect, or happiness,
made subjects more risk averse, in comparison with those in a control group. They sug-
gest that persons who are feeling good tend to protect the pleasant positive state, making
potential losses seem more aversive.
Taking a more fundamental approach, one might turn to evolution in order to explore
the origins of a relation between social status and risk aversion. Such an evolutionary
approach may suggest that agents are hardwired to accept higher risks in case of feelings of
inferiority, as a human mechanism. The emotion of inferiority may have evolved to moderate
the emotion of fear, as risk tolerance serves as a signal for non-observable quality in the
reproductive cycle.
6
In this case, one would expect winners to become more risk averse.
An eect of awards on individual-level decisions may suggest a change in risk aversion,
and not merely a rational adjustment to risk taking. One direct measure of CEO risk pref-
5
See Loewenstein et al. (2001) for an interdisciplinary survey on the determinants of fear. The determi-
nants of fear are more complex than an assessment of the severity and likelihood of the possible outcomes
of choice alternatives, as expected utility theory assumes.
6
Evolutionary biology highlights the importance of social status in the reproductive cycle, as well as its
relation to risky choices. While avoiding unnecessary risks is crucial for survival, risk tolerance may also serve
as a signal for gene quality. Given this tradeo, it is possible that the human brain is hardwired to accept
higher risks in case of the feeling of inferiority. I follow Grafen (1990), who develops an evolutionarily stable
signaling equilibrium deduced through the process of choice over members of the opposite sex. Evolution
dictates that the surviving organisms and strategies are those that succeed in maximizing reproductive
success. As Grafen shows, evolution shapes a signaling rule-that is, a scaled-response gene that in eect
instructs its bearer: \If you nd yourself in a state X, emit a big signal. If the opposite, emit a small signal".
The innovation in the behavioral story I suggest is that risk tolerance may serve as a signal for quality in
such a system. One of the mechanisms through which agents signal high gene quality is by exerting the
minimum level of risk aversion and disease avoidance (Fessler, Pillsworth, and Flamson [2004]). For example,
consider the behavior of peacocks: the male peacock's tail is taken to be a signaling device to prospective
mates (Niman [2006]). One view is that the exuberance of the tail is an attractive quality exactly because
it makes the peacock more vulnerable to predators, and therefore signals the male's condence and quality.
This hypothesis was originally proposed by biologist Amotz Zahavi (1975). Zahavi's \handicap principle"
suggests that reliable signals must be costly to the signaler, costing the signaler in the trait being signaled
in a manner that an individual with less of that trait could not aord. Risk tolerance was the sole signal for
gene quality for most of our own species' history, and the human brain may have evolved to be hardwired
to accept higher risks in case of the feeling of inferiority. Evolutionary eects persist to the present day
even though human reproduction is now largely divorced from the factors that governed it for most of our
species' history, and humans are unaware of any connection between these dimensions and reproductive
success. Modern society has developed alternative signals for status, such as wealth or visible consumption,
which neutralize the need to take higher risks. The relation between modern signals for status should thus
be negatively related to risk aversion.
29
erence could be extracted from the CEO's personal portfolio. The overcondence literature
uses share ownership and option exercise activity as measures for overcondence, inspired by
Hall and Murphy (2003) who study the subjective value of compensation for undiversied
risk-averse managers.
I focus on ownership as a proxy for risk preferences. CEO ownership is used in the over-
condence literature as a measure for managerial risk aversion, as it is related to the sub-
jective level of under-diversication of the CEO's personal portfolio. Under-diversication
means that a very high share of the CEO's personal wealth is invested in the company
he works for. The level of under-diversication depends on the managerial subjective risk
tolerance, as this concentrated investment exposes them to company-specic risk. A visual
inspection of gure 1.3 suggests that award-winning CEOs decrease their share ownership
positions. The decrease is economically signicant, as it accounts for more than 20% from
the pre-award ownership level.
Table 1.7 shows that the decrease is also statistically signicant one year after the
award and onwards. Panel A displays changes in share ownership, based on the `SHROWN'
variable from ExecuComp.
7
It seems that predicted winners may also decrease their ownership, but not as much
as winners do. One concern is that winners may optimally adjust their ownership level
in response to higher option compensation. Managers who receive more stock and option
grants and own more shares have a greater incentive to sell equity for diversication reasons
(Ofek and Yermack [2000]). If winners receive higher compensation, they may exercise more
options (which I nd that they do; not reported), which in turn increases their share own-
ership. In many cases however, the executive will sell immediately once he or she exercises,
either in the open market or directly back to the rm. To address this concern, I study
changes in total equity holding, dened as the total dollar value of direct share ownership
and option holdings, normalized by market capitalization. This accounts for the substi-
7
The `SHROWN' variable is said to include restricted stock but does not account for option holdings,
though it seems that ExecuComp is inconsistent with regard to the inclusion of restricted stock.
30
0.2
0.4
0.6
0.8
1
1.2
-3 -2 -1 0 1 2 3
Ownership (%)
Year
Share ownership Total equity holding
Figure 1.3: Median ownership of award-winning CEOs
Graph plots median share ownership and total equity holding of winners. Share ownership equals the
number of shares held (excluding restricted stock), normalized by shares outstanding. Total equity
holding equals the total dollar value of direct share ownership (including restricted stock) and option
holdings, normalized by market capitalization. I estimate the value of options held at the end of
each year from ExecuComp using the procedure outlined in Murphy (1999). For consistency, the
graph includes only executives for which data are available for the full window [-3:+3] (N=83).
tution between stocks and options, and thus adjusts for any dierences in compensation
between winners and predicted winners. Surprisingly, the results presented in Panel B show
that total holding of winners decrease in the year in which the award was granted. This
suggests that winners sell more stocks than what they get through stock grants and option
exercise combined. Moreover, winners decrease their total holding by more than predicted
winners do.
31
Table 1.7: Share ownership of award-winning CEOs
Panel A: Share ownership
Share ownership equals the number of shares held (excluding restricted
stock), normalized by shares outstanding. Bias-adjusted dierence
uses an auxiliary regression of the outcome variable on the matching
covariates following Abadie-Imbens.
Predicted Bias-adjusted
N Winners winners Dierence dierence
di[-1,+0] 147 -0.2032

0.2525 -0.4558 -0.4837
(-2.66) (0.69) (-1.22) (-1.23)
di[-1,+1] 110 -0.2758

0.2499 -0.5257 -0.9515

(-1.72) (0.62) (-1.22) (-1.94)
di[-1,+2] 83 -0.565

0.3139 -0.8789 -2.0756

(-2.69) (0.49) (-1.31) (-2.84)
di[-1,+3] 65 -0.9023

0.6552 -1.5575 -4.3443

(-2.88) (0.56) (-1.29) (-2.99)
Panel B: Total equity holding
Total equity holding equals the total dollar value of direct share own-
ership (including restricted stock) and option holdings, normalized by
market capitalization. I estimate the value of options held at the end
of each year from ExecuComp using the procedure outlined in Mur-
phy (1999). Bias-adjusted dierence uses an auxiliary regression of the
outcome variable on the matching covariates following Abadie-Imbens.
Predicted Bias-adjusted
N Winners winners Dierence dierence
di[-1,+0] 147 -0.2065

0.9512 -1.1577 -1.1196
(-2.8) (1.36) (-1.65) (-1.52)
di[-1,+1] 110 -0.2724 0.8938 -1.1662 -1.349
(-1.66) (1.15) (-1.47) (-1.56)
di[-1,+2] 83 -0.5493

0.3071 -0.8564 -1.7799

(-2.53) (0.36) (-0.98) (-1.88)
di[-1,+3] 65 -0.9801

0.3112 -1.2913 -2.9972

(-3.06) (0.28) (-1.13) (-2.34)
An alternative motive for changes in share ownership may be driven by portfolio re-
balancing. For example, managers have an increased incentive to sell shares after their
inside holdings have appreciated in value (Jenter [2005]). However, MT nd that rms with
award-wining CEOs underperform the market, and so the rebalancing argument does not
hold. On the other hand, winners may trade on private information regarding their future
underperformance. The insider trading literature nds mixed evidence. Jenter (2005) nds
that insider trades do not predict subsequent returns. On the other hand, Aboody and
32
Lev (2000) nd that insider gains in R&D-intensive rms are substantially larger than in-
sider gains in rms without R&D, suggesting that R&D is an important source of private
information leading to information asymmetry and insider gains. I therefore split rms
with award-winning CEOs into low- and high-R&D intensity rms, as measured by R&D
expenditure normalized by total assets. The decrease in ownership does appear more signif-
icant in high-R&D intensity winners, yet it is still signicant at the 5% level for low-R&D
intensity rms (not reported).
A major caveat for the use of holdings as a proxy for risk preferences is that there are ex-
plicit and implicit restrictions on insider trading. An alternative proxy for risk preferences
is the relation between option-based compensation and stock-return variability. Option
compensation is the principal component of the CEO's Vega, which measures the extent to
which changes in risk aect the CEO's wealth. The relation between option compensation
and rm-level risk taking is moderated by the executive's risk aversion. Firm risk may
change for various reasons, most of which cannot be controlled by the executive. There-
fore, risk shifting in response to option grants may be attributed mostly to the executive's
preferences. I therefore use the degree of risk shifting in response to option grants as a
proxy for changes in risk aversion. If award winners become more risk averse, their option
compensation will not induce risk taking as much as expected. I test this in a regression
framework in table 1.8. I rst estimate the value of options held at the end of each year
from ExecuComp using the procedure outlined in Murphy (1999). I then estimate Vega
elasticity, which measures the extent to which changes in rm risk aect the CEO's wealth.
More specically, Vega elasticity equals the percentage change in value of outstanding op-
tions for a one percentage-point increase in volatility. The dependent variable is annual
return standard deviation.
Table 1.8 shows that in general option compensation induces risk taking, which is con-
sistent with previous literature (e.g., Cohen, Hall, and Viceira [2000]). The panel includes
all rms with award-winning CEOs, as well as all other rms common to CRSP, CompuStat
and ExecuComp. The post-award dummy is not signicant, consistent with the observa-
33
Table 1.8: Vega elasticity and return variability
Panel regression of return standard deviation on Vega elasticity.
Vega elasticity equals the percentage change in value of outstand-
ing options for a one percentage-point increase in volatility, and
is estimated at the end of each year from ExecuComp using the
procedure outlined in Murphy (1999). The post-award dummy
is set to 1 only during the 3 years following an award. Regres-
sion includes rm and year xed eects, and standard errors are
clustered by rm.
Parameter Estimate t Value Pr >jtj
Intercept 40.56

146,897 0.0001
Award dummy (last 3 years) 1.14 1.09 0.2768
Vega elasticity 3.57

13.58 0.0001
Vega elasticity * Award dummy -166.61

-2.17 0.0298
Firm xed-eects Yes
Year xed-eects Yes
R-square 0.7359
Observations 19,622
Vega elasticity*(1+ Award) -163.04

-2.13 0.0335
tion that awards don't seem to aect total stock return variability (table 1.6, panel A).
However, award-winning CEOs display a negative and signicant sensitivity during the 3
years following the award. I interpret the negative interaction term (Vega elasticity*Award
dummy) as evidence for a lower degree of risk shifting as a result of option grants by award
winners as compared with non-winners. Note that the coecients should be interpreted as
in a dierence-in-dierences model, since I control for rm xed eects and the post-award
dummy is set to 1 only during the 3 years following an award.
To summarize, I nd some evidence suggesting that award-winning CEOs become more
risk averse. The individual-level eects reported support a more general behavioral eect
governing a relation between status and underlying risk preferences, not just observed risk
taking. The social-science literature, including business and economics, is still debating
the relation between status and risk preferences. This paper contributes to this literature
34
by providing support for a positive relation between status and risk aversion.
8
Putting
all results together, it seems that both a behavioral eect by which award-winning CEOs
become more risk averse and a rational eect driven by the tournament are at play. That
is, a behavioral eect by which award-winning CEOs become more risk averse may coexist
with an eect driven by the tournament.
1.6 Direct and indirect eects on compensation
I study eects on compensation separately from other rm-level decisions because the eects
that awards have on compensation are complex and dicult to interpret.
First, compensation adjustments following the award may be driven by the board of
directors, in an attempt to aect CEO eort and/or risk taking. The board of directors can
adjust compensation and its composition in response to changes in CEO motives and/or
CEO preferences. For example, award-winning CEOs may face better outside options, and
so higher compensation is required to keep them from leaving the rm. The board of
directors of rms with such CEOs would thus like to support retention and preserve man-
agerial eort. Alternatively, winner CEOs may face lower termination risk, as the board
fo directors will be reluctant to re a superstar, and so higher incentives are required as
an alternative governance mechanism. Alternatively, the board of directors of rms with
winner CEOs may want to lower the eects of reduced risk taking by the CEO. The board
may be concerned that the CEO may no longer have an incentive to take additional risk
and therefore may decrease the risk exposure of their rms. This may result in suboptimal
decisions such as abstaining from growth opportunities if a desirable project (i.e. with a
positive Net Present Value) is turned down due to the risk involved. According to classical
principal-agent theory, the cash component in an optimal contract is increasing with the
8
It would be interesting to more directly test for a behavioral eect by which agents are hardwired to
accept higher risks in case of feelings of inferiority, as a human mechanism. It may be possible to develop
an fMRI experiment, focusing on the interplay between brain regions associated with risk perception and
emotions. The idea would be to control for a feeling of status/inferiority and the riskiness of investment
opportunities, and then test whether brain regions associated with risk preferences are aected solely by the
elicited emotion.
35
agent's risk aversion. The intuition is that when the agent is more risk averse, the cost
of alignment using incentives goes up. In these models, however, it is assumed that the
agent cannot aect rm risk. Cash compensation, however, may be more costly because
of Internal Revenue Service Regulation 162(m) (which limits a company's ability to deduct
more than $1 million in cash salary for top executives from their taxes). The board may
thus instead choose to grant more stock options to the CEO, imposing a convex preference
on rm performance. Executives cannot simply hedge these new option grants, commonly
unvested for several years, because such trades are restricted by regulation. In this case,
one may expect boards in rms with higher growth opportunities to grant more options
intentionally, since in these rms the manager's risk aversion can aect investment deci-
sions more signicantly. Good-governance rms may be less concerned with a decrease in
managerial risk taking, since in these rms the manager cannot aect investment decisions
easily.
On the other hand, award-winning CEOs may use their increased power to aect their
compensation level and structure (Belliveau, O'Reilly, and Wade [1996]). MT nd mixed
evidence, as increases in winners' equity-based compensation are only apparent in rms with
weak pre-existing corporate governance. The authors suggest that award-winning CEOs use
their increased power to extract greater rents in the form of equity-based compensation.
If CEOs can control their compensation structure to a large extent, it may be attributed
to their personal preferences, or more specically, their risk preferences. If managers become
more risk averse, they require more options to keep their subjective utility from compen-
sation at the same level. This is a certainty-equivalent (CE) argument since the CE is
decreasing with risk aversion. Lord and Saito (2006) report a negative relation between
cash and total pay. According to standard utility theory, a risk-averse manager who re-
ceives a cash component in his or her compensation contract could be given a package with
a lower expected value than one who receives only risky stock compensation. While it is
possible that award winners use their increased power to increase the level of their pay, it
may be more dicult to explain why their increased power would yield higher cash weights
36
relative to non-winners with the same level of total pay. It is interesting therefore to test
whether award winners display a higher cash-weight-in-total-compensation when compared
with non-winners with the same level of total pay.
Second, the eects of compensation on risk taking are unclear. For example, most of the
literature assumes complete markets, in which the options' Vega is positive, and so options
elicit risk taking. Coles, Daniel, and Naveen (2006) nd that higher Vega (the sensitivity
of CEO wealth to stock volatility) leads to riskier policy choices, including relatively more
investment in R&D and less investment in property, plant, and equipment (PPE). On
the other hand, Ross (2004) suggests and Cadenillas, Cvitanic, and Zapatero (2005) show
that options may have the opposite eect, as they excessively expose risk-averse executives
to rm-specic risk. Whichever of these eects prevails, it should be stronger for award
winners, as they face a lower probability of termination. A lower probability of termination
means that newly granted options will become exercisable and will not be lost in case of
termination during their vesting period. This makes options more valuable on expectation,
as the probability of staying in the rm long enough to exercise the unexercisable options
goes up.
1.6.1 Empirical results for executive compensation
In gure 1.4, I shows an increase in mean compensation, while medians show that com-
pensation in unaected by awards in general. This suggests that there might be a strong
eect but only for a small subsection of winners. The gure also suggests that most of the
increase in mean compensation is driven by an increase in option grants. These increases
however are not signicant (not reported) and are likely driven by rms with weak corporate
governance. MT split the sample by governance and show that only bad-governance rms
show a signicant increase in option compensation while good-governance rms do not.
I next study the compensation structure, following Lord and Saito (2006). According to
standard utility theory, the certainty equivalent of equity-based compensation is lower than
that of cash. A manager who receives a higher cash component in his or her compensation
37
0
5,000
10,000
15,000
20,000
25,000
30,000
-3 -2 -1 0 1 2 3
Compensation ($1,000s)
Year
Total Compensation (mean) Total Compensation (median)
Options Granted (mean) Options Granted (median)
Figure 1.4: Total compensation and option compensation of award-winning CEOs
Graph plots mean and median total compensation and option compensation of award-winning CEOs.
Total Compensation includes Salary + Bonus + Other Annual + Restricted Stock Grants + LTIP
Payouts + All Other + Value of Option Grants. Option compensation is the aggregate value of stock
options granted to the executive during the year as valued using Standard & Poor's Black-Scholes
method. For consistency, the graph includes only rms for which data are available for the full
window [-3:+3] (N=64).
contract could be given a package with a lower expected value than the one who receives all
risky stock compensation. Lord and Saito (2006) report a negative relation between cash
weight and total pay. In table 1.9, I show that cash-weight-in-total-compensation increases
for winners more than it does for predicted winners.
Since total compensation levels between winner and predicted winners dier, I use a
more general panel regression in table 1.10. The panel includes all rms with award-winning
CEOs, as well as all other rms common to CRSP, CompuStat and ExecuComp. Award
38
Table 1.9: Cash-weight-in-compensation of winners vs. predicted winners
Cash-weight-in-compensation is dened as Salary + Bonus + All Other
Compensation that is paid or payable in cash, divided by total compen-
sation (EXECUCOMP (SALARY +BONUS +ALLOTHPD)=TDC1).
Bias-adjusted dierence uses an auxiliary regression of the outcome variable
on the matching covariates following Abadie-Imbens.
Predicted Bias-adjusted
N Winners winners Dierence dierence
di[-1,+0] 226 -0.011 -0.036

0.0256 0.0291
(-0.59) (-1.92) -0.97 -1.11
di[-1,+1] 169 -0.015 -0.088

0.0739

0.0889

(-0.61) (-3.97) -2.26 -2.7
di[-1,+2] 128 -0.032 -0.053

0.0208 0.0356
(-1.14) (-1.83) -0.52 -0.91
di[-1,+3] 90 -0.074

-0.147

0.0727 0.0927

(-2.24) (-3.74) -1.42 -1.88
dummy is 1 if the current CEO received an award in the last three years, and zero otherwise.
Missing lagged award dummies are assumed to be zero, in order to include the rst three
years of the sample. This indeed creates a measurement error; however, since the value
is always assumed to be zero the model is consistent and unbiased. This imputation only
makes it harder to get signicant results.
Table 1.10: Cash-weight-in-compensation
Panel regression of cash weight in compensation (EXECUCOMP
(SALARY +BONUS +ALLOTHPD)=TDC1) on total compensa-
tion (EXECUCOMPTDC1). Regression includes year and rm xed
eects.
Parameter Estimate t Value Pr >jtj
Award dummy (last 3 years) -0.0327

-2.85 0.0044
Total compensation -7.10E-06

-34.8 0.0001
Total compensation * Award dummy 4.37E-06

13.88 0.0001
R-Square 0.4867
Observations 21,837
Total compensation*(1+Award dummy) -2.70E-06

-10.77 0.0001
The results in table 1.10 show that winners display a negative relation as standard utility
theory predicts, yet more interestingly it is signicantly less negative as compared with
39
non-winners with the same level of total pay. While it seems plausible that award winners
use their increased power to aect the level of their pay, it is dicult to explain why their
increased power would yield a higher cash weight compared with non-winners with the same
level of total pay. In addition, the decrease in ownership reported earlier is not consistent
with increased CEO power, as more powerful CEOs will prefer to maximize ownership
and use it to expropriate as much as possible. I also nd that the higher cash weight in
compensation is not concentrated in bad-governance rms, as reported in table 1.11. I use
the governance index provided by Gompers, Ishii, and Metrick (2003) to split the rms into
three groups. If compensation structure is driven by CEOs' power to aect their pay, I
expect this eect to be stronger in, if not unique to, bad-governance rms. However, in
table 1.11 I nd the eect to be uncorrelated with governance. This supports an alternative
argument, by which boards are adjusting compensation of winning CEOs following the
award to elicit risk taking in an attempt to mitigate managers'
ight to safety.
1.7 Conclusion
This paper tests the hypothesis that social status concerns aect risk taking. I test whether
changes in status aect risk taking as they are manifested in business decisions of award-
winning CEOs. I nd that CEO awards aect rm-level decisions and outcomes. Firms
with award-winning CEOs invest less in R&D relative to a matched sample of non-winning
CEOs. A consistent eect in the decomposition of stock returns further supports the risk-
taking tournament argument. Winners avoid idiosyncratic investments and cling on to their
industry. I interpret the results as evidence for the signicance of social status and com-
petition, which govern CEO behavior over and above other factors, such as compensation,
that are commonly considered in the literature. These ndings shed some light on our
understanding of managerial risk taking.
In a more general sense, I provide further evidence that CEOs matter, i.e. they can
aect rm policy, and also that the media matters, i.e. it aects managers.
40
Table 1.11: Cash-weight-in-compensation by corporate governance
Panel regression of cash-weight-in-compensation (EXECUCOMP (SALARY +BONUS +ALLOTHPD)=TDC1) on total
compensation (EXECUCOMP TDC1) and rm and year xed eects, by corporate governance
Bad-governance rms (GIM > 9) 7 < GIM <= 9 Good-governance rms (GIM <= 7)
Parameter Estimate t Value Pr >jtj Estimate t Value Pr >jtj Estimate t Value Pr >jtj
Award dummy -0.0529

-2.98 0.0029 -0.08597

-3.69 0.0002 -0.065

-2.36 0.0182
Total compensation -1.30E-05

-27.87 0.0001 -8.50E-06

-17.54 0.0001 -1.00E-05

-17.67 0.0001
Total comp * Award 8.08E-06

9.73 0.0001 6.81E-06

11.28 0.0001 5.44E-06

5.21 0.0001
R-Square 0.5244 0.5942 0.6
Observations 7,757 4,463 4,445
Total comp*(1+Award) -5.20E-06

-7.39 0.0001 -1.70E-06

-4 0.0001 -4.70E-06

-5.13 0.0001
41
Chapter 2
Thou Shalt not Covet Thy
(suburban) Neighbor's Car
2.1 Introduction
The notion that individual agents are in
uenced in their economic decisions by the con-
sumption or wealth of some comparison group (like neighbors, co-workers or relatives) has
been present in the social sciences in general, and in economics in particular, for a long
time. This type of behavior has been labeled \keeping up with the Joneses" and, arguably,
is motivated by the objective to signal a certain level of economic status. In his path-
breaking work, Veblen (1899) introduced the notion of \conspicuous consumption" and
argued that individual agents spend resources on luxurious goods that indicate a certain
status. Duesenberry (1949) postulates that the utility of a consumer depends on the ratio
of the consumption of this agent to a weighted average of of a reference group. He fur-
ther argues that people with whom the consumer has social contacts will have more weight
than those with whom the consumer only has casual contacts. There seems to be strong
macroeconomic evidence of investment in conspicuous goods. Hirsch (1976) calls \posi-
tional economy" this type of activity. In an in
uential paper, Frank (1984) argues that
income comparison eects explain why the dispersion in wages is lower than the dispersion
in marginal productivity. Mason (2000) oers a survey of some of the literature on this
topic, as well as recommended economic policies. More recently, the availability of data
42
on individual consumption, has permitted the study of the eects of individual purchases
decisions on the consumption decisions of neighbors. Grinblatt, Keloharju and Ikaheimo
(2008) study the purchase of cars in two Finnish provinces and nd evidence of the eect
of individual purchases on the decisions of neighbors. Ravina (2007) nds similar evidence
on consumption documented by credit card purchases.
In this paper we analyze a new dimension that we conjecture might aect \keeping
up with the Joneses" behavior: population density. We predict that population density
aects the \strength" of the \keeping up with the Joneses" behavior. In particular, in
areas of low population density, the consumption decisions of individual agents are more
likely to be in
uenced by the consumption of their neighbors. The argument in favor of
this conjecture is that in areas of low population density, there is a natural peer group that
economic agents can compare to (neighbors), and it is also easier to ascertain economic
information about this peer group and observe conspicuous consumption. To the best of
our knowledge, this has not been directly studied before, although Hong, Kubik and Stein
(2008) and G omez, Priestley and Zapatero (2010) provide some indirect evidence through
the equilibrium properties of security prices.
We use data on car purchases for three large counties which include areas with a large
range of diversity in population density and other economic and social dimensions. In par-
ticular, we study whether there is more clustering of car purchases of higher price segments
in areas of lower population density than in areas of higher population density, controlling
for household income. Our empirical analysis documents that there is strong evidence of
such pattern, and we therefore conclude that population density aects the intensity of the
\keeping up with the Joneses" behavior.
The paper is structured as follows. In section 2.2 we articulate the idea in the context
of the related literature on social comparisons. In section 2.3 we describe the data, and in
section 2.4 we present and discuss the results. section 2.5 concludes.
43
2.2 Hypothesis
There is ample evidence of consumption in conspicuous goods whose main purpose is to
denote statues since ancient times. As Mason (2000) points out, \Sumptuary laws were
often introduced to suppress excessive levels of ostentatious display," (see Hunt, 1996, for a
history of sumptuary laws). However, standard models of utility maximization in the last
decades ignore the quest for status and the value of investing in conspicuous consumption.
Some authors, starting with Veblen (1899), Frank (1985) and Robson (2001) argue that
status seeking has evolutionary basis. In particular, the rate of success in nding mates in
many species is higher for individuals endowed with characteristics associated with higher
probability of survival. Arguably, wealth is, and has been for centuries, a predictor of
survival (or longevity) in the human race. The quest for status as an indicator of wealth
and, therefore, a survival predictor is hard-wired in the human being, according to these
authors. Frank (1985) postulates that status should be part of the utility function. In fact,
the inclusion of relative wealth concerns in the utility function has become a frequent device
to explain asset prices since Abel (1990) rst suggested it. In an in
uential paper, Campbell
and Cochrane (1999) introduce the notion of \external habit formation". This additional
parameter in the utility function has been interpreted as relative wealth concerns by most
scholars. However, these are standard asset pricing models, based on a single consumption
good, which rules out the possibility of considering dedicated investment in conspicuous
goods.
In this paper, we do not postulate (or need) any particular rationalization for the con-
sumption of conspicuous goods. However, based on the overwhelming empirical evidence,
we take it as given that economic agents signal status by engaging in conspicuous con-
sumption. According to the Longman Dictionary of Contemporary English
1
, conspicuous
consumption is: \The act of buying a lot of things, especially expensive things that are not
necessary, in order to impress other people and show them how rich you are."
1
http://www.ldoceonline.com/dictionary/conspicuous-consumption
44
In particular, we focus on car purchases, as status-signaling decisions. Of course, cars
do not necessarily t the denition of conspicuous goods we just provided: for many people
a car is just as important for their normal participation in society as proper clothes or
adequate dwelling. However, it is also clear that above a certain threshold, the car becomes
a luxury good (there is a category labeled \luxury cars") and some of the price is related to
car attributes \that are not necessary." See for example Choo and Mokhtarian (2004) for
evidence of purchase of luxury cars as a status-signaling device. In addition, the literature
has also documented a peer eect in the car purchase decision. Grinblatt, Keloharju and
Ikaheimo (2008) show that a car purchase decision in
uences future car purchase decisions of
neighbors in a careful empirical analysis using data from Finland. The following quote from
the New York Times, explaining why someone had decided to buy a $190,000 fully electric
Tesla sports car, provides some anecdotal evidence of the peer in
uence in the decision to
buy a car:
\We asked him how he heard of Tesla and why he bought the car," said Rachel Konrad,
a Tesla spokeswoman. \He said, `Well, three other guys on my block have them.' " (New
York Times, Feb 15 2010).
In this paper we want to move a step forward and study the eect of population density
on the neighbor's eect we just discussed. As we discussed before, Duesenberry (1949)
supports the inclusion of other people's consumption in the utility function of economic
agents. Furthermore, he argues that \any particular consumer will be more in
uenced by
the consumption of people with whom he has social contacts than by that of people with
whom he has only casual contacts." Following this insight, we postulate that in areas of
lower population density neighbors are on average likely to have more intense interaction
than in areas of high population density.
2
These people are likely to interact in multiple
ways, as a result of possibly having children who attend the same school, shopping in the
2
With \lower population density" we mean groups of population that live close enough to each other to
have the possibility to chat or wave hello when stepping out of their residences, as opposed to areas in which
people are so far apart from each other than they might to have to drive to interact. This will become clear
when we describe our data.
45
same places, attending the same church, and even working for the same employer. This
can create a sense of belonging to a community that provides an obvious reference for their
members. Of course there might be other reference groups that are also in
uential, like
family and co-workers. However, there does not seem to be a reason why the peer pressure
should come from just one reference group. In this paper we will focus on neighbors, but
we do not rule out other possible sources of in
uence.
The main empirical challenge for our analysis is the existence of several reasons, other
than \keeping up with the Joneses" behavior, that might in
uence the purchase of a car.
The most obvious is possibly the information channel: buyers who are happy with their
decision after driving the car for a few days or weeks, might express their satisfaction to
their neighbors and in
uence their choice of brand on purely consumer satisfaction grounds.
In our empirical analysis, we control for this \information" eect in two ways: i) we use
income dispersion as a control variable in our analysis; lack of dispersion will be associated
with more homogenous groups and will facilitate communication; ii) we study the eect
across dierent brands, i.e. how purchases of luxury brands aect purchases of other luxury
brands dierent from the original. Of course there will be also an income eect in the
purchase decision, especially of luxury cars, and we do control for the level of income, along
with the dispersion. Finally, there are also seasonal eects that tend to lump car purchases
around certain times of the year and this might give the false impression of in
uence in
purchase decisions. For that reason we also control for seasonality in purchases. In next
section we describe our data in detail.
2.3 Data
We use information from a dataset from R. L. Polk & Co. that records all car purchases, new
and used, from most Department of Motor Vehicles (DMV) in the US. For each purchase
we have the model, make and year of the car, price and date of purchase. For privacy
reasons, it is not possible to obtain the exact address of the buyer, but we get the census
46
block group (BG), which is more detailed than ZIP codes. BGs are delimited by the US
Census Bureau. They contain between 600 and 3,000 people, with an optimum size of 1,500
people. This seems precise enough for our purposes. We merge the Polk dataset with data
from the 2000 US census, which includes demographical information at the BG level.
In particular, we have information on all car purchases for three years, 2004-2006, in
three large adjacent counties in Southern California: Los Angeles, Orange and Riverside
(Orange County is contiguous to both Los Angeles and Riverside; the last two are separated
by a narrow sleeve of land belonging to San Bernardino County). Our objective is to
compare purchase patterns across dierent areas with dierent population density, within
these three counties. We have to note that, overall, these are highly populated areas, and
\low density" typically represents a suburban neighborhood, usually with relatively high
household income. Therefore, in what we call \low population density," neighbors are likely
to know each other and have the possibility to communicate with each other easily (as
opposed to areas where neighbors are so far apart that direct communication might require
an extra eort).
2.3.1 Descriptive statistics
Table 2.1 includes descriptive statistics on all three counties. Overall, we have over 7 million
observations. Our population unit is a block group. In gure 2.1 we illustrate that the
delimitation of the BGs is based on population, not area. In that histogram we have used
the number of households per BG, but population per BG yields a similar graph. Figure 2.2
provides a histogram of the distribution of population density across BGs, summarized in
panel B of table 2.1 for each of the three counties. Clearly, we have enough dispersion of
density across our sample to test whether population density aects how purchase decisions
of agents in
uence the purchase decisions of their neighbors. Similarly, gure 2.3 shows
that we have enough dispersion in the distribution of household income across the BGs.
We need dispersion, rst so that controlling for income (a main factor in the type of car
people buy) is meaningful, but also in order to generate a proxy for homogeneity: areas of
47
low dispersion of household income tend to be more homogeneous and, arguably, will show
more communication among neighbors.
Table 2.1: Descriptive statistics
Panel A: Counties
Los Angeles Orange Riverside All counties
Census 2000
Number of Block Groups 6,351 1,826 804 8,981
Total population 9,519,338 2,846,289 1,545,387 13,911,014
Total household units 3,270,909 969,484 584,674 4,825,067
Area in sq. meters (millions) 10,517 2,044 18,667 31,229
Area in acres 2,598,957 505,219 4,612,716 7,716,892
Car registrations in 2004-2006
Used 2,720,491 787,919 554,287 4,062,697
New 2,038,502 610,846 362,885 3,012,233
All 4,758,993 1,398,765 917,172 7,074,930
Panel B: Block Group medians
Los Angeles Orange Riverside
Area in sq. meters 318,407 454,918 1,353,677
Area in dunam 318 455 1,354
Area in acres 79 112 335
Population density per dunam 3.81 3.08 1.26
Per capita income in 1999 17,296 25,738 16,761
Median family income in 1999 46,685 64,710 44,829
2.4 Results
With this data we can study the time series of purchases and compare empirically dierent
patterns across dierent areas, especially areas with dierent population density. The main
challenge of our analysis is the need to control for a number of variables that are possibly
relevant in purchase decisions, like dispersion of household income. For this purpose, we
merge the information of our database with data from the 2000 US Census to control for
other variables.
In addition, we need to establish that population density is the reason that explains a
given purchase pattern in a BG, as opposed to alternative explanations. In particular, we
48
04:10 Thursday, March 31, 2011 1
100 700 1,300 1,900 2,500 3,100 3,700 4,300 4,900 5,500
0
5
10
15
20
25
30
35
Percent
Housing Unit Count (100%)
Figure 2.1: Household units per block group
need to distinguish between informational and behavioral eects: good word of mouth from
neighbors who bought a car might explain why some people decide to buy the same model.
We address this problem in our empirical tests. We perform several tests that we explain
next.
2.4.1 Counts
In our rst exercise we want to establish the BGs are a relevant unit of analysis and that
some of the eects we have discussed before are present in our data. At this stage we do not
try to establish the source of the eects, that is, whether they are due to status-signaling
reasons or to communication, but whether the factors we are going to use, population
density and dispersion of income, are relevant at the BG level.
49
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Figure 2.2: Population density per block group, by county
In this test we do not distinguish among dierent car segments. We proceed as follows:
we count the number of car registrations within each BG by car make (i.e. Honda, Toyota
etc.) during our sample period. Since we want to verify that the BG is a relevant unit
for our analysis, we match each BG is with the ten nearest block groups. This allows us
to control for general market trends and general local characteristics. The total number of
car purchases in the 10 closest BGs, divided by 10, gives us the \expected count" of car
purchases of a given make if the BG is a perfect replica of the area in which it is located.
3
3
Since the population may be dierent across the BGs (1,500 people for BG only on average), the expected
counts based on the 10 nearest block groups are adjusted both by population and by number of household
units.
50
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C
o
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t
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Figure 2.3: Median family income per block group, by county
If the BG is an adequate unit of analysis, the prole of the car purchases in a BG will
deviate from the prole of purchases in the area in which it is located; in addition, we
want to study if the deviations are explained by the factors we are going to use in our
tests, population density and income distribution. We run a test for heteroskedasticity in
table 2.2: We test whether transaction counts, controlling for the expected count based on
the 10 nearest BGs, are more dispersed in areas with low population density, that is, we
test whether the residuals increase in absolute size with our factors.
Panel A of table 2.2 shows the rst-step regression, used to estimate dierences in
transaction counts between each BG and its 10 nearest BGs. The absolute residuals from
this rst-step regression are then used as the dependent variable in Panel B. Each column
corresponds to a dierent model specication. We employ both a linear regression and
51
Table 2.2: Car purchase counts, population density and income distribution
Panel A: 1st stage
Count Count
(population adjusted) (household unit adjusted)
Model Linear Fixed eects Linear Fixed eects
Intercept 11.40338

5.3845

13.13196

6.94765

Expected count 0.50214

0.50128

0.39833

0.39767

Population density -0.29935

-0.24561

Family income HI -7.31151

-9.44962

Low density (Tercile 0) 6.15713

5.92586

Medium Density (Tercile 1) -0.85209 -1.10987
Low income HI (Tercile 0) 5.04348

5.68326

Medium income HI (Tercile 1) 1.01223 1.20981
Panel B: Heteroskedasticity test
Count Count
(population adjusted) (household unit adjusted)
Model Linear Fixed eects Linear Fixed eects
Intercept 5.08142

0.88247 8.9194

4.08308

Expected count 0.47455

0.47275

0.35941

0.35803

Population density -0.52244

-0.42659

Family income HI 12.30069

6.7579

Low density (Tercile 0) 9.04715

8.63821

Medium Density (Tercile 1) 0.16688 -0.52084
Low income HI (Tercile 0) 2.60507

4.10363

Medium income HI (Tercile 1) -1.00446 -0.48131
a density xed-eect model (note that in the xed eect model, the highest rank is the
baseline). Although we do not dierentiate across dierent models within a given car make,
we also control for dispersion of income, as an important source of heterogeneity, that might
aect the transmission of information. We use the Herndahl index (HI) of family income
(based on 16 income groups within each BG) as a proxy for heterogeneity. We also use both
linear regression and a xed-eect model for income distribution (with the highest value
of the index being the baseline). The results in Panel B show that transaction counts of
dierent makes are more dispersed in areas with low population density. This evidence is
consistent with higher crowding in specic makes (at the expense of other makes that t the
neighborhood prole) in areas with low population density. In other tests we explore the
52
possible channels through which population density translates into concentration in these
makes.
2.4.2 Intervals
Next we explore the intervals between transactions within a BG during our sample period.
For each transaction, we compute the number of days between consecutive transactions of
the same car make within a BG. We focus on car make and not on specic models, as model
eects may be driven by information exchange to a larger degree than the car make. We
test whether the interval between transactions is correlated with population density. We
control for the expected interval, dened as the total number of days in the sample divided
by the total number of transactions of the same car make within the same block group.
The results for cars of the same make are collected in gure 2.4. In gure 2.5, we focus
only on luxury car makes (BMW, LEXUS and MERCEDES-BENZ), for which the eect
is expected to be stronger. Since even make level eects may be driven by information
exchange, we also explore only transactions that follow a luxury car (BMW, LEXUS and
MERCEDES-BENZ) of a dierent make in gure 2.6. That is, purchases of a car of a given
make in this group followed by purchases of a dierent make within the same group.
Table 2.3 tests the signicance of the results collected in the previous plots. In particular,
if intervals between car purchases are shorter in lower density areas and/or lower income
dispersion. Table 2.3 shows a strong eect of population density: lower population density
increases the in
uence of the purchase of a given make on the decision of the neighbors.
This is the case both for same make purchases of all cars and for luxury car purchases.
With respect to income heterogeneity, low income dispersion is positively correlated with
the expected number of days to purchase any car of the same make (more homogeneity
and more communication increases in
uence of a purchase on neighbors' decisions), and,
consistent with this rst result, it is negatively correlated when cars might be of a dierent
make (columns two and three). The density eect survives when we control for income
heterogeneity. The magnitude of the eect is stronger in luxury cars. Notably, the eect is
53
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t
H
i
g
h
Excess days between transactions
R
a
n
k
f
o
r
V
a
r
i
a
b
l
e
d
e
n
s
i
t
y
Figure 2.4: Days between transactions of the same make, by density
the strongest for luxury cars of a dierent make, which provides support for the relevance
of status signaling eects.
2.4.3 Logit
We use a Logit model to study the decision whether to buy a luxury car or not. In this
test we focus on luxury cars, for which the behavioral eect is expected to be stronger; as
such cars are clearly more conspicuous. As in the previous test, we also study whether a
purchase decision of a luxury car (of the class we dened before) has an eect on purchase
decisions of neighbors of a dierent luxury make. The dependent variable equals 1 if at least
one luxury car of a specic make was purchased in a specic block group within a period
of 3 months (calendar quarters). The Logit model includes quarter xed-eects in order to
54
04:10 Thursday, March 31, 2011 1
0
10
20
30
40
P
e
r
c
e
n
t
L
o
w
0
10
20
30
40
P
e
r
c
e
n
t
M
e
d
i
u
m
-197.5-152.5-107.5 -62.5 -17.5 27.5 72.5 117.5 162.5
0
10
20
30
40
P
e
r
c
e
n
t
H
i
g
h
Excess days between transactions
R
a
n
k
f
o
r
V
a
r
i
a
b
l
e
d
e
n
s
i
t
y
Figure 2.5: Days between transactions of any luxury make, by density
Table 2.3: Car purchase intervals, population density and income distribution
Interval Interval Interval
(same make) (any luxury) (dierent luxury)
Observations Used 6,141,309 613,261 395,163
Model Linear FE Linear FE Linear FE
Intercept 4.63

6.3

2.79

3.32

3.83

4.36

Expected interval 0.76

0.76

0.78

0.77

0.47

0.47

Population density 0.013

0.11

0.14

Family income HI 7.08

-3.04

-5.96

Low density (Tercile 0) -0.6

-1.33

-1.83

Medium Density (Tercile 1) 0.45

0.04 -0.19

Low income HI (Tercile 0) -1.18

0.14

0.13
Medium income HI (Tercile 1) -0.43

0.34

0.43

55
04:10 Thursday, March 31, 2011 1
0
5
10
15
20
25
30
35
P
e
r
c
e
n
t
L
o
w
0
5
10
15
20
25
30
35
P
e
r
c
e
n
t
M
e
d
i
u
m
-197.5 -152.5 -107.5 -62.5 -17.5 27.5 72.5 117.5 162.5
0
5
10
15
20
25
30
35
P
e
r
c
e
n
t
H
i
g
h
Excess days between transactions
R
a
n
k
f
o
r
V
a
r
i
a
b
l
e
d
e
n
s
i
t
y
Figure 2.6: Days between transactions of dierent luxury make, by density
control for within-year seasonality, as it is widely known that there are times of the year
that are more popular for car purchases (right before summer, for vacation traveling, and
at the beginning of fall, when new models are rolled out). This can produce some lumping
of purchases of luxury cars independent of communication and/or status signaling reasons.
Table 2.4 shows that the likelihood of buying a luxury car is aected by previous trans-
actions involving luxury cars within the same BG. The magnitude of this relation depends
on its interaction with population density. More interestingly, the eect is strong even if
the previous transaction involves a dierent luxury make. Arguably, eects across dierent
makes are driven by status signaling reasons, rather than information exchange. Notably,
this eect is present controlling for seasonal eects.
56
Table 2.4: Logit model per make and block group, 3 months intervals, luxury cars
Parameter Estimate Standard Error Wald Chi-Square
Intercept -1.578

0.0201 6,189.28
Family income 0.000021

1.97E-07 10,989.06
Population density 0.0252

0.00255 97.97
SameMaket1 1.5051

0.0202 5,550.68
DierentMaket1 0.6777

0.0218 965.16
Samet1 Density -0.0182

0.00291 39.06
Dierentt1 Density -0.00916

0.00319 8.24
Quarter xed-eects Yes
R-Square 0.1324
Observations Used 295,020
2.5 Conclusion
In this paper we explore whether population density has an eect on \keeping up with
the Joneses" preferences. We use a database of car purchases for areas with dierent
population density. We nd strong evidence that car purchases in
uence the purchase
decisions of neighbors and this eect is stronger in areas of lower population density. We
control for household income and we use income disparity as a proxy for heterogeneity:
low income dispersion (i.e., homogeneous population) will be associated with more intense
information exchange. The eect of population density persists even after we control for
income distribution (as a proxy for homogeneity) and for seasonal eect.
57
Chapter 3
The Weekend Eect in Equity
Option Returns
3.1 Introduction
The weekend eect in the stock market represents one of the earliest and most studied
pieces of evidence against the Ecient Market Hypothesis, yet the eect has received little
attention in recent literature. The explanation seems to be that the weekend eect has
disappeared, at least in equity markets, sometime during the last two decades. Why the
eect disappeared, or whether there ever was a weekend eect to begin with, as Sullivan,
Timmermann, and White (2001) have questioned, remain open questions.
Although the modern weekend eect literature began with the article of French (1980),
evidence on the eect was reported 50 years earlier by Fields (1931). Similar eects have
been observed in international equity indexes (e.g. Jae and Westereld (1985)), in a variety
of government bond returns (e.g. Gibbons and Hess (1981), Flannery and Protopapadakis
(1988)), and in U.S. equities as far back as 1885 (Bessembinder and Hertzel (1993)). The
robustness of the nding was short-lived, however, as authors such as Connolly (1989) and
Chang, Pinegar, and Ravichandran (1993) suggested that the eect started disappearing
in the 1970s or 80s. Kamara (1997) showed that the disappearance happened the soonest
for the largest rms. Chen and Singal (2003) argued that it is the introduction of options
on a rm's stock that led to the elimination of the weekend eect in a specic rm. Since
58
options tended to be introduced rst for large capitalization rms, this oers a potential
explanation of Kamara's result.
The Chen and Singal (2003) nding deserves further investigation because it implies that
the weekend eect may not have disappeared, but merely changed addresses. Their story is
actually related to the original intuition of Fields (1931), who conjectured that risk-averse
equity investors might want to close out their positions on Friday afternoon and open them
back up on Monday morning. Chen and Singal modify this intuition by suggesting that it
is the short sellers that are most interested in closing positions before the weekend. Their
reasoning is simple { with unbounded downside risk, naked short positions require constant
monitoring, which becomes dicult if not impossible to perform over the weekend.
Chen and Singal (2003) support their hypothesis with the observation that the weekend
eect was most pronounced in stocks with high levels of short interest and the nding that
the weekend eect disappeared only for those stocks on which options are traded. Their
result is also consistent with the decline in the weekend eect for US Treasuries, for which
derivative products are widely used.
The same intuition implies another eect that remains unexplored. If investors are
generally averse to holding positions with unbounded risk over the weekend, then speculators
who have written call option positions should also attempt to close out these positions
unless they receive additional compensation for that risk in the form of declining option
premia. Put option writers, while not exposed to a completely unbounded risk, still face the
possibility of losses that are far in excess of those that likely to occur in an equity position,
for example. For this reason we believe that the Chen and Singal (2003) hypothesis has the
straightforward implication that we should see a weekend eect in call and put options, with
weekend option returns being substantially lower than returns over the rest of the week.
We view this story only as one possible motivation for examining weekday eects in
equity option markets. More generally, options represent one of the last unexplored asset
classes for assessing the survival of the weekend eect. Knowing whether or not such an
eect exists has substantial implications for a number of literatures. Besides providing an
59
additional test of the Chen and Singal (2003) hypothesis, an unambiguous result from the
options market would directly address the view of Sullivan, Timmermann, and White (2001)
that the weekend eect was most likely the result of data mining.
Finding a weekend eect in option returns might also provide a new direction for the
option pricing literature in its search for models capable of explaining upward-sloping term
structures and smile-shaped cross sections in Black-Scholes implied volatilities. This liter-
ature is divided over the importance of jumps versus stochastic volatilities and the correct
risk premia to attribute to each (e.g. Pan (2002), Broadie, Chernov, and Johannes (2007)).
A weekend eect in option returns would indicate that the risks that are more prevalent or
less manageable over the weekend are the ones that require the largest risk premia.
We look for a weekend eect in option returns using simple methods. Using the Op-
tionMetrics dataset over the period from January 1996 to June 2007, we form portfolios of
options. Portfolios are formed on the basis of option maturity, moneyness, or both. Puts
and calls are put in dierent portfolios. We experiment with a variety of sampling and
weighting schemes. In addition, we examine returns separately for each year in our sample
period.
The results are clear cut. The weekend eect in individual equity option returns is large
and negative. We observe the eect in unhedged returns, but an analysis of delta-hedged
returns suggests that little of the eect is due to any weekend eect in the underlying stock
returns. All results are highly statistically signicant, often with t-statistics exceeding 10.
We nd similar eects in puts and calls and across almost all maturity and moneyness
categories.
After an adjustment to quote implied volatilities in terms of trading time rather than
calendar time, we nd a weekly seasonal in implied volatilities that is even more signif-
icant than that of the option returns. We also examine a measure we refer to as \total
implied volatility", which is simply the Black-Scholes implied volatility of the stock price
at expiration, not reported per unit of time. As an option moves closer to expiration, it's
total volatility tends to decrease as the length of time before expiration decreases. Over
60
the weekend, total implied volatility declines over twice as much as any other day of the
week, which is inconsistent with the observation, rst made by French and Roll (1986) and
conrmed in our sample below, that the actual volatility of Friday close to Monday close
returns is no greater than the volatility of returns over any other close-to-close interval.
Our results are unaected when we restrict the sample to the most liquid options and
to options on rms that are members of the S&P 100. We do not, however, nd strong
evidence of a weekend eect in S&P 500 Index options.
We investigate a number of potential explanations for the eect. One is that our results
are due to data mining, a concern articulated by Sullivan, Timmermann, and White (2001).
Another is that the margins required to write options are more costly to maintain over the
weekend than during the week. Although the underlying equity returns do not appear any
riskier over the weekend, we do nd limited evidence that option returns are slightly more
volatile, suggesting that higher risk may be partly responsible for the eect. We do not
nd evidence that our results can be attributed to the biases that result from measurement
errors in prices, as in Blume and Stambaugh (1983). Finally, we nd no evidence or weekly
patterns in volume or open interest that might suggest other liquidity-based explanations
of our results.
Regressions reveal that the eect is substantially stronger for expiration weekends (week-
ends that follow the last day of trading for front month contracts). It appears to exist to a
lesser extent for mid-week holidays as well, though the evidence for this nding is weaker,
most likely because of low incidence of mid-week holidays. In addition, the weekend eect
is more negative in times when S&P 500 Index volatility and the TED spread are high.
Since higher values of these two variables should make arbitrage strategies more dicult
to implement, we interpret these ndings as providing evidence for a limits to arbitrage
explanation as to why the eect persists.
We know of only one other paper, Sheikh and Ronn (1994), that investigates weekly
patterns in options markets. In examining short-term at-the-money options on 30 stocks
over a period of just 21 months, Sheikh and Ronn nd some evidence of a weekly seasonal
61
in which call returns are highest on Wednesdays, but they do not nd a weekend eect in
calls or in puts. Furthermore, after adjusting option returns by subtracting Black-Scholes
model-implied returns, the pattern in calls disappears, though a signicant weekend eect
arises in adjusted put returns. Our paper therefore resolves the ambiguity of their ndings,
showing that weekend eects are present in both calls and puts over a far more extensive
sample.
The paper is organized as follows. In Section 3.2 we describe our data, sampling meth-
ods, and portfolio construction. Section 3.3 contains results that document weekly patterns
in returns, implied volatilities, and liquidity measures. Section 3.4 examines the determi-
nants of weekend and weekday returns in a regression setting. Section 3.5 concludes.
3.2 Data and methods
Our primary data source is the Ivy DB data set from OptionMetrics. This data set includes
all US listed options on equities, indexes, and ETFs. In our paper we generally restrict our
attention to individual equity options, though for a few results we examine S&P 500 Index
options.
Throughout our analysis, we form portfolios of options on the basis of maturity and/or
delta. The delta we use is lagged an extra day, i.e. if we are forming a portfolio at day t 1
to hold until dayt, then we use the delta that was observed on dayt2. We do this so that
if there are measurement errors in deltas they are not correlated with the returns on the
same assets. We consider ve maturity ranges and six delta ranges so that all options in a
given portfolio are at least roughly comparable and all portfolios have a reasonable number
of options included. Finally, we have separate portfolios for calls and puts.
We compute portfolio returns by taking the equal or value weighted average of the
returns, either hedged or unhedged, of each option in that portfolio. Since our dataset
includes bid-ask quotes rather than transaction prices, we compute returns from quote
midpoints. Since options have zero net supply, the concept of value weighting must be
62
reinterpreted, and what we call value weighted portfolios are actually weighted by the
dollar value of open interest for each option. We usually examine excess returns, where
we compute riskless returns using the shortest maturity yield provided in the Ivy DB zero
curve le.
We impose a number of lters to try to eliminate a number of sources of noise. We nd
many large errors on the rst day an option is introduced, so we exclude the rst observation
for each contract. Large return reversals (2000% followed by -95% or vice versa) are also
eliminated. Because large bid-ask spreads are likely to be less informative, and to deal
with obvious data errors, we exclude the day t return on an option if any of the following
conditions hold:
day t 2 bid price is less than $0.50 or 0.1% of the price of the underlying stock
day t 2 bid-ask spread is more than 25% of the midpoint
day t 1 or t bid-ask spread is more than $5.00 or 200% of the midpoint
day t 1 or t ask price is less than the bid or more than twice the price of the
underlying stock
The rst two conditions represent lters that are implemented prior to the return interval.
These focus our attention away from the least liquid segment of the options market, which
tends to be deep out-of-the-money contracts. Note that if the day t 2 values that these
lters are based on are measured with error, then this error should at least be uncorrelated
with the subsequent return from day t 1 to t. The last two conditions are included to
eliminate a small number of major outliers that we do not catch otherwise. These might be
data recording errors or non-competitive \stub" quotes posted by a market maker who does
not want to trade. We also eliminate quotes in which the bid or ask is set to what appears
to be an undocumented missing value code (e.g. 999). Finally, we eliminate observations in
which there was a stock split between day t 1 and dayt. Together, these lters eliminate
the largest and most suspicious outliers in our sample. We note, however, that all of our
main results are robust to dropping all of these lters.
63
The implied volatilities in our analysis are provided by Ivy DB (with some adjustments
we describe below). They are computed using a binomial tree approach that accounts for
dividends. (Because they are equivalent to Black-Scholes values for stocks that pay no
dividends, we will refer to the implied volatilities and Greeks as \Black-Scholes" values.)
The delta of each option is also computed with the Black-Scholes model using the implied
volatility from that same option.
In many cases the OptionMetrics database does not include an implied volatility. Most
often, this is because an option contract appears to have negative intrinsic value, making
the implied volatility undened. As discussed by Battalio and Shultz (2008), apparent
arbitrage opportunities in options data are typically the result of microstructure issues and
measurement errors. If we were to discard options with negative intrinsic values, we would
be systematically excluding options with observed prices that are below their true values.
Duarte and Jones (2008) demonstrate that this will result in an downward bias for option
returns.
The solution proposed by Duarte and Jones is to \ll in" missing implied volatilities
with those of similar contracts. If a call option's implied volatility is missing, then we
use the implied volatility of the put contract written on the same underlying rm with
the same maturity and strike price. If both put and call implied volatilities are missing,
then we use the value from the same contract on the previous day. It is worth noting that
this procedure of lling in missing implied volatilities relies only on current and lagged
information. A portfolio strategy that uses the implied volatilities from this procedure for
portfolio formation and for computing hedge ratios is therefore fully implementable.
Option returns and excess returns are dened as
C
t
C
t1
C
t1
and
C
t
C
t1
C
t1
r
t1
ND
t1;t
;
64
respectively, where C
t
is the option bid-ask midpoint, r
t
is the riskless return per day, and
ND
t1;t
is the number of calendar days between date t 1 andt. Given that the change in
value of a delta-hedged portfolio is
C
t
C
t1
(S
t
S
t1
);
we dene delta-hedged returns as
C
t
C
t1
C
t1

S
t1
C
t1
S
t
S
t1
S
t1
and delta-hedged excess returns as
C
t
C
t1
C
t1
r
t1
ND
t1;t

S
t1
C
t1

S
t
S
t1
S
t1
r
t1
ND
t1;t

:
This may be viewed as the excess return on a portfolio that combines one option contract
with a zero-cost position in shares worth of single-stock futures.
We view our use of the Black-Scholes model as relatively benign. Even if the delta we
use to compute hedged returns is incorrect, those hedged returns nevertheless represent
the returns on a feasible investment strategy (abstracting from transactions costs). Delta
hedging, while not perfect, can be expected to remove at least the majority of the option's
exposure to the underlying stock. Hull and Suo (2002) claim, in fact, that Black-Scholes
works about as well as any other model in this regard. When we examine weekday eects
in Black-Scholes implied volatilities, our results may also be slightly skewed by model mis-
specication. Nevertheless, it is hard to imagine how this form of misspecication could
causes systematic patterns across dierent days of the week.
Summary statistics describing our sample are included in Table 3.1. The table exam-
ines the excess returns on equal weighted portfolios of unhedged and delta-hedged option
positions, where portfolios are formed on the basis of option delta.
65
Table 3.1: Summary statistics
This table reports summary statistics of unhedged and delta-hedged excess returns. Portfolios are equally weighted across contracts and
are formed on the basis of delta. \All Delta" portfolios include options regardless of delta, even those that are less than .01 or greater
than .99 in absolute value. Data are daily from January 4, 1996, through June 31, 2007.
Unhedged Delta-hedged
Standard Excess Standard Excess Avg. # of
Mean Deviation Skewness Kurtosis Mean Deviation Skewness Kurtosis Contracts
Puts & Calls All Deltas 0.03 0.91 3.4 37.6 0.06 0.72 3.3 31.5 59,563
Puts All Deltas -0.18 5.10 0.7 3.2 0.02 0.68 1.8 17.1 29,444
-.01 > Delta > -.10 -0.17 10.30 1.8 11.9 0.15 3.30 3.2 30.9 353
-.10 > Delta > -.25 -0.17 8.07 1.2 6.6 0.04 1.81 3.3 36.1 2,676
-.25 > Delta > -.50 -0.22 6.53 0.8 3.7 0.01 1.08 2.2 25.6 7,010
-.50 > Delta > -.75 -0.20 5.36 0.6 2.3 0.03 0.62 1.1 11.8 7,146
-.75 > Delta > -.90 -0.18 4.24 0.4 1.9 0.04 0.36 1.9 23.1 5,564
-.90 > Delta > -.99 -0.19 3.24 0.2 2.4 -0.01 0.20 1.6 17.6 6,006
Calls All Deltas 0.25 6.29 0.4 3.2 0.10 0.89 4.3 44.0 30,119
.01 < Delta < .10 1.42 27.19 5.5 81.0 0.60 16.35 8.5 151.0 37
.10 < Delta < .25 0.70 12.45 1.1 6.0 0.35 3.76 2.9 23.4 953
.25 < Delta < .50 0.40 8.90 0.5 2.6 0.14 1.78 2.8 25.0 5,204
.50 < Delta < .75 0.26 6.79 0.2 1.8 0.08 0.88 3.5 35.0 8,039
.75 < Delta < .90 0.18 5.44 -0.1 1.9 0.08 0.47 4.0 41.9 6,399
.90 < Delta < .99 0.12 4.00 -0.3 2.5 0.03 0.20 2.7 27.2 8,120
66
Several stylized facts are immediately apparent. First, portfolios of unhedged call op-
tions have positive average returns, while unhedged puts have negative average returns,
which is consistent with calls having positive market betas and puts having negative betas.
Second, all portfolios of unhedged option positions have returns that display positive skew-
ness and substantial excess kurtosis. Delta-hedged option returns are even more fat-tailed.
This is the result of delta hedging being more eective for small changes in stock prices.
Large changes in stock prices, which are often the source of extreme option returns, cannot
be hedged due to the convexity of option payos. We also see a systematic relation between
moneyness and volatility. Out-of-the-money (OTM) options are substantially more risky
than in-the-money options. This is the direct result of OTM options representing more
highly leveraged exposures to the underlying securities.
Another regularity in Table 3.1 is that average delta-hedged returns are almost all
positive, for most option deltas and for both puts and calls. We believe that these positive
means are likely the result of an upward bias arising from measurement errors in observed
prices. This bias, discussed rst by Blume and Stambaugh (1983) and more recently by
Duarte and Jones (2008), is a signicant problem when measuring average returns. We
believe that our results, which focus on the dierences between Monday and non-Monday
returns, should be unaected by this bias. Nevertheless, we address the issue below in
Section 3.4.1.
Finally, Table 3.1 contains the average number of options in our sample and in each
delta-sorted portfolio. Our sample contains, on a typical day, almost 60,000 contracts,
representing several dozen puts and calls of dierent deltas and maturities for the average
rm. Portfolios that are formed on the basis of delta are generally well populated, usually
containing 5,000 contracts or more. A few portfolios, namely the deep out-of-the-money
puts and calls, contain many fewer contracts. As discussed above, this is the direct result
of the data lters we impose. The contracts that pass our lters and remain in these
portfolios, while limited in number, should hopefully provide a more accurate assessment
of the performance of deep OTM contracts.
67
3.3 Weekday patterns in option markets
3.3.1 Main ndings
Our main results are presented in Tables 3.2 and 3.3. Table 3.2 displays average excess
returns across dierent days of the week on portfolios of puts and calls sorted by delta.
When we average across all options, both puts and calls, we see an average Monday return
of -0.58%, indicating that the average option loses more than half of 1% of its value each
weekend. The corresponding t-statistic is -16.
1
The average returns for other days of the
week are all positive. Similar results are obtained for portfolios of puts or calls that are
sorted on delta. Monday returns are in all cases negative, though their statistical signicance
is sometimes only marginal.
2
Table 3.3 presents corresponding results for delta-hedged excess returns. A subset of
these results is reported graphically in Figure 3.1. These results show that delta-hedged
returns exhibit an even stronger weekend eect with markedly increased statistical precision.
This suggests two conclusions. One is that the weekend eect in option returns is not the
result of a weekend eect in the underlying stocks. If it was, then delta hedging would
eliminate at least the majority of that weekly pattern. Second, delta-hedged returns are
substantially less volatile than unhedged returns, so standard errors on average hedged
returns are much smaller.
Because we observe the same eect in delta-hedged returns, and because we see that
eect much more clearly, our subsequent analysis will be focused on delta-hedged positions.
In addition, we simply feel that looking at delta-hedged returns is also more interesting.
The literature has already examined weekend eects in stock returns, so if delta hedging at
least substantially eliminates the portion of the option return that is due to the underlying
1
All tables report asymptotic t-statistics. We have also computed p-values for all our key results using
bootstrap distributions, and we nd these results to be essentially identical. Additional nonparametric
results, reported in Section 3.3.6, also addresses nite sample issues.
2
The higher levels of statistical signicance for the pooled portfolio of unhedged puts and calls is due to
the reduction in variance that comes from the osetting deltas of puts and calls, which has approximately
the same eect as delta hedging.
68
Table 3.2: Unhedged excess returns, delta-sorted portfolios
This table reports average excess returns of portfolios of unhedged equity options. Portfolios are equally weighted across contracts
and are formed on the basis of delta. \All Delta" portfolios include options regardless of delta, even those that are less than .01
or greater than .99 in absolute value. Data are daily from January 4, 1996, through June 31, 2007. Values that are statistically
signicant at the 10%, 5%, an 1% levels are denoted by one, two, or three stars, respectively.
Means T-statistics
Mon Tues Weds Thurs Fri Mon Tues Weds Thurs Fri
Puts & Calls All Deltas -0.58

0.11

0.25

0.24

0.08

-16.03 2.48 6.76 7.82 2.53
Puts All Deltas -0.45

0.02 -0.20 -0.02 -0.29 -1.82 0.11 -1.01 -0.11 -1.45
-.01 > Delta > -.10 -1.38

0.30 0.11 0.43 -0.41 -2.53 0.74 0.28 1.07 -1.06
-.10 > Delta > -.25 -1.12

0.19 -0.03 0.33 -0.28 -2.75 0.58 -0.10 1.01 -0.90
-.25 > Delta > -.50 -0.79

0.02 -0.18 0.11 -0.34 -2.48 0.09 -0.70 0.43 -1.34
-.50 > Delta > -.75 -0.43

-0.02 -0.25 -0.02 -0.31 -1.68 -0.07 -1.18 -0.07 -1.50
-.75 > Delta > -.90 -0.13 -0.07 -0.28 -0.12 -0.28

-0.66 -0.40 -1.63 -0.65 -1.71
-.90 > Delta > -.99 -0.03 -0.12 -0.33

-0.23 -0.26

-0.19 -0.89 -2.53 -1.64 -2.03
Calls All Deltas -0.75

0.23 0.69

0.51

0.50

-2.72 0.84 2.72 1.99 2.01
.01 < Delta < .10 -0.60 1.29 2.48

1.95

1.84

-0.40 1.17 2.53 1.77 1.73
.10 < Delta < .25 -2.28

0.64 2.25

1.58

1.10

-4.54 1.15 4.26 3.13 2.28
.25 < Delta < .50 -1.56

0.37 1.33

0.99

0.74

-4.09 0.95 3.65 2.73 2.13
.50 < Delta < .75 -0.89

0.25 0.78

0.55

0.52

-2.96 0.85 2.86 1.98 1.95
.75 < Delta < .90 -0.44

0.16 0.46

0.30 0.37

-1.78 0.71 2.13 1.33 1.77
.90 < Delta < .99 -0.10 0.09 0.23 0.13 0.22 -0.52 0.54 1.49 0.77 1.42
69
Table 3.3: Delta-hedged excess returns, delta-sorted portfolios
This table reports average excess returns of portfolios of delta-hedged equity options. Portfolios are equally weighted across contracts
and are formed on the basis of delta. \All Delta" portfolios include options regardless of delta, even those that are less than .01 or
greater than .99 in absolute value. Data are daily from January 4, 1996, through June 31, 2007.
Means T-statistics
Mon Tues Weds Thurs Fri Mon Tues Weds Thurs Fri
Puts & Calls All Deltas -0.50

0.12

0.26

0.27

0.08

-13.48 4.36 10.85 11.67 3.43
Puts All Deltas -0.60

0.09

0.24

0.24

0.07

-17.95 3.45 11.27 10.67 3.22
-.01 > Delta > -.10 -1.08

0.36

0.69

0.63

0.08 -5.78 2.83 5.80 5.49 0.62
-.10 > Delta > -.25 -1.26

0.17

0.53

0.54

0.13

-12.64 2.51 9.27 8.98 1.98
-.25 > Delta > -.50 -0.97

0.12

0.38

0.38

0.09

-17.36 2.91 11.71 10.89 2.47
-.50 > Delta > -.75 -0.60

0.10

0.25

0.25

0.09

-20.13 4.45 13.65 11.81 4.36
-.75 > Delta > -.90 -0.25

0.07

0.15

0.16

0.07

-14.86 5.81 12.87 10.01 5.43
-.90 > Delta > -.99 -0.12

-0.01 0.01

0.03

0.00 -12.54 -0.94 2.06 2.92 0.38
Calls All Deltas -0.40

0.17

0.28

0.32

0.10

-8.49 4.59 9.07 10.34 3.25
.01 < Delta < .10 -0.82 1.01

1.20

1.28

0.23 -0.81 1.70 2.43 2.00 0.35
.10 < Delta < .25 -1.54

0.60

1.12

1.16

0.25

-7.74 3.92 8.01 8.64 2.00
.25 < Delta < .50 -1.05

0.29

0.58

0.65

0.15

-11.40 3.93 9.69 10.79 2.56
.50 < Delta < .75 -0.52

0.15

0.28

0.34

0.08

-11.45 4.17 10.09 11.16 2.67
.75 < Delta < .90 -0.17

0.11

0.15

0.20

0.07

-6.61 5.59 9.92 11.30 4.24
.90 < Delta < .99 0.01 0.04

0.03

0.06

0.03

0.94 4.58 3.72 8.16 3.26
70
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Figure 3.1: Average Delta-Hedged Excess Return by Day of the Week
The returns used for this plot come from equal weighted portfolios of all delta-hedged calls or puts.
Data are daily from January 4, 1996, through June 31, 2007.
stock, then whatever returns remain should re
ect risks that have thus far received much
less attention in the literature.
Table 3.4 performs the same analysis on delta-hedged excess returns, only now the
portfolios are sorted on the basis of maturity rather than delta. Here we see that the
eect is strong for all maturities except the longest. Even the 1-10 day maturity range,
which many studies discard because of expiration-day concerns, displays the weekend eect
strongly.
The results in Tables 3.2- 3.4 demonstrate large negative and highly signicant Monday
returns, but they are not completely satisfactory for three reasons. First, they do not
directly assess the statistical signicance of the dierences between average returns on
dierent days of the week, which would represent the most direct evidence of a weekend
eect. Second, the presence of Monday holidays means that weekend returns are sometimes
not observed until Tuesday, so the interpretation of Monday returns as weekend returns
is not always correct. Finally, in order to present these results in a reasonable amount of
space we are limited to one-way sorts on the basis of either maturity or delta, resulting in
highly aggregated portfolios whose constituents may dier widely.
71
Table 3.4: Delta-hedged excess returns, maturity-sorted portfolios
This table reports average excess returns of portfolios of delta-hedged equity options. Portfolios are equally weighted
across contracts and are formed on the basis of maturity. Data are daily from January 4, 1996, through June 31, 2007.
Means T-statistics
Mon Tues Weds Thurs Fri Mon Tues Weds Thurs Fri
Puts 1-10 days -1.16

0.26

0.45

0.44

0.05 -16.20 4.02 8.07 6.83 0.76
11-53 days -0.82

0.09

0.29

0.28

0.06

-19.31 2.73 11.13 10.86 2.11
54-118 days -0.41

0.08

0.20

0.20

0.10

-13.88 3.66 11.30 10.49 5.14
119-252 days -0.30

0.06

0.16

0.16

0.09

-12.11 3.40 10.10 9.54 5.21
253+ days 1.23 0.22 0.53

0.02 0.23

0.92 0.73 1.76 0.10 1.85
Calls 1-10 days -0.78

0.46

0.59

0.58

0.19

-8.22 5.03 6.53 7.54 1.95
11-53 days -0.60

0.20

0.36

0.40

0.10

-9.61 4.20 9.02 10.42 2.60
54-118 days -0.25

0.13

0.22

0.27

0.11

-5.84 4.26 8.95 10.05 4.32
119-252 days -0.16

0.09

0.16

0.21

0.11

-4.73 3.86 7.95 9.17 4.99
253+ days -0.28

0.20 0.11 -0.76 0.11 -2.05 0.55 0.67 -1.11 1.13
72
To address all three of these issues, we next examine the dierences between weekend
and non-weekend returns for portfolios sorted on the basis of both maturity and delta, where
the weekend return is dened as the return from the last trading day of one week to the
rst trading day of the next. The results, presented in Table 3.5, show that average returns
are lower over weekends for almost all portfolios, and most of these results are statistically
signicant at very high condence levels. For the disaggregated portfolios of both calls
and puts, average dierences range from around zero to more than -3%, with the typical
portfolio having an average dierence of about -1%.
A potential concern is that our returns are calculated assuming no early exercise. Early
exercise can be optimal for put options and, in the case of stocks about to pay dividends,
for call options as well. In these cases, our computed returns should understate the returns
to a portfolio in which exercise decisions are made optimally. For puts, the value of early
exercise comes from the possible benet of accelerating the xed option premium forward in
time. While this can have a signicant eect on option value, the loss in value that results
from delaying exercise by one day should be small, as it is at most the loss of one day of
interest on the option payo.
For calls, failing to exercise prior to a large dividend could have a substantial eect
on the one-day option return. This cannot explain our results for two reasons. First,
rms do not have any tendency to go ex dividend over the weekend, with Wednesdays and
Thursdays containing about 60% of all ex dividend dates in our sample. Thus, if failing
to account for early exercise is biasing any of our average returns downward, it is the non-
weekend returns, so accounting for early exercise would only magnify the dierence between
weekend and weekday returns.
Most importantly, early exercise cannot explain our results because it is only optimal for
call and put options that are signicantly in the money. Since we nd large weekend eects
across all moneyness levels, early exercise due to dividends or any other factor cannot be a
primary explanation of our ndings.
73
Table 3.5: First day of the week versus other days
This table reports dierences between the average excess returns on delta-hedged equity options on the rst day of the
week (Monday unless it is a holiday) and the remainder of the week. Portfolios are equally weighted across contracts and
are formed on the basis of delta. \All Delta" portfolios include options regardless of delta, even those that are less than
.01 or greater than .99 in absolute value. Data are daily from January 4, 1996, through June 31, 2007.
Means T-statistics
All 11-53 54-118 119-252 All 11-53 54-118 119-252
exp. days days days exp. days days days
Puts & Calls All Deltas -0.70

-0.94

-0.51

-0.37

-20.95 -21.38 -18.30 -16.77
Puts All Deltas -0.78

-1.03

-0.58

-0.43

-25.07 -25.34 -22.66 -20.99
-.01 > Delta > -.10 -1.55

-2.66

-1.48

-1.06

-9.03 -6.28 -9.96 -7.44
-.10 > Delta > -.25 -1.64

-3.50

-1.34

-0.83

-18.81 -19.55 -18.12 -18.40
-.25 > Delta > -.50 -1.24

-2.40

-0.87

-0.53

-25.59 -26.91 -23.35 -20.58
-.50 > Delta > -.75 -0.79

-1.19

-0.43

-0.28

-28.95 -29.59 -23.92 -20.07
-.75 > Delta > -.90 -0.37

-0.39

-0.17

-0.12

-22.39 -21.86 -17.25 -10.61
-.90 > Delta > -.99 -0.13

-0.12

-0.08

-0.08

-13.75 -12.58 -10.78 -5.24
Calls All Deltas -0.63

-0.87

-0.45

-0.31

-15.01 -15.43 -12.51 -11.43
.01 < Delta < .10 -1.69

-2.57

-1.13

-0.90

-2.06 -2.17 -2.14 -1.96
.10 < Delta < .25 -2.30

-3.67

-1.67

-1.04

-12.28 -11.16 -12.08 -9.88
.25 < Delta < .50 -1.48

-2.63

-1.01

-0.63

-18.08 -18.74 -16.14 -14.10
.50 < Delta < .75 -0.75

-1.29

-0.46

-0.29

-19.24 -20.96 -15.34 -13.43
.75 < Delta < .90 -0.31

-0.42

-0.15

-0.09

-14.12 -14.87 -9.24 -5.67
.90 < Delta < .99 -0.03

-0.03

-0.01 0.00 -2.95 -3.25 -0.91 0.14
74
3.3.2 Weekday eects in other variables
Table 3.6 looks at weekday eects in other variables to determine whether we see eects
that are consistent with those found in equity option excess returns. We rst examine
\simple" returns, which are identical to the returns we examined previously but do not
subtract the riskless rate. We start with simple returns to exclude the possibility that our
results arise from the way we are computing riskless returns. Averages of simple unhedged
and delta-hedged returns, shown in the top rows of the table, demonstrate the same weekly
patterns that we observed for excess returns. Thus, the weekend eect in excess returns
cannot simply be attributed to the fact that excess returns over weekends are reduced by
three days of riskless return.
We next investigate average changes in several dierent measures of implied volatility.
While changes in implied volatilities would seem somewhat mechanically related to option
returns, it is not necessarily the case that patterns in returns and implied volatilities will
mirror each other. As a simple example, consider the case in which investors are risk neutral
and volatility changes deterministically. In this case, changes in implied volatilities will be
predictable, but all expected excess returns are zero. A model that generates an eect in
returns, as we have observed, but not in implied volatilities is somewhat more dicult to
construct but is nevertheless a theoretical possibility.
3
Table 3.6 reports results for three dierent measures of implied volatility. The rst is the
\unadjusted" implied volatility that is provided in Ivy DB. This measure of volatility tends
to rise as options approach expiration, most likely re
ecting a misspecication of the Black-
Scholes model. Surprisingly, however, we see that the rise is greatest on Mondays. While
such a result is theoretically possible, it is nevertheless unintuitive that implied volatility
could rise, indicating higher option values, when returns are most negative.
The answer to this apparent contradiction is in how Ivy DB computes implied volatilities.
In the Black-Scholes formula, it is the total amount of volatility until the expiration date
3
One possibility is a stochastic volatility model in which opposite weekly seasonals in the volatility drift
and the volatility risk premium oset to produce no seasonal in the risk neutral volatility process.
75
Table 3.6: Weekday eects in other variables
This table reports weekday eects in ve variables. For each, we report equal weighted averages across all contracts. The simple
unhedged and delta-hedged returns are identical to the returns used above except that they are not in excess of the riskless rate.
The change in unadjusted implied volatility is the average rst dierence of the implied volatilities as calculated by OptionMetrics.
The change in adjusted implied volatility uses implied volatilities that are quoted in terms of business days rather than calendar
days. The change in total implied volatility looks at the change in cumulative-until-expiration implied volatility. Data are daily from
January 4, 1996, through June 31, 2007.
Means T-statistics
Mon Tues Weds Thurs Fri Mon Tues Weds Thurs Fri
Simple Puts & Calls -0.54

0.12

0.26

0.25

0.09

-15.09 2.81 7.08 8.19 2.91
unhedged Puts -0.41

0.04 -0.19 -0.01 -0.28 -1.68 0.18 -0.95 -0.05 -1.39
return Calls -0.71

0.24 0.70

0.53

0.51

-2.59 0.89 2.77 2.04 2.06
Simple Puts & Calls -0.48

0.13

0.26

0.28

0.09

-13.04 4.60 11.06 11.88 3.64
delta-hedged Puts -0.41

0.17

0.31

0.30

0.14

-12.17 6.90 14.24 13.56 6.04
return Calls -0.55

0.10

0.23

0.27

0.05 -11.81 2.79 7.41 8.71 1.62
Change in Puts & Calls 0.77

0.37

0.32

0.31

0.22

23.48 19.06 20.13 18.77 12.14
unadjusted Puts 0.73

0.36

0.32

0.28

0.23

18.44 14.50 13.25 11.74 8.30
implied vol Calls 0.79

0.37

0.32

0.33

0.21

26.59 18.45 21.29 21.14 12.85
Change in Puts & Calls -0.61

0.62

0.97

1.45

0.68

-19.36 17.02 27.36 23.81 24.01
adjusted Puts -0.66

0.62

0.98

1.42

0.70

-16.37 14.73 22.31 21.70 17.69
implied vol Calls -0.54

0.61

0.95

1.45

0.66

-19.32 17.15 29.18 24.28 25.82
Change in Puts & Calls -8.53

-3.73

-3.15

-3.44

-2.82

-42.08 -22.55 -27.28 -24.83 -21.71
total Puts -8.90

-3.75

-3.17

-3.73

-2.70

-35.05 -18.03 -18.34 -20.38 -13.89
implied vol Calls -8.13

-3.70

-3.12

-3.14

-2.90

-43.59 -23.24 -27.23 -22.40 -23.00
76
Table 3.7: Weekday eects in S&P 500 Index options
This table reports mean excess returns and changes in implied volatility of portfolios of delta-hedged S&P 500 Index options. Portfolios
are equally weighted across contracts. Data are daily from January 4, 1996, through June 31, 2007.
Means T-statistics
Mon Tues Weds Thurs Fri Mon Tues Weds Thurs Fri
Excess Puts & Calls -0.60

-0.02 -0.16 -0.13 -0.43

-4.30 -0.14 -1.36 -1.08 -3.22
unhedged Puts -1.30

-0.49 -0.66 -0.05 -0.85 -1.90 -0.72 -1.14 -0.08 -1.33
return Calls 0.34 0.47 0.26 -0.13 0.05 0.63 0.84 0.49 -0.26 0.11
Excess Puts & Calls -0.28 -0.11 -0.14 0.03 -0.27

-1.43 -0.70 -1.36 0.25 -2.00
delta-hedged Puts -0.85

-0.27 -0.07 0.11 -0.65

-3.78 -1.06 -0.40 0.55 -3.05
return Calls 0.22 0.11 -0.21 -0.06 0.11 0.88 0.65 -1.39 -0.36 0.58
Change in Puts & Calls 0.62

0.97

1.61

1.18

0.51

6.51 10.08 10.07 13.79 6.47
adjusted Puts 0.32

0.45

1.26

0.82

0.09 3.32 4.96 7.35 8.77 0.85
implied vol Calls 0.84

1.44

1.76

1.42

0.90

4.73 7.67 7.15 9.65 6.03
77
that determines option value, not the amount of volatility per unit of time. In other words,
every place the volatility parameter appears it is multiplied by the square root of the time
to expiration. Ivy DB measures the time to expiration in terms of calendar time, so that
Monday has three days less time to maturity than the Friday that immediately preceded
it. There is nothing incorrect about this approach { quoting in terms of calendar time is
just a convention { but the interpretability of this convention is slightly problematic. The
reason is that the interval from Friday close to Monday close is about as volatile as any
other close-to-close period, as demonstrated by French and Roll (1986). It certainly is not
more volatile by a factor of
p
3, which is what we would expect if weekends and weekdays
were equally risky. Hence, when the time to maturity declines by three days but only one
day of actual volatility actually accrues, implied volatility appears to rise.
We address this in two ways. First, we adjust the implied volatility so that it is quoted
in terms of trading days rather than calendar days. Second, we examine \total implied
volatility", which is the implied volatility of the log stock price at expiration, not reported
per unit of time. This is computed simply by taking the product of the unadjusted implied
volatility and the square root of the time to expiration (measured in calendar time). With
both of these modications, we see highly signicant changes in implied volatility that are
lower on Mondays than they are for the rest of the week.
Finally, we also look for a weekend eect in S&P 500 Index options. Intuitively, one
might expect index options to be driven by the same systematic risk factors that aect
individual equity options. However, the two dier signicantly in that index options are
options on a portfolio rather than a portfolio of options. They are therefore aected by
correlations as well as volatilities. Risk factors that drive correlations, as in the model of
Driessen, Maenhout, and Vilkov (2009), should therefore aect only options on the index.
On the other hand, systematic movements in average idiosyncratic volatility will aect
portfolios of individual options but will have little eect on options on the index. Such
systematic movements have been documented by Campbell, Lettau, Malkiel, and Xu (2001)
and have been found by Goyal and Santa-Clara (2003) to drive aggregate risk premia. If
78
the risk premium on this factor has a weekly seasonal, then this will generate a weekend
eect only in individual equity options.
Our results for S&P 500 options, reported in Table 3.7, are somewhat inconclusive. The
average Monday return on the portfolio of all puts is signicantly negative and is lower than
the average return over the rest of the week. However, the average Friday return on the
same portfolio is also low, suggesting that Monday returns are not special. Furthermore,
there is no weekend eect observed at all for index call options. Finally, more disaggregated
portfolios, which we do not report in the table, yield weak or nonexistent eects.
3.3.3 Midweek holidays, long weekends, and expiration weekends
Having established that weekend returns are signicantly dierent from weekday returns,
we now examine midweek holidays, long weekends, and expiration weekends. If the weekend
eect is related to non-trading, then we should also see negative option returns over midweek
holidays, and we might also expect that the eect would be stronger over long weekends.
We also examine whether expiration weekends are dierent from non-expiration week-
ends. Early studies by Stoll and Whaley (1986, 1987) documented that expiration weekends
were associated with higher than normal levels of trading volume, as well as some evidence
of unusual price behavior in the underlying index. More recently, Ni, Pearson, and Potesh-
man (2005) document that returns on underlying stocks over expiration weekends appear
to be altered by price manipulation and hedge rebalancing. By controlling for expiration
weekends we can conrm that our nding is not simply driven by option expirations, which
also occur on weekends, but is in fact related to weekend non-trading in general.
We investigate these issues in a regression framework. In all the regressions we run, the
dependent variable is the excess return on a portfolio of delta-hedged option positions. We
consider both equal weighted and value weighted portfolios, where value weighted (VW)
portfolios weight contacts by the dollar value of their open interest. In every case, the unit
of observation is a portfolio, either of puts or calls, that is formed on the basis of a double
sort on both delta and maturity.
79
The independent variables in these regressions consist of four dummy variables. The
rst is set to one if the return is computed over any interval that includes a non-trading
period. These are, of course, most often weekends, but they include mid-week holidays as
well. The second dummy is set to one if the non-trading period is a mid-week holiday. This
variable therefore represents the incremental eect of the non-trading period being a mid-
week holiday. The third dummy variable is equal to one if the non-trading period is a long
weekend of three or more days. As with the previous variable, this represents a incremental
eect rather than the total eect of the three-day weekend on returns. Finally, we include a
dummy variable that is equal to one if the return interval includes an expiration weekend.
Again, the coecient on this variable captures the incremental eect of expiration over and
above the eect that comes from the fact that expiration takes place over the weekend.
4
All regressions use ordinary least squares and pool all observations of all double-sorted
portfolios of puts and calls. Because of signicant cross-correlations, standard errors are
clustered by date. The so-called Rogers clustering we use also adjusts the standard errors
for conditional heteroskedasticity. In addition, to account for portfolio-level heterogeneity,
we include portfolio xed eects. This has virtually no eect on any of our results except
to increase the R-squares.
In addition to regressions based on the full sample, we also report results based on more
liquid subsamples. In one pair of regressions, we only include options on stocks that are
members of the S&P 100. In another pair, we only include option contracts that had positive
trading volume for ve days in a row prior to the day on which the return is computed.
In both cases, the additional lter has the eect of concentrating the sample on the most
liquid options in the market. Results that use these lters should alleviate concerns that
our results are driven solely by illiquid contracts that do not trade.
Table 3.8 contains the results of these regressions. In every case, the non-trading dummy
is highly signicant, with t-statistics ranging from 3.76 to 8.92 in absolute value. The size of
4
We note that expiring options do not have market prices on the Monday following expiration weekend,
so our regressions only include options that are not expiring. The dummy variable therefore represents the
eect of expiration weekend on non-expiring contracts.
80
the eect is fairly consistent across specications as well, with non-trading periods having
returns that are lower by about one percent. The results for value weighted portfolios are
moderately weaker than those of the equal weighted portfolios, and the eect in the more
liquid subsamples is just slightly reduced from the full sample, but for all portfolios the
non-trading dummy remains highly signicant.
Table 3.8: Mid-week holidays, long weekends, and expiration weekends
This table reports the results of pooled regressions in which delta-hedged excess re-
turns on various portfolios of equity options are regressed on four dummy variables.
Dependent variables are the excess delta-hedged returns on portfolios formed on the
basis of delta and maturity. Equal weighted (EW) portfolios weight all option contracts
evenly, while value weighted (VW) portfolios weight contacts by the market value of
their open interest. The rst explanatory variable is a dummy that is equal to 1 if
the return is computed over an interval that includes any non-trading period. The
second is a dummy equal to 1 if the non-trading period is a mid-week holiday. The
third dummy variable is set to 1 if the non-trading period is a long weekend of three or
more days. The last is a dummy that takes the value 1 if the return is computed over
an option expiration weekend. The bottom of the table reports sums of some of the
coecients. Data are daily from January 4, 1996, through June 31, 2007. Standard
errors are computed with clustering by date, and all regressions include portfolio xed
eects. T-statistics are in parentheses.
All options Liquid subsample S&P 100 stocks
EW VW EW VW EW VW
Intercept 2.05 -0.07 -1.93 -0.86 0.20 0.17
(1.04) (0.04) (0.36) (0.15) (7.45) (6.16)
Non-trading period dummy -1.33 -0.70 -1.15 -0.70 -1.01 -0.70
(8.92) (4.41) (6.42) (3.76) (8.67) (5.32)
Mid-week holiday dummy 0.72 0.05 0.30 0.04 0.39 0.15
(3.02) (0.20) (0.97) (0.12) (1.07) (0.41)
Long weekend dummy 0.40 0.67 0.47 0.53 0.58 0.52
(1.09) (1.68) (0.97) (1.11) (1.08) (1.36)
Expiration weekend dummy -0.38 -0.94 -0.98 -1.09 -0.82 -1.10
(2.07) (4.64) (4.07) (4.30) (4.97) (6.22)
Regression R-squared (in %) 0.32 0.49 0.56 0.77 0.78 0.39
Non-trading + mid-week -0.61 -0.65 -0.85 -0.66 -0.62 -0.55
(3.06) (3.03) (3.19) (2.35) (1.78) (1.57)
Non-trading + long weekend -0.93 -0.03 -0.68 -0.17 -0.43 -0.18
(2.55) (0.08) (1.43) (0.35) (0.78) (0.48)
81
The fact that the non-trading dummy is signicant even when the expiration weekend
dummy is included implies that the weekend eect is not simply driven by the fact that
expirations take place over the weekend. However, the expiration weekend dummy is signif-
icant in all regressions, suggesting that expiration does have an incremental eect over and
above the eect that comes from non-trading. The expiration eect is stronger for value
weighted relative to equal weighted portfolios, and it is also stronger in the more liquid sub-
samples. The fact that the expiration eect is stronger in contracts that are more widely
held suggests the possibility that new option purchases by holders of expiring contracts
might result in high closing prices going into expiration weekend.
The coecient on the mid-week holiday dummy is only signicant for the equal weighted
portfolios from the full sample, but its positive sign suggests that mid-week holidays are
signicantly dierent from weekends. Specically, mid-week holidays have average returns
that are not as negative as weekends, consistent with the fact that mid-week holidays usually
represent a non-trading period that is just half as long as a regular weekend. The long
weekend dummy is never signicant, possibly the result of usually having a small number
of extended weekends each year.
The bottom of the table reports sums of some of the coecients as well as t-statistics
for those sums. These sums represent the total eect of having a mid-week holiday or a
long weekend rather than the incremental eect over and above the generic non-trading
eect. The results here are not always signicant, again probably due to the low numbers
of mid-week holidays and long weekends. Despite the small sample sizes, however, we can
still reject in half the cases that the total eect of a mid-week holiday is zero. This suggests
that our ndings are more accurately described as a \non-trading" rather than \weekend"
eect.
3.3.4 Robustness
We now ask whether these results are sensitive to changes in our empirical approach. Ta-
bles 3.9 and 3.10 replicate 3.2 and 3.3 but, instead of equal weighting, weight options by
82
the dollar value of their open interest. Weighting by open interest has two purposes. One is
that it puts more emphasis on contracts that are likely more liquid and more representative
of the options market as a whole. Second, it should reduce the measurement error bias
identied by Blume and Stambaugh (1983), though this is a bit uncertain since the the bias
in delta-hedged returns is somewhat more complex than the bias in simple returns, as noted
by Duarte and Jones (2008).
Overall, Tables 3.9 and 3.10 show that average Monday returns are only slightly smaller
for value weighted portfolios than they are for equal weighted portfolios. T-statistics are
generally about the same as those from equal weighted portfolios, more so for delta-hedged
returns. This indicates that negative weekend returns are pervasive in contracts that are
widely held, and not just in puts and calls that exist only on paper.
However, average returns on non-Mondays are noticeably dierent from results under
equal weighting. In Table 3.3, for instance, we saw signicantly positive non-Monday returns
for most portfolios of delta-hedged calls and puts. Once combined with the negative Monday
returns, the non-Monday returns were suciently positive such that cumulative weekly
returns were positive as well, indicating that the simple strategy of delta-hedging long option
positions would result in high positive rates of return. In contrast, Table 3.10 shows that
there is little evidence of systematically positive non-Monday returns, and the cumulative
weekly returns implied from Table 3.10 are generally close to zero or slightly negative.
We believe that the most likely explanation of the dierences between equal weighted and
value weighted non-Monday returns is a reduction in the Blume-Stambaugh bias, and that
the positive non-Monday returns in Table 3.3 were most likely spurious. Since our nding
of signicant negative Monday returns is, in contrast, robust to the weighting scheme, we
nd it unlikely that it could be driven by the same bias. Nevertheless, we will return to the
issue brie
y in Section 3.4.1.
An alternative robustness check is to alter our sample selection approach to focus on the
most liquid contracts in the market. As in Table 3.8, we report results based on (i) options
83
Table 3.9: Unhedged excess returns, delta-sorted portfolios, value-weighted
This table reports average excess returns of portfolios of unhedged equity options. Portfolios are value weighted and are
formed on the basis of delta, where the value of each option contract is taken to be the market value of open interest. \All
Delta" portfolios include options regardless of delta, even those that are less than .01 or greater than .99 in absolute value.
Data are daily from January 4, 1996, through June 31, 2007.
Means T-statistics
Mon Tues Weds Thurs Fri Mon Tues Weds Thurs Fri
Puts & Calls All Deltas -0.10 -0.04 0.16

0.06 0.02 -0.87 -0.38 1.65 0.64 0.24
Puts All Deltas -0.46 -0.13 -0.45

0.07 -0.22 -1.57 -0.52 -1.85 0.26 -0.96
-.01 > Delta > -.10 -1.75

-0.38 -0.09 0.44 -0.36 -2.70 -0.83 -0.20 0.96 -0.84
-.10 > Delta > -.25 -1.46

-0.29 -0.37 0.58 -0.30 -2.83 -0.72 -1.01 1.42 -0.80
-.25 > Delta > -.50 -0.93

-0.20 -0.44 0.30 -0.29 -2.31 -0.60 -1.38 0.87 -0.94
-.50 > Delta > -.75 -0.43 -0.14 -0.47

0.05 -0.24 -1.35 -0.50 -1.81 0.19 -0.94
-.75 > Delta > -.90 -0.13 -0.08 -0.44

-0.15 -0.19 -0.55 -0.35 -2.07 -0.69 -0.99
-.90 > Delta > -.99 -0.05 -0.13 -0.53

-0.23 -0.20 -0.24 -0.77 -3.04 -1.23 -1.29
Calls All Deltas -0.17 0.00 0.43

0.22 0.03 -0.65 0.01 1.75 0.87 0.15
.01 < Delta < .10 0.87 -0.45 1.21 0.17 -0.03 0.36 -0.41 1.21 0.17 -0.02
.10 < Delta < .25 -1.52

-0.05 1.88

0.81 -0.18 -2.62 -0.09 3.17 1.49 -0.36
.25 < Delta < .50 -0.95

0.08 1.30

0.64 0.03 -2.24 0.19 3.13 1.59 0.08
.50 < Delta < .75 -0.29 0.08 0.75

0.30 0.10 -0.85 0.25 2.44 0.97 0.34
.75 < Delta < .90 -0.01 0.08 0.40

0.10 0.14 -0.03 0.32 1.71 0.41 0.63
.90 < Delta < .99 0.13 0.03 0.12 0.04 0.08 0.72 0.19 0.74 0.23 0.49
84
Table 3.10: Delta-hedged excess returns, delta-sorted portfolios, value-weighted
This table reports average excess returns of portfolios of delta-hedged equity options. Portfolios are value weighted and are formed
on the basis of delta, where the value of each option contract is taken to be the market value of open interest. \All Delta" portfolios
include options regardless of delta, even those that are less than .01 or greater than .99 in absolute value. Data are daily from January
4, 1996, through June 31, 2007.
Means T-statistics
Mon Tues Weds Thurs Fri Mon Tues Weds Thurs Fri
Puts & Calls All Deltas -0.29

0.01 0.09

0.11

-0.05

-8.55 0.28 4.49 5.29 -2.39
Puts All Deltas -0.49

-0.02 0.14

0.14

-0.07

-10.91 -0.53 5.09 4.31 -2.56
-.01 > Delta > -.10 -0.89

0.06 0.43

0.29

-0.05 -3.11 0.37 2.69 1.89 -0.32
-.10 > Delta > -.25 -1.13

-0.08 0.36

0.39

-0.17

-7.26 -0.94 4.19 4.28 -1.89
-.25 > Delta > -.50 -0.85

-0.04 0.27

0.27

-0.14

-10.41 -0.79 5.48 4.97 -2.98
-.50 > Delta > -.75 -0.50

-0.01 0.17

0.17

-0.07

-11.77 -0.34 5.66 5.10 -2.68
-.75 > Delta > -.90 -0.23

0.00 0.09

0.07

-0.01 -11.10 0.21 4.41 3.23 -0.56
-.90 > Delta > -.99 -0.11

-0.02 -0.02 0.00 -0.01 -8.47 -1.49 -1.18 0.22 -0.55
Calls All Deltas -0.24

0.02 0.09

0.11

-0.05

-5.66 0.76 3.61 4.81 -1.77
.01 < Delta < .10 -0.25 -0.15 0.11 0.09 -1.14 -0.15 -0.28 0.23 0.16 -1.39
.10 < Delta < .25 -1.53

-0.07 0.38

0.67

-0.45

-5.17 -0.40 2.17 3.80 -2.40
.25 < Delta < .50 -0.94

0.03 0.33

0.44

-0.22

-7.15 0.35 4.27 5.45 -2.72
.50 < Delta < .75 -0.39

0.06

0.16

0.22

-0.07

-6.32 1.67 4.68 6.14 -1.96
.75 < Delta < .90 -0.15

0.05

0.06

0.09

-0.01 -5.54 2.90 3.48 5.28 -0.41
.90 < Delta < .99 -0.01 0.01 -0.01 0.01 0.00 -1.49 1.51 -0.76 1.13 0.09
85
on rms that are members of the S&P 100 and (ii) options that had positive trading volume
for ve days in a row prior to the day on which the return is computed.
The results, reported in Table 3.11, conrm our earlier conclusion that the weekend
eect is not simply a gment of thinly-traded contracts. In particular, the results for the
S&P 100 sample are about the same as those from the sample of all rms. For the sample
of contracts with ve consecutive days of positive volume, our main result is unaected and
possibly even stronger than before.
Finally, we move in the opposite direction and include all options in the data set, even
those that we previously ltered out because of large price reversals or bid-ask spreads.
In this sample, all average returns are higher, a result we attribute to the upward bias in
average returns that results from larger measurement errors. Nevertheless, in this sample
Monday returns are still the lowest, generally by the same margin as before.
3.3.5 Subsample results
In Table 3.12 we examine each year in our sample separately. We do so for several reasons.
First, nding a consistent eect across years would indicate that our nding is robust and
unlikely to be the result of data mining. Second, if we nd that our weekend eect persists
in years, like 2002 and 2003, when both interest rates and interest rate spreads were close to
zero, then it is unlikely that the eect can be attributed to the costs of maintaining margin
requirements, which might be higher over the weekend.
86
Table 3.11: Alternative sampling procedures
This table reports average excess returns and average changes in adjusted implied volatility of portfolios of delta-hedged equity
options. Portfolios are equally weighted across contracts and are formed on the basis of delta. \All Delta" portfolios include options
regardless of delta, even those that are less than .01 or greater than .99 in absolute value. Data are daily from January 4, 1996,
through June 31, 2007.
Means T-statistics
Mon Tues Weds Thurs Fri Mon Tues Weds Thurs Fri
Delta-hedged excess returns
Only rms Puts & Calls -0.45

0.06

0.21

0.28

0.08

-7.83 1.78 7.72 8.45 2.40
that are in Puts -0.58

0.04 0.23

0.29

0.09

-10.42 1.14 7.68 8.12 2.74
the S&P 100 Calls -0.34

0.08

0.20

0.27

0.07

-4.95 2.03 6.23 7.05 1.97
Only options w/ 5 Puts & Calls -1.20

0.21

0.58

0.60

-0.19

-9.72 2.49 7.37 7.69 -2.28
consecutive days Puts -1.51

0.16

0.62

0.53

-0.33

-12.24 1.77 7.02 6.14 -3.83
of volume > 0 Calls -1.05

0.25

0.58

0.65

-0.12 -7.64 2.68 6.80 7.46 -1.34
No lters to Puts & Calls 0.34

1.40

1.49

1.69

1.24

2.53 11.75 17.98 14.01 9.57
exclude errors & Puts 0.08 1.26

1.52

1.60

1.13

0.75 12.43 17.03 14.22 13.96
large spreads Calls 0.60

1.54

1.45

1.79

1.36

2.58 6.74 8.65 8.11 5.20
Changes in adjusted implied volatilities
Only rms Puts & Calls -0.27

0.51

0.75

1.13

0.50

-9.44 17.23 24.81 22.60 22.33
that are in Puts -0.30

0.47

0.68

1.08

0.53

-7.42 13.37 18.03 19.83 15.71
the S&P 100 Calls -0.24

0.53

0.80

1.15

0.46

-7.93 15.27 22.94 21.88 18.48
87
Table 3.12: Average delta-hedged excess returns for each year of the sample
This table reports average excess returns of portfolios of delta-hedged equity options. Portfolios are equally weighted across
contracts. Data are daily from January 4, 1996, through June 31, 2007.
Means T-statistics
Mon Tues Weds Thurs Fri Mon Tues Weds Thurs Fri
1996 Puts & Calls -0.68

0.24

0.28

0.29

0.17

-8.68 2.84 5.61 4.63 2.67
Puts -0.82

0.16

0.30

0.28

0.16

-10.78 2.12 6.39 4.18 2.04
Calls -0.56

0.31

0.28

0.30

0.18

-5.71 2.82 3.62 4.10 2.81
1997 Puts & Calls -0.47

0.26

0.26

0.31

0.21

-2.45 2.16 6.15 5.73 3.83
Puts -0.64

0.21

0.24

0.26

0.27

-3.21 2.74 4.90 4.42 4.15
Calls -0.33

0.31

0.30

0.36

0.16

-1.71 1.74 5.14 5.02 2.49
1998 Puts & Calls -0.48

0.27

0.36

0.58

0.29

-2.97 2.65 5.00 4.02 3.20
Puts -0.66

0.23

0.32

0.47

0.20

-5.78 2.70 4.70 4.54 2.74
Calls -0.25 0.35

0.42

0.73

0.40

-0.98 2.27 4.38 3.44 3.00
1999 Puts & Calls -0.74

0.21

0.39

0.37

0.11

-8.95 2.28 6.02 6.82 1.93
Puts -0.79

0.20

0.48

0.37

0.14

-8.76 1.84 5.98 5.06 2.32
Calls -0.70

0.22

0.32

0.38

0.09 -7.76 2.54 4.94 6.90 1.34
2000 Puts & Calls -0.60

0.59

0.78

0.67

0.48

-4.85 3.88 5.66 5.94 2.67
Puts -0.69

0.46

0.64

0.63

0.42

-6.12 3.46 5.12 5.57 2.90
Calls -0.51

0.73

0.95

0.74

0.55

-3.52 3.97 5.60 5.24 2.44
2001 Puts & Calls -0.67

-0.11 0.32

0.26

-0.01 -2.80 -1.22 2.46 3.11 -0.13
Puts -0.74

-0.12 0.20

0.22

-0.06 -3.94 -1.45 2.29 3.07 -0.76
Calls -0.59

-0.10 0.46

0.32

0.05 -1.83 -0.88 2.50 2.73 0.40
2002 Puts & Calls -0.41

0.19

0.26

0.26

0.04 -4.45 2.12 3.24 3.72 0.57
Puts -0.47

0.12 0.21

0.18

0.00 -5.42 1.64 3.32 2.64 0.06
Calls -0.33

0.30

0.33

0.38

0.09 -2.79 2.40 2.76 4.03 0.96
Continued on next page
88
Table 3.12 (Continued)
Means T-statistics
Mon Tues Weds Thurs Fri Mon Tues Weds Thurs Fri
2003 Puts & Calls -0.47

-0.15

0.04 0.03 -0.12

-7.41 -2.96 0.93 0.55 -2.85
Puts -0.46

-0.15

0.02 0.04 -0.13

-6.47 -2.78 0.34 0.68 -2.24
Calls -0.49

-0.15

0.06 0.02 -0.11

-7.31 -2.68 1.29 0.27 -2.24
2004 Puts & Calls -0.37

-0.05 0.09

0.11

-0.02 -6.16 -1.06 2.08 2.89 -0.45
Puts -0.44

-0.05 0.13

0.07

0.00 -6.73 -1.21 2.45 1.65 -0.08
Calls -0.31

-0.05 0.07 0.15

-0.04 -4.56 -0.82 1.23 3.16 -0.58
2005 Puts & Calls -0.40

-0.01 0.12

0.17

-0.04 -8.81 -0.31 2.56 3.53 -0.92
Puts -0.49

-0.07 0.16

0.18

-0.03 -9.84 -1.44 3.13 3.73 -0.60
Calls -0.33

0.04 0.08 0.17

-0.04 -5.34 0.95 1.36 2.69 -0.94
2006 Puts & Calls -0.26

-0.03 0.04 0.06 -0.10

-3.66 -0.55 0.90 1.18 -2.13
Puts -0.40

0.01 0.05 0.04 -0.12

-5.98 0.15 0.92 0.81 -2.06
Calls -0.13 -0.07 0.04 0.07 -0.08 -1.37 -0.96 0.54 1.09 -1.34
2007 Puts & Calls -0.33

0.01 -0.05 0.07 -0.08 -3.08 0.04 -1.08 0.98 -1.09
Puts -0.57

-0.01 0.07 -0.02 -0.01 -4.89 -0.04 0.85 -0.20 -0.07
Calls -0.12 0.02 -0.16

0.15 -0.14 -0.98 0.08 -1.83 1.42 -1.19
89
The ndings are amazingly consistent across years. In every year, the average return
on all options is signicantly negative on Mondays. Some Tuesdays are also signicantly
negative, but with much less regularity. Notably, the average returns are about as negative
in 2002 and 2003 as they are in the rest of the sample. Figure 3.2 shows that during this
period T-bill yields were extremely low, and the TED spread (3-month Eurodollars minus
3-month T-bills) was stuck below 25bps. If the cost of maintaining margin is related to
interest rates or interest rate spreads, then that cost cannot explain the weekend eect in
options, at least completely.
3.3.6 Nonparametric tests
Thus far, all of our test statistics have been computed based on asymptotic approximations.
In a recent paper, Broadie, Chernov, and Johannes (2009) nd that asymptotic standard
errors can be misleading when applied to average returns on S&P 500 Index options. They
instead advocate a parametric bootstrap approach that is more successful at accounting for
tail events that may be absent from the sample.
Given that the asymptotic t-statistics that result from our analysis are much larger than
those that Broadie et al. nd unconvincing, we feel it is unlikely that our results would be
overturned using the approach that they suggest in their paper. Of course, it would be
preferable to demonstrate this via our own parametric bootstrap, but such an undertaking
is impossible given the size of our sample, which is several orders of magnitude larger than
the one considered by Broadie et al.
An alternative approach towards obtaining exact nite sample inferences is to focus on
nonparametric tests for which distributional assumptions are unnecessary. As motivation
for the kind of test we consider, Figure 3.3 plots the frequencies with which each day of
the week has the lowest return of all the days in that week. The returns used for this plot
come from equal weighted portfolios of all delta-hedged calls or puts. Regardless of the
distribution of underlying returns, if that distribution is xed for all days of the week then
90
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
0
2
4
6
8
3ï Month Treasury Bill Yield
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
0
0.5
1
1.5
2
TED Spread: 3 ï Month Eurodollar Rate minus 3 ï Month Treasury Bill Yield
Figure 3.2: 3-Month Treasury Yield and TED Spread
The TED Spread is dened as 3-month Eurodollars minus 3-month T-bills. Data are daily from
January 4, 1996, through June 31, 2007.
we would expect these frequencies to be approximately equal.
5
Instead, what we see is that
the put portfolio has its lowest return of the week on Monday about 75% of the time, the
call portfolio about 60%.
Since Monday is not always the rst day of the week, as a more direct examination of
weekend returns we focus on the frequency with which the return on the rst trading day of
the week is the lowest of that week. For a typical week, regardless of the return distribution,
any distribution that is identical across days of the week implies that this frequency should
be one in ve. Given the presence of holidays in our sample, the correct expectation is
5
Actually, Monday should contain the lowest return of the week less often than other days due to the
higher frequency of Monday holidays.
91
Mon Tues Weds Thurs Fri
0
0.2
0.4
0.6
0.8
Puts
Mon Tues Weds Thurs Fri
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Calls
Figure 3.3: Frequency of Lowest Delta-Hedged Excess Returns by Day of the Week
This gure plots the frequencies with which each day of the week has the lowest return of all the days
in that week. The returns used for this plot come from equal weighted portfolios of all delta-hedged
calls or puts. Data are daily from January 4, 1996, through June 31, 2007.
that this frequency should be around 21%. We can test this null using a simple chi-square
test. The results are shown in the left panel of Table 3.13, where stars indicate the level of
statistical signicance.
Amazingly, the portfolio of all puts and calls has its lowest return over the weekend
in over 82% of the weeks in our sample, which is overwhelmingly statistically signicant.
While portfolios of puts or calls with dierent deltas and maturities have somewhat lower
frequencies, they are all above 21% and are almost all highly signicant.
Were it the case that weekend returns were the lowest of the week just slightly more that
21% of the time, then it would be possible that this could be attributed to higher weekend
volatility. However, this would imply that weekend returns should also be the highest of
the week with probability greater than 21%. The right panel of Table 3.13 shows, however,
that weekend returns are rarely the highest of the week, with frequencies generally below
10% and never above 21%.
While these results do not necessarily imply that mean weekend returns are lower than
those of the rest of the week, they leave little doubt that weekend returns are typically low,
and that this phenomenon is not attributable to errors in nite sample inference.
92
Table 3.13: Frequencies of lowest and highest returns
The left panel of the table reports the fraction of weeks in which the rst day of the week is the day with the lowest return.
The right panel reports the fraction in which the rst day has the highest return. For most portfolios, the fraction that would
be expected under the null hypothesis that all days are equivalent is about 0.21, slightly higher than one in ve due to the
presence of weeks with fewer than ve trading days. Stars indicate p-values from Chi-square tests of this null hypothesis,
where values that are statistically signicant at the 10%, 5%, an 1% levels are denoted by one, two, or three stars, respectively.
In all cases, portfolios are equally weighted across contracts and are formed on the basis of delta and/or option maturity.
\All Delta" portfolios include options regardless of delta, even those that are less than .01 or greater than .99 in absolute
value, and \All exp." portfolios include all options regardless of maturity. Data are daily from January 4, 1996, through
June 31, 2007.
Lowest Highest
All 11-53 54-118 119-252 All 11-53 54-118 119-252
exp. days days days exp. days days days
Puts & Calls All Deltas 0.824

0.824

0.809

0.781

0.054

0.054

0.043

0.052

Puts All Deltas 0.813

0.813

0.781

0.742

0.040

0.040

0.037

0.040

-.01 > Delta > -.10 0.522

0.453

0.515

0.478

0.112

0.149

0.099

0.079

-.10 > Delta > -.25 0.746

0.721

0.759

0.716

0.042

0.055

0.038

0.042

-.25 > Delta > -.50 0.823

0.826

0.816

0.768

0.037

0.037

0.027

0.038

-.50 > Delta > -.75 0.826

0.841

0.754

0.682

0.033

0.033

0.028

0.042

-.75 > Delta > -.90 0.657

0.647

0.530

0.478

0.047

0.057

0.050

0.065

-.90 > Delta > -.99 0.465

0.438

0.408

0.368

0.087

0.094

0.089

0.105

Calls All Deltas 0.659

0.689

0.632

0.580

0.072

0.064

0.072

0.079

.01 < Delta < .10 0.346

0.441

0.406

0.383

0.187 0.184

0.175

0.176

.10 < Delta < .25 0.582

0.589

0.579

0.477

0.094

0.107

0.090

0.105

.25 < Delta < .50 0.711

0.722

0.682

0.624

0.069

0.062

0.069

0.074

.50 < Delta < .75 0.709

0.761

0.642

0.574

0.054

0.045

0.062

0.072

.75 < Delta < .90 0.572

0.617

0.443

0.375

0.070

0.057

0.102

0.115

.90 < Delta < .99 0.276

0.273

0.232 0.236 0.152

0.140

0.154

0.184
93
3.4 Potential explanations
In this section we examine several possible explanations for low weekend returns. These
include statistical biases, risk compensation, and limits to arbitrage. We also explain why
our results cannot be attributed, at least in a rational market, to time decay in option
values.
The result of this analysis is to identify a number of conditioning variables that forecast
the magnitude of weekend returns. However, none of these variables is successful at \ex-
plaining" our basic nding that weekend returns are the lowest of the week. The weekend
is not a proxy for any other variable that we have considered.
3.4.1 Weekly patterns in liquidity
As we have discussed, if observed prices are subject to measurement errors then average
returns will be upward biased, as noted by Blume and Stambaugh (1983). The errors in
Blume and Stambaugh's paper arose from the use of transactions prices rather than \true"
prices or fundamental values. While our price data consist of bid-ask midpoints, which
should potentially be less error-prone than transactions prices, Duarte and Jones (2008)
show that measurement errors are still prevalent and appear strongly related to the size
of the bid-ask spread. Large spreads mean that the midpoint is less likely to re
ect true
value, and as the result a concern arises that systematic patterns in bid-ask spreads might
generate a weekend eect as an artifact of pure statistical bias.
Table 3.14 reports average bid-ask spreads of options relative to quote midpoints. On
a relative basis, option spreads can be very large, averaging up to 17% for deep out-of-the-
money puts and over 24% for deep out-of-the-money calls. These spreads provide at least
a partial explanation for the generally positive cumulative weekly returns found for equal
weighted portfolios in Table 3.3.
6
Attributing positive weekly returns to statistical bias is
6
For example, if the true option price is uniformly distributed between the bid and the ask, then measure-
ment errors in prices will have a standard deviation that is approximately 29% of the width of the spread.
For an option with a 10% spread, this would cause returns to be upward biased by approximately 8 basis
points per day, which would increase the observed weekly return by 40 basis points.
94
consistent with our nding that value weighted portfolio returns, which should be largely
immune from the Blume-Stambaugh bias, have cumulative weekly returns that are close to
zero.
Table 3.14: Relative bid-ask spreads, maturity-sorted portfolios
This table reports average bid-ask spreads, measured as a percent-
age of the bid-ask midpoint, of portfolios of equity options. All
gures represent equally weighted averages across contracts. Data
are daily from January 4, 1996, through June 31, 2007.
Means
Mon Tues Weds Thurs Fri
Puts All Deltas 8.9 8.9 8.9 8.9 8.8
-.01 > Delta > -.10 17.2 17.1 16.8 16.8 16.6
-.10 > Delta > -.25 14.6 14.6 14.4 14.3 14.2
-.25 > Delta > -.50 11.5 11.5 11.4 11.4 11.2
-.50 > Delta > -.75 8.9 8.9 8.9 9.0 8.8
-.75 > Delta > -.90 7.6 7.6 7.7 7.8 7.5
-.90 > Delta > -.99 4.9 4.9 5.0 5.1 4.8
Calls All Deltas 8.9 8.9 8.7 8.8 8.7
.01 < Delta < .10 23.7 23.8 22.8 22.2 22.1
.10 < Delta < .25 18.3 18.5 17.8 17.6 17.4
.25 < Delta < .50 13.6 13.6 13.3 13.3 13.1
.50 < Delta < .75 9.8 9.8 9.7 9.7 9.6
.75 < Delta < .90 7.8 7.8 7.8 7.9 7.7
.90 < Delta < .99 5.4 5.4 5.5 5.5 5.4
What we are more interested in, however, is whether Friday spreads are small relative
to other days of the week. In this case, the upward bias in Friday to Monday returns will
be lower than the bias on other days, which could lead to an observed weekend eect. The
bottom line from Table 3.14 is that Friday spreads are not smaller, except possibly to a
degree that is so small that it would have no eect beyond one or two basis points. We
conclude that bid-ask spreads do not oer any explanations for the weekend eect, either
related to the Blume and Stambaugh bias or otherwise.
Our second reason to examine liquidity measures follows from the hypothesis of Chen
and Singal (2003). If option writers are averse to holding positions over the weekend, as their
story would suggest, then we might expect systematic dierences in open interest or trading
95
volume on dierent days of the week. We emphasize that this prediction is ambiguous due
to the fact that in equilibrium the motive to trade around the weekend may be suppressed
by higher weekend risk premia. It is therefore possible that negative weekend returns are
low enough to keep both volume and open interest stable across the week.
Nevertheless, we examine both volume and open interest in Table 3.15. In order to try
to standardize volume and open interest across option written on very heterogeneous rms,
we report dollar open interest and volume as a percentage of the market capitalization of
the rm. A visual inspection of the numbers in Table 3.15 reveals no observable patterns
whatsoever. Whatever the explanation for the weekend eect is, it is not to be found in
this table.
3.4.2 Time decay
A rst reaction to the above results might be to attribute low weekend returns to the neg-
ative time decay, or \theta," in option values. We seek to dispel this apparent explanation
here.
In a Black-Scholes world, the price C
t
of an option satises
dC
t
=
@C
t
@S
t
dS
t
+
@C
t
@t
dt +
1
2
@
2
C
t
@S
2
t
Var(dS
t
):
Since the partial derivative
@Ct
@t
, often referred to as \theta," is negative, the option value
will decrease over time if the price of the underlying asset remains constant.
The theta of an option, at least in the Black-Scholes model, has two components, both
of which are negative:
@C
t
@t
=rKe
r
(d
2
)
S
t
(d
1
)
2
p

The rst term represents the cost of leverage. Any call option represents a levered equity
position, and this term represents the cost of the borrowing that would take place in a
portfolio that replicated the value of the option.
96
Table 3.15: Open interest and trading volume, maturity-sorted portfolios
This table reports average levels of open interest and trading volume, measured as a percentage of the
market capitalization of the underlying rm, of portfolios of equity options. All gures represent equally
weighted averages across contracts. Data are daily from January 4, 1996, through June 31, 2007.
Open interest Trading volume
Mon Tues Weds Thurs Fri Mon Tues Weds Thurs Fri
Puts All Deltas 5.75 5.82 5.65 5.70 5.73 0.17 0.21 0.20 0.19 0.18
-.01 > Delta > -.10 1.25 1.28 1.34 1.35 1.31 0.05 0.06 0.07 0.06 0.05
-.10 > Delta > -.25 2.49 2.59 2.52 2.56 2.52 0.14 0.14 0.15 0.14 0.13
-.25 > Delta > -.50 4.90 5.00 4.80 4.89 4.90 0.25 0.27 0.26 0.27 0.26
-.50 > Delta > -.75 6.94 7.05 6.81 6.88 6.93 0.21 0.22 0.23 0.23 0.23
-.75 > Delta > -.90 7.54 7.61 7.41 7.39 7.55 0.14 0.15 0.16 0.16 0.14
-.90 > Delta > -.99 5.78 5.72 5.59 5.53 5.71 0.11 0.22 0.15 0.15 0.12
Calls All Deltas 6.48 6.55 6.44 6.47 6.50 0.28 0.30 0.29 0.30 0.29
.01 < Delta < .10 0.75 0.82 0.95 1.27 1.14 0.09 0.06 0.05 0.12 0.13
.10 < Delta < .25 2.03 2.00 2.03 2.07 2.07 0.16 0.14 0.16 0.15 0.14
.25 < Delta < .50 5.00 5.06 5.00 5.09 5.08 0.39 0.38 0.39 0.39 0.37
.50 < Delta < .75 7.69 7.79 7.57 7.66 7.71 0.43 0.44 0.44 0.44 0.43
.75 < Delta < .90 7.07 7.17 6.99 7.01 7.09 0.24 0.27 0.26 0.26 0.26
.90 < Delta < .99 6.45 6.49 6.43 6.38 6.43 0.14 0.17 0.15 0.16 0.15
97
Since borrowing costs are three times higher over the weekend than they are over a
single day, this term might be expected to contribute to the weekend eect. However, these
implicit borrowing costs are small for most maturities and deltas, even in high interest
rate environments, and we observe a weekend eect even during time periods when interest
rates are near zero. More importantly, however, all interest rate eects are eliminated by
examining excess returns, and our results for excess returns on delta-hedged options are
no weaker than our results for simple (i.e. not in excess of the riskless rate) delta-hedged
returns.
The second component of theta,S
t
(d
1
)= (2
p
), represents the option value that
is lost as the amount of volatility remaining until expiration is reduced by the passage of
time. There are two reasons why this component of theta is also incapable of explaining the
weekend eect. The rst reason is based on the observation that the loss in option value is
not due to time per se but rather is due to the lower amount of volatility remaining over the
option's life as the option moves closer to expiration. Empirically, French and Roll (1986)
observed that the amount of volatility over a three-day weekend is no greater, on average,
than the amount of volatility that occurs during a weekday. Below, we conrm the same
result in our sample. Hence, the loss in option value should be no greater over the weekend
than it is over any other period with identical underlying volatility.
Moreover, even if the weekend were signicantly more volatile than a weekday, the
second component of theta would still not explain our ndings. The reason is that this
component is exactly equal to the \gamma" eect,
1
2
@
2
C
t
@S
2
t
Var(dS
t
):
That is, the loss in option value that occurs when we x the price of the stock is exactly
oset by the gain that is due to the fact that the stock price is never xed!
Intuitively, theta mostly comes from the fact that the total volatility until expiration
decreases from one trading day to the next, and with less volatility remaining over the life
98
of the contract there is a lower probability of ending up deeper in the money. By denition,
however, that total volatility until expiration is reduced exactly by the volatility that is
realized between these two dates, which itself increases the probability of ending up deeper
in the money, leading to higher expected payos.
7
In markets that are incomplete, either because of discreteness or additional risk factors,
option thetas could be substantially more complex. Nevertheless, we do not believe that it
is productive to think about theta as a determinant of expected option returns. Fundamen-
tally, we know that all assets' expected returns are the sum of the riskless interest rate and
a risk premium. If systematic dierences in excess returns are observed for dierent days
of the week, then the only explanation is variation in risk premia. Attributing returns to
the theta of a more complex model may be possible, but to us it seems more direct to ex-
amine whether weekly patterns in risk could make time variation in risk premia a plausible
explanation. We turn to this issue next.
3.4.3 Weekly patterns in risk
If delta-hedging is imperfect, then delta-hedged returns might retain exposures to systematic
risk factors, and delta-hedged returns could therefore oer higher or lower expected returns
7
To formalize this discussion, note that the delta-hedged gain on the call is
@Ct
@t
dt +
1
2
@
2
Ct
@S
2
t
Var(dSt):
Replacing derivatives with Black-Scholes \Greeks," this gain is written as

rKe
r
(d2)
St(d1)
2
p

dt +
1
2
(d1)
S
p

2
S
2
t
dt
The gamma eect cancels out the second term in theta, simplifying the gain to be
rKe
r
(d2)dt
The riskless return on the same notional amount would be

Ct
@Ct
@St
St

rdt

St(d1)e
r
K(d2)

St(d1)

rdt
=re
r
K(d2)dt
Hence the rst term of theta is exactly canceled out when we subtract the corresponding riskless return.
99
if those risk factors are priced. In the literature on equity index options, delta-hedged
option returns are found to be quite negative on average, a result that is often interpreted
as compensation for stochastic volatility and jump risks borne by the option writer. If this
is the case, then a greater level of unhedgeable risk over the weekend might explain our
results. We address this issue in two ways. First, we ask whether there is any evidence
that the underlying stocks are riskier over the weekend, either in terms of higher standard
deviation or greater departures from normality. Second, we ask whether the option portfolio
returns are themselves more volatile.
Table 3.16 examines the moments of the S&P 500 Index, the average moments of the
individual stocks in our sample, and also the moments of rst dierences in the VIX in-
dex. Specically, the numbers in the tables represent average values of sample moments
calculated separately for each rm-year based on daily returns on the underlying asset. We
average the sample moments cross sectionally before computing the time series averages
and standard errors reported in the table. An advantage of computing moments for each
rm-year is that we implicitly weight rms with longer histories more heavily.
Table 3.16: Stock return and VIX moments
This table reports average rm-year moments for S&P 500 Index and individual equity returns
as well as rst dierences in the VIX Index. Data are daily from January 4, 1996, through
June 31, 2007, though one year of data must be used to compute open interest weights, so only
sample moments starting in 1997 are included in the averages.
Mon -
Mon Tues Weds Thurs Fri T-F T-F
S&P 500 Index
Mean (bps.) 4.98 5.07 3.81 1.79 0.72 2.85 2.13
(1.39) (0.55) (0.54) (0.32) (0.13) (1.25) (0.64)
Standard Deviation (%) 1.14 1.11 1.03 1.09 1.06 1.08 0.07
(8.70) (9.61) (9.14) (10.79) (9.26) (10.15) (0.89)
Skewness -0.46 0.28 0.14 0.33 -0.16 0.15 -0.61
(1.30) (1.67) (0.99) (3.28) (1.71) (2.95) (1.66)
Excess Kurtosis 3.01 0.76 0.59 0.85 0.53 0.68 2.32
(2.27) (1.50) (1.75) (2.77) (2.63) (2.95) (1.89)
Continued on next page
100
Table 3.16 (Continued)
Mon -
Mon Tues Weds Thurs Fri T-F T-F
Equal weighted stock average
Mean (bps.) -5.22 4.71 8.96 10.44 19.73 10.94 -16.17
(0.98) (0.77) (1.88) (2.18) (5.55) (4.70) (3.70)
Standard Deviation (%) 4.09 4.06 4.07 4.08 3.98 4.05 0.04
(11.95) (11.69) (11.74) (11.99) (11.11) (11.64) (1.70)
Skewness 0.32 0.38 0.41 0.40 0.42 0.40 -0.08
(9.19) (12.71) (12.92) (11.21) (12.01) (13.46) (2.31)
Excess Kurtosis 3.01 3.26 3.41 3.45 3.42 3.39 -0.38
(30.46) (41.93) (33.45) (31.48) (31.48) (35.64) (3.37)
Value weighted stock average
Mean (bps.) 2.43 4.69 6.11 3.75 3.41 4.48 -2.05
(0.71) (0.56) (0.89) (0.70) (0.72) (2.31) (0.74)
Standard Deviation (%) 2.35 2.33 2.39 2.38 2.25 2.34 0.02
(9.21) (8.77) (8.76) (9.21) (8.78) (8.92) (0.40)
Skewness -0.02 0.18 0.21 0.17 0.08 0.16 -0.18
(0.28) (3.92) (5.53) (4.57) (1.61) (5.90) (2.26)
Excess Kurtosis 2.11 1.87 2.19 2.21 2.13 2.10 0.01
(13.40) (18.63) (21.09) (16.42) (12.75) (19.68) (0.03)
Open interest weighted stock average
Mean (bps.) 3.22 2.67 10.23 7.21 -2.81 4.32 -1.10
(0.64) (0.23) (0.97) (0.84) (0.34) (1.30) (0.29)
Standard Deviation (%) 2.94 2.93 3.07 3.06 2.82 2.97 -0.03
(8.77) (8.22) (7.44) (8.28) (8.34) (8.10) (0.40)
Skewness 0.01 0.22 0.25 0.22 0.14 0.21 -0.20
(0.08) (4.69) (3.53) (6.18) (2.89) (9.99) (2.34)
Excess Kurtosis 1.92 1.65 2.26 2.31 2.19 2.10 -0.18
(9.75) (11.68) (13.66) (11.06) (9.90) (13.24) (0.81)
Continued on next page
101
Table 3.16 (Continued)
Mon -
Mon Tues Weds Thurs Fri T-F T-F
VIX Index (rst dierences)
Mean (bps.) 46.74 -7.81 -10.54 -2.21 -25.29 -11.46 58.21
(6.15) (1.03) (1.78) (0.28) (3.82) (6.25) (6.24)
Standard Deviation (%) 1.24 1.21 1.08 1.25 1.21 1.19 0.06
(8.29) (8.21) (10.28) (9.01) (9.22) (9.72) (0.58)
Skewness 0.24 0.33 0.24 -0.04 0.63 0.29 -0.06
(0.68) (1.19) (1.81) (0.13) (2.66) (4.07) (0.15)
Excess Kurtosis 3.82 2.02 1.66 2.42 2.34 2.11 1.71
(3.24) (1.86) (4.02) (2.34) (2.49) (3.13) (1.15)
For the S&P 500 and the VIX, the cross sectional average is trivial, as there is just one
asset in the cross section. For stocks, the cross sectional average is performed three ways:
equally weighted, weighted by rm market value (value weighted) at the end of the previous
year, and weighted by the average dollar open interest in all options on that rm in the
previous year (open interest weighted). Since one year of data must be used to compute
open interest weights, the rst sample moments included in the averages are from 1997.
A number of ndings here deserve mention. First, we nd some evidence that the
weekend eect in stocks, reported by Fields (1931) and French (1980), persists through our
sample, but only in the equal weighted averages of individual stock moments. The eect is
absent from the S&P 500 Index and is undetectable in rm value weighted and open interest
weighted averages, suggesting that whatever weekend eect remains in stocks is conned to
the smallest rms, for which option open interest is generally small. Nevertheless, for these
options the weekend eect must remain fairly large. The average Monday return is around
-5bps for the equal weighted portfolio, a full 15bps below the average value for the rest of
the week.
While a weekend eect in small stock returns is notable, it cannot explain our nd-
ings in the option market for several reasons. First, as noted above, a weekend eect in
the underlying stock return might explain some patterns in unhedged option returns, but
102
the eect should be mostly absent from delta-hedged returns. This is not what we nd.
Furthermore, the weekend eect we nd in options exists even for rms in the S&P 100
Index, which represent the largest rms in the market, and for option contracts that have
the greatest open interest.
It is more plausible that weekly patterns in second and higher moments of stock returns
would explain the weekend eect in option returns, but we nd little evidence of such a
pattern. The average return standard deviation is very
at across all days of the week,
conrming French and Roll's (1986) nding that Friday-to-Monday returns are not much
dierent from those of any other close-to-close interval despite being computed over two
additional days. This is true both for S&P 500 volatility and for all the averages of individual
stock standard deviations.
Skewness does seem slightly lower on Mondays than it is for the rest of the week, though
it is still usually positive. Kurtosis is slightly lower over the weekend, at least in the equally
weighted results. To the extent that negative skewness is undesirable from the perspective
of an option writer, low Monday skewness could cause negative weekend returns. Note,
however, that negative skewness is only desirable for buyers of out-of-the-money puts and
in-the-money calls, the latter since they can be transformed into out-of-the-money puts via
put-call parity. In contrast, buyers of out-of-the-money calls and in-the-money puts benet
from positive skewness. Since we see weekend eects for puts and calls of all deltas, skewness
cannot explain our ndings completely, even if the market's perception of weekend skewness
is that it is substantially more negative than our estimates. Furthermore, if lower skewness
is contributing to negative weekend returns, this should be at least somewhat oset by the
slightly lower excess kurtosis, which should make deep out-of-the-money options less risky
from the perspective of the option writer.
One intriguing result at the bottom of the table jumps out, namely that changes in the
VIX Index are systematically higher on Mondays relative to the rest of the week. This turns
out to be due to the same technical eect that results from the use of calendar rather than
trading time. As described by the CBOE (2009), the VIX Index computes maturity as the
103
amount of calendar time until expiration. Despite the fact that the VIX is \model-free"
and not a Black-Scholes implied volatility, it nevertheless is measured per unit of time, and
the time convention chosen ensures that it will rise predictably over the weekend.
There is no evidence that the volatility of VIX changes is higher over the weekend, which
should rule out the possibility that the weekend eect in options is due to time variation in
the quantity of variance risk. Since variance risk has been shown by Bakshi, Cao, and Chen
(1997) and others to be an important determinant of S&P 500 Index option risk premia,
nding that the level of this risk is higher over the weekend might explain our result. No
such pattern can be detected.
A more direct examination of the risk-return explanation is to look at the standard
deviations of portfolios of delta-hedged options. We do so in Table 3.17 and nd that
Mondays are in fact associated with slightly higher levels of riskiness in option returns,
particularly among deep out-of-the-money contracts. Given that the underlying stocks have
essentially no more volatility over the weekend than they do over a single weekday, greater
weekend volatility in delta-hedged option returns implies that delta hedging is somewhat
less eective over the weekend than it is during the week. Compensation for non-hedgeable
risk could therefore contribute or possibly even explain the weekend eect in options.
There are two problems, however, with option portfolio risk as an explanation for low
weekend returns. The rst is that the level of volatility in option returns over the weekend
is simply not that much higher than it is during the week, and it is hard to see how such a
modest dierence could result in the magnitude of the weekend eect that we nd. Second,
if risk is greater on weekends, and if that risk is priced, then it likely represents some
systematic factor that should also drive S&P 500 Index options. For example, if the higher
kurtosis we observed for S&P 500 Index returns on Mondays is the explanation for the
weekend eect in individual equities, then it seems natural to expect a similar eect in
options on the index. Our earlier results for the S&P 500 Index, reported in Table 3.7,
were somewhat inconclusive. There were some signicantly negative Monday returns, but
104
Table 3.17: Risk of portfolios of delta-hedged excess option returns
This table reports standard deviations of excess returns of portfolios of
delta-hedged equity options. Portfolios are equally weighted across con-
tracts and are formed on the basis of delta. \All Delta" portfolios include
options regardless of delta, even those that are less than .01 or greater than
.99 in absolute value. Data are daily from January 4, 1996, through June
31, 2007.
Standard deviations
Mon Tues Weds Thurs Fri
Puts & Calls All Deltas 0.86 0.69 0.57 0.57 0.59
Puts All Deltas 0.78 0.62 0.52 0.53 0.55
-.01 > Delta > -.10 4.36 3.06 2.91 2.74 2.97
-.10 > Delta > -.25 2.32 1.62 1.40 1.46 1.54
-.25 > Delta > -.50 1.30 0.97 0.78 0.84 0.84
-.50 > Delta > -.75 0.69 0.55 0.45 0.51 0.47
-.75 > Delta > -.90 0.39 0.29 0.28 0.39 0.29
-.90 > Delta > -.99 0.22 0.17 0.17 0.22 0.18
Calls All Deltas 1.10 0.88 0.75 0.75 0.76
.01 < Delta < .10 23.22 14.25 11.80 15.28 15.55
.10 < Delta < .25 4.64 3.70 3.38 3.24 3.05
.25 < Delta < .50 2.14 1.80 1.46 1.46 1.42
.50 < Delta < .75 1.06 0.90 0.68 0.74 0.70
.75 < Delta < .90 0.59 0.48 0.37 0.42 0.41
.90 < Delta < .99 0.24 0.20 0.17 0.18 0.19
no weekend eect was obviously apparent, as one might have expected if options were
systematically more risky over the weekend.
Nevertheless, we do not believe that the risk explanation should be dismissed completely.
In the next section we include several risk measures as possible determinants of average
option returns.
3.4.4 Market conditions and non-trading returns
In this section we examine the relation between non-trading returns and a number of vari-
ables that represent current conditions in the underlying and option markets. Given the
relationship between risk and weekend returns that was suggested by previous results, two
of these variables are measures of volatility in option or underlying returns.
105
An alternative motivation for examining the relation between volatility and expected
returns is that high volatility may represent an impediment to arbitrageurs attempting to
exploit the weekend anomaly. For the weekend eect to persist in markets where traders
are aware of its existence, it seems natural to imagine that there are limits to arbitrage of
the sort discussed by Shleifer and Vishny (1997). In fact, Venezia and Shapira (2007) nd
that the weekend eect in equity markets appears to be driven by an increase in the trading
activity of individual investors around the weekend. Professional investors, in contrast,
decrease their trading around the weekend, suggesting that they may face impediments to
trade that limit their ability to capitalize on weekend mispricings.
Another potential limit to arbitrage is the cost of borrowing. Specically, as we discussed
above, the cost of maintaining the margin required to write options should be related to
interest rate spreads since T-bills can be held as collateral in a margin account. Though we
found that the weekend eect persists in periods when the TED spread is low, there still
may be a relation that is not apparent from casual inspection. We therefore consider the
TED spread as an additional explanatory variable for option returns.
As in Table 3.8, regressions are run in which the unit of observation is a portfolio that
is formed on the basis of maturity and delta and the dependent variable is the delta-hedged
excess return on a given portfolio. Regressions on equal weighted portfolios are presented in
Table 3.18, while results for value weighted portfolios are in Table 3.19. All regressions use
ordinary least squares, and standard errors are clustered by date. Portfolio xed eects are
included, but all the results we discuss are obtained without them as well. In all regressions
we control for the non-trading and expiration eects already documented in Table 3.8, and
regressions that include only these eects are repeated in the rst columns of regression
coecients in Tables 3.18 and 3.19.
In the previous section we saw that the volatility of delta-hedged option returns was
modestly higher over the weekend than it was for weekdays. This suggests the possibility
that negative weekend option returns represent compensation for the riskiness of portfolios
of delta-hedged option positions.
106
Table 3.18: Explaining delta-hedged excess option returns, equal weighted portfolios
This table reports the results of pooled regressions in which the dependent variable is the
delta-hedged excess return on various portfolios of equity options. The dependent and rst
four independent variables are described in Table 3.8. In addition, the independent variables
include a 44-day rolling window standard deviation from the returns on an open interest
weighted portfolio of all delta-hedged option positions, a 44-day rolling volatility computed
from S&P 500 Index returns, and the TED spread (Eurodollar minus T-bill yields). All three
of these variables are also interacted with the non-trading period dummy. Data are daily
from January 4, 1996, through June 31, 2007. Standard errors are computed with clustering
by date, and all regressions include portfolio xed eects. T-statistics are in parentheses.
Intercept 2.05 1.90 1.33 1.45 0.94 1.23
(1.04) (0.95) (0.67) (0.73) (0.47) (0.62)
Non-trading period dummy -1.33 -1.08 -0.51 -0.55 -0.02 -1.31
(8.92) (3.51) (1.82) (2.10) (0.07) (8.41)
Mid-week holiday dummy 0.72 0.71 0.73 0.72 0.70 0.72
(3.02) (2.99) (3.06) (2.83) (2.79) (2.94)
Long weekend dummy 0.40 0.37 0.35 0.40 0.37 0.40
(1.09) (0.98) (0.94) (1.08) (0.96) (1.07)
Expiration weekend dummy -0.38 -0.40 -0.38 -0.39 -0.40 -0.39
(2.07) (2.10) (2.05) (2.12) (2.15) (2.04)
Option volatility 0.35 -0.63 -0.47
(1.57) (1.35) (1.20)
Option volatility non-trading dummy -0.44 0.78
(1.00) (1.11)
S&P 500 volatility 0.61 0.79 0.59
(3.78) (2.58) (2.35)
S&P 500 volatility non-trading dummy -0.77 -0.95
(2.91) (2.30)
TED spread 1.10 0.92 0.54
(4.67) (3.83) (2.22)
TED spread non-trading dummy -1.93 -1.73
(2.55) (2.30)
Regression R-squared (in %) 0.32 0.33 0.35 0.35 0.38 0.35
107
Table 3.19: Explaining delta-hedged excess option returns, value weighted portfolios
This table reports the results of pooled regressions in which the dependent variable is the
delta-hedged excess return on various portfolios of equity options. The dependent and rst
four independent variables are described in Table 3.8. In addition, the independent variables
include a 44-day rolling window standard deviation from the returns on an open interest
weighted portfolio of all delta-hedged option positions, a 44-day rolling volatility computed
from S&P 500 Index returns, and the TED spread (Eurodollar minus T-bill yields). All three
of these variables are also interacted with the non-trading period dummy. Data are daily
from January 4, 1996, through June 31, 2007. Standard errors are computed with clustering
by date, and all regressions include portfolio xed eects. T-statistics are in parentheses.
Intercept -0.07 -0.19 -0.34 -0.46 -0.67 -0.47
(0.04) (0.12) (0.21) (0.28) (0.41) (0.29)
Non-trading period dummy -0.70 -0.31 -0.19 -0.24 0.22 -0.67
(4.41) (0.99) (0.62) (0.86) (0.56) (4.17)
Mid-week holiday dummy 0.05 0.07 0.06 0.05 0.07 0.05
(0.20) (0.29) (0.25) (0.19) (0.26) (0.19)
Long weekend dummy 0.67 0.65 0.62 0.67 0.65 0.67
(1.68) (1.58) (1.53) (1.67) (1.56) (1.65)
Expiration weekend dummy -0.94 -0.94 -0.94 -0.94 -0.94 -0.93
(4.64) (4.57) (4.64) (4.68) (4.63) (4.53)
Option volatility 0.23 -0.07 -0.12
(1.06) (0.28) (0.52)
Option volatility non-trading dummy -0.68 -0.25
(1.46) (0.40)
S&P 500 volatility 0.23 0.22 0.15
(1.74) (1.36) (1.07)
S&P 500 volatility non-trading dummy -0.48 -0.31
(1.78) (0.93)
TED spread 0.70 0.66 0.43
(3.16) (3.10) (1.91)
TED spread non-trading dummy -1.13 -1.05
(1.47) (1.37)
Regression R-squared (in %) 0.49 0.52 0.50 0.51 0.55 0.53
108
If risk in hedged positions commands a negative risk premium, then a negative risk-
return relation should be expected more generally, and not just on weekends. As a measure
of this risk, we construct a 44-day rolling window standard deviation from the returns on an
value weighted portfolio of all delta-hedged option positions in our dataset. This volatility
is included separately and interacted with a non-trading dummy variable.
Our regression results, presented in the second columns of Tables 3.18 and 3.19, reveal
no signicant relation between delta-hedged returns and option volatility, either separately
or interacted with the non-trading dummy. The absence of a consistently negative relation
between option risk and return suggests that risk does not provide an explanation for
negative weekend returns.
We nevertheless consider a 44-day rolling volatility computed from S&P 500 Index re-
turns as an alternative measure of volatility.
8
As before, this volatility is included separately
and interacted with the non-trading dummy. The results for equal weighted portfolios in
Table 3.18 and value weighted portfolios in Table 3.19 are fairly consistent. Aggregate stock
market risk is positively, rather than negatively, related to future option returns, though
the eect is stronger in equal weighted portfolios. The positivity of this relation is also
inconsistent with a risk based explanation of negative weekend returns.
What is surprising in these results, at least in the case of the equal weighted portfolios,
is the negative coecient on the interaction between S&P 500 volatility and the non-trading
dummy. Thus, while volatility in general has a positive eect on option risk premia, the
eect switches sign over the weekend.
The sign of the risk premia underlying these coecient estimates is determined by the
sign of the covariance between delta-hedged option returns and the aggregate pricing kernel.
Since the covariance between marginal utility and option returns is negative for option
buyers but positive for sellers, the correlation between returns and the pricing kernel, which
will be a weighted average of the two marginal utilities, is indeterminate. One possible
8
Another possibility would have been to use the VIX Index instead, but the mechanically-induced weekly
seasonal in VIX discussed in Section 3.4.3 makes the interpretation of results using the VIX problematic.
109
explanation of the changing regression coecient is that as we move from weekday to
weekend the marginal utility of the option writer becomes more volatile as the eectiveness
of his hedging strategy deteriorates from the inability to rebalance. If option sellers hedge
but option buyers do not, then the ability to hedge eectively when markets are open
means that the behavior of the pricing kernel will mimic that of the option buyer. Over
the weekend, ineective hedging causes the option writer's marginal utility to dominate
the pricing kernel, causing the covariance of the pricing kernel with returns to switch from
negative to positive. If risk premia are of greater magnitude when volatility is higher, we
should obtain the observed result.
The eect of the TED spread on average returns also changes sign when it is interacted
with the non-trading dummy. During the week, higher TED spreads predict higher option
returns. Over the weekend or during other non-trading periods, high TED spreads fore-
cast lower returns. Both eects are statistically signicant, at least marginally, in all the
specications in which they appear.
In summary, we nd that the weekend eect is strongest when market volatility and
TED spreads are high, both of which suggest that limits to arbitrage prevent the eect's full
exploitation. We note that the results in Tables 3.18 and 3.19 include a number of cases in
which the inclusion of other variables eliminates the signicance of the non-trading dummy.
This does not mean that the regression \explains" the weekend eect, because the variables
that must be added to make the non-trading dummy insignicant are themselves interaction
terms with the same dummy. When we include all the explanatory variables except the
interaction terms, reported in the last column of the two tables, the signicance of the non-
trading dummy is as strong as it was without the additional explanatory variables. Rather
than oering an explanation of the weekend eect, these regressions are more accurately
interpreted as measuring the magnitude of the eect in dierent market conditions.
110
3.5 Conclusions
We have demonstrated that a weekend eect exists in the returns, both hedged and un-
hedged, and implied volatilities of individual equity options. The nding is robust to sample
period, the method of portfolio construction, and the selection of the sample.
Regression results suggest that the eect exists during mid-week holidays as well, likely
with a somewhat smaller magnitude. Returns are especially negative over expiration week-
ends and during non-trading periods in which TED spreads and market volatilities are high.
We argue that these results are consistent with limits to arbitrage that prevent option writ-
ers from fully proting from anomalous weekend returns.
We believe that our results lend some support to the Chen and Singal (2003) hypothesis
that investors try to close out positions that expose them to unbounded downside risk
prior to the start of the weekend. In stock markets, the unbounded risk faced by short
sellers was eliminated when those investors could instead take short positions by purchasing
put options. In options markets, the unbounded risks are borne by option writers, and
compensation for their risks takes the form of negative weekend option returns. Support
for the hypothesis is strengthened by the nding that variables that proxy for limits to
arbitrage forecast future weekend returns in a manner consistent with that theory.
The fact that option returns have a weekly seasonal has two other implications. One is
that option pricing models that rely on risk premia for stochastic volatility or jumps must
also explain why such premia are primarily manifested over weekends. This seems to us like
a challenging restriction that most models would likely fail.
In addition, we believe that our results make the data mining explanation of the original
weekend eect, as articulated by Sullivan, Timmermann, and White (2001), somewhat
less appealing. While the weekend eect may have disappeared from equity markets, its
continued existence in option markets suggests that the eect was real and indicative of
economic forces that continue to operate today in a somewhat dierent environment.
111
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Abstract (if available)

Abstract This dissertation is comprised of three essays.

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Asset Metadata

Creator Shemesh, Joshua (author)

Core Title Essays in behavioral and financial economics

School Marshall School of Business

Degree Doctor of Philosophy

Degree Program Business Administration

Degree Conferral Date 2011-05

Publication Date 04/21/2011

Defense Date 03/17/2011

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

Tag behavioral finance,OAI-PMH Harvest,relative concerns,weekend effect

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Zapatero, Fernando (committee chair), John, Richard S. (committee member), Jones, Christopher (committee member), Ozbas, Oguzhan (committee member)

Creator Email joshua.shemesh@gmail.com,shemesh@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m3765

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