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Essays on real options

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Content Essays on Real Options Davidson Heath USC Marshall School of Business Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Finance and Business Economics August 2015 1 Acknowledgments I owe a huge debt of gratitude to my committee chair Wayne Ferson, a true scientist, who has forgotten more than I’ll ever know about finance. My first chapter was inspired by the incisive work and the encouragement of Scott Joslin. My second chapter was inspired by the far-sighted work and the encouragement of Gordon Phillips and Gerard Hoberg. My approach to research, which is to devote one’s energy to being creative, pragmatic, careful, and humble, is directly inspired by Kenneth Ahern and the other members of my committee. My parents, John and Ann, are the best anyone could wish for. I aspire to live up to the example they set me as scientists, as parents and as people. My brothers Mark George and Earl, my sister-in-law Milena and my mother-in-law Bogdanka provided much love, inspiration and support. Finally I wish to dedicate this work – and every day of my life – to my brilliant and beautiful wife Jelena and my beautiful and brilliant boys Johnny and Tommy. 2 Contents I Unspanned Macroeconomic Risks in Oil Futures 7 1 Introduction 8 2 Data and Forecasting Regressions 11 2.1 Futures Price Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Macro Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Evidence for Unspanned Macro Risks . . . . . . . . . . . . . . . . . . . . . . 13 3 Model 18 3.1 Stochastic Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4 Model Estimates 22 4.1 Model Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2 Historical Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.2.1 Oil Futures and Economic Activity . . . . . . . . . . . . . . . . . . . 27 4.2.2 Oil Futures and Inventories . . . . . . . . . . . . . . . . . . . . . . . 28 4.2.3 Impulse Response Functions . . . . . . . . . . . . . . . . . . . . . . . 29 4.3 Risk Neutral Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.4 Risk Premiums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.5 A Simple Model of Oil Risk Premia . . . . . . . . . . . . . . . . . . . . . . . 34 5 Further Applications 37 5.1 Other Macro Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.1.1 Financialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3 5.1.2 Rig Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 5.1.3 Subcomponents of GRO . . . . . . . . . . . . . . . . . . . . . . . . . 42 5.1.4 Positive vs Negative Growth Regimes . . . . . . . . . . . . . . . . . . 44 5.2 Other Commodities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 6 The Cost of Carry 47 6.1 Comparison with the Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 6.2 Variation in c t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 7 Real Options 53 8 Conclusion 57 A Model Specification and Risk Premiums 69 A.1 P t Measured Without Error . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 A.2 Rotating to s t and c t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 A.3 Risk premiums and s t , c t : . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 B JPS Parametrization 75 B.1 Observational Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 B.2 Uniqueness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 C Estimation 80 D Comparison with other Futures Models 82 E Real Option Valuation 83 4 References 59 F Robustness Checks 84 F.1 Excluding the Financial Crisis . . . . . . . . . . . . . . . . . . . . . . . . . . 84 F.2 Time varying volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 F.3 Real vs Nominal Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 F.4 Inflation as a Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 II Technology and Real Options: Evidence from Patent Text 93 1 Introduction 94 1.1 Prior Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 2 Data and Methodology 96 2.1 Patent Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 3 Firm-year Technology Positions 99 3.1 Firm Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3.2 Firm-year Technology Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . 100 3.3 Technological Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 3.4 Comparison with Hoberg-Phillips TNIC . . . . . . . . . . . . . . . . . . . . 104 3.5 Correlation with Firm Characteristics . . . . . . . . . . . . . . . . . . . . . . 107 3.5.1 TFP and techdiff based on Census data . . . . . . . . . . . . . . . . . . . . . . 108 4 Model 111 5 Returns 114 6 Conclusion 119 5 References 120 A Selecting Ngrams 130 B Patent Reassignments 131 C Individual Patents 132 C.1 Technology Measures by Individual Patent . . . . . . . . . . . . . . . . . . . 132 C.2 Validation: Patent Renewals . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 D Simulation 135 E Measuring Technology Using Patent Classes 135 6 Part I Unspanned Macroeconomic Risks in Oil Futures Abstract This paper constructs a macro-finance model for commodity futures. I document a negative feedback relationship between crude oil prices and real economic activity. The channel from real activity to oil prices is unspanned – meaning not identified in current futures prices – consistent with oil futures as a hedge asset against supply shocks. Unspanned macroeconomic risks have first order effects on risk premiums and the value of real options. The model also yields a precise estimate of the cost of carry that is strongly related to physical inventories. 7 1 Introduction Commodity futures are claims on direct inputs into production and consumption, and are among the most active markets in the world. 1 Understanding the interaction of the real economy with futures prices can shed light on equilibrium production and consumption, forecasting, hedging, risk premiums, and the values of real options. There is a gap in the current literature between time series analyses of commodity prices and the economy, which are silent on risk premiums and the term structure of futures prices, and pricing models that contain no macroeconomic data. This paper fills the gap by developing a macro-finance model for futures – to my knowl- edge, the first – that incorporates both pricing and macroeconomic factors. The approach is tractable and nests previous models as special cases. It can be applied to any commodity and any set of economic data. I estimate models with state variables that span oil futures prices, economic activity and physical oil inventories. I concentrate on oil because it is the single most important commodity to the U.S. and world economy as reflected in its trading volume, media coverage and academic and industry attention. I find evidence of both macro-to-futures and futures-to-macro links. There is a negative feedback relationship between oil prices and U.S. economic activity and a strong relationship betweentheslopeofthefuturescurveandphysicaloilinventories. Theestimatessuggestthat previous models miss a large component of risk premiums and the values of real options. The estimates also imply that the cost of carry – the quantity that ties futures prices to physical inventories – is pinned down precisely by the data. A key empirical question that this paper raises is which macroeconomic risks are spanned 1 In October 2014 the average trading volume across the two benchmark crude oil futures, WTI and Brent, was $120 billion per day compared to $129 billion per day for all NYSE and NASDAQ stocks. 8 by commodity futures and which are material but unspanned. An unspanned macro risk is a state variable that is relevant to expected returns and/or price forecasts, but is not identified in contemporaneous futures prices. Vector autoregressions (VARs) that include a single commodity price cannot address this question. Previous pricing models for commodity derivatives assume that all relevant risks in the economy are spanned, which imposes strong restrictions on the joint behavior of macro information, futures prices, and futures returns. In particular, perfect spanning implies that conditional on current futures prices no other information can forecast oil prices or returns or the macroeconomic variables. I find that this restriction is strongly rejected in the data. A high spot price of oil forecasts lower real economic activity, consistent with the find- ings of Hamilton (1983), Bernanke etal. (1997) and Kilian (2009) that oil shocks forecast recessions. The effect is conditional on the market’s forecast of how long the shock will last: persistent shocks to oil prices lower real activity persistently, while transient shocks lower real activity transiently. Conversely, a high level of real activity forecasts higher oil prices. Although shocks to real activity dissipate in less than a year the market forecasts that their effect on oil prices persists for decades, perhaps because oil is a nonrenewable resource. Moreover, economic activity forecasts oil prices over and above the information in oil futures – equivalently, the spotriskpremiuminoilfutureshasanunspannedprocyclicalcomponent. Thisfindingaligns with those of Ludvigson and Ng (2009), Duffee (2011) and Joslin, Priebsch and Singleton (2014) of unspanned countercyclical risk premia in bonds, but in the opposite direction. I argue that the results are consistent with oil futures as a hedge asset against supply shocks. Allowing the spot risk premium to vary with unspanned real activity raises its monthly volatility almost tenfold, which suggests that spanned-risk pricing models may miss much of 9 the variation in commodity risk premiums. By definition unspanned macro risks cannot affect the prices of financial options or other derivatives, but they may affect the valuation and exercise of real options. In a calibrated example I find that adding unspanned macro risk increases the value of a hypothetical oil well over the corresponding spanned-risk model by 35% to 400% depending on the well’s current cost of extraction. There are two channels by which unspanned macro risks raise real option values: their dynamics with futures prices and their risk premiums. In the example the dynamics effect dominates, while the effect of unspanned risk premiums on real option values is much smaller. The model estimates further imply that the cost of carry is pinned down precisely by the data. The cost of carry is the marginal cost of physical storage for one period, equal to storage costs plus the risk free rate minus the convenience yield. In empirical studies, the basis – the percent spread between the first- and second-nearest maturity futures prices – is often used as a proxy for the cost of carry. I find that the cost of carry differs significantly from the basis. Its monthly standard deviation is 40% lower and it mean reverts more than twice as slowly. The cost of carry is more strongly associated with inventories than the basis is, and in a horse race of forecasting changes in inventories it drives out the basis entirely. Moreover, the cost of carry estimated from North Sea oil futures drives out the U.S. basis as a predictor of U.S. inventories. These results suggest that the additional variation in the basis over and above the cost of carry is not linked to physical storage. There are two strands of prior literature in commodity futures that this paper builds on. In the first, commodity futures prices are modeled as affine functions of latent state variables. ClassicexamplesareGibson andSchwartz(1990), Schwartz(1997), and CasassusandCollin- Dufresne (2005). More recent examples include Casassus, Liu and Tang (2013) and Hamilton 10 and Wu (2014). None of the previous studies of this type incorporate explicit macroeconomic data. Second, these models implicitly assume that all relevant information in the economy is spanned by futures prices and no other information can contribute incremental forecasting power. I find that real economic activity has material effects on risk premiums and forecasts of oil prices that are unspanned in the futures curve. The second strand uses VARs to explore the time series relations of oil prices with the real economy; examples include Hamilton (1983); Hamilton (2003); Kilian (2009); Alquist and Kilian (2010); Kilian and Vega (2011). These studies generally include a single state variable based on the spot price of oil. A limitation of this approach is that it does not incorporate the full set of futures prices of different maturities. The model in this paper imposes the additional assumption that risk premiums are “essentially affine” in the state variables which lets us bring the full futures curve to bear on returns, price forecasts, and the spanning of macroeconomic risks. 2 Data and Forecasting Regressions InthissectionIdescribethedata,whichconsistofcrudeoilfuturespricesandmacroeconomic data, and investigate to what extent the macroeconomic data are spanned by futures prices. In addition to being an empirical question in its own right, the distinction between spanned and unspanned risks drives the modelling strategy. I conclude that, first, two linear factors suffice to summarize the oil futures curve, and second, the macro factors, in particular economic activity, contain relevant information that is unspanned by oil futures. 11 2.1 Futures Price Data I use closing prices for West Texas Intermediate (WTI) oil futures with maturities of one to twenty four months, on the last business day of each month from January 1986 to July 2013. The futures price data is denoted f j t = log(F j t ), j = 1...J, t = 1...T f t = f 1 t f 2 t ... f J t 0 whereF j t is the closing price at end of montht of the future that expires in montht +j, t = 1 corresponds to 1/1986, T = 331 corresponds to 7/2013, and J = 24. 2.2 Macro Factors I use the Chicago Fed National Activity Index, hereafter labelled GRO, as the first macro factor. The index is released toward the end of each month and is a weighted combination of 74 U.S. economic indicators, similar in spirit to the real economic activity indexes of Stock andWatson(1999)andLudvigsonandNg(2009). Theindexisintendedasaforward-looking indicator of U.S. economic activity and is used in macro-finance models of bond yields (cf. Joslin, Priebsch and Singleton (2014)). From January 2001 onward I use the real-time values of the index, although the results using the revised values are very similar. I also use changes in the Conference Board’s Leading Economic Index (LEI) as an alternative proxy and obtain similar results. The second macro factor is the inventory, or quantity in readily available storage. I use the log of the Energy Information Administration (EIA)’s “Total Stocks of Commercial 12 −4 −3 −2 −1 0 1 2 1985 1990 1995 2000 2005 2010 2015 2 2.5 3 3.5 4 4.5 5 GRO INV f t 1−12 Figure 1: The figure plots the time series of log futures prices for Nymex crude oil f 1−24 t , the Chicago Fed National Activity Index GRO, and the log of the EIA’s monthly U.S. oil inventory INV. Crude Oil excluding the Strategic Petroleum Reserve” as a measure of the readily available U.S. inventory of crude oil, hereafter labelled INV. The EIA’s storage report is released weekly, and I use the most recent data as of the last business day of each month. The macro factors are thus M t = [GRO t , INV t ] 0 . Figure 1 plots the time series of the twelve constant-maturity log futures prices, overlaid with the time series of GRO and INV. 2.3 Evidence for Unspanned Macro Risks Previous commodity pricing models assume complete spanning of the state variables and are estimated using financial data only. As Duffee (2011) and Joslin, Le and Singleton (2013) observe in the context of bond yields, this assumption has strong implications for the joint behavior of futures prices and the economy. First, it implies that the state vector can be rotated so that the state variables equal the prices of arbitrary linearly independent 13 0 2 4 6 8 10 12 −0.4 −0.2 0 0.2 0.4 0.6 Futures maturity in months Loading PCs of Log Oil Price Levels PC1 −− 99.79% PC2 −− 0.20% PC3 −− 0.01% 0 2 4 6 8 10 12 −0.4 −0.2 0 0.2 0.4 0.6 Futures maturity in months Loading PCs of Log Oil Price Changes PC1 − 97.15% PC2 − 2.56% PC3 − 0.23% Figure 2: Loadings of the first three principal components of the levels (panel A) and changes (panel B) of log oil futures prices, monthly from 1/1986 - 7/2013. The legend displays the fraction of total variance explained by each of the principal components. portfolios of futures contracts. Second, it implies that those portfolios capture log futures pricesuptoidiosyncraticpricingerrors. Third, itimpliesthatallrelevantinformationisfully summarized by those portfolios’ prices and no other information can contribute incremental forecasting power. I first document that the first two principal components, level and slope, account for well over 99% of the variation in both levels and changes of log futures prices. There are more than two sources of aggregate uncertainty in the world, so the natural hypothesis is that some relevant economic state variables are unspanned by oil futures. A) Oil futures prices display a low dimensional factor structure Figure 2 plots the loadings of the first three principal components (PCs) of log oil futures prices. The figure also displays the fraction of the variance that is accounted for by the PCs. The first two PCs – level and slope – account for 99.9% of the variation in log price levels and 99.7% of variation in log price changes. 14 Second, I find that the macro factorsM t , in particular the economic activity indexGRO, are not well summarized by futures prices. B) M t is mostly unspanned by oil futures I projectM t on the time series of the first five principal components of log oil futures prices, and label the residual UM t : M t =α +γ 1−5 PC 1−5 t +UM t The R 2 of the projection is 14.5% for GRO and 30.0% for INV. If I instead project M t on the log prices of all 24 futures contracts, the R 2 is 22.9% for GRO and 37.9% for INV. These results are consistent with the hypothesis that M t is unspanned by oil futures. However,M t might be measured with error or some component ofM t might be irrelevant to the oil market. In this case the test of whether M t is unspanned is not the projection R 2 , but whether the residualsUM t are economically meaningful over and above the information in futures prices. Third, I find that UM t contributes incremental forecasting power for oil prices and returns. C) M t forecasts prices and returns over and above information in the futures curve Table 1 Panel A shows the results of forecasting log returns to oil futures contracts using the first five principal components PC 1−5 and then adding the residual UM t . The results suggest that the economic growth time series contributes additional forecasting power over and above information in the futures curve. For log returns to the one month and twelve 15 month futures contracts over a one month holding period, the coefficient on UGRO t is positive and significant at the 5% level. The adjusted R 2 s increase from 0.7% and 0.3% to 3.0% and 2.7% respectively. The coefficients of returns on UGRO increase over holding periodsofthreeandsixmonths, thoughtheyarenotsignificantstatistically, andtheadjusted R 2 increases in every case. Panel B shows the results of forecasting changes in the level and slope factors of the oil futures curve using PC 1−5 and then adding the macro factors. The results again suggest that UM t has incremental forecasting power. Higher levels of growth forecast a higher level to the futures curve and the coefficient increases with the forecast horizon. The incremental increase in the adjusted R 2 for the change in the level factor is significant over one, six and twelve month horizons. Similar results obtain for both returns and PC changes if I use all 12 log futures prices in place of the principal components. The results are not driven by the big swings in 2008-2009: Appendix F shows the results are similar when I estimate on a subsample that ends in 2007. Previous studies of oil prices and the macroeconomy generally use VARs. The most closely related to my results is Kilian and Vega (2011), who generally find no consistent predictive power of macroeconomic news for the spot price of crude oil at a monthly horizon andconcludethatrelevantinformationismoreorlessimmediatelyreflectedinthespot price. Kilian and Vega examine a variety of macroeconomic data that are mostly backward looking. They do not examine the Chicago Fed National Activity Index, and for the most closely related forward-looking time series that they examine – the Conference Board’s Leading Economic Index – they find that it does in fact forecast oil prices at a monthly horizon (p< 0.01) and I replicate their finding in untabulated results. Another way in which our approaches differ is that Kilian and Vega (2011) and others 16 Table 1: Panel A shows the results of forecasting returns to oil futures. Panel B shows the results of forecasting changes in the level and slope, PC1 and PC2 respectively, of the oil futures curve. The data are monthly from from 1/1986 to 7/2013. The forecasting variables are the first five principal components of log futures prices, PC 1−5 , and the residuals of the Chicago Fed National Activity Index and U.S. oil inventory projected on PC 1−5 . The standard errors are Hansen-Hodrick. ∗ :p< 0.10, ∗∗ :p< 0.05, ∗∗∗ :p< 0.01. Panel A: Forecasting Returns to Futures r t→t+horizon =α +β 1−5 PC 1−5 t +β UGRO,UINV UM t + t Horizon 1 month 6 months 12 months Futures maturity 1 m 12 m 1 m 12 m 1 m 12 m β UGRO 0.025 ∗∗ 0.017 ∗∗ 0.032 0.023 0.042 0.033 (0.010) (0.007) (0.039) (0.030) (0.055) (0.043) β UINV 0.028 0.003 -0.170 -0.328 -0.112 -0.542 (0.087) (0.059) (0.510) (0.385) (0.860) (0.664) Adjusted R 2 (PC 1−5 ) 0.7% 0.3% 6.9% 0.7% 13.0% 1.3% Adj. R 2 (PC 1−5 +UM t ) 3.0% 2.7% 7.1% 2.0% 13.2% 3.2% F-ratio 9.6 ∗∗∗ 4.9 ∗∗∗ 1.4 3.0 ∗∗ 2.2 ∗ 4.0 ∗∗ Panel B: Forecasting Changes in Level and Slope ΔPC (n) t→t+horizon =α +β 1−5 PC 1−5 t +β UGRO,UINV UM t + t Horizon 1 month 6 months 12 months Principal Component Level Slope Level Slope Level Slope β UGRO 0.068 ∗∗ -0.008 0.091 0.001 0.071 -0.002 (0.028) (0.005) (0.144) (0.016) (0.107) (0.009) β UINV 0.040 -0.032 -1.615 -0.124 -1.047 -0.073 (0.236) (0.047) (2.267) (0.191) (1.386) (0.162) Adjusted R 2 (PC 1−5 ) -0.6% 8.0% 4.0% 50.0% 2.2% 34.3% Adj. R 2 (PC 1−5 +UM t ) 1.7% 8.5% 5.2% 50.0% 3.0% 34.0% F-ratio 9.5 ∗∗∗ 1.9 6.1 ∗∗ 0.9 4.6 ∗∗ 0.4 17 regress monthly changes in the spot price on their macro factors. This approach lumps together the spanned and unspanned effects of macroeconomic news. Specifically, GRO is positively correlated with the futures price f 1 t and negatively correlated with the basis f 2 t −f 1 t . Thus a high realization ofGRO is accompanied by a more downward-sloping curve, and the latter naturally forecasts a lower realization of Δs =s t+1 −s t . If we instead regress the log returnrf =f 1 t+1 −f 2 t onUGRO as in Table 1 Panel A then we isolate the incremental effect of the growth index on the forecast. 3 Model Motivated by the empirical findings in Section 2, in this section I develop a macro-finance model for commodity futures that admits unspanned macroeconomic risks. Macro-finance models that investigate the interaction of bond markets with the real economy are an active area of research starting with Ang and Piazzesi (2003). Let X t denote a vector of N state variables that summarize the economy. X t includes macroeconomic risk factors such as expected economic growth, and factors specific to the commodity such as hedging pressure, inventories, and expectations of supply and demand. The stochastic discount factor is given by e Λ 0 t t+1 =e (Λ 0 +Λ 1 Xt) 0 t+1 (1) The state vector follows a Gaussian VAR, X t+1 =K P 0X +K P 1X X t + Σ X P t+1 (2) where P t+1 ∼N(0, 1 N ). 18 Previous models such as Gibson and Schwartz (1990); Schwartz (1997); Casassus and Collin-Dufresne (2005) assume that X t is spanned i.e. fully reflected in contemporaneous futures prices. As is well known for bond yields (Duffie and Kan (1996)), Appendix B shows that the spanning assumption implies that X t can be replaced by an arbitrary set of linear combinations of log futures prices: P N t =Wf t where W is any full rank real valued N×J matrix. This assumption has the following implications for the interaction of the futures market and the macroeconomy: 1. Futures prices are described up to idiosyncratic errors by the N factorsP N t . 2. The projection of X t onP N t has R 2 of one. 3. Conditional onP N t , no other information forecasts X t or futures prices or returns. I instead assume that a subspace of X t is spanned, while its complement is unspanned but observed by the econometrician. Suppose that contemporaneous futures prices are deter- mined by a set of linear combinationsL t =Vf t whereV is a real valuedN L ×J matrix and N L <N. That is, the spot price and its evolution under the risk neutral measure are: s t =δ 0 +δ 0 1 L t (3) L t+1 =K Q 0L +K Q 1L L t + Σ L Q t+1 (4) where Q t+1 ∼ N(0, 1 N L ) and Σ L = V Σ X . The spanned components L t may be observed or latent. Finally, I assume that the unspanned componentsL ⊥ t ofX t are observed by the econome- trician. There are N M =N−N L of these factors. Label them UM t =L ⊥ t – the unspanned 19 components of observed macroeconomic information – and rewrite     L t UM t     =K P 0 +K P 1     L t UM t     + Σ P t+1 By construction, the factors UM t are not spanned by contemporaneous futures prices: this specification is in the class of macro-finance models explored by Diebold, Rudebusch and Aruoba (2006); Duffee (2011); Joslin, Priebsch and Singleton (2014) for bonds. By the same rationale as before, we can replace L t with N L linear combinations of log prices, P L t =W L f t where W L is any full rank N L × J real valued matrix. In contrast to the spanned-risk formulation, this model has the implications that: 1. Futures prices are described up to idiosyncratic errors by N L <N factors. 2. The projection of X t onP L t has R 2 less than one. 3. Conditional onP L t , other information may forecast X t or futures prices or returns. Motivated by the variance decompositions in the previous section, I assume the number of spannedstatevariablesN L = 2. AppendixBdescribestheparametrizationandestimationof the model. After estimating, I rotate and translate so that the state variables are the model implied spot price and cost of carry (s t , c t ) and the macroeconomic seriesM t =SM t +UM t . 2 The model can then be described in just two equations: 1) the law of motion for the state variables: 2 Appendix A.2 presents the definitions of s t and c t . 20         s t+1 c t+1 M t+1         =     K P 0sc K P 0M     +     K P sc,sc K P sc,M K P M,sc K P MM             s t c t M t         + Σ P t+1 (5) 2) the dynamics of (s t , c t ) under the risk neutral measure:     s t+1 c t+1     = K Q 0 +K Q 1     s t c t     + Σ sc Q t+1 (6) where • s t is the spot price and c t is the one-period cost of carry • M t are the macro state variables • K P 0sc , K P 0M are 2× 1 and N M × 1 real valued matrices • K P sc,sc , K P sc,M , K P M,sc , K P MM are 2× 2 , 2×N M , N M × 2 and N M ×N M real valued matrices • K Q 0 , K Q 1 are 2× 1 and 2× 2 real valued matrices • Σ isN M + 2×N M + 2, lower triangular, and Σ sc is the upper left 2× 2 submatrix of Σ. The model is a canonical form, that is, any affine model with two spanned state variables and N M ≥ 0 macroeconomic variables can be written in the form above. Extending the model to more than two spanned state variables is straightforward. 21 3.1 Stochastic Volatility The Gaussian assumption in the model is a strong one, because the volatility of commodity futures markets varies over time (Trolle and Schwartz (2009)). Stochastic volatility alters futures prices directly via the convexity term and could alter price forecasts or expected returns. If these effects are present, in general they will be reflected in the reduced-form (pricing)factorsbecausethemodelidentifiesthespannedstatevariablesdirectlyfromfutures prices in an agnostic way. Thus, any spanned effects of stochastic volatility are generally compatible with the model estimates and do not confound my findings. Unspanned stochastic volatility does not appear to drive the results in this paper. Chi- ang etal. (forthcoming) find that exposure to an oil volatility factor estimated from options on futures has a positive risk premium attached to it in the returns of equities, but not in oil futures or options. Consistent with their findings, Appendix F Table 13 shows the results of forecasting regressions that include two indexes of time-varying volatility, the first estimated from the time series and the second from options on futures. Both volatility factors are insignificant in the regressions and their inclusion does not alter the forecasting power of GRO. 4 Model Estimates This section presents the estimates of the macro-finance model with two spanned (“pricing”) factors and two macroeconomic factors: the monthly Chicago Fed National Activity Index (GRO) and log U.S. oil inventories (INV). Figure 3 Panel A plots the spanned and unspanned components of GRO as well as the log spot price. We see that essentially all of the monthly and yearly variation in GRO 22 1990 1995 2000 2005 2010 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 CFNAI index in % SGRO UGRO 1990 1995 2000 2005 2010 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 log U.S. Inventory in Barrels SINV UINV Figure 3: Panel A plots the components of the monthly Chicago Fed National Activity Index that are spanned (SGRO) and unspanned (UGRO) by oil futures prices, as well as the log spot price of oil s t . Panel B plots the components of monthly log U.S. oil inventories that are spanned (SINV ) and unspanned (UINV ) by oil futures prices. 23 appears in the unspanned component. Figure 3 Panel B plots the spanned and unspanned components of log oil inventories INV. Compared toGRO, much more of the monthly and yearly variation in INV is spanned by futures prices. The spanned component of inventory loads exclusively, and strongly, on the cost of carry. Table 2 presents the maximum likelihood estimate of the model using the monthly data from January 1986 to July 2013. 4.1 Model Fit The risk neutral parametersK Q 0 ,K Q 1 are estimated relatively precisely for two reasons. First, they use the entire futures curve data; on each date, the set of futures prices represents a “snapshot” of risk-neutral expectations. Second, a linear factor model holds closely in the futures curve: our two affine factors fit the futures curve closely, so the pricing errors relative to the fitted model are small and idiosyncratic. By contrast, the historical measure parameters K P 0 , K P 1 , Σ are estimated less precisely because their estimation uses only the time series of the state variables. Each month represents a single observation, and the R 2 of the best-fit forecast is low. Risk prices Λ =K P −K Q inherit the lower precision of K P 0 ,K P 1 . The values of both s t and c t are precisely estimated. Figure 4 plots the fitted values of s t and c t with 95% confidence intervals, which are too small to see. A flip side of this observation is thats t andc t as affine state variables do a good job of summarizing oil futures prices 3 . The principal components that we used in Section 2 do the best possible job by construction, and it is not guaranteed thats t andc t with their AR(1) structure will perform 3 This observation does not contradict the conclusions of Schwartz (1997) and Casassus and Collin- Dufresne (2005) that a three-factor model is necessary to summarize commodity futures prices. The three- factor models in those papers have two latent factors – spot price and convenience yield – and a spanned interest rate that is estimated separately. Interest rates are very slow moving compared to futures prices, so they contribute almost no extra explanatory power. 24 Table 2: Maximum likelihood (ML) estimate of the macro-finance model for Nymex crude oil futures. s, c are the spot price and annualized cost of carry respectively. GRO is the monthly Chicago Fed National Activity Index. INV is the log of the private U.S. crude oil inventory as reported by the EIA. The coefficients are over a monthly horizon, and the state variables are de-meaned. ML standard errors are in parentheses. Coefficients in bold are significant at the 5% level. Historical (P) Measure K P 0 K P 1 s t c t GRO t INV t s t+1 0.008 0.994 0.061 0.025 0.038 (0.006) (0.009) (0.033) (0.008) (0.082) c t+1 -0.007 0.016 0.874 -0.015 -0.045 (0.005) (0.008) (0.031) (0.008) (0.078) GRO t+1 0.001 -0.115 0.051 0.618 -0.194 (0.030) (0.046) (0.171) (0.043) (0.433) INV t+1 0.002 0.000 0.032 -0.002 0.888 (0.002) (0.002) (0.009) (0.002) (0.023) Risk Neutral (Q) Measure K Q 0 K Q 1 s t c t s t+1 -0.004 1.000 0.083 (0.008) (0.004) (0.011) c t+1 0.001 -0.004 0.892 (0.012) (0.010) (0.029) Shock Volatilities [off-diagonal = % correlations] s c GRO INV s 0.103 c -81% 0.057 GRO 5% -2% 0.530 INV -22% 27% 4% 0.028 25 1990 1995 2000 2005 2010 −1.5 −1 −0.5 0 0.5 1 1.5 Log Spot Price A) Log Spot Price st 95%CI s SCHWARTZ t 1990 1995 2000 2005 2010 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 Cost of Carry B) Annualized Cost of Carry ct 95%CI c SCHWARTZ t Figure 4: The figure plots the fitted values of the log spot price s t and the annualized cost of carryc t in Nymex oil futures from the canonical model, with 95% (±two standard errors) confidence intervals. The figure also plots the fitted values of s t and c t from the Schwartz (1997) two factor model for comparison. as well. I find that s t ,c t explain 99.97% of variation in futures prices and the residuals (pricing errors) explain 0.03% of the total variation. These observations hold for the canonical model with no auxiliary restrictions. But because they are a product of the strong factor structure in the data, they also hold for other models. Figure 4 also plots s t and c t implied by the two factor model of Schwartz (1997), which corresponds to our model with no macro factors and five auxiliary restrictions: • The rate of mean reversion ofc t underQ does not depend ons t i.e. the lower left entry of K Q 1 is zero • Risk premiums are non time varying i.e. K P 1 =K Q 1 . These restrictions change the estimated historical measure dynamics materially and the risk neutral dynamics slightly, but leave the fitted values of s t and c t virtually unchanged. 26 4.2 Historical Dynamics The models of Schwartz (1997) and Schwartz and Smith (2000) impose that s t is unit-root. Without that restriction and using data from 1990 to 2003, Casassus and Collin-Dufresne (2005) estimate thats t has a long run mean to which it reverts with a halflife of around two years, so the expected spot price of oil in ten years is essentially constant. Our unrestricted estimate which adds ten years of subsequent data is more consistent with Schwartz (1997). The AR(1) coefficient for s t of 0.994, which is close to the largest eigenvalue of K P 1 , is very close to unity. 4 Thecostofcarryrevertstoaslightlynegativemeanwithahalf-lifeoffivemonths. Shocks to the spot price and the cost of carry are strongly negatively correlated (ρ =−81%), so a higher spot price is accompanied by a more downward sloping curve, but spot price shocks are essentially permanent while the cost of carry shock decays within a few years. As a result, about half of a typical move in the oil spot price disappears after two to three years, while the other half is expected to persist effectively forever. 4.2.1 Oil Futures and Economic Activity Shocks to economic activity are almost uncorrelated with shocks to the spot price and the cost of carry. Looking down the third column of the transition matrix, a one percent shock to economic activity predicts a 2.5% higher spot oil price the next month but only a 1.5% lower cost of carry. Thus, the effects of economic activity on oil prices are forecast by the market to be persistent – higher activity raises both the short run and the expected long run price of oil. 4 The estimates all use nominal futures prices. Inflation was relatively constant over the period from 1986 to 2013, relative to the movement in oil prices, so it does not drive the high AR(1) coefficient of s t . Using futures prices deflated by the CPI or PPI does not materially change any of the results. 27 Looking across the third row of the transition matrix, a higher spot price of oil predicts lower economic activity. A higher cost of carry – higher expected prices in future – forecasts slightly higher economic activity, but the effect is not significant, and c t also forecasts a higher spot price. The impulse response functions in section 4.2.3 make clear that the net effect of c t on GRO is negative. As a result, a shock to the spot price that the market expects to persist has a more negative effect on growth than a shock that is expected to be transitory. These results are not driven by the big swings in 2008-2009: Appendix F shows the results are similar when I estimate on a subsample that ends in 2007. Taken together, there is a negative feedback relationship between the spot price of oil and growth. A positive growth shock forecasts persistent higher oil prices, while a positive oil price shock forecasts slower growth, and the effect is stronger for oil price shocks that the market expects to persist. 4.2.2 Oil Futures and Inventories Shocks to log inventories are negatively correlated with the spot price and positively corre- lated with the cost of carry. Both of these observations are consistent with the Theory of Storage – higher inventories signal that the market is moving up the supply-of-storage curve. The correlation between shocks to inventory and the cost of carry (27%) is relatively modest; in the frictionless storage model of Working (1949) and others, INV t and c t are collinear. Looking across the bottom row of the transition matrix, a higher cost of carry strongly pre- dicts higher inventories the next month. This relationship further suggests adjustment costs in physical storage: the futures curve adjusts to relevant information first and inventories respond with a lag. Looking down the last column of the transition matrix, unspanned crude oil inventory 28 does not forecast any of the other variables. In particular, periods of higher inventory do not have much effect on the forecast of either the spot price or the cost of carry. This finding is consistent with the fundamental drivers of oil inventory such as precautionary storage and expected physical supply and demand being fully spanned by oil futures prices. 4.2.3 Impulse Response Functions Figure 5 plots the impulse response functions (IRFs) to shocks to oil prices and economic ac- tivity. Theorderingofthevariablesfortheimpulseresponsefunctionsis (GRO, s t , c t , INV ). GRO is first because innovations in the unspanned component, which dominates the varia- tion inGRO, can be thought of as exogenous to contemporaneous oil prices and inventories. We analyze s t and c t simultaneously so their relative ordering is not important. Finally, it is intuitive and also supported by the estimates and regressions that the oil futures curve adjusts to new information faster than physical inventory does. Panel A plots the response to a unit shock to the log spot price, which is correlated with a negative shock to the cost of carry and a more downward-sloping curve. A unit shock to s t means a doubling of the spot price of oil. About half of the increase decays within two years, while the other half is effectively permanent, and forecasts an economic activity index that is 0.2% lower effectively forever. This effect is material: the index averaged -1.66% in 2009 during the depths of the financial crisis, while it averaged 0.02% in 2006. The higher spot price and lower cost of carry also produce a fall in inventories. PanelBplotstheresponsetoajointshocktos t andc t suchthatthespotpriceisexpected to fully revert to the pre-shock baseline. The response of economic activity is transient as well, and in fact GRO recovers to the baseline faster than s t does. Comparing to Panel A, which only differs in the size of the shock to c t , makes clear that the net effect of c t on 29 0 5 10 15 20 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 Horizon (months) Impulse Response Unit shock to s t GRO s t c t INV 0 5 10 15 20 −2 −1.5 −1 −0.5 0 0.5 1 1.5 Horizon (months) Impulse Response Transient shock to s t GRO s t c t INV 0 5 10 15 20 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 Horizon (months) Impulse Response Unit shock to GRO GRO s t c t INV Figure 5: Panel A shows the impulse response functions (IRFs) of the four state variables to a unit shock to the log spot price of oil s t . Panel B shows the IRFs for a transient shock for which the spot price of oil fully reverts to the baseline. Panel C shows the IRFs for a unit shock to economic growth, GRO. The order of the variables is (GRO,s t ,c t ,INV ). 30 expected growth is negative. Note that the fact that the forecast of the long-run spot price is unchanged in Panel B does not mean that long maturity futures prices will be unchanged – the two are equivalent only in the case that oil risk premiums are non time varying. Thus, a VAR that includes a long-maturity futures price or spread will not in general recover the correct dynamics of the state variables. Panel C plots the response to a shock to economic activity. The index mean reverts rapidly and the shock decays back to the baseline within a year. However, a transient shock to GRO produces a near permanently higher spot price of oil – perhaps because oil is a nonrenewable resource. The magnitude of the effect is large: a one-period shock to economic activity of one percent produces a spot price of oil that is 5.1% higher than the baseline, ten years later. 4.3 Risk Neutral Dynamics By definition, c t is the annualized forecast of the change in the spot price under the Q- measure. Thus, the top row of K Q 1 by definition equals [1, 1 12 ]. Any mean reversion of the spot price under the risk neutral measure is thus rotated into the bottom-left entry ofK Q 1 . In our estimate the entry is small (-0.004) and not statistically significant, so the risk neutral forecast of c t is almost uncorrelated with the level of s t . This implies that the shape of the futures curve does not vary with the price level, which corroborates our observation in Section 2 that the first two principal components explain the vast majority of the variation in log futures prices. The cost of carry mean-reverts under the risk neutral measure at a similar speed to that under the physical measure. 31 4.4 Risk Premiums Several recent studies (for example Erb and Harvey (2006); Etula (Forthcoming); Gorton, Hayashi and Rouwenhorst (2013); Yang (2013)) investigate the returns to commodity futures by sorting cross sections of individual near-maturity contracts on different commodities. Singleton (2013) and Hamilton and Wu (Forthcoming) run return forecasting regressions for individual futures maturities. The model in this paper contributes to this literature as well, as it offers a simple way to utilize the full futures curve data for each commodity. Szymanowska etal. (2013) decompose futures returns into two components. The spot premium corresponds to going long near-maturity futures, while the term premium corre- sponds togoinglong near-maturity futuresand shortdistant-maturity futures(a termspread position). Appendix A describes the correspondence of their decomposition to the risk pre- miums in my model. Their spot premium equals the risk premium attached to the spot price plus a small convexity term, while their term premium equals the risk premium attached to the cost of carry minus the conditional expected cost of carry. Table 3 displays the estimates of the parameters governing risk premiums. The uncon- ditional spot risk premium for oil is positive, while the unconditional cost of carry premium is negative. Only one entry in the time-varying loadings of risk premiums Λ 1 is statistically significant: higher economic activity is associated with a higher spot risk premium in oil. Similar results obtain using the monthly change in the Conference Board’s Leading Eco- nomic Index as an alternate proxy for growth, including longer maturity futures prices, or estimating on a subsample that stops in 2007 and omits the wide swings of 2008-9. The effect of economic activity on the spot risk premium in oil futures is material. Figure 6 plots the implied spot premiums for the macro-finance model and the two-factor nested 32 Table 3: Maximum Likelihood (ML) estimates of risk premiums in the macro-finance model for U.S. crude oil futures. s, c are the spot price and annualized cost of carry respectively. GRO andINV are the Chicago Fed National Activity Index and log U.S. crude oil inventory respectively. The coefficients are standardized to reflect a one standard deviation change in each variable over a monthly horizon, and the state variables are de-meaned. ML standard errors are in parentheses. Coefficients in bold are significant at the 5% level. " Λ s Λ c # t = Λ 0 + Λ 1 h s t c t M t i 0 Λ 0 Λ 1 s c GRO INV Λ s 0.012 -0.001 -0.001 0.013 0.001 (0.014) (0.002) (0.003) (0.004) (0.002) Λ c -0.010 0.003 -0.001 -0.008 -0.001 (0.017) (0.002) (0.004) (0.004) (0.002) 1990 1995 2000 2005 2010 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 Spot risk premium Unspanned Macro Model Spanned Risk Model 3 month realized returns Figure 6: The figure compares the model implied spot premium for the macro-finance model versus the two-factor model which enforces spanning. Also displayed is the average log return to all active oil futures over the subsequent three month horizon. NBER recessions are shaded in grey. 33 model that enforces spanning 5 , as well as the average realized returns for oil futures in the sample over the following three months. The model predictions differ most noticeably during 1990-1991, 2001-2002 and 2008-2009: slumps in real activity forecast lower oil prices. The risk premium for exposure to the spot price of oil is procyclical. The unspanned procyclical component dominates the variation in the model-implied spot risk premium; the standard deviation of changes in Λ s t in the unspanned macro model is 1.5% per month compared to 0.16% per month in the spanned-risk model, an increase in volatility of almost ten times. This forecast is attached to the unspanned component of real activity because it is not reflected in the futures curve at the time. Per the estimates in Table 2, a fall in GRO is weakly correlated with a rise, not a fall, in the cost of carry. In other words, in economic downturns the oil futures curve “fails” to forecast the subsequent fall in the spot price. This observation aligns with the findings of unspanned countercyclical risk premia in bonds by Ludvigson and Ng (2009), Duffee (2011) and Joslin, Priebsch and Singleton (2014), but in the opposite direction. 4.5 A Simple Model of Oil Risk Premia A potential explanation is as follows. Suppose a representative agent consumes oil and a general consumption good, with V t =E " ∞ X t=0 β t u(A t ) # u(A t ) = A 1−γ t 1−γ 5 That is, the unrestricted two factor model with UM t =∅. 34 A(C t ,O t ) = h C 1−ρ t +ωO 1−ρ t i 1 1−ρ I assume thatγ >ρ> 1, that is, the general consumption good and oil are complements, and investors’ risk aversion for total consumption is stronger than the elasticity between the two goods. Normalize the price of the consumption good to 1 and P o t the price of a barrel of oil. The intratemporal equilibrium is P o t =ω C t O t ρ and the stochastic discount factor is M t+1 =β C t+1 C t −γ " 1 +ωO 1−ρ t+1 /C 1−ρ t+1 1 +ωO 1−ρ t /C 1−ρ t # ρ−γ 1−ρ Log-linearizing: 6 m t ≈K− (γ−ω (γ−ρ)) Δc t+1 −ω (γ−ρ) Δo t+1 Thus the expected return of any asset in this economy is: E[r] =κ + (γ−ω (γ−ρ))cov(r, Δc t+1 ) +ω (γ−ρ)cov(r, Δo t+1 ) Thus assets pay a consumption risk premium for exposure to Δc t and an oil risk premium for exposure to Δo t . 6 This derivation follows, e.g., Yogo (2006) 35 For a one period oil future which pays p O t+1 , r FUT =κ o t +ρΔc t+1 −ρΔo t+1 cov(r, Δc) =ρ cov(r, Δo) =−ρ Hence,alongpositioninoilfuturespaysaconsumptionriskpremiumforitspositiveexposure to “demand shocks” and collects an oil hedge premium for its negative exposure to “supply shocks”. Nowsupposeriskaversionγ ishigherinbadtimes–thismeansthatboththeconsumption risk premium and the oil risk premium are countercyclical. The latter induces procyclical variation in expected futures returns, consistent with our empirical observations. There is an additional aspect in which the model is consistent with the data. Both regressions and model estimates indicate that innovations to real activity are unspanned by contemporaneous futures prices. The existence of state variables that are meaningful for bond risk premiums yet unspanned by bond prices is an active question in the term structure literature (Duffee (2011); Joslin, Priebsch and Singleton (2014)). In our setting, it corresponds to the state variable having offsetting effects on oil risk premiums and the oil price forecast. This is again consistent with oil futures as a hedge against oil supply shocks. A negative growth shock raises risk premiums including λ oil t , which raises futures prices ceteris paribus. At the same time, it forecasts reduced demand and a lower spot price of oil, which acts to lower futures prices. If these two effects are of comparable magnitude and expected duration then innovations in growth could be unspanned or – more likely – the net effect on the futures curve could be small enough that we do not detect it. 36 5 Further Applications 5.1 Other Macro Factors 5.1.1 Financialization A major debate in recent years is the consequences of increased participation in commodity futures markets by hedge funds, index funds and other purely financial participants, also known as ’financialization’. Hamilton and Wu (2014) analyze a spanned-risk model of oil futures risk premia and find evidence of a structural break in 2004, which they interpret as consistent with the claim that financialization caused a change in the behavior of oil futures markets. However, they do not formally test the hypothesis using a measure of financialization, and controlling for other things that may have differed pre and post 2004. Singleton (2013) finds that changes in imputed positions of commodity index funds forecast returns on individual oil futures; however, his individual regressions do not use the full information available in the panel of futures prices. InthissectionIevaluatetheeffectsoffinancializationonoilriskpremiausingexplicittime series data in the macro-finance framework. The proxy for financialization is the imputed positions of commodity index funds in oil futures, available from 1/2006 to 12/2011 7 . Figure 7 plots the time series of the financialization proxy FIN, the real activity index GRO and the model implied spot price of crude oils. There appear to be parallel movements in the time series of s t and FIN. However, the projection of FIN on the first two PCs of log futures prices has an R 2 of 0.31, so FIN is not well spanned contemporaneously by the futures curve. Table 4 shows the estimated coefficients of the time-varying risk premia Λ t and shock 7 Many thanks to James Hamilton for sharing his data and calculations. 37 2006 2007 2008 2009 2010 2011 2012 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 st FIN t GROt Figure 7: The figure plots the model implied spot price of oil along with the Hamilton-Wu- Masters measure of index fund positions and the real activity measure GRO, monthly from 1/2006 to 12/2012. matrix Σ. Shocks to fund positions FIN are positively correlated contemporaneously with the spot prices t and hence the overall futures price level. Consistent with Singleton (2013)’s forecasting regressions, shocks to index fund positionsFIN forecast higher returns to futures positions – equivalently, a higher spot price that was not forecast by the contemporaneous futures curve. The coefficient of GRO for the forecast of s t is imprecisely measured due to the huge volatility in GRO during this subperiod, but the point estimate is positive and GRO does not extinguish the strong coefficient on FIN. Thus, it appears that index fund positions in crude oil futures did raise crude oil risk premia – equivalently, forecast higher spot prices in a way that was not reflected in the contemporaneous futures curve. Although shocks to fund positions were correlated with higher levels of oil prices, the pattern in returns corresponds to futures prices that were too low conditional on the con- temporaneous index fund position. Singleton (2013) suggests this wrong-way finding is due to an “expectations effect” where index fund flows drove expectations in the market which 38 Table 4: Estimates of risk premiums and shock volatilities in the macro-finance model in which s, c are the spot price and annualized cost of carry in oil futures and GRO and FIN are the Chicago Fed National Activity Index, and the log imputed positions of index funds in oil futures, respectively. The data are from 1/2006 to 12/2011. The coefficients are standardized to reflect a one standard deviation change in each variable over a monthly horizon, and the state variables are de-meaned. ML standard errors are in parentheses. Coefficients in bold are significant at the 5% level. " Λ s Λ c # t = Λ 0 + Λ 1 h s t c t M t i 0 Λ 0 Λ 1 s c FIN GRO Λ s 0.047 -0.082 -0.021 0.020 0.004 (0.049) (0.022) (0.008) (0.007) (0.007) Λ c -0.014 0.019 0.000 -0.006 -0.006 (0.028) (0.011) (0.004) (0.003) (0.003) Shock Volatilities [off-diagonal = % correlations] s c FIN GRO s 0.212 c -96% 0.033 FIN 14% -14% 0.088 GRO 0% 0% 10% 0.472 39 are not fully rational. The estimated effect is economically meaningful: an 8.8% (one stan- dard deviation) increase in index fund positions forecasts a 2% higher return to oil futures over the following month. Due to the huge volatility of oil prices over the period, however, this corresponds to a puny conditional Sharpe ratio. 5.1.2 Rig Activity Since 1975 the firm Baker-Hughes has published weekly counts of the number of rotary rigs, the main extraction technology, that are in operation worldwide. This is a useful index of the short-run supply of crude oil, as distinct from the inventory in storage. For each monthly observation from 1986-2013 I take the log of the most recent weekly rig count and denote the time series RIG. Projecting RIG on the first two PCs of log oil futures prices, the R 2 is 75.8% so the majority of variation in the rig count is spanned by oil futures prices, in particular the level factor. Table 5 presents theP-dynamics of the macro-finance model using the two time series RIG and INV as macro factors. Note that although the coefficient of s t+1 on s t is greater than one, the eigenvalues ofK P 1 are all within the unit circle, so the estimated dynamics are stationary. Although shocks to the rig count and the oil market factors s t , c t are effectively uncor- related they also show evidence of a strong feedback relationship. A shock to the spot price forecasts a higher rig count and a shock to the rig count forecasts a lower spot prices t : both of these relationships are intuitive. However, the fact that the ability of RIG to forecast higher oil prices comes from its unspanned component is notable. While the rig count re- sponds strongly to a higher spot price, it responds much less, indeed slightly negatively to a higher cost of carry and thus an upward-sloping futures curve. To my knowledge this is a 40 Table 5: Maximum likelihood (ML) estimate of the macro-finance model for Nymex crude oil futures. s, c are the spot price and annualized cost of carry respectively. RIG is the log number of rotary oil rigs operating worldwide; INV is the log U.S. inventory of crude oil storage excluding the SPR. The coefficients are over a monthly horizon, and the state variables are de-meaned. ML standard errors are in parentheses. Coefficients in bold are significant at the 5% level. Historical (P) Measure K P 0 K P 1 s t c t RIG t GRO t s t+1 0.009 1.030 0.109 -0.108 0.027 (0.006) (0.015) (0.035) (0.039) (0.008) c t+1 -0.007 -0.004 0.865 0.048 -0.014 (0.004) (0.011) (0.026) (0.028) (0.006) RIG t+1 -0.003 0.057 -0.023 0.870 0.015 (0.003) (0.007) (0.017) (0.018) (0.004) GRO t+1 -0.001 -0.076 0.001 -0.115 0.618 (0.031) (0.082) (0.196) (0.213) (0.043) Shock Volatilities [off-diagonal = % correlations] s c RIG GRO s 0.108 c -86% 0.043 RIG -5% 0% 0.045 GRO 5% -3% 5% 0.529 novel observation and suggests that the opening and closing of oil rigs (short-term supply) is driven by short-horizon concerns. At the same time, we observe that storageINV is forecast to be higher when the spot price is lower, when the cost of carry is higher, and when the oil supply (rig count) is higher, which are all intuitive relationships. 41 5.1.3 Subcomponents of GRO The Chicago Fed National Activity Index (GRO) is the first principal component of 85 indicators of real economic activity (Stock and Watson (1999)). The Chicago Fed groups the indicators into four subcomponents of the index: Production & Income, Employment Unemployment & Hours, Personal Consumption & Housing, and Sales Orders & Inventories. The strongest interactions of the oil spanned factors with the four subcomponents are with Product & Income (PI) and Personal Consumption & Housing (PCH). Notably, their interactions with oil markets are quite distinct. Table 6 presents the model estimate using those two subcomponents as the macro factors. PI, which contains manufacturing, construc- tion and industrial production, is contemporaneously correlated with a higher spot price and a more downward-sloping curve and higher PI forecasts a higher spot price of oil. However, shocks to oil prices do not significantly forecast PI. PCH contains housing starts, personal consumption and retail sales. Shocks to PCH are uncorrelated with contemporaneous move- ments in oil prices (though positively correlated with PI) and do not forecast oil prices. However, higher oil prices forecast lower PCH. Thus, the subcomponents suggest that the feedback effect between GRO and oil futures is in fact the result of two separate channels. In the first channel shocks to industrial activity, whether due to real business cycles or anticipated consumption or waves of sentiment, are correlated with higher oil prices and also forecast higher oil prices. In the second channel shocks to the oil price, whether due to supply news or political developments or financial speculation, forecast lower consumer spending. 42 Table 6: Maximum likelihood (ML) estimate of the macro-finance model for Nymex crude oil futures. s, c are the spot price and annualized cost of carry respectively. PI is the monthly Chicago Fed National Activity Index’s subcomponent “Production & Income”. PCH is the monthly CFNAI’s subcomponent of “Personal Consumption & Housing”. The coefficients are over a monthly horizon, and the state variables are de-meaned. ML standard errors are in parentheses. Coefficients in bold are significant at the 5% level. Historical (P) Measure K P 0 K P 1 s t c t PI t PCH t s t+1 0.009 0.993 0.069 0.049 0.017 (0.006) (0.010) (0.029) (0.018) (0.040) c t+1 -0.008 0.017 0.863 -0.030 -0.016 (0.005) (0.009) (0.028) (0.017) (0.038) PI t+1 0.003 -0.017 0.082 0.286 0.195 (0.017) (0.029) (0.086) (0.053) (0.119) PCH t+1 -0.001 -0.014 -0.016 -0.015 0.910 (0.003) (0.006) (0.017) (0.011) (0.024) Shock Volatilities [off-diagonal = % correlations] s c PI PCH s 0.103 c -81% 0.057 PI 14% -10% 0.295 PCH 4% -2% 24% 0.057 43 5.1.4 Positive vs Negative Growth Regimes The effects of economic activity on the spot risk premium in oil appear to be concentrated in economic downturns. To investigate this possibility I split GRO into two components: GRO + equals GRO in months when its value is positive and zero otherwise, while GRO − equals GRO in months when its value is negative, and zero otherwise. This split lets the coefficients of risk premiumsGRO differ when the world is in a positive-growth regime versus a negative-growth regime. Table (7) presents the estimated risk prices when GRO is split in this way. The size of the coefficients on GRO + and GRO − are not directly comparable to the previous table because all of the coefficients are standardized to reflect a one standard deviation change, and GRO + and GRO − naturally have lower standard deviations than GRO. The message of the table is that the response of the spot risk premium to growth shocks is symmetric on the upside and the downside: the coefficient on GRO − is 0.008 per month compared to 0.007 per month for GRO + . Contrary to our impression from Figure 6, the effect of growth on the oil price forecast is relatively symmetric in good times versus bad. 5.2 Other Commodities Oil is the single most important commodity to any modern economy as reflected in its trading volume, media coverage and academic and industry attention. The ’macro-finance’ framework in this paper can be applied to any commodity and any set of macro factors. In this section I illustrate the application to another futures market, copper. Copper is a key industrial input and copper futures are perceived to be a forward-looking indicator of industrial growth: commentators refer to the market as “Doctor Copper” for 44 Table 7: Estimates of risk premiums in the macro-finance model in which s, c are the spot price and annualized cost of carry in oil futures and GRO + and GRO − are the monthly Chicago Fed National Activity Index in months when the index is positive and negative respectively. The coefficients are standardized to reflect a one standard deviation change in each variable over a monthly horizon, and the state variables are de-meaned. ML standard errors are in parentheses. Coefficients in bold are significant at the 5% level. " Λ s Λ c # t = Λ 0 + Λ 1 h s t c t M t i 0 Λ 0 Λ 1 s c GRO + GRO − Λ s 0.013 -0.001 -0.001 0.007 0.008 (0.017) (0.002) (0.002) (0.006) (0.004) Λ c -0.011 0.003 -0.002 -0.003 -0.005 (0.020) (0.002) (0.004) (0.006) (0.004) its ability to “...diagnose the health of the global economy”. 8 To investigate the interaction of copper futures with the economy, I estimate the model using copper futures prices with maturities from one to twenty-four months from January 1998 to July 2013. As macro factorsIuseU.S.monthlyrealactivityGRO andmonthlyAmericancopperstocksindelivery warehouses, INV C . The dynamics of the spot price for copper is similar to that of crude oil, but for copper the cost of carry varies less and is much more persistent than it is for oil. Moreover, the data do not support the popular view that copper prices are tightly tied to the economy – at least to U.S. real activity. Shocks to GRO and the priced factors s, c for copper futures are effectively uncorrelated. Moreover, GRO has no power to forecast s or c or vice versa. The relationship of futures with copper inventories is strong, however. Contemporaneously higher inventories are negatively correlated with the spot price and positively correlated with the cost of carry, and a higher cost of carry strongly forecasts higher inventories the next 8 http://www.cnbc.com/id/101800965# 45 Table 8: Maximum likelihood (ML) estimate of the macro-finance model for Comex copper futures. s,c are the spot price and annualized cost of carry respectively. GRO is the monthly Chicago Fed National Activity Index. INV C is the log of the U.S. warehouse inventory of copper as reported by the LME. The coefficients are over a monthly horizon, and the state variables are de-meaned. ML standard errors are in parentheses. Coefficients in bold are significant at the 5% level. Historical (P) Measure K P 0 K P 1 s t c t GRO t INV C t s t+1 0.005 0.991 -0.104 0.008 0.001 (0.007) (0.010) (0.109) (0.009) (0.005) c t+1 0.000 0.001 0.984 -0.003 -0.002 (0.002) (0.003) (0.028) (0.002) (0.001) GRO t+1 -0.031 -0.013 -1.065 0.751 0.032 (0.036) (0.052) (0.578) (0.048) (0.025) INV C t+1 0.094 -0.087 3.379 -0.035 0.839 (0.046) (0.066) (0.728) (0.061) (0.032) Risk Neutral (Q) Measure K Q 0 K Q 1 s t c t s t+1 -0.002 1.000 0.083 (0.005) (0.001) (0.010) c t+1 -0.001 -0.002 0.965 (0.002) (0.001) (0.013) Shock Volatilities [off-diagonal = % correlations] s c GRO INV C s 0.084 c -48% 0.020 GRO 3% 0% 0.445 INV C -9% 11% 0% 0.557 46 month. Indeed, the coefficient is larger than unity – a 10% higher cost of carry forecasts a 34% higher inventory level next month. 6 The Cost of Carry 6.1 Comparison with the Basis The model estimates say that s t and c t are precisely pinned down by the data. Empirical studies usually proxy for these quantities with futures prices and spreads. Fama and French (1987); Gorton, Hayashi and Rouwenhorst (2013); Singleton (2013) and others use some version of the log spread or “basis”, f 2 t −f 1 t , as a proxy for the cost of carry. 9 By definition, c t equals the difference between the model implied values of f 1 t and s t . The model fits an AR(1) process to (s t ,c t ) using the full futures curve at each date. The basis does not model the behavior or number of state variables but instead assumes that the errors on f 1 t and f 2 t are zero and that f 2 t −f 1 t is closely correlated with c t . The normalization and estimation in this paper, based on the recent advances of Joslin, Singleton and Zhu (2011) in term structure modelling, are exceedingly stable and tractable: estimates converge in a few seconds. Thus it is practical to use the model estimated c t instead of the basis. There are several reasons why fitting the model could yield more accurate estimates of the cost of carry. First, producers and consumers plan and hedge their activities more than two months in advance, in which case longer dated futures prices will contain relevant information. Second, market microstructure issues like congestion at delivery points or financial order flows could add noise to individual prices. Third, because 9 Fama and French (1987) and others subtract a short term Treasury bill rate from the spread. The short rate is slow moving relative to the spread, and defining the basis as f 2 t −f 1 t −r f t gives the same results. 47 the cost of carry is mean reverting, when the futures curve slopes in either direction f 2 t −f 1 t is biased toward the mean as a proxy for f 1 t −s t . Figure 8 Panel A plots the model implied log spot prices t against the one month futures log pricef 1 t in the sample. The two are almost collinear with a correlation in levels (monthly changes) of 0.999 (0.995). Thus, the one month futures prices is a close proxy for the spot price although they occasionally differ by as much as 5%. Figure 8 Panel B plots the model implied cost of carry c t against the annualized basis. The two series have similar unconditional averages but their correlation in levels (monthly changes) is 0.79 (0.60) and their values differ significantly throughout the sample. In partic- ular, c t is much more slow moving. Monthly innovations in c t have a standard deviation of 10.0% compared to 16.9% for the basis. The AR(1) coefficient of c t+1 on c t is 0.88 (half-life of 5.5 months) compared to 0.74 (half-life of 2.3 months) for the basis, and the differences in variances and AR(1) coefficients are significant at the 1% and 5% level respectively. Thus,c t implies that the net convenience yield for oil varies less and returns to its mean more slowly than the basis implies. Whetherc t orthebasisisabettermeasureofthecostofcarryisansweredbylinkingthem with the inventory data. In models of storage without adjustment costs, the cost of carry and the quantity stored are perfectly correlated. c t is modestly more correlated with contempo- raneous inventories INV t than the basis is: corr(c t , INV t ) is 0.52 while corr(basis t , INV t ) is 0.42, and the difference in correlations is significant at the 10% level. Table 9 Panel A presents a horse race regressing the change in inventories on c t , the basis, and the current inventory level. We see that c t is a stronger predictor of future inventories, and in the joint regressionc t drives out the basis entirely. Thus,c t is more tightly linked to both present and future storage decisions than the basis is. Similar results obtain if I winsorize the basis at 48 1990 1995 2000 2005 2010 −1.5 −1 −0.5 0 0.5 1 1.5 Log price Implied spot price st f 1 t 1990 1995 2000 2005 2010 −1 −0.5 0 0.5 1 1.5 Instantaneous cost of carry Implied cost of carry ct Basis Figure 8: Panel A plots the model implied log spot price of oil s t and the one-month log futures price f 1 t . Panel B plots the model implied cost of carry c t and the annualized basis 12× (f 2 t −f 1 t ). 49 Table 9: Comparison between the model implied cost of carryc t and the basis 12× (f 2 t −f 1 t ) as predictors of log U.S. inventories of crude oil INV. The standard errors are Newey-West with six lags. ∗ :p< 0.10, ∗∗ :p< 0.05, ∗∗∗ :p< 0.01. Panel A: Cost of Carry from WTI Futures, 1/1986-7/2013 ΔINV t+1 c t 0.031 ∗∗∗ 0.038 ∗∗∗ (0.008) (0.010) basis t 0.016 ∗ -0.009 (0.009) (0.012) INV t −0.112 ∗∗∗ −0.088 ∗∗∗ −0.112 ∗∗∗ (0.022) (0.023) (0.022) adj.R 2 6.4% 3.9% 6.2% T 330 330 330 Panel B: Cost of Carry from Brent Futures, 1/1990-7/2013 ΔINV t+1 c BRENT t 0.039 ∗∗∗ -0.027 0.035 ∗∗ (0.011) (0.037) (0.015) c t 0.062 ∗∗ (0.030) basis t 0.004 (0.013) INV t −0.105 ∗∗∗ −0.127 ∗∗∗ −0.107 ∗∗∗ (0.026) (0.023) (0.028) adj.R 2 6.3% 7.4% 6.0% T 281 281 281 50 the 1% or 5% level in both tails, indicating that the stronger performance of c t is not driven by a few extreme observations in the basis. To further investigate the validity of the model implied cost of carry, I estimate the model using the prices of Brent crude oil futures from one to twelve months maturity, from January 1990 to July 2013. The WTI contract delivers oil in Cushing, Oklahoma, while the Brent contract delivers oil on shipboard in the North Sea approximately 4,500 miles away. The two markets are naturally linked, but can diverge materially. The correlation of the WTI basis with the Brent basis is 77.8%, while the correlation of c t withc BRENT t is 95.2%. Thus, there is considerable market-specific variation in the basis, while the slopes of the futures curves are more closely linked. The question is whether the market-specific variation in the basis is economically meaningful in relation to storage. Table (9) Panel B, Column 1 shows that c BRENT t is a strong predictor of future U.S. inventories. Column 2 shows that c BRENT t is driven out entirely by c t computed from U.S. oil futures, so some variation between the markets is relevant to storage. But Column 3 shows that c BRENT t completely drives out the U.S. futures basis as a predictor of U.S. inventories. These results suggest, first, that the model’s estimation of c t picks up as much or more of the market-specific variation in the cost of carry than the basis does, and second, that the additional market-specific variation in the basis is not related to storage. 6.2 Variation in c t From 1986 to 2013, the cost of carry in oil futures was negative 56% of the time – oil futures for later delivery had lower prices. From 1998 to 2013, the cost of carry in copper futures was negative 33% of the time. This ’backwardation’ is a puzzle, because it means marginal storage at a loss. The standard explanation is convenience yield (Kaldor (1939); Working 51 (1949), a nonmonetary benefit of holding physical inventory. It is usually motivated via the risk of a stockout (Deaton and Laroque (1996); Bobenrieth etal. (2002)) – firms suffer a deadweight loss if demand increases and they have insufficient inventory. This motivation is hard to square with the inventory data – U.S. oil inventories over those 28 years do not change much month to month and have never fallen below 60% of their maximum. It is also hard to believe that the risk of a stockout varies so much month to month as to produce such monthly volatility in the convenience yield. An alternative theory (Benirschka and Binkley (1995); Brennan, Williams and Wright (1997)) is that the illusion of convenience yield results from physical adjustment costs. A simple version is as follows. We are in a risk neutral world with two periods and three locations: A, a futures delivery point and shipping hub, B an inland hub, and overseas markets. Both domestic locations have perfectly elastic storage at unit cost c > 0. The overseas demand, which is perfectly inelastic, rises in period 0 and raises the spot price at A until all the inventories there are depleted (with no ’convenience’ loss to storage firm A). Moving oil from B to A costs a 0 at time 0 and a 1 at time 1, and the long run elasticity of transport is higher a 0 > a 1 . Thus, in period 0, inventory at B is moved to A and then shipped overseas until equilibrium is reached: s B 0 =s A 0 −a 0 E[s B 1 ] =s B 0 −c E[s A 1 ] =E[s B 1 ] +a 1 Substituting we arrive atf 0 =f 1 +c− (a 0 −a 1 ). Ifa 0 −a 1 >c then the futures curve slopes down, yet the total inventory in the system is still positive. 52 Both the stockout-risk and adjustment-cost hypotheses imply that higher demand or lower supply should result in higher prices, lower inventories and a higher convenience yield (lower cost of carry c t ). A further implication of the stockout hypothesis is that the cost of carry should vary positively with volatility. In times of greater volatility, the risk of a spike in demand causing a stockout is higher and prompts a higher convenience yield and greater precautionary storing. In the adjustment-costs model, volatility does not directly affect the cost of carry. To the extent that higher uncertainty raises physical adjustment costs, it should increase the variability of c t , but there is no clear prediction of its effect on the level of c t . Figure 9 is a scatterplot of each month’s estimated cost of carry c t versus the implied volatility from options on oil futures (panel A) and copper future (panel B). There is no clear relation, and indeed the point estimate is that higher volatility is accompanied by a higher cost of carry. The coefficient of the best-fit line is 0.042 (t-statistic = 0.6) for crude oil and 0.021 (t-statistic = 0.2) for copper. The results are the same when I winsorize the option volatilities, that is, the positive coefficient is not driven by the outlying observations in the upper right corner. Thus, in this respect, the data are inconsistent with the stockout-risk model. 7 Real Options Firms’ capacity to adjust investment or production ex post – their real options – make up a substantial part of firm value, and evaluating and managing these adjustments is a primary role of firm management (Pindyck (1988); Berk, Green and Naik (2004)). Previous studies (Brennan and Schwartz (1985); Schwartz (1997); Casassus and Collin-Dufresne (2005)) have 53 0.5 1 1.5 2 2.5 3 3.5 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 Option Implied Volatility Model Implied c t Panel A: Crude Oil Cost of Carry vs Option Volatility Best−fit 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 −0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 Option Implied Volatility Model Implied c t Panel B: Copper Basis vs Option Volatility Best−fit Figure 9: Panel A plots the monthly cost of carry of crude oil against the one-month implied volatility from options on crude oil futures for 1/1986 - 7/2013. Panel B plots the monthly cost of carry of copper against the one-month implied volatility from options on copper futures for 9/2003 - 7/2013. explored what commodity derivatives can tell us about the valuation of real options. These previous studies make the strong assumption that the economy is spanned by commodity futures. One exception is Trolle and Schwartz (2009), in which a latent stochastic volatility factor is unspanned by futures but identified in options prices. By contrast, if a factor M t is unspanned in the sense of this paper then it cannot be identified from commodity futures or options data. Unspanned factors of this type are still relevant to real options, however, when the option payoff depends on M t . For example, an oil well is often presented as the right to pump oil out of the ground at a fixed cost per barrel, analogous to a purely financial option. But for a real oil well, the costs of extraction are uncertain. Moel and Tufano (2002) find that for gold mines, changes in extraction costs over time are a significant predictor of mine openings and closings after controlling for the spot price, convenience yield and price volatility of gold. 54 More generally, commodity prices are only one element of a firm’s decision process. For example, in an airline’s decision to purchase more fuel efficient planes, the cost savings will vary with oil prices while revenues will vary with aggregate economic activity. Pindyck (1993) makes this argument and points out that the risk premiums of all risk factors will also affect real option valuation 10 . To illustrate the effects of unspanned macroeconomic risks on real options valuation, I model an oil well as a ten year strip of European options on an oil field that produces 1000 barrels of oil per month when open. The oil is extracted at lifting cost l t and sold at the spot price s t each month that it is open. Thus, it is open whenever s t > l t . In the model that is used to generate the data, the log lifting cost l t has both spanned and unspanned components plus idiosyncratic noise. The dynamics of the state variables (s,c,GRO) are a simplified version of the estimates presented earlier. Appendix E describes the setting in detail. I assume that the unspanned macro variable GRO carries a non time varying risk premium λ. Figure 10 plots the value of wells with different current lifting costs L 0 using different models. The lower two lines represent option values for spanned-risk models in which all relevant risks are assumed to be spanned by oil futures. This means l t must be a linear combination of s t and c t plus an error term (Joslin, Le and Singleton (2013)). Whether the error term is modelled as an i.i.d. or AR(1) process is essentially irrelevant to option value. The upper two lines represent option values for unspanned-risk models. We see that the spanned-risk models miss a large component of option value due to the contribution of unspanned macro risk. To emphasize, the monthly volatility of shocks to l t in the spanned- 10 “... this effect [of uncertainty on option value and exercise] is magnified when fluctuations in construction costs are correlated with the economy, or, in the context of the Capital Asset Pricing Model, when the ‘beta’ of cost is high... [A] higher beta raises the discount rate applied to expected future costs, which raises the value of the investment opportunity as well as the benefit from waiting rather than investing now.” 55 20 40 60 80 100 120 140 0 2 4 6 8 10 12 Current Lifting Cost $/bbl Real Option Value ($M) M t Spanned, iid Errors M t Spanned, AR(1) Errors M t Unspanned, Unpriced M t Unspanned, Risk Premium>0 Figure 10: Examples of real options valuation with unspanned risks. An oil well is modelled as a strip of European options that are exercised when the stochastic log extraction costl t is less than the log spot prices t . l t covaries withs t and the unspanned macro riskGRO t . The current spot price of oil is $80, and the x-axis indexes the current lifting cost L 0 of different oil wells. 56 risk models is the same as it is in the unspanned-risk models. The difference is that l t ’s dependence on GRO adds persistent time variation in lifting costs that can interact with the spot price and cost of carry (recall the impulse response functions presented in Section 4.2.3). This addition has a large effect on option valuation: Adding the unpriced (λ = 0) unspanned macro risk raises the real option value by 35% for an ’in the money’ well with current lifting cost = $20 per barrel and 405% for an ’out of the money’ well with current lifting cost of $150 per barrel. The risk premium (Pindyck) effect is that the option value is higher when GRO, and hence L t , carries a positive risk premium (λ > 0). This effect on valuation is present but minor in the example, increasing the well’s value by only 0.99% for the ’in the money’ well with L 0 = 20 and by 1.27% for the ’out of the money’ well with L 0 = 150. 8 Conclusion Thispaperdevelopsanaffinemacro-financemodelforfuturesthatadmitsunspannedmacroe- conomic variables. The model includes many existing commodity futures models as spe- cial cases, and represents a middle ground between studies that use vector autoregressions (VARs) on the one hand and affine latent-factor models on the other. The model can be applied to any commodity and any set of macro factors. I apply it to crude oil futures prices and investigate their interaction with economic growth and oil inventories. I find novel evi- dence that higher real activity forecasts higher oil prices and that this forecast is unspanned in contemporaneous futures prices. At the same time, higher oil prices forecast lower real activity, especially when the price increase is forecast by the market to be persistent. Thus, there is a negative feedback relationship between oil prices and the economy. The implied 57 spot risk premium in the model estimate differs, particularly in recessions, from the spot risk premium in a model that omits growth as an unspanned risk factor. These results high- light the importance of using information beyond that contained in the futures curve when studying futures returns and price forecasts. The model also has applications to real options valuation. By assumption, the unspanned macro factors do not affect the prices of commodity futures or any other financial derivatives. However, when the payoff of a real option such as an oil well depends on macroeconomic factors beyond the oil price, then those factors can have a large effect on option value and exercise. In a calibrated example I show that both the dynamics and the risk premiums of unspanned macro risks have large effects on real options valuation. The model estimates imply that the spot price and cost of carry in the oil market are precisely pinned down by futures prices. The model cost of carry differs significantly from the basis, which is commonly used as a proxy for the cost of carry. In particular, the model cost of carry is 40% less volatile month-to-month, and reverts to its mean more than twice as slowly as the basis does. The model cost of carry is more strongly related to both current and future oil inventories than the basis, and the cost of carry based on North Sea futures is more strongly related to U.S. inventories than the U.S. basis. 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Yogo, M., ‘A consumption-based explanation of expected stock returns’, Journal of Finance, 61 (2006):2, p.539–580. 68 A Model Specification and Risk Premiums Consider a Gaussian model where the log spot price s t of a commodity is a function of N L spanned state variables L t , which may be latent or observed, and N M unspanned state variables M t that are observed:     L t+1 M t+1     = K P 0X +K P 1X X t + Σ X P t+1 L t+1 = K Q 0L +K Q 1L L t + Σ L Q t+1 s t = δ 0 +δ 0 1 L t (7) where • P denotes dynamics under the historical or data generating measure • Q denotes dynamics under the risk neutral measure • Q L,t+1 ∼N(0, I N L ), P t+1 ∼N(0, I N ) • Σ L is the top left N L ×N L block of Σ X ; Σ L , Σ X are lower triangular The model is written in discrete time but all results follow in continuous time as well. (7) is equivalent to specifying the equation for s t and the P-dynamics plus a lognormal affine discount factor with ’essentially affine’ prices of risk as in Duffee (2002). For N M = 0 the model includes existing models such as Gibson and Schwartz (1990); Schwartz (1997); Schwartz and Smith (2000) as special cases (see Appendix D). Standard recursions show that (7) implies affine log prices for futures, f t =A +BX t (8) 69 f t = f 1 t f 2 t ... f J t 0 where f j t is the price of a j period future and J is the number of futures with different maturities. Estimating the model as written presents difficulties; with two latent factors and two macro factors there are 40 free parameters. Different sets of parameter values are observa- tionally equivalent due to rotational indeterminacy of the latent factors. Discussing models of the form (7) for bond yields, Hamilton and Wu (2012) refer to “tremendous numerical challenges in estimating the necessary parameters from the data due to highly nonlinear and badly behaved likelihood surfaces.” In general, affine models for futures identify the model by specifying dynamics that are less general than (7) and risk prices that are zero or non time varying. Joslin, Priebsch and Singleton (2014) note that if N L linear combinations of bond yields are measured without error, then any model of yields of the form (7) implies a model with observable factors in place of the latent factors. They construct a minimal parametrization where no sets of parameters are redundant - models in the “JPS form” are unique. Thus the likelihood surface is well behaved and contains a single global maximum. Their results hold to a very close approximation if the linear combinations of yields are observed with relatively small and idiosyncratic errors. Section B demonstrates the same result for futures pricing: if N L linear combinations of log futures prices are measured without error, P t =Wf t (9) 70 for any full rank N L × J matrix W, then any model of the form (7) is observationally equivalent to a unique model of the form     ΔP t+1 ΔUM t+1     = ΔZ t+1 = K P 0 +K P 1 Z t + Σ Z P t+1 ΔP t+1 = K Q 0 +K Q 1 P t + Σ P Q t+1 s t = ρ 0 +ρ 1 P t (10) parametrized by θ = (λ Q , p ∞ , Σ Z , K P 0 , K P 1 ), where • λ Q are the N L ordered eigenvalues of K Q 1 • p ∞ is a scalar intercept • Σ Z is the lower triangular Cholesky decomposition of the covariance matrix of innova- tions in the state variables • Σ P Σ 0 P = [Σ Z Σ 0 Z ] N L , the top left N L ×N L block of Σ Z Σ 0 Z A.1 P t Measured Without Error In this paper I assume that while each of the log futures maturities is observed with iid measurement error, the pricing factorsP 1 t andP 2 t are measured without error. f j t =A j +B j P t +ν j t , ν j t ∼N(0,ζ 2 j ) The use of the first two PCs of log price levels is not important: in unreported results I find that all estimates and results are effectively identical using other alternatives such as the 71 first two PCs of log price changes or of returns, or a priori weights such as W =     1 ... 1 0 ... 12     The identifying assumption that N L linear combinations of yields are measured without error is common in the bond yields literature beginning with Chen and Scott (1993). Given themodelparameters, valuesofthelatentfactorsateachdatearethenextractedbyinverting the relation (8). The same assumption is used to identify previous latent factor models for commodity futures (see Gibson and Schwartz (1990); Casassus and Collin-Dufresne (2005); Hamilton and Wu (2014)). In unreported results I find that all estimates and results are effectively identical if the pricing factors are estimated via the Kalman filter. A.2 Rotating to s t and c t Once the model is estimated in the JPS form, I rotate (P 1 t ,P 2 t ) to be the model implied log spot price and instantaneous cost of carry, (s t , c t ). For s t this is immediate: s t =ρ 0 +ρ 1 P t Forc t the definition is as follows. Any agent with access to a storage technology can buy the spot commodity, sell a one month future, store for one month and make delivery. Add up all the costs and benefits of doing so (including interest, costs of storage, and convenience yield) and express them as quantity c t where the total cost in dollar terms = S t (e ct − 1). 72 Then in the absence of arbitrage it must be the case that F 1 t =S t e ct f 1 t =s t +c t =E Q [s t+1 ] + 1 2 σ 2 s c t =E Q [Δs t+1 ] + 1 2 σ 2 s =ρ 1 [K Q 0 +K Q 1 P t ] + 1 2 σ 2 s A.3 Risk premiums and s t , c t : Szymanowska etal. (2013) define the per-period log basis y n t ≡f n t −s t , and define two risk premiums based on different futures trading strategies; the spot premium π s,t and the term premium π n y,t . The spot premium is defined as π s,t ≡E t [s t+1 −s t ]−y 1 t =E t [s t+1 ]−f 1 t =E P t [s t+1 ]−E Q t [s t+1 ]− 1 2 σ 2 s ⇒π s,t = Λ st − 1 2 σ 2 s The term premium is defined as π n y,t ≡y 1 t + (n− 1)E t h y n−1 t+1 i −ny n t =f 1 t + (n− 1)E t h f n−1 t+1 i −nf n t 73 The one month term premium is always zero, because storing for one month is riskless. π (1) y,t =f 1 t + 0−f 1 t = 0 π (2) y,t =c t +E P t [c t+1 ]− 2E Q t [s t+2 −s t+1 +s t+1 −s t ] =E P t [c t+1 ]−E Q t [c t+1 ]−E Q t [s t+2 −s t+1 ]−c t ⇒π (2) y,t = Λ ct − c t +E Q t [c t+1 ] Thus the spot premium and term premium of Szymanowska etal. (2013) each have a natural expression in our affine framework. The spot premium is exactly the risk premium attached to shocks to the log spot price s t plus a small constant. The term premium is the risk premium attached to shocks to the cost of carry minus the (risk-neutral) total expected cost of carry. 74 B JPS Parametrization I assume that N L linear combinations of log futures prices are measured without error, P L t =Wf t for any full-rank real valued N L ×J matrix W, and show that any model of the form     ΔL t+1 ΔM t+1     = ΔX t+1 = K P 0X +K P 1X X t + Σ X P t+1 ΔL t+1 = K Q 0L +K Q 1L X t + Σ L Q L,t+1 s t = δ 0 +δ 0 1 X t (11) is observationally equivalent to a unique model of the form     ΔP L t+1 ΔM t+1     = ΔZ t+1 = K P 0 +K P 1 Z t + Σ Z P Z,t+1 ΔP L t+1 = K Q 0 +K Q 1 Z t + Σ P Q t+1 s t = ρ 0 +ρ 0 1 Z t (12) which is parametrized by θ = (λ Q , p ∞ , Σ Z , K P 0 , K P 1 ). The proof that follows is essentially the same as that of Joslin, Priebsch and Singleton (2014). Joslin, Singleton and Zhu (2011) demonstrates the result for all cases including zero, repeated and complex eigenvalues. Assume the model (11) under consideration is nonredundant, that is, there is no observa- tionally equivalent model with fewer thanN state variables. If there is such a model, switch to it and proceed. 75 B.1 Observational Equivalence Given any model of the form (11), the J× 1 vector of log futures prices f t is affine in L t , f t =A L +B L L t Hence the set of N L linear combinations of futures prices,P L t , is as well: P L t =W L f t =W L A L +W L B L L t Assume that the N L ordered elements of λ Q , the eigenvalues of K Q 1L , are real, distinct and nonzero. There exists a matrix C such that K Q 1L = Cdiag(λ Q )C −1 . Define D = Cdiag(δ 1 )C −1 , D −1 =Cdiag(δ 1 ) −1 C −1 and Y t =D[L t + K Q 1L −1 K Q 0L ] ⇒ L t =D −1 Y t − K Q 1L −1 K Q 0L Then ΔY t+1 =DΔL t+1 =D[K Q 0L +K Q 1L (D −1 Y t − K Q 1L −1 K Q 0L ) + Σ L Q L,t+1 ] = diag(λ Q )Y t +DΣ L Q L,t+1 76 and     ΔY t+1 ΔM t+1     =     D 0 0 I M     [K P 0X +K P 1X (     D −1 0 0 I M         Y t M t     −     K Q 1L −1 K Q 0L 0     )+Σ X P t+1 ] =K P 0Y +K P 1Y     Y t M t     +     D 0 0 I M     Σ X P t+1 and p t =δ 0 +δ 0 1 L t =δ 0 +δ 0 1 D −1 Y t −δ 0 1 K Q 1L −1 K Q 0L =p ∞ +ι·Y t where ι is a row of N L ones. f t =A Y +B Y Y t P L t =Wf t =WA Y +WB Y Y t The model is nonredundant⇒ WB Y is invertible: Y t = (WB Y ) −1 P L t − (WB Y ) −1 WA Y ·P L t+1 =WB Y ΔY t+1 =WB Y diag(λ Q )[(WB Y ) −1 P L t − (WB Y ) −1 WA Y ] +WB Y DΣ L Q L,t+1 =K Q 0 +K Q 1 P L t + Σ P Q t+1 77 Further, ΔZ t+1 =     ·P L t+1 ΔM t+1     =     WB Y 0 0 I M         ΔY t+1 ΔM t+1     =     WB Y 0 0 I M         K P 0Y +K P 1Y     Y t M t     +     D 0 0 I M     Σ X P t+1     =K P 0 +K P 1 Z t + Σ Z P t+1 p t =p ∞ +ι·Y t =p ∞ +ι· (WB Y ) −1 P L t −ι· (WB Y ) −1 WA Y =ρ 0 +ρ 0 1 P L t QED.Collectingtheformulas: givenanymodeloftheform(7), thereisanobservationally equivalent model of the form (10), parametrized by θ = (λ Q , p ∞ , Σ Z , K P 0 , K P 1 ), where • D =Cdiag(δ 1 ) −1 C −1 • Σ Z =     WB Y D 0 0 I M     Σ X , Σ P = [Σ Z ] LL • B Y =         ι 0 [I L+M +diag(λ Q )] . . . ι 0 [I L+M +diag(λ Q )] J         • A Y =         p ∞ + 1 2 ι 0 Σ P Σ 0 P ι . . . A Y,J−1 + 1 2 B Y,J−1 Σ P Σ 0 P B 0 Y,J−1         • K Q 1 =WB Y diag(λ Q )(WB Y ) −1 , K Q 0 =−K Q 1 WA Y • ρ 0 =p ∞ −ι· (WB Y ) −1 WA Y , ρ 0 1 =ι· (WB Y ) −1 In estimation I adopt the alternate form 78 • ΔY t+1 =     p ∞ 0     +diag(λ Q )Y t +DΣ X Q t+1 • p t =ι·Y t • A Y =             p ∞ + 1 2 ι 0 Σ P Σ 0 P ι . . . A Y,J−1 +B Y,J−1     p ∞ 0     + 1 2 B Y,J−1 Σ P Σ 0 P B 0 Y,J−1             • K Q 1 =WB Y diag(λ Q )(WB Y ) −1 , K Q 0 =WB Y     p ∞ 0     −K Q 1 WA Y • ρ 0 =−ι· (WB Y ) −1 WA Y , ρ 0 1 =ι· (WB Y ) −1 which is numerically stable when λ Q (1)→ 0. See the online supplement to JSZ 2011. B.2 Uniqueness We consider two models of the form (10) with parametersθ and ˆ θ = ( ˆ λ Q , ˆ p ∞ , ˆ Σ Z , ˆ K P 0 , ˆ K P 1 ) that are observationally equivalent and show that this implies θ = ˆ θ. Since Z t =     P L t M t     are all observed,{Σ Z , K P 0 , K P 1 } ={ ˆ Σ Z , ˆ K P 0 , ˆ K P 1 }. Since f t =A +BZ t are observed, A(θ) =A( ˆ θ), B(θ) =B( ˆ θ). Suppose λ Q 6= ˆ λ Q . Then by the uniqueness of the ordered eigenvalue decomposition, B j Y (λ)6=B j Y ( ˆ λ)∀j ⇒WB Y (λ)6=WB Y ( ˆ λ)⇒ (WB Y (λ)) −1 6= (WB Y ( ˆ λ)) −1 79 ⇒ρ 1 (λ)6=ρ 1 ( ˆ λ)⇒B(λ)6=B( ˆ λ) , a contradiction. Hence λ Q = ˆ λ Q . Then A(λ Q , p ∞ ) =A( ˆ λ Q , ˆ p ∞ )⇒p ∞ = ˆ p ∞ . C Estimation Given the futures prices and macroeconomic time series{f t , M t } t=1,...,T and the set of port- folio weights W that define the pricing factors: P t =Wf t weneedtoestimatetheminimalparametersθ = (λ Q , p ∞ , Σ Z , K P 0 , K P 1 )intheJPSform. The estimation is carried out by maximum likelihood (ML). If no restrictions are imposed (i.e. we are estimating the canonical model (11)), then K P 0 , K P 1 do not affect futures pricing and are estimated consistently via OLS. Otherwise K P 0 , K P 1 are obtained by GLS taking the restrictions into account. The OLS estimate of Σ Z is used as a starting value, and the starting value for p ∞ is the unconditional average of the nearest-maturity log futures price. Both were always close to their ML value. Finally I search over a wide range of values for the eigenvalues λ Q , and the ML values were always of reasonable magnitude, real valued, and distinct. After the ML estimate of the model in the JPS form is found, I rotate and translate the spanned factors fromP 1 t ,P 2 t tos t , c t as described in A.2. I rotate and translateUM t toM t , so that the estimate reports the behavior of the actual macro time series M t instead of their 80 subcomponents:         s t c t M t         =         ρ 0 1 2 σ 2 s +ρ 1 K Q 0 α MP         +         ρ 1 0 1×N M ρ 1 K Q 1 0 1×N M 0 N M ×1 β MP             P t UM t     where M t =α MP +β MP P t +UM t 81 D Comparison with other Futures Models The model (7) is a canonical affine Gaussian model, so any affine Gaussian model is a special case. For example, discretized, the Gibson and Schwartz (1990); Schwartz (1997); Schwartz and Smith (2000) two factor model can be written   Δs t+1 Δδ t+1   =   μ κα   +   0 −1 0 −κ     s t δ t   +   σ 1 0 0 σ 2     1 ρ ρ 1   1/2 P t+1 (13)   Δs t+1 Δδ t+1   =   r κα−λ   +   0 −1 0 −κ     s t δ t   +   σ 1 0 0 σ 2     1 ρ ρ 1   1/2 Q t+1 (14) which is clearly a special case of (7). The Casassus and Collin-Dufresne (2005) model, discretized, is:     ΔX t+1 Δ ˆ δ t+1 Δr t+1     =     κ P X θ P X +κ P Xr θ P r +κ P X ˆ δ θ P ˆ δ κ P ˆ δ θ P ˆ δ κ P r θ P r     +     −κ P X −κ P X ˆ δ −κ P Xr 0 −κ P ˆ δ 0 0 0 −κ P r         Xt ˆ δt rt     +     σ X 0 0 0 σ ˆ δ 0 0 0 σr         1 ρ Xδ 1 ρ Xr ρ δr 1     1/2 P t+1 (15)     ΔX t+1 Δ ˆ δ t+1 Δr t+1     =     α X θ Q X + (αr− 1)θ Q r +θ Q ˆ δ κ Q ˆ δ θ Q ˆ δ κ Q r θ Q r     +     −α X −1 1−αr 0 −κ Q ˆ δ 0 0 0 −κ Q r         Xt ˆ δt rt     +     σ X 0 0 0 σ ˆ δ 0 0 0 σr         1 ρ Xδ 1 ρ Xr ρ δr 1     1/2 Q t+1 (16) (see their formulas 7, 12, 13 and 27, 28, 30) which is the Schwartz three factor model with more flexible risk premiums. 82 Table 10: Parameters of the model for the purpose of real option valuation K P 0 K P 1 s t c t GRO t s t+1 0.00 1.00 0.083 0.03 c t+1 0.00 0.00 0.90 0.00 GRO t+1 0.00 -0.10 0.00 0.60 K Q 0 K Q 1 s t c t GRO t s t+1 0.00 1.00 0.08 0.00 c t+1 0.00 0.00 0.90 0.00 GRO t+1 −λ -0.10 0.00 0.60 Σ s c GRO s 0.10 c -0.08 0.06 GRO 0 0 0.50 E Real Option Valuation The lifting cost is l t =κ l + 0.1s t + 0.01GRO t + l t , l t ∼N(0,σ l ) , that is, l t varies with both s t and GRO t as well as having an i.i.d idiosyncratic compo- nent. Notice the third row of K Q 1 , which was not there in the previous estimates. When we consider assets with payoffs that depend onM t , the risk neutral dynamics ofM t are material. In principle one can estimate them with a mimicking portfolio forGRO (Lamont 2001), but here I simply assume that exposure to GRO carries a non time varying risk premium equal to λ. I compute option values for different starting values of L 0 = exp(l 0 ), with S 0 = exp(s 0 ) equal to $80 per barrel and c 0 = 0. This is meant to mimic an oil firm evaluating wells that differ in their cost and difficulty of extraction, conditional on today’s oil prices. 83 F Robustness Checks F.1 Excluding the Financial Crisis A natural question from Figure 1 is whether my results are driven by the huge swings in oil prices and real activity during 2008-2009. Table 11 presents the model estimate on a subsample from January 1986 to December 2007. The subsample estimate is similar to the full-sample estimate, and the key coefficients of GRO t+1 on s t , s t+1 on GRO, and INV t+1 on c t are virtually unchanged and remain statistically significant at the 5% level. Table 12 shows that the regression results using the principal components of log prices are also similar, and indeed the incremental predictability from the macro factors is slightly stronger, when we omit the financial crisis from the data. F.2 Time varying volatility Table 13 shows the results of the forecasting regressions in Table 1 when I add two indexes of time-varying volatility: the monthly volatility of the one month log futures price estimated as an GARCH(1,1) process, garchvol, and the implied volatility of the one month futures price based on the prices of at-the-money call options, optionvol. Neither volatility factor is significant in the forecasting regressions, neither raises the adjusted R 2 , and their inclusion does not alter the forecasting power of GRO. F.3 Real vs Nominal Prices As oil prices make up an important fraction of consumers’ and firms’ expenditures, the interaction of this paper’s results with inflation is a natural question. In particular, the return predictability or dynamics of oil prices with the real economy that I document might 84 Table 11: Maximum likelihood (ML) estimate of the macro-finance model for Nymex crude oil futures, using data from 1/1986 to 12/2007. s, c are the spot price and annualized cost of carry respectively. GRO is the monthly Chicago Fed National Activity Index. INV is the log of the private U.S. crude oil inventory as reported by the EIA. The coefficients are over a monthly horizon, and the state variables are de-meaned. ML standard errors are in parentheses. Coefficients in bold are significant at the 5% level. Historical (P) Measure K P 0 K P 1 s t c t GRO t INV t s t+1 0.011 0.996 0.058 0.029 -0.006 (0.007) (0.014) (0.036) (0.011) (0.107) c t+1 -0.013 0.026 0.864 -0.012 0.031 (0.007) (0.015) (0.037) (0.011) (0.111) GRO t+1 0.056 -0.171 0.633 0.427 -1.571 (0.035) (0.070) (0.178) (0.054) (0.533) INV t+1 0.002 -0.008 0.031 -0.003 0.855 (0.002) (0.004) (0.010) (0.003) (0.031) Risk Neutral (Q) Measure K Q 0 K Q 1 s t c t s t+1 -0.003 1.000 0.083 (0.007) (0.005) (0.011) c t+1 0.000 -0.008 0.885 (0.012) (0.013) (0.031) Shock Volatilities [off-diagonal = % correlations] s c GRO INV s 0.102 c -85% 0.057 GRO 7% 0% 0.500 INV -23% 31% 4% 0.028 85 Table 12: Panel A shows the results of forecasting returns to oil futures. Panel B shows the results of forecasting changes in the level and slope, PC1 and PC2 respectively, of the oil futures curve. The data are monthly from from 1/1986 to 12/2007. The forecasting variablesarethefirstfiveprincipalcomponentsoflogfuturesprices,PC 1−5 , andtheresiduals of the Chicago Fed National Activity Index and U.S. oil inventory projected onPC 1−5 . The standard errors are Hansen-Hodrick. ∗ :p< 0.10, ∗∗ :p< 0.05, ∗∗∗ :p< 0.01. Panel A: Forecasting Returns to Futures r t→t+horizon =α +β 1−5 PC 1−5 t +β UGRO,UINV UM t + t Horizon 1 month 6 months 12 months Futures maturity 1 m 12 m 1 m 12 m 1 m 12 m β UGRO 0.028 ∗∗ 0.022 ∗∗∗ 0.034 0.034 0.015 0.026 (0.010) (0.006) (0.036) (0.023) (0.068) (0.045) β UINV -0.027 -0.001 −0.727 ∗ −0.58 ∗∗ -1.161 −1.12 ∗∗ (0.119) (0.072) (0.414) (0.27) (0.800) (0.55) Adjusted R 2 (PC 1−5 ) -0.2% 0.7% 4.1% 2.6% 6.8% 2.9% Adj. R 2 (PC 1−5 +UM t ) 2.1% 4.1% 7.6% 8.9% 10.0% 10.8% F-ratio 7.9 ∗∗∗ 5.6 ∗∗∗ 5.7 ∗∗∗ 9.7 ∗∗∗ 11.2 ∗∗∗ 11.8 ∗∗∗ Panel B: Forecasting Changes in Level and Slope ΔPC (n) t→t+horizon =α +β 1−5 PC 1−5 t +β UGRO,UINV UM t + t Horizon 1 month 6 months 12 months Principal Component Level Slope Level Slope Level Slope β UGRO 0.082 ∗∗∗ -0.007 0.104 0.007 0.059 0.023 (0.027) (0.006) (0.085) (0.012) (0.151) (0.020) β UINV -0.011 0.012 −2.04 ∗ 0.106 -3.54 0.127 (0.302) (0.071) (1.06) (0.187) (1.92) (0.182) Adjusted R 2 (PC 1−5 ) -0.3% 8.5% 1.6% 35.0% 0.3% 51.2% Adj. R 2 (PC 1−5 +UM t ) 2.5% 8.3% 6.7% 34.8% 6.7% 51.8% F-ratio 9.5 ∗∗∗ 0.7 15.8 ∗∗∗ 0.6 19.7 ∗∗∗ 2.7 ∗ 86 Table 13: Panel A shows the results of forecasting returns to U.S. oil futures. Panel B shows the results of forecasting changes in the level factor PC 1 in oil futures. The data are monthly from from 1/1986 to 7/2013. The forecasting variables are 1) the first two principal components of log oil futures prices, 2) the unspanned components UM t = M t − Proj(M t |PC 1,2 t ) of the Chicago Fed National Activity IndexGRO t and log U.S. oil inventory INV t , and 3) the unspanned componentsUVOL t =VOL t −Proj(VOL t |PC 1,2 t ) of an index of time varying volatility. VOL garch t is the conditional volatility of Δf 1 t estimated as a GARCH(1,1) process. VOL option t is the implied volatility based on the prices of at-the-money options on one month futures. Variable being Forecast r 1 t+1 r 12 t+1 ΔPC 1 t+1 UGRO t 0.029 ∗∗∗ 0.023 ∗∗ 0.019 ∗∗∗ 0.016 ∗∗ 0.077 ∗∗∗ 0.063 ∗∗ (0.010) (0.010) (0.007) (0.007) (0.028) (0.028) UVOL garch t 0.001 0.001 0.009 (0.009) (0.006) (0.024) UVOL option t -0.009 -0.003 -0.011 (0.017) (0.011) (0.045) Spanned Factors: PC 1,2 PC 1,2 PC 1,2 PC 1,2 PC 1,2 PC 1,2 Adjusted R 2 (P t +UM t ) 4.5% 4.1% 4.0% 3.8% 3.1% 2.8% Adj. R 2 (P t +UM t +UVOL t ) 4.3% 3.9% 3.7% 3.5% 2.9% 2.5% F-ratio 0.0 0.4 0.1 0.1 0.2 0.1 Robust standard errors are in parentheses. ∗ :p< 0.10, ∗∗ :p< 0.05, ∗∗∗ :p< 0.01 87 be driven by inflation or inflation expectations. This would not invalidate the results but might call into question the interpretation. For example, periods of high inflation might also be periods of high oil prices and low future growth. Procylical nominal returns to oil futures might reflect not risk premiums but higher (expected) inflation in booms versus busts. Table 14 reproduces the forecasting regressions from Section 2 using futures prices that have been deflated by the monthly Consumer Price Index (CPI) and thus represent real prices and returns. Table 15 and Table 16 display the model estimate and the model implied risk premiums using real prices. In all cases the results using real prices are very similar to those using nominal prices. The real results are also very similar to the nominal results if I instead deflate by the core CPI which excludes food and energy, by the producer price index (PPI) or by the core PPI. These observations are consistent with the claim that inflation does not drive the results in the paper – in particular, that the two-way relationship between oil prices and real activity and the procylical unspanned behavior I observe in oil futures are non nominal phenomena. F.4 Inflation as a Factor Another question is to what extent oil futures markets interact with inflation – that is, what happens when we treat inflation as a macro factor. More than 80% of monthly variation in the CPI and PPI are due to changes in energy prices, so there is a potential simultaneity issue with using those measures alongside movements in oil futures. Hence, Table 17 presents the model estimates using WTI crude oil futures, the real activity indexGRO, and inflation measured as the 12 month change in the core CPI. We see that there is no strong relation between core inflation and the oil price fac- tors, either contemporaneously (the correlations of their shocks are insignificant) nor over 88 Table 14: Results of forecasting real returns to oil futures and changes in the level and slope, PC1 andPC2 respectively, of the real oil futures curve after deflating by the monthly CPI. The data are monthly from from 1/1986 to 10/2013. The forecasting variables are the first five principal components of log futures prices, PC 1−5 , and the residuals of the Chicago Fed National Activity Index and U.S. oil inventory projected onPC 1−5 . The standard errors are Hansen-Hodrick. ∗ :p< 0.10, ∗∗ :p< 0.05, ∗∗∗ :p< 0.01. Panel A: Forecasting Returns to Futures r t→t+horizon =α +β 1−5 PC 1−5 t +β UGRO,UINV UM t + t Horizon 1 month 6 months 12 months Futures maturity 1 m 12 m 1 m 12 m 1 m 12 m β UGRO 0.023 ∗∗ 0.016 ∗∗ 0.027 0.018 0.033 0.025 (0.010) (0.007) (0.037) (0.029) (0.052) (0.041) β UINV 0.037 0.000 -0.062 -0.309 0.074 -0.542 (0.087) (0.061) (0.532) (0.411) (0.839) (0.679) Adjusted R 2 (PC 1−5 ) 1.0% 0.2% 9.6% 1.9% 17.4% 3.4% Adj. R 2 (PC 1−5 +UM t ) 3.1% 2.2% 9.5% 2.8% 17.3% 5.0% F-ratio 9.0 ∗∗∗ 4.3 ∗∗ 0.9 2.5 ∗ 1.5 3.6 ∗∗ Panel B: Forecasting Changes in Level and Slope ΔPC (n) t→t+horizon =α +β 1−5 PC 1−5 t +β UGRO,UINV UM t + t Horizon 1 month 6 months 12 months Principal Component Level Slope Level Slope Level Slope β UGRO 0.063 ∗∗ -0.008 0.054 -0.001 0.062 0.002 (0.027) (0.005) (0.102) (0.009) (0.140) (0.015) β UINV 0.044 -0.045 -0.929 -0.136 -1.584 -0.209 (0.239) (0.047) (1.472) (0.166) (2.301) (0.175) Adjusted R 2 (PC 1−5 ) -0.3% 8.2% 3.9% 36.0% 6.4% 52.1% Adj. R 2 (PC 1−5 +UM t ) 1.6% 8.9% 4.3% 36.2% 7.3% 52.6% F-ratio 8.5 ∗∗∗ 2.2 3.4 ∗∗ 1.3 5.3 ∗∗∗ 2.7 ∗ 89 Table 15: Maximum likelihood (ML) estimate of the macro-finance model for Nymex crude oil futures, using futures prices deflated by the monthly CPI. s, c are the spot price and annualized cost of carry respectively. GRO is the monthly Chicago Fed National Activity Index. INV is the log of the private U.S. crude oil inventory as reported by the EIA. The coefficients are over a monthly horizon, and the state variables are de-meaned. ML standard errors are in parentheses. Coefficients in bold are significant at the 5% level. Historical (P) Measure K P 0 K P 1 s t c t GRO t INV t s t+1 0.006 0.986 0.062 0.024 0.045 (0.006) (0.012) (0.032) (0.008) (0.083) c t+1 -0.007 0.026 0.880 -0.014 -0.064 (0.005) (0.011) (0.031) (0.008) (0.079) GRO t+1 0.000 -0.161 0.011 0.618 -0.079 (0.030) (0.062) (0.171) (0.043) (0.438) INV t+1 0.002 0.003 0.033 -0.002 0.884 (0.002) (0.003) (0.009) (0.002) (0.024) Risk Neutral (Q) Measure K Q 0 K Q 1 s t c t s t+1 -0.003 1.000 0.083 (0.007) (0.004) (0.011) c t+1 0.000 -0.004 0.892 (0.012) (0.012) (0.030) Shock Volatilities [off-diagonal = % correlations] s c GRO INV s 0.102 c -81% 0.057 GRO 5% -2% 0.530 INV -22% 27% 4% 0.028 90 Table 16: Maximum Likelihood (ML) estimates of risk premiums for U.S. crude oil futures using real prices deflated by the monthly CPI. s,c are the spot price and annualized cost of carry respectively. GRO andINV are the Chicago Fed National Activity Index and log U.S. crude oil inventory respectively. The coefficients are standardized to reflect a one standard deviation change in each variable. Standard errors are in parentheses. Coefficients in bold are significant at the 5% level. " Λ s Λ c # t = Λ 0 + Λ 1 h s t c t M t i 0 Λ 0 Λ 1 s c GRO INV Λ s 0.009 -0.002 -0.001 0.012 0.001 (0.013) (0.002) (0.003) (0.004) (0.002) Λ c -0.007 0.004 -0.001 -0.007 -0.002 (0.016) (0.003) (0.004) (0.004) (0.002) time (neither significantly forecasts the other). The relationship between oil prices and real activity is unchanged and still strongly significant both ways. We do observe a relation- ship between real activity and inflation and their respective forecasts. Although shocks to GRO and Δ 12m cCPI are not significantly correlated, a higher level of real activity forecasts higher core inflation, while higher core inflation forecasts lower real activity. The estimate thus suggests interesting dynamics running from oil prices to real activity to core inflation, and perhaps vice versa, but no clear relation between oil prices and core inflation directly. 91 Table 17: Maximum likelihood (ML) estimate of the macro-finance model for Nymex crude oil futures, using futures prices deflated by the monthly CPI. s, c are the spot price and annualized cost of carry respectively. GRO is the monthly Chicago Fed National Activity Index. Δ 12m cCPI isthe12monthchangeinthecoreCPI.Thecoefficientsareoveramonthly horizon, and the state variables are de-meaned. ML standard errors are in parentheses. Coefficients in bold are significant at the 5% level. Historical (P) Measure K P 0 K P 1 s t c t GRO t Δ 12m cCPI t s t+1 0.009 0.986 0.064 0.023 -0.008 (0.006) (0.011) (0.028) (0.008) (0.006) c t+1 -0.008 0.020 0.867 -0.014 0.004 (0.005) (0.010) (0.026) (0.008) (0.006) GRO t+1 -0.001 -0.212 -0.038 0.589 -0.097 (0.030) (0.057) (0.146) (0.044) (0.034) Δ 12m cCPI t+1 -0.010 0.015 -0.025 0.024 0.996 (0.007) (0.014) (0.036) (0.011) (0.008) Shock Volatilities [off-diagonal = % correlations] s c GRO Δ 12m cCPI s 0.102 c -81% 0.057 GRO 4% -1% 0.524 Δ 12m cCPI 6% -4% 3% 0.129 92 Part II Technology and Real Options: Evidence from Patent Text Abstract I measure U.S. firms’ technological areas using textual analysis of their patents. Firms’ technological position forecasts their future product market position. Greater technological differentiation is associated with higher total factor productivity, prof- itability, investment and market-to-book ratio. Consistent with a model of real options on heterogeneous assets, firms that are more technologically differentiated have lower stock returns and this effect is concentrated in small growth firms. 93 1 Introduction Technological innovation is a major and persistent component of productivity growth at both the aggregate and firm level (Solow (1962); Romer (1990)). In this paper I construct new measures of innovation using the text of all 6.2 million utility patents granted by the U.S. Patent and Trademark Office (USPTO) from 1926 to 2010. These new measures open the “black box” of simply counting patents and present a more detailed picture of the nature of innovation at the patent and firm level. I use these measures to estimate the connections between firms’ innovation, productivity and stock returns. I map patents and firm-years to vectors in “word space”. At the firm-year level I measure firms’ technological differentiation relative to other firms. I find that technological differ- entiation is strongly positively associated with market-to-book ratio, Tobin’s Q, return on assets, investment, and total factor productivity. These relations persist after controlling for measures of market power and product market differentiation and after sweeping out industry and firm fixed effects. Relative to standard measures of technology the text-based measures contribute substantial explanatory power. I compare my text-based measures in detail with those of Hoberg and Phillips (2010), who locate firms in word space using the business description section of their 10-K filings. There is substantial overlap between Hoberg and Phillips (2010)’s product market positions and my technological positions, but there is also considerable discrepancy between firms’ patenting activities and their operating activities. Technological differentiation is one way that firms can achieve product market differen- tiation by inventing new products. I solve a simple model in which innovation yields real options to introduce novel products. Novel products have less volatile cash flows and are less risky (Hou and Robinson (2006)) and this effect is magnified when the product is not yet 94 implemented, because real options are levered relative to assets in place (Berk, Green and Naik (2004)). In the model, while firms’ market to book ratio reflects their product market positionitdoesnotfullyreflecttheirtechnologicalposition. Consistentwiththemodel, Ifind that technological differentiation predicts lower returns conditional on standard benchmarks and measures of firms’ product market position. The predictable component of returns due to technological differentiation is concentrated in firms with a higher ratio of growth options to assets in place. Previous studies document that firms with high Tobin’sQ or market-to-book ratio (Fama and French (1992)) or high TFP (Imrohoroglu and Tuzel (2014)) have lower stock returns in the cross-section. The results in this paper support the hypothesis that cross-sectional differences in Q and TFP, and the differences in stock returns that accompany them, are related to firms’ technology. 1.1 Prior Literature This paper joins other recent studies that apply textual analysis to measure aspects of firm behavior beyond the standard accounting variables. The closest related paper is Hoberg and Phillips (2010) who locate firms in product market space based on key words in the business description section of their 10-K filings. Hoberg and Phillips (2010)’s TNIC measures are available for publicly traded firms from 1997 onward. By contrast, I collect the text of all U.S. patents granted to individuals, public firms, and private firms since 1926. Section I.4 compares my measure to theirs in detail. Packalen and Bhattacharya (2012) analyze U.S. patent text: their focus is on the changing nature of technology over time, and they do not link their text based measures to the CRSP/Compustat data. Alexopoulos (2011) finds that innovative activity as measured by the publication of computer- and telecommunications- 95 related technical manuals is followed by growth in GDP, TFP, investment and hours worked at the aggregate level. InPastorandVeronesi(2003)andGarleanu,PanageasandYu(2012),anewtechnological eraarrivesandisgraduallyadoptedintheeconomy. Here, Isupposethatfirmsarepositioned in a multidimensional “technology space” that is a precursor to their position in product market space cf. Hotelling or Hoberg-Phillips. Hirshleifer, Hsu and Li (2012); Hirshleifer, Hsu and Li (2013); Cohen, Diether and Malloy (2013) find that firms with diverse patents, high-quality patents and high research productiv- ity have high subsequent returns. Their interpretation is that the market is slow to recognize innovativefirms’superiority, sothedocumentedreturnspreadsrepresentmispricing. Bycon- trast, I find that firms with more technological differentiation have lower subsequent returns, and I offer a simple rational explanation based on the leverage effect of growth options on the risk premiums of the underlying assets. 2 Data and Methodology 2.1 Patent Text I use the full text of all U.S. utility patents granted from 1926 to 2010 from the U.S. Patent and Trademark Office, which is cross hosted at the Google Patents project 11 . Figure 11 plots the number of patents granted each year that appear in the sample, compared to the official grant numbers by year from the USPTO which are available starting in 1963. The sample covers well over 99% of all U.S. utility patents every year from 1963 to 2009 and 85% of those granted in 2010. The sample comprises 6,237,597 patents and 240GB of text which 11 http://www.google.com/googlebooks/uspto-patents-grants-text.html 96 corresponds to roughly 134 million pages. Figure 11: Number of patents each year in the sample from 1926-2010 and number of patents granted by the USPTO from 1963-2013. For each patent I take the full body text and extract all words (1-grams) and two and three word phrases (2-grams and 3-grams). For each calendar year from 1960 to 2009, I select a set of informative words and phrases (’ngrams’) using patent text from previous years. The details of how I select the ngrams are in Appendix A. Table 18 lists some common ngrams by their vintage (the application year of the first patent that mentions the ngram) for the years 1950, 1960, and so on up to 2000, which illustrates the changes in technology over the period. The vintages support the conclusion of Griliches (1990) that patents are applied for early in the inventive process. “GPS system” first appears in a patent in 1980; the first functioning GPS satellite was not launched until 1989. “Notebook computer” is first mentioned in 1990 when such portable computers were quite unusual. “Picture experts” and “picture experts group”, which first appear in a patent in 1990, refer to the MPEG digital video format, which was first discussed in 1988 and the first MPEG format was officially released in 1993. 97 Table 18: The table shows the most common ngrams (one, two or three word noun phrases) by their vintage (year of first mention) for vintages 1950, 1960, 1970, 1980, 1990 and 2000. 1950 1960 1970 control circuitry system memory acid sequences clock cycle glass transition temperature methodologies substrate material status information software components epoxy resins immune response bus interface computer networks control module programming languages command signal calf serum interface card remote computer fibroblast plasma display enantiomers error message browsers breast cancer disclosure bulletin management information polymer matrix logic device cpu controls 1980 1990 2000 program product email address communication media computer cytokines notebook computer wireless media combinations fusion protein remote memory storage computer communication media protein expression notebook computers laptop devices multiprocessor flash chromatography email messages systems methods features hybridization conditions picture experts methods components materials gps system picture experts group access protocol soap angioplasty email addresses amplification markers necrosis factor sound card server data stores cdna clones multiple servers valdecoxib For each patent, I evaluate if each ngram is present (1) or absent (0) out of the set of ngrams corresponding to the year the patent was granted. This yields a Boolean vector for each patent. I only count the presence or absence of each ngram because patents vary greatly in their length and structure – mechanical patents are short with many diagrams, while biotech patents run to hundreds of pages. Thus, above its presence or absence, the number of times an ngram is mentioned in a patent is uninformative. 98 Some patent documents are almost entirely diagrams of the invention. I exclude patents from the analysis if they contain fewer than 10 ngrams as these are likely more noise than signal. About 46,000 patents fall into this category, almost all of them from the early (pre- 1960) years of the sample. After these filters, the word space is populated by 6.2 million vectors representing the vast majority of U.S. utility patents granted from 1926 to 2010. Appendix C describes the construction of quality and vintage scores at the level of indi- vidual patents. Briefly, I find that patents’ quality and vintage positively predict whether the patent holders pay fees to renew them over and above standard measures of quality like citations. This suggests that my ngram selection and vectorization are capturing meaningful information about the patents. 3 Firm-year Technology Positions 3.1 Firm Data Annual firm data is from domestic (U.S.) firms in Compustat. I drop utility, financial and government firms (firms whose SIC codes begin with 49 or 6 or 9) from the sample. I drop firm-years with missing or negative assets or book equity and winsorize all ratios at the 1% and 99% levels. The main departure from the full CRSP / Compustat sample is that my patent-based measures require a firm has at least one patent to its name. Hence, firms appear in the panel in the year that they are granted their first patent. Table 19 presents summary statistics for the sample compared to the full Compustat cross section. Firms holding patents represent 25-45% of all Compustat firms in any year, and the overall distribution of firm characteristics is similar between the subsample and the full set. Relative to the set of all Compustat firms 99 those with patents are somewhat larger, higher Q, and older. They have similar investment as a fraction of book assets and are more R&D intensive. I map patents to firms using the database of Kogan etal. (2014), which extends the patent-to-firm mapping in the NBER database (Hall, Jaffe and Trajtenberg (2001)) in two ways. First, they extend the mapping backward in time as far as 1960 and forward in time to 2010. Second, they map to firms some previously unmapped patents which were granted to subsidiaries of Compustat firms. I extend the Kogan etal. (2014) map in one way. Both the NBER and Kogan etal. (2014) databases assign patents to firms as of the patent’s grant date. However, patents are often reassigned to a new legal owner via mergers, acquisitions, or sales of IP assets. I collected the USPTO data and incorporated reassignments into my patent-to-firm map. The details are in Appendix B. Table 19: Summary statistics of the Compustat firm-years sample. Patenting Firms 1961-2009 All Compustat Firms 1961-2009 Mean Median St. Dev. p 10 p 90 Mean Median St. Dev. p 10 p 90 log(AT) 5.67 5.45 1.90 3.33 8.27 4.94 4.66 1.74 2.88 7.40 Average Q 1.93 1.38 1.64 0.83 3.60 1.74 1.27 1.44 0.80 3.10 Firm Age 12.8 10 10.6 1 29 10.3 8 9.5 1 24 CAPX/AT 0.065 0.053 0.050 0.018 0.125 0.072 0.051 0.071 0.013 0.155 R&D/AT 0.059 0.026 0.092 0.000 0.152 0.034 0.000 0.078 0.000 0.108 Firms per Year 858.2 849 290.9 429 1295 2922.8 3117 1223.6 956 4687 3.2 Firm-year Technology Vectors I sum the text based vectors of the patents granted to each firm in each year. Thus, the entries of the firm-year vectors are integer counts of how many firm patents contained each 100 ngram. This is in contrast to the approach for individual patents where all that matters is if an ngram is present (1) or absent (0). At the firm-year level each patent represents a separate invention, so the number of the firm’s patents that mention a given ngram is informative about the firm’s research program. Small firms often have several patents one year and zero the next. I fill the resulting gaps in the panel in two ways. The first way is to construct word stock vectors: these vectors are a rolling stock of the count vector from the focal year plus the stock from the prior year, which is depreciated by some amount δ≥ 0. The second way is to fill the firm-year vectors forward: when a firm had no patents in some year, but did have patents in a prior year, I copy the most recent prior year’s vector. I present the results using word stock vectors with depreciation rate δ = 0.2 which is used to construct R&D and patent stocks in previous literature (Chan, Lakonishok and Sougiannis (2001); Hirshleifer, Hsu and Li (2013)). The results in the paper are robust to using other depreciation rates or filling forward instead. 101 (a) Yahoo (b) Google (c) Coca-Cola (d) Intel Figure 12: Word clouds for Google, Yahoo, Coca-Cola and Intel in 2000. The clouds display the twenty ngrams that appear in the largest number of patents that each firm applied for in 2000. The size of the ngram increases with the fraction of the firm’s patents that mention the ngram. Figure 12 displays “word clouds” based on the patent text vectors of four firms for the year 2000: Google, Yahoo, Coca-Cola and Intel. Note that Google was a private firm as of the year 2000 and did not go public until 2004. The word clouds display the 20 most common ngrams for each firm and the size of the typeface increases with the fraction of the firm’s patents in which the ngram appeared. The word clouds appear to be reflective of the firms’ technological areas. 102 3.3 Technological Differentiation Using the normalized word vectors, I compute cosine similarities between all patents (private and public) in each year, cos ij =wordvec it ·wordvec jt the differentiation for each patent as one minus the 99th quantile of the cosine similarities techdiff i = 1−quantile j 99 (cos ijt ) (i.e. among 20,000 other patents granted that year, how close was the 200th closest patent to the focal patent). Relative to other measures like the median similarity, the 99th quantile is a relatively local measure of differentiation. For each firm-year I define its technological differentiation as: techdiff it =median p∈P{i,t} (techdiff p ) , that is, the median differentiation of all patents mapped to the firm in that year. Similar results obtain for different summary statistics such as the mean techdiff or the 90% quantile of the techdiff. The higher the techdiff, the farther firm i’s patents are from other patents in the same general area, and the more technologically differentiated it is. The techdiff scores for the firms in Figure 12 are GOOG 0.81, YHOO 0.76, INTL 0.35, KO 0.20. Thus, in 2000 Google had the highest techdiff and Coca-Cola the lowest. 103 3.4 Comparison with Hoberg-Phillips TNIC This section compares my patent-based similarity measures with the Hoberg and Phillips (2010) TNIC classifications, which map firms’ product market position based on their 10- K product descriptions. The conclusion is that 10-K text captures where firms are, while patent text captures where firms are heading. To compare the overlap between the two data measures, in this section I drop years prior to 1997 from my data and years after 2007 from the Hoberg-Phillips data. I retain only firm-years that appear in both data sets, so firm i in year t is only present if firm i filed a 10-K in year t and if it had at least one patent in or prior to year t. As the raw similarity scores for the Hoberg-Phillips product market network are not available, I change my similarity scores into a neighbor network to facilitate comparison in this section. For each firm-firm pair in each year, I assign them to be technology (“TECH”) neighbors if their cosine similarity based on patent text is higher than 0.17. This cutoff rule produces a network that, distributionally, is a very close match to that of the Hoberg-Phillips product market (“PROD”) network. Figure 13 plots the histograms of the number of TECH neighbors and PROD neighbors that each firm-year has in the data. 104 0 .005 .01 .015 .02 Density 0 100 200 300 400 Number of T neighbors 0 .005 .01 .015 .02 Density 0 100 200 300 400 Number of PM neighbors Figure 13: Histograms of the degree (number of network neighbors) of all firm-years for the technology (TECH) and Hoberg-Phillips (PROD) networks. The mean and median degree of the TECH network are 80.1 (68), those of the PROD network are 79.3 (71). Averaged across the years, any two firms have a 3.7% (3.5%) unconditional chance of being TECH neighbors (PROD neighbours). Conditional on being TECH neighbors, any two firms have a 32.3% chance of also being PROD neighbors; the chance of PROD neighbors also being TECH neighbors is 33.5%. Thus, there is overlap between the two networks far in excess of what we would expect by chance, but firms’ TECH and PROD neighbor lists also differ significantly. 105 Figure 14: Technology and product market neighbors of Apple Computer in 2006. The technology neighbors are based on similarities in firms’ patent text, while the product market neighbors are based on similarities in firms’ 10-K product descriptions (Hoberg and Phillips (2010)). As an illustration, Figure 14 displays the largest five firms that were TECH or PROD neighbors or both of Apple Computer in 2006. In 2006, Apple Computer produced personal computers and personal music players (iPods). The long rumored iPhone was announced on January 9, 2007. Several of Apple’s patents in 2005 and 2006 dealt with cellular phone technology, with the result that AT&T, Sprint, and Motorola are all TECH-neighbors but not PROD-neighbors. For the same reason, Google was also a TECH-neighbor of Apple in 2006, although neither firm was officially involved in the mobile phone market at the time. In November 2007, Google announced the Android mobile operating system and in 2010 it launched its own line of Nexus smartphones and tablets. Google and Apple first became Hoberg-Phillips (PROD) neighbors in 2010. 106 3.5 Correlation with Firm Characteristics Table 20 shows the results of regressingln(Q) by firm-year ontechdiff and other covariates. Column 1 shows that bothtechdiff and the log of patents granted are positively correlated with Tobin’sQ within industries over time; Column 2 shows thattechdiff is also correlated with Q when the identifying variation is within-firm over time. Both coefficients are eco- nomically sizeable – a one standard deviation increase intechdiff is associated with a 1.8% or 1.4% higher average Q. Imrohoroglu and Tuzel (2014) impute total factor productivity (TFP) for Compustat firms using semiparametric methods 12 . They document that high TFP firms tend to be large growth firms that are younger, less levered, and whose capital and labor grow more rapidly than low TFP firms. Table 20 columns 3 and 4 show that TFP is strongly positively correlated with technological differentiation. As with firm Q, the size of the coefficient is again large: a one standard deviation increase intechdiff is associated with a 1.9% to 2.7% higher TFP for that firm-year relative to the firm’s sample average. Table 20 columns 5 and 6 show that techdiff is also positively associated with investment (capex over total assets) although the coefficient is more modest. 12 Many thanks to Selale Tuzel and Ayse Imhoroglu for sharing their firm-year TFP measurements. 107 Table 20: The table regresses log of Tobin’s average Q, firm TFP and capital expenditures over assets on techdiff plus other control variables and fixed effects. The independent variables have been standardized to have zero mean and unit variance. The standard errors are clustered by firm and year. (1) (2) (3) (4) (5) (6) VARIABLES logQ logQ TFP TFP CAPX_AT CAPX_AT techdiff 0.018** 0.014* 0.019*** 0.027*** 0.0011** 0.0014* (0.0075) (0.0080) (0.0070) (0.0058) (0.00055) (0.00074) logpat 0.047*** -0.0098* -0.011** -0.029*** 0.0010* -0.0020*** (0.0065) (0.0059) (0.0058) (0.0058) (0.00055) (0.00049) RD/AT 0.13*** 0.037*** -0.061*** -0.17*** 0.0021*** 0.0048*** (0.010) (0.0089) (0.015) (0.016) (0.00059) (0.00066) ln(Total Assets) -0.026* -0.14*** 0.20*** 0.21*** 0.0040*** 0.0041*** (0.013) (0.020) (0.014) (0.020) (0.00072) (0.0015) Industry HHI -0.0037 0.0097 -0.021*** -0.014** 0.00088 3.8e-06 (0.0062) (0.0072) (0.0053) (0.0065) (0.00055) (0.00063) Observations 58,761 58,312 43,472 43,094 58,197 57,741 R-squared 0.061 0.017 0.114 0.055 0.006 0.005 Industry FE Yes No Yes No Yes No Firm FE No Yes No Yes No Yes Year FE Yes Yes Yes Yes Yes Yes Number of gvkey 4,928 3,731 4,910 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 3.5.1 TFP and techdiff based on Census data There are potential problems with the TFP imputed by Imrohoroglu and Tuzel (2014) from Compustat data. In particular, Compustat lacks detailed data on inputs and outputs, mak- ing it impossible to compute TFP directly and the imputation of TFP based on aggregate data is prone to (possibly systematic) error. To investigate this possibility I make use of plant-level TFP estimated from the Census Longitudinal Research Database (LRD) 13 . The LRD is a detailed database of public and private manufacturing firms (SIC 20-39) from 1972 to 2006. In particular the LRD contains 13 Any opinions and conclusions expressed herein are those of the author(s) and do not necessarily represent the views of the U.S. Census Bureau. All results have been reviewed to ensure that no confidential informa- tion is disclosed. Support for this research at the Los Angeles RDC from NSF(ITR-0427889) is gratefully acknowledged. 108 plant-level input and output data and thus is suited to accurate estimation of TFP. There are approximately 1.4 million plant-year observations and 125,000 firm-years in the data which corresponds to an average of nine yearly observations for each of 14,000 unique firms 14 . I compute firm-year TFP using three different approaches: 1. Industry (SIC3) fixed effects and aggregating to firm level weighted by total employ- ment 2. Industry (SIC3) fixed effects and aggregating to firm level weighted by total value of shipments (revenues) 3. Industry (SIC3) random effects and aggregating to firm level weighted by total em- ployment I map patents to LRD firm-years using the bridge file developed by Kerr and Fu (2008). I then compute the median techdiff score for each firm-year in the data as for the previous (CRSP/Compustat) sample. I also compute plant-level TFP using Table 21 shows the results. Unlike the results in the previous section, TFP as measured from the Census is not associated with technological differentiation in any of the specifications. 14 Due to disclosure limitations all count data from the sample is rounded to the nearest 1000. 109 Table 21: The table regresses firm-level TFP estimated from Census LRD data on techdiff plus other control variables and fixed effects. log(TVS) is the total value of shipments for that firm-year. log(K/L) is the capital-labor ratio. All independent variables have been standardized to have zero mean and unit variance. The standard errors are clustered by firm and year. TFP TFP TFP TFP TFP TFP techdiff -0.0347 -0.021 -0.0296 0.0029 0.0059 0.005 (0.021) (0.027) (0.021) (0.022) (0.024) (0.022) log(TVS) 1.6301*** 3.0257*** 1.2290*** 1.5810*** 2.6810*** 1.4142*** (0.150) (0.209) (0.145) (0.146) (0.188) (0.145) log(K/L) 0.5916*** 1.1776*** 0.4488*** 0.3672*** 0.6486*** 0.3184*** (0.071) (0.102) (0.068) (0.041) (0.063) (0.040) TFP Calculation Fixed Effects Fixed Effects Random Effects Fixed Effects Fixed Effects Random Effects TFP Aggregation Employment TVS Employment Employment TVS Employment Fixed Effects Year + SIC3 Year + SIC3 Year + SIC3 Year + Firm Year + Firm Year + Firm R 2 0.08 0.16 0.05 0.02 0.03 0.01 R 2 adj 0.08 0.16 0.05 -0.09 -0.07 -0.1 N 125000 125000 125000 123000 123000 123000 Why the discrepancy? There are three main differences between the LRD sample and the Compustat (main) sample. First, the LRD sample contains detailed plant-level informa- tion from every firm and thus a very accurate and granular estimation of TFP is possible: this is not possible using the broad firm-level data in the Compustat sample. Second, the LRD sample contains data from both public and private firms, while the Compustat sample contains data from public firms only. Third, the LRD sample contains data from manufac- turing firms (SIC 20-39) only, while the Compustat sample contains data from firms of all industries. To allow a cleaner comparison I regress TFP ontechdiff in the Compustat sample using only firms in SICs 20-39. Table 22 shows the results, which find again that techdiff is positively associated with Compustat-based TFP in manufacturing firms. I also reran the 110 analysis in the LRD sample using only firms that were publicly listed, and obtained similar results to Table 21 i.e. no significant relation with firm-level TFP. Thus the difference between the Compustat and LRD results is not due to sample composition, but rather to how TFP is measured. Most likely, imputing TFP using the LRD data is more accurate, and the true relationship is nonsignificant as in Table 21. Table 22: The table regresses log of Tobin’s average Q, firm TFP and capital expenditures over assets on techdiff plus other control variables and fixed effects, for firms in manufac- turing industries (SIC 20-39) only. The independent variables have been standardized to have zero mean and unit variance. The standard errors are clustered by firm and year. (1) (2) (3) (4) (5) (6) VARIABLES logQ logQ TFP TFP CAPX_AT CAPX_AT techdiff 0.0060 0.0075 0.021*** 0.023*** 0.0013** 0.0012* (0.0087) (0.0071) (0.0064) (0.0052) (0.00057) (0.00068) logpat 0.053*** -0.020*** -0.012* -0.034*** 0.0023*** -0.0022*** (0.0084) (0.0072) (0.0065) (0.0063) (0.00068) (0.00059) RD/AT 0.12*** 0.042*** -0.048*** -0.17*** 0.0024*** 0.0051*** (0.011) (0.0098) (0.016) (0.018) (0.00067) (0.00073) ln(Total Assets) 0.0026 -0.12*** 0.17*** 0.21*** 0.0035*** 0.0046*** (0.013) (0.019) (0.014) (0.019) (0.00074) (0.0015) Industry HHI -0.0010 0.012 -0.021*** -0.015** 0.00060 0.00039 (0.0065) (0.0075) (0.0051) (0.0064) (0.00053) (0.00062) Observations 55,210 54,927 42,040 41,802 55,296 55,010 R-squared 0.071 0.017 0.098 0.055 0.009 0.005 Industry FE Yes No Yes No Yes No Firm FE No Yes No Yes No Yes Year FE Yes Yes Yes Yes Yes Yes Number of gvkey 3,937 3,003 3,934 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 4 Model If R&D immediately converts into new products, firms’ technological and product market positions are always identical. There is reason to think that the real optionality in firms’ strategy is material, however, starting with McDonald and Siegel (1986). In this section, I develop a model that characterizes the effects that real options on new products have on the 111 cross section of expected returns. Consider a set of n≥ 1 products that are substitutes (if n > 1). The firm producing product i pays a fixed cost of production c i and faces demand q i = q ˜ X   α i − X j6=i γ ij α j   −p i + X j6=i γ ij p j The demand function is that of a representative consumer who has generalized quadratic utility from consumption of a set of products with quality α i and elasticity of substitution γ ij (Vives (2001); Vives (2008); Phillips and Zhdanov (2013)). For simplicity, assume the product market is symmetric γ ij = γ, α i = α, c i = c. Then the industry equilibrium is: p i = (1−γ(n− 1))α √ ˜ X 2−γ(n− 1) ∀i q i = (1−γ(n− 1)) α q ˜ X−p ∀i π i = (1−γ(n− 1)) α q ˜ X−p ( (1−γ(n− 1))α √ ˜ X 2−γ(n− 1) )−c = (γ(n− 1)− 1) 2 (γ(n− 1)− 2) 2 α 2 ˜ X−c =B ˜ X−c , where the support of the demand shock ˜ X is bounded below so that prices, quantities and profits π are always positive. Profits π and the coefficient B are both increasing in α and decreasing in γ and n. π decreases with c, but changing c does not change B. The product market resolves and profits are paid at t = 1. At t = 0 the CAPM holds (for example because investors have quadratic preferences over final wealth). I set the risk free rate to zero for simplicity. X contains an industry or product-specific demand shock 112 and also covaries one for one with the return on the wealth portfolio: ˜ X = e A +r m The value at time t = 0 of an existing product is: V n =E[π n ]−Bμ The market beta of the asset is β = B V n = 1 E[ ˜ X]−c/B−μ Products with higher quality (highα), less close substitutes (lowγ) and fewer competing products (low n) have lower beta and lower expected returns. Products with higher costs of production c have higher beta and expected returns, due to “operating leverage” (e.g. Carlson, Fisher and Giammarino (2004)). At t = 0 an outside firm (that does not currently produce in the industry) has a real option to introduce a new product at costI. Att = 0 + ,I is revealed as eitherI hi >V n+1 or I lo <V n+1 with equal chance. Thus there is a 50% chance that the project is in the money. The realization of I is unrelated to the market return. At t = 0 the value of the real option is thus V opt = 0.5(V n+1 −I lo ) and the beta of the real option with the market is β opt = B V n+1 −I lo >β Holding an option on the asset rather than the asset itself creates further leverage: the 113 option’s beta is strictly greater than the asset’s beta and is increasing in the cost of imple- menting the project I. The CAPM still prices the option correctly, because the implemen- tation cost I creates a pure leverage effect just like an operating cost, so its beta is just a multiple of the asset beta. If as in Da Guo Jagannathan the option payoff is nonlinear in the market return then the (unconditional) CAPM can fail to price it correctly. Maximizing firm value means that firms wish to create new products, and alter existing products,tohavehighquality(higherα),highdifferentiation(lowerγ andn),andlowcostsc. Whether applied to existing products or new products, all four forms of successful innovation result in lower systematic risk and lower expected returns. The model uses the CAPM but themarketreturncanbereplacedwithanysystematicfactor(s)thatarepositivelycorrelated with consumer demand. Thus, it appears to be a robust prediction that: 1. Successfulinnovation(inparticular,technologicaldifferentiation–products/technologies with few substitutes and competitors) predicts lower returns 2. The effects of technology on returns are strongest in firms with the highest ratio of growth options to assets in place, that is, small firms, young firms, and growth (low book to market) firms. 5 Returns Monthly stock returns are from CRSP. I retain only U.S. firms traded on the NYSE, NAS- DAQ and AMEX from 1961 to 2010. I follow standard practice and update firms’ accounting data at the end of June, using data from the fiscal year ending in the previous December at the latest. I drop any firms with a market value or book value of assets that is missing or negative. 114 Table 23 presents the results of Fama-MacBeth regressions of monthly excess returns on techdiff along with other variables and standard benchmarks. The first column shows that techdiff is negatively associated with subsequent returns after controlling for firm size (market cap), market-to-book ratio, operating profits, asset growth, one month reversal and six month momentum. The second column shows that the relationship persists after controllingforR&Dintensity(Chan, LakonishokandSougiannis(2001), innovativeefficiency (Hirshleifer, Hsu and Li (2013)) and innovative diversity (Hirshleifer, Hsu and Li (2012)) which have been previously found to be associated with excess returns. These results are consistent with prediction #1 of the model. The third column of Table 23 shows that measures of product market differentiation do not predict returns. These results are consistent with prediction #2 of the model, that the risk of assets in place is well measured by accounting variables. 115 Table 23: Coefficients of Fama-MacBeth regressions of monthly excess returns for patenting firms from 1961-2010 on text-based technological differentiation (techdiff), measures of product market differentiation, and other variables. The dependent variable is annualized monthly excess returns, (rtn t+1 −r f t )×12. All independent variables have been standardized to have zero mean and unit variance. (1) (2) (3) VARIABLES rtnrf rtnrf rtnrf techdiff -0.021*** -0.011** -0.014** (0.0065) (0.0055) (0.0060) logME -0.045*** -0.045*** -0.044*** (0.012) (0.011) (0.012) logBM 0.023** 0.0082 0.022** (0.0098) (0.0092) (0.011) logOP 0.025*** 0.020*** 0.037*** (0.0086) (0.0075) (0.012) logINV -0.031** -0.026*** -0.021* (0.013) (0.0065) (0.012) RDMEw 0.030*** 0.026 (0.0076) (0.040) l1rtn -0.099*** -0.11*** -0.10*** (0.013) (0.0083) (0.012) l12rtn 0.019 0.0063 0.013 (0.014) (0.011) (0.014) ID1 0.0050 (0.0045) IE1 -1.31** (0.62) herf -0.0043 (0.0027) herf_naics -0.0022 (0.0047) Observations 628,496 387,256 628,496 R-squared 0.090 0.061 0.100 Number of groups 583 432 583 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 116 Table 24 shows that the association of technological differentiation with lower returns is concentrated in small firms (market cap less than the median across all firms in that year) and young firms (firm age less than the median across all firms in that year). These results are consistent with the model. Columns 1 and 2 show that the association of techdiff with lower returns is concentrated in value firms not growth firms, which is inconsistent with the model’s predictions. Table 24: Coefficients of Fama-MacBeth regressions of monthly excess returns for patenting firms from 1961-2010 on text-based technological differentiation (techdiff) for subsets of the sample. Growth, Small and Young firms are those below the median firm book-to-market, size and age within each year. The dependent variable is annualized monthly excess returns, (rtn t+1 −r f t )× 12. All independent variables have been standardized to have zero mean and unit variance. (1) (2) (3) (4) (5) (6) VARIABLES Growth Value Small Big Young Old techdiff -0.020 -0.034*** -0.045*** -0.013 -0.027*** 0.011 (0.012) (0.0089) (0.011) (0.0093) (0.0078) (0.031) Observations 297,592 330,904 298,953 329,543 266,094 362,402 R-squared 0.117 0.101 0.096 0.123 0.108 0.109 Number of groups 583 583 583 583 583 583 Other Controls Yes Yes Yes Yes Yes Yes Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 117 Table 25: Panel A shows monthly portfolio returns from 1961-2010 after independent sorts on size (market value of equity) and techdiff . Panel B shows portfolio betas against the techdiff HML factor. Panel A: Excess Returns by Portfolio techdiff Portfolio 1 2 3 4 5 HML 1 0.0200 0.0178 0.0156 0.0163 0.0134 −0.0065 ∗ (0.0051) (0.0037) (0.0035) (0.0033) (0.0029) (0.0037) 2 0.0146 0.0113 0.0103 0.0089 0.0091 −0.0059 ∗∗ Size (0.0043) (0.0033) (0.0030) (0.0030) (0.0028) (0.0029) Portfolio 3 0.0117 0.0100 0.0073 0.0072 0.0076 −0.0045 ∗∗ (0.0035) (0.0030) (0.0029) (0.0028) (0.0027) (0.0021) 4 0.0104 0.0082 0.0065 0.0053 0.0076 −0.0033 ∗∗ (0.0029) (0.0027) (0.0026) (0.0026) (0.0026) (0.0015) 5 0.0066 0.0056 0.0046 0.0067 0.0051 -0.0015 (0.0022) (0.0023) (0.0024) (0.0023) (0.0023) (0.0013) Panel B: Betas against techdiff HML returns techdiff Portfolio 1 2 3 4 5 1 -1.12 -0.34 -0.30 -0.24 -0.09 (0.03) (0.04) (0.04) (0.03) (0.03) 2 -1.13 -0.48 -0.31 -0.29 -0.11 Size (0.04) (0.04) (0.04) (0.04) (0.04) Portfolio 3 -1.07 -0.47 -0.42 -0.20 -0.07 (0.05) (0.05) (0.05) (0.05) (0.05) 4 -0.85 -0.45 -0.25 -0.33 0.07 (0.07) (0.07) (0.07) (0.07) (0.07) 5 -0.24 -0.05 -0.07 0.27 0.72 (0.07) (0.07) (0.09) (0.07) (0.08) Table 25 shows the results of monthly independent double sorts on size (market capi- talization) and techdiff. Panel A shows sizeable differences in monthly returns between the highest and lowesttechdiff quintile, up to 1.16% per month in the second-smallest size quintile. The return difference is primarily among the smallest firms by market cap, and is absent in the largest size quintile. Panel B shows betas of each of the portfolios against the monthly returns of the high- 118 minus-lowtechdiff portfolio. We see that there is a nearly monotonic relationship between the betas and techdiff quintiles, which is generally consistent with the “risk” story in this paper and less consistent with a “mispricing” story. 6 Conclusion This paper uses patent text to impute firms’ technological positions. Firms’ location in technology space is related to but reliably different from their location in product market space per Hoberg and Phillips. I find that firms’ degree of technological differentiation predicts future product differentiation, but the reverse is not true. 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Yang, Fan, ‘Investment Shocks and the Commodity Basis Spread’, Journal of Financial Economics, Forthcoming (2013)hURL: http://www.sciencedirect.com/science/ article/pii/S0304405X13001360i, ISSN 0304–405X. Yogo, M., ‘A consumption-based explanation of expected stock returns’, Journal of Finance, 61 (2006):2, p.539–580. 129 A Selecting Ngrams To select words and phrases that summarize patents into vectors, I do the following: For each patent: 1. Select body text (background, description and claims sections) 2. Remove words that are only numbers or only contain ATCG (genetic code) 3. Extract all single words and all two word phrases (collectively, ’ngrams’) 4. Filter out standard stopwords such as articles, prepositions, and place names 5. Compare each word in each ngram to the Wordnet lexicon to see if it can be used as an English noun 6. Keep only ngrams made up of English nouns Across the corpus, for each year (“focal year”) from 1960 to 2010: 1. For every ngram count the number of documents (patents) granted in or before the focal year in which the ngram occurs. 2. Select the 50,000 most common ngrams that appear in no more than 1% of all patents in the sample up to the focal year. The process yields a dictionary (list of ngrams) for each year from 1960 to 2010, using the text of patents granted up to and including that year. Each patent is then represented as a Boolean vector using the dictionary for its year, with a one in positions where the patent contains that word or phrase and a zero if not. Patents are dropped if they contain fewer than 10 ngrams. 130 The limit of 50,000 ngrams per year is due to computational limits. Using 40,000 instead or a 0.5% or 2% upper bound for ngram frequency gives very similar results. B Patent Reassignments Both the NBER and Kogan etal. (2014) databases assign patents to firms as of the patent’s grant date. However, patents are often reassigned to a new legal owner via mergers, acquisi- tions, or sales of IP assets. Recently, data on patent reassignments (when a patent is legally reassigned from one firm to another in the USPTO’s ledger) have become available online. I mapped post-grant-date reassignments to CRSP PERMNOs using a fuzzy string match of the reassignment records with the grant-date matches of Kogan et al. The data suggest that patents are frequently reassigned. From 1980 to 2010 there were 229,000 reassignments for which at least one of the assignor and assignee were publically traded (CRSP) firms. I thus augment the Kogan etal. (2014) map in the following way. Whenever a patent is reassigned I subtract the patent’s depreciated Boolean vector from the selling firm’s patent stock vector and add it to the acquiring firm’s stock vector. Relative to just using the Kogan etal. (2014) map, the augmented map does not alter any of the results in the paper and in most cases, makes them slightly stronger. 131 C Individual Patents C.1 Technology Measures by Individual Patent I compute the cosine similarity of each patent vector with every other patent vector. This is a commonly used measure of two documents’ similarity; for patent vectors i and j it equals the dot product cos ij = pvec i kpvec i k ! · pvec j kpvec j k ! The first patent-level measure I calculate is patent quality. This measure is based on two sub-measures: influence, which is the median similarity of the focal patent to the 100 nearest neighbouring patents from subsequent years, and originality, which is one minus the median similarity of the focal patent to the 100 nearest neighbouring patents from previous years. Originality measures how uncommon a patent’s ngrams – and the specific mix of ngrams in the patent – were in patents that precede it. Influence measures how common they were in patents that follow. Text-based quality is originality plus influence – or equivalently, the difference in similarity of patents that postdate the focal patent minus those that predate the focal patent. For example, ngrams relating to the Internet do not appear at all in the 1970s and 80s but appear increasingly often in the 1990s and 2000s. Thus, a patent related to the internet that appears in the 1990s will be generally scored as having high originality, influence, and quality. Patents’ originality and influence scores are strongly negatively correlated (ρ =−0.71), because some ngrams are more common than others throughout the sample. A patent related to microprocessors or recombinant DNA tends to have both low originality and high influence, relative to a patent related to hockey helmets. The quality measure avoids this issue: if a patent’s similarity to its decedents and antecedents is the sum of a patent-specific 132 component and a non time varying component specific to its area, then quality differences out the latter. The second patent-level measure is vintage. For each ngram in the list, I note the first year that that word or phrase appears in any patent. vintage is defined as the dot product of a patent’s Boolean vector with the vector of first-mention years, divided by the number of entries in the vector: vintage i = pvec 0 i ·firstmention pvec 0 i ·1 vintage is thus the average year of first mention across all the ngrams contained in the patent. It reflects how current the language in the patent is, without direct reference to other patents. C.2 Validation: Patent Renewals A patent is valid for up to twenty years; for all patents granted after December 1981, the patent expires at four, eight and twelve years unless a renewal fee is paid. In 2013 the fees were $1600, $3600 and $7400. Thus, one measure of whether or not a patent’s value exceeds some minimal value is whether it was renewed or not. Of the 1.6 million patents granted between 1982 and 1998, 84%, 63% and 44% were renewed after four, eight and twelve years respectively. Table 26 shows the results of regressing a dummy variable that equals one if the patent was renewed after twelve years on our measures of patent quality. Citations are strongly correlated with renewal. Some of this is likely a selection effect because both are ex post outcomes: conditional on patent value, a patent that is not renewed is less likely to be cited. 133 Text-basedquality andvintage are potentially subject to a similar critique, because they are based on the list of informative ngrams which are selected from their usage throughout the entiresample. Butbecausetheselectioneffectisatthelevelofngramsratherthanthepatent itself, the bias for the text-based measures is likely to be less than it is for citations. We see that both text-based measures are strongly positively correlated with subsequent renewal. A one standard deviation increase inquality orvintage is associated with an increase in the likelihood that the patent will be renewed after 12 years by 3.6% and 7.0%, respectively. Table 26: Logit regressions of patent renewal on text based measures, for all U.S. utility patents granted from 1982 to 1998. The dependent variable is a dummy variable that equals one if the patent is renewed at the twelve year mark. The independent variables are standardized to unit variance, and the coefficients report the estimated marginal effects. The standard errors are clustered by year. Logit Logit Logit 12yr Renew 12yr Renew 12yr Renew quality i 0.036*** 0.014*** (0.0040) (0.0029) vintage i 0.070*** 0.062*** (0.0043) (0.0043) ln(cites i ) 0.099*** 0.084*** (0.0030) (0.0023) Observations 1,617,938 1,617,938 1,617,938 Fixed Effects Year Year Year Pseudo R-squared 0.032 0.026 0.043 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 134 D Simulation To illustrate the effects of growth options on the cross section of expected returns, I simulate a cross section of 1000 firms. In the economy the CAPM holds withμ = 0.06,r f = 0. There are two types of products. Type 1 products are nondifferentiated (β = 1.5), Type 2 products are differentiated (β = 0.5). Otherwise the products are identical with parameters I = 1, σ = 0.2, ν =−0.02, D initial = 1. Firms have arrival probabilities of innovations that are drawn from a uniform joint distribution on [0, 0.1]× [0, 0.1]. Each step consists of: 1. Cash flow shocks arrive for all existing products and options 2. Firms exercise options with D t >D ∗ j 3. New innovations arrive 4. Firms update their book values I simulate 1000 firms for 10,000 steps which is enough to reach the stationary distribution. E Measuring Technology Using Patent Classes In a seminal study, Jaffe (1986) characterized firms’ technological positions using count vectors of patent classes. The USPTO assigns each patent to one primary and any number of secondary technology classes that characterize the type of innovation being patented. In Jaffe (1986) if there are five patent classes and firm i has five patents whose primary classes are #1, #1, #2, #5 and #5, then firm i’s technology position is ( 2 3 , 1 3 , 0, 0, 2 3 ) 0 . Bena and Li (2013) compute the relatedness between merging firms using the cosine similarity of firms’ 135 patent class vectors. Hirshleifer, Hsu and Li (2012) measure firms’ innovative diversity using the Herfindahl of their patent classes. There are three potential measurement issues with using technological classes. First, the classes are designed to expedite the USPTO examiners’ search for prior art and as a result they reflect the technological nature of the patent and not its intended use. Schmookler (1972) cites the class “Dispensing: solids” which contains patents for both toothpaste tubes and commercial manure spreaders. Second, some classes are enormously more active than others. For example, since 1960 there have been 96,639 patents in “Drug, bio-affecting and body treating compositions” and three in “Land vehicles: animal draft”. Third, new technologies are often slotted into old classes, which causes the composition of classes to change over time. The patent from the year 2000 for Google’s PageRank algorithm is in class 715, “Data Processing: presentation processing of document, operator interface processing, and screen saver display processing” whichalsocontainsU.S.Patent#3325786, “Machinefor composing ideographs”, a 1964 patent on a physical machine that translates a typewriter’s input into Chinese characters. Thus, a firm in the year 2000 pursuing 1960s-era mechanical technology (or 1990s-era screen savers) would be coded as highly similar to Google. Using the text of individual patents produces a more accurate picture of the evolution of technology. First, a patent’s text describes both the technology and its intended use; using textual measures, toothpaste tubes will be grouped with dental innovations and manure spreaders with agricultural innovations. Second, the resolution of the picture is much higher: I examine the incidence of over 60,000 key words and phrases compared to 430 patent classes. Third, new words and phrases (and more subtly, new combinations of old words and phrases) are incorporated de novo and not allocated to preexisting categories. The second and third concerns (resolution and novelty) loom particularly large in mea- 136 suring technological originality or differentiation at the firm level. Due to comparative ad- vantage, large mature firms will pursue smaller more applied innovations while small firms will pursue larger more disruptive innovations (Schumpeter (1942)). Large mature firms also have more diverse operations. Thus, large mature firms will pursue incremental innovations across many areas and small startups will pursue original innovations in one specific area. In this sketch of the economy, measuring firms’ innovation by the diversity of their patent classes, or measuring their similarity in terms of the similarity of their patent classes, may confuse size and/or diversity with originality. Text-based measures are subject to similar concerns because firms with more diverse projects will use more diverse words. But the concern is less, for two reasons. First, text has much higher resolution. Second, new words and phrases are incorporated into the analysis as new. Ultimately whether patent classes or patent text is a better measure of firms’ technology is an empirical question. To answer it, I re-map firms using the Jaffe approach. I characterize each patent by a vector with a one signifying its primary USPTO technology class and zero elsewhere (the results are the same if I include secondary classes). I sum the patent vectors by firm-year, and fill missing observations and construct ’rolling stock’ as for the text-based measures. I compute firm-firm cosine similarities (“Jaffe similarity”) within each year and define “Jaffe differentiation” jaffediff as one minus the 99th quantile of Jaffe similarity for each firm-year in the sample. Notably, the correlation of jaffediff with the text-based measure techdiff is−0.24: using the same patent data, the two measures of firms’ technological differentiation are negatively correlated. In 2005 the techdiff score for Google was 0.69 compared to 0.36 for Intel. Google’s jaffediff score was 0.09 compared to 0.46 for Intel. Thus the text-based 137 measure suggests that Google was 2.8 standard deviations more original in 2005 than Intel 15 , while the class-based measure suggests the opposite. Table 27 shows thatjaffediff is positively correlated with firms’ age, book assets, sales, and book to market ratio. The correlations are opposite for techdiff. Table 28 presents the results of regressing log Q, TFP, ROA and investment on jaffediff and other firm characteristics. Recall from Section I.5 Table 20 that the text-based measure techdiff is positively related to all four. In contrast, jaffediff is negatively related to Q, TFP, and ROA and effectively uncorrelated with firm investment. Thus, measuring firms’ technology by their patent classes implies that the most techno- logically differentiated firms in the economy are large, old, value firms with low Q , TFP and ROA. The techdiff text-based measure, on the other hand, suggests that the most differentiated firms are small, young firms with high Q, TFP, ROA and investment. The results fortechdiff agree with our intuition, and suggest that techdiff is a better measure for our purposes. Table 27: Correlations of measures of technological differentiation with contemporaneous firm characteristics, for all Compustat firm-years with patents outstanding from 1976-2010. jaffediff techdiff jaffediff 1 techdiff -0.24 1 age 0.43 -0.44 ln(assets) 0.34 -0.58 ln(sales) 0.40 -0.49 BooktoMkt 0.18 0.00 15 The standard deviations of techdiff and jaffediff are 0.12 and 0.22 respectively in 2005. 138 Table 28: The table regresses log Q, ROA, capex and TFP imputed by firm-year on the technology class-based measurejaffediff plus other firm-year characteristics. All indepen- dent variables are standardized to have zero mean and unit variance. The standard errors are clustered by firm and year. (1) (2) (3) (4) (5) (6) (7) (8) VARIABLES logQ logQ logTFP logTFP ROA ROA CAPX/AT CAPX/AT jaffediff -0.037*** -0.024*** -0.037*** -0.017** -0.0061*** -0.0046*** -0.0015** 0.00026 (0.0073) (0.0076) (0.0059) (0.0070) (0.0020) (0.0018) (0.00061) (0.00063) ln(patent stock) 0.035*** -0.059*** -0.054*** -0.10*** -0.011*** -0.018*** -0.00087 -0.0058*** (0.0093) (0.012) (0.0085) (0.013) (0.0027) (0.0027) (0.00074) (0.00088) RD/AT 0.11*** 0.033*** -0.082*** -0.17*** -0.10*** -0.083*** 0.0028*** 0.0057*** (0.010) (0.010) (0.019) (0.020) (0.0032) (0.0039) (0.00068) (0.00080) ln(Total Assets) -0.027* -0.16*** 0.22*** 0.22*** 0.063*** 0.022*** 0.0049*** 0.0038** (0.016) (0.026) (0.019) (0.026) (0.0057) (0.0064) (0.0010) (0.0018) Industry HHI 0.028*** 0.013 -0.013* -0.0051 -0.0033* -0.0046** 0.0030*** 0.0018** (0.0087) (0.0082) (0.0070) (0.0069) (0.0020) (0.0019) (0.00088) (0.00077) Observations 30,214 29,489 24,307 23,735 30,165 29,442 29,898 29,177 R-squared 0.043 0.028 0.099 0.062 0.410 0.178 0.007 0.010 Industry FE Yes Yes Yes Yes Year FE Yes Yes Yes Yes Yes Yes Yes Yes Number of gvkey 3,249 2,526 3,248 3,241 Firm FE Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 139

Abstract (if available)

Abstract This paper constructs a macro‐finance model for commodity futures. I document a negative feedback relationship between crude oil prices and real economic activity. The channel from real activity to oil prices is unspanned—meaning not identified in current futures prices—consistent with oil futures as a hedge asset against supply shocks. Unspanned macroeconomic risks have first order effects on risk premiums and the value of real options. The model also yields a precise estimate of the cost of carry that is strongly related to physical inventories.

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Creator Heath, Davidson (author)

Core Title Essays on real options

School Marshall School of Business

Degree Doctor of Philosophy

Degree Program Finance

Publication Date 06/09/2015

Defense Date 05/16/2015

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

Tag affine,Commodities,futures,innovation,OAI-PMH Harvest,Patents,real options,stock returns,textual

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Ferson, Wayne (committee chair), Ahern, Kenneth (committee member), Hoberg, Gerard (committee member), Joslin, Scott (committee member), Phillips, Gordon M. (committee member)

Creator Email davidsontheath@gmail.com,dheath@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-569378

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