Limits to Arbitrage and Hedging: Evidence from Commodity Markets

Transcription

1 Limits to Arbitrage and Hedging: Evidence from Commodity Markets Viral Acharya, Lars Lochstoer, and Tarun Ramadorai Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 1 / 44

2 Motivation: Limits-to-arbitrage and hedging pressure A measure of arbitrage capital employed in the Crude Oil futures market versus the component of the futures risk premium due to producer hedging pressure (from one of our measures) data annual, overlapping at quarterly frequency, variables normalized Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 2 / 44

3 Managers maximize rm value (no role for futures market) Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 3 / 44

4 Managers maximize rm value BUT also wants to minimize variance a role for futures market hedging decisions have no impact on commodity spot or futures prices Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 4 / 44

5 Real-world markets have frictions. An important one: Limits to Arbitrage. Shleifer and Vishny, 1997; Gromb and Vayanos, 2002; Brunnermeier and Pedersen, Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 5 / 44

6 Paper summary Propose simple equilibrium model that formalizes the "limits-to-hedging"-argument Managers of commodity producing rms aim to maximize share value, but also averse to price risk Financial intermediaries in commodity futures market capital constrained These features a ect producers desire and economic cost of inventory hedging, which in turn a ects spot and futures prices Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 6 / 44

7 Paper summary Propose simple equilibrium model that formalizes the "limits-to-hedging"-argument Managers of commodity producing rms aim to maximize share value, but also averse to price risk Financial intermediaries in commodity futures market capital constrained These features a ect producers desire and economic cost of inventory hedging, which in turn a ects spot and futures prices Novel empirical analysis Propose measures of producers default risk as proxies for managers desire to hedge price risk: "The amount of production we hedge is driven by the amount of debt on our consolidated balance sheet and the level of capital commitments we have in place." - St. Mary Land & Exploration Co., in their 10-K ling for (Average market value of equity in 2006 was $2.5 billion.) Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 6 / 44

8 Paper summary () We con rm model predictions in U.S. Crude Oil, Heating Oil, Gasoline, and Natural Gas commodity markets 1 A 1 st.dev. increase in aggregate producer fundamental hedging demand -> a 4% increase in the quarterly futures risk premium 2 Similar e ect for expected spot price changes 3 Aggregate commodity inventory decreasing in both producer hedging demand and speculator capital constraints 4 nteraction between arbitrage capital and hedging demand on futures risk premium and inventory levels Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 7 / 44

9 Outline of Talk 1 The Model 2 Evidence of producer hedging 3 Price impact of producer hedging 4 nteraction of producer hedging and speculative demand Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 8 / 44

10 The model Two periods (empirical analysis focuses on short-term futures): 1 Supply of commodity, g t, pre-determined 2 r = 1/E [Λ] 1; d 2 [0, 1) Consumers inverse demand function: 1/ε At S t = ω, Q t where: Q t = g t t + (1 d) t 1 ln A t ln A t 1 N µ, σ 2 is demand shock S t is the commodity spot price ω and ε are positive constants. Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 9 / 44

11 Producers Competitive, price-takers. Representative rm: max f,h p g S 0 (g 0 ) + E [Λ fs 1 ((1 d) + g 1 ) + h p (F S 1 )g]... subject to γ p 2 Var [S 1 ((1 d) + g 1 ) + h p (F S 1 )] 0, where γ p governs the degree of aversion to variance in future earnings. Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 10 / 44

12 Producers Competitive, price-takers. Representative rm: max f,h p g S 0 (g 0 ) + E [Λ fs 1 ((1 d) + g 1 ) + h p (F S 1 )g]... subject to γ p 2 Var [S 1 ((1 d) + g 1 ) + h p (F S 1 )] 0, where γ p governs the degree of aversion to variance in future earnings. Note: if E [Λ (S 1 F )] > 0, costly in terms of rm value to hedge by going short Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 10 / 44

13 Representative Speculator Objective Function Capital constraints (e.g., due to VaR constraint as in Danielsson, Shin, and Zigrand (2008)) in the form of variance penalty: max h S h s E [Λ (S 1 F )] γ s 2 Var [h s (S 1 F )] Equilibrium: Futures and spot market clears, producer and speculator FOCs hold (σ f = σ S /F ): S1 E F F = Corr (Λ, S 1 ) Std (Λ) σ {z f } usual risk term + γ p γ s γ p + γ s σ 2 f FQ 1 {z } price pressure Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 11 / 44

14 Comparative Statics and Empirical Predictions 1 ncreasing producer risk aversion (fundamental hedging demand), γ p : 1 ncreases optimal number of short futures contracts (hedging) 2 ncreases futures risk premium 3 Decreases inventory 4 Decreases current spot price and increases expected future spot price 2 ncreasing speculator risk tolerance, γ s : 1 Decreases futures risk premium 2 ncreases inventory 3 ncreases current spot price 3 nteraction between speculator risk tolerance and e ect of hedging demand on risk premium, spot price, and inventory. Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 12 / 44

15 Overview of Empirical Approach 1 Measures of Default Risk proxy for time-varying fundamental hedging demand (γ p ) (Gilson, 1989; Haushalter, 2000; Fehle and Tsyplakov, 2005). 1 Data limitations force commodity selection: Crude Oil, Heating Oil, Gasoline, and Natural Gas. 2 Provide rm level and aggregate evidence that producers hedging activity indeed is related to default risk measures 3 Construct commodity sector average default risk measures from rm-level data and test model s pricing implications 4 Control for other possible omitted determinants of futures risk premium 1 Controls: Standard predictive variables 2 Volatility nteraction (implied by model) 3 Hedgers versus non-hedgers 4 Producers versus re ners Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 13 / 44

16 Controls Aggregate: 1 Slope of the Treasury bond term structure (5yr - 1yr yields) 2 The quarterly T-bill rate 3 Aggregate default spread (Baa - Aaa spread on corporate bonds) 4 Analyst GDP growth forecasts Commodity speci c: 1 Basis 2 nventory level 3 Lagged futures return Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 14 / 44

17 Proxies for Hedging Demand Very poor data for most rms in terms of actual hedging positions E.g., do not report direction, only notional, only VaR, etc. iral Acharya, Lars Lochstoer, and Tarun Ramadorai () 15 / 44

18 Proxies for Hedging Demand Very poor data for most rms in terms of actual hedging positions E.g., do not report direction, only notional, only VaR, etc. 1 Zmijewski-score (Zmijewski, 1984): Zmijewski-score = Netnc/TotAssets TotDebt/TotAssets CurrentAssets/CurrentLiabilities. iral Acharya, Lars Lochstoer, and Tarun Ramadorai () 15 / 44

19 Proxies for Hedging Demand Very poor data for most rms in terms of actual hedging positions E.g., do not report direction, only notional, only VaR, etc. 1 Zmijewski-score (Zmijewski, 1984): Zmijewski-score = Netnc/TotAssets TotDebt/TotAssets CurrentAssets/CurrentLiabilities. 2 Naive EDF (Bharath and Shumway, 2004): ln(v /F ) + (µ 0.5σ 2 EDF = Φ V )T!! p σ v T Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 15 / 44

20 Proxies for Hedging Demand Very poor data for most rms in terms of actual hedging positions E.g., do not report direction, only notional, only VaR, etc. 1 Zmijewski-score (Zmijewski, 1984): Zmijewski-score = Netnc/TotAssets TotDebt/TotAssets CurrentAssets/CurrentLiabilities. 2 Naive EDF (Bharath and Shumway, 2004): ln(v /F ) + (µ 0.5σ 2 EDF = Φ V )T!! p σ v T 3 3-year average stock return (Gilson, 1989): ThreeYearAvg i,t = ln (1 + R i,t k ) k =0 Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 15 / 44

21 Data Sample Main analysis (maximum) sample period: 1980Q1-2006Q4. Varies across commodities given data availability (DataStream; NYMEX) Quarterly, commodity producer balance sheet data (Compustat and Edgar) Aggregate U.S. inventory data from Energy nformation Administration. Aggregate "hedger" positions per commodity from CFTC. Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 16 / 44

22 Data Sample Main analysis (maximum) sample period: 1980Q1-2006Q4. Varies across commodities given data availability (DataStream; NYMEX) Quarterly, commodity producer balance sheet data (Compustat and Edgar) Aggregate U.S. inventory data from Energy nformation Administration. Aggregate "hedger" positions per commodity from CFTC. n the following, often show regression results only from regressions that are pooled across the four commodities Rogers (1993) standard errors; HAC, 3 lags Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 16 / 44

23 Data Sample Main analysis (maximum) sample period: 1980Q1-2006Q4. Varies across commodities given data availability (DataStream; NYMEX) Quarterly, commodity producer balance sheet data (Compustat and Edgar) Aggregate U.S. inventory data from Energy nformation Administration. Aggregate "hedger" positions per commodity from CFTC. n the following, often show regression results only from regressions that are pooled across the four commodities Rogers (1993) standard errors; HAC, 3 lags 1 "ControlVariables": The controls listed before as well as quarterly dummies to control for seasonalities 2 "HedgeVar": One of the three measures of default risk as proxies for fundamental hedging demand Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 16 / 44

24 Macro Evidence of Producer Hedging and Default Risk CFTC data on aggregate short "hedger" positions NetShortHedgers t = βhedgevar t + ControlVariables t + ε t CFTC Hedger Positions: Pooled HedgeVar: Zm score Naïve EDF avg3yr HedgeVar 0.140** 0.147** 0.090** (0.062) (0.072) (0.045) R2 18.3% 20.2% 17.4% # obs Controls? yes yes yes Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 17 / 44

25 Commodity Futures Return (NYMEX contracts) Excess return from the end of month t to t + 1 is calculated as: F t+1,t F t,t, F t,t where F t,t is nearest contract that matures after time t + 1. Quarterly return is constructed from monthly data (Hayashi, Gorton, and Rouwenhorst, 2008) These are most liquid contracts + avoid issues related to delivery. Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 18 / 44

26 Futures Forecasting Regressions FuturesReturns t+1 = βhedgevar t + ControlVariables t + ε t+1 Futures return: Pooled HedgeVar: Zm score Naïve EDF avg3yr HedgeVar 0.038** 0.036*** 0.040** (0.016) (0.009) (0.016) R2 11.4% 9.8% 12.8% # obs Controls? yes yes yes Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 19 / 44

27 Futures Forecasting Regressions - Volatility nteraction Model predicts interaction between futures return volatility and producers fundamental hedging demand (γ p ) S F E F = R f Cov (Λ, S/F ) + R f γ p γ s γ p + γ s σ 2 S /F FQ Futures return: Pooled HedgeVar: Zm score Naïve EDF avg3yr Realized Variance (RV) *** (0.030) (0.015) (0.019) HedgeVar: 0.057*** 0.068*** 0.052*** (0.019) (0.012) (0.014) HedgeVar*RV 0.041* 0.066** 0.034*** (0.022) (0.028) (0.010) R % 17.2% 13.1% # obs Controls? yes yes yes Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 20 / 44

28 Futures Forecasting Regressions - Producers vs. Re ners Classi cation based on information from annual/quarterly reports Futures return: Crude Oil Zm score Naïve EDF avg3yr All firms 0.107*** 0.055* 0.153*** (0.026) (0.033) (0.049) Refiners 0.051*** * (0.018) (0.024) (0.054) R2 18.8% 19.0% 19.1% # obs Controls? yes yes yes Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 21 / 44

29 Futures Forecasting Reg s - Hedgers vs. Non-Hedgers Classi cation based on information from annual/quarterly reports Use sum of three proxies for each rm as hedging measure (each proxy normalized to have unit variance) FutRet t+1 = b 1 (Hedger t + NonHedger t ) + b 2 NonHedger t + ContVars t + ε t+1 b1 (Hedger + b2 Non Hedger) (Non Hedger) Controls? R 2 # obs (1) Hedger measure constructed 0.055*** 0.057** yes 13.0% 343 using all hedgers (0.016) (0.026) (2) Hedger measure constructed 0.054*** 0.045** yes 12.2% 343 using small hedgers (0.015) (0.019) Also, in paper show that it is the default risk of "hedgers" and not that of "non-hedgers" that is related to the aggregate CFTC positions Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 22 / 44

30 Spot Forecasting Regressions Model predicts common component in spot and futures return Hedging measures should predict changes in spot price as well: Spot "return": Pooled HedgeVar: Zm score Naïve EDF avg3yr HedgeVar 0.037** 0.033*** 0.037** (0.016) (0.011) (0.016) R2 15.2% 16.7% 15.3% # obs Controls? yes yes yes Magnitudes cannot explain crude prices going from $40 to $147 to $40 Not suprising, since argument is one of risk-sharing (second order e ects) Still, highlights a channel that is not based on information about future supply/demand where speculator activity in the futures market a ects spot prices Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 23 / 44

31 Spot Prices and Speculator Activity Are commodity spot prices a ected by speculator risk preferences / speculative activity? "Pension funds and other large institutions are holding over $250 billion in commodities compared to their $10 billion holding in 2000." - Financial Times, July "Non-fundamental price pressure in futures market responsible for spot price increase." - Michael Masters, George Soros Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 24 / 44

32 Measures of Speculator Risk Tolerance Adrian and Shin (2008), Etula (2009): growth in Broker-Dealer assets relative to Household Assets Scaled by ratio of Broker-Dealer assets to Household assets (Flow of Funds data) Growth in CTA assets relative to household assets CTA = Commodity Trading Advisors (Commodity hedge funds; TASS, HFR and CSDM consolidated database) Measure scaled by ratio of CTA assets to household assets Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 25 / 44

33 Futures return, Spot, and nventory Testing model implications including the measures of speculator capital constraints: B D measure CTA measure Pooled Futures Spot Annual Futures Spot Annual forecasting regs: return % change nventory return % change nventory Spec_measure 0.058*** 0.061*** 0.014*** 0.061*** 0.035** 0.015* (0.014) (0.017) (0.004) (0.017) (0.017) (0.009) avgedf 0.025** 0.022*** 0.034*** 0.038*** 0.029*** 0.058*** (0.009) (0.008) (0.007) (0.013) (0.009) (0.017) R % 22.6% 76.9% 22.8% 18.1% 81.0% # obs Controls? yes yes yes yes yes yes Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 26 / 44

34 Hedging Pressure vs. Arbitrage Activity (94Q1-06Q4) Both speculator and hedger measures orthogonalized wrt controls; extract non-systematic component Create hedging component of FRP as an R 2 : ln βhedgevar orthogonal 2 t / β 0 AllControls 2 Rolling annual, overlapping quarterly Hedging pressure is high when arbitrage activity is low... Stronger relation later in sample Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 27 / 44

35 Updated analysis: Crude Oil 1994Q2-2009Q3 Lots of variation in hedging demand and speculator capital More precise measure of speculator capital ows Energy CTA s only Controlling for spot price movements important Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 28 / 44

36 Updated regressions: 1994:Q2-2009:Q3 Crude oil only: quarterly crude futures return Quarterly crude inventory level Zm score( 1) 0.058*** RP( 1) 0.294*** (0.022) (0.073) CTA_Energy( 1) RP 0.172** (0.016) (0.085) Zm( 1)*CTA( 1) 0.054** (0.024) R2adj 67.3% 62.1% R2adj 10.9% controls: realized variance, spot price controls: lagged inventory, spot, realized variance, quarterly dummies 1 Hedging pressure stronger when speculator risk-tolerance is low 2 Estimated crude oil risk premium (RP) negatively related to aggregate inventory holdings Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 29 / 44

37 Conclusion Asset pricing implications of corporate hedging demand hard to uncover Commodity markets: natural hedgers, low basis risk Find that corporate hedging policy a ects asset prices and vice versa economically signi cant e ect: predictability in commodity futures and spot returns, inventory Support for limits-to-arbitrage / market segmentation interaction with producer hedging demand speculator capital supply in the futures market has real e ects recent debate: increased risk appetite of speculators decreases cost of hedging, which increases inventory, which increases spot prices. Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 30 / 44

38 Data: nventory vs. spot and basis (Crude Oil) Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 31 / 44

39 Producers Competitive, price-takers. Representative rm: max f,h p g S 0 (g 0 ) + E [Λ fs 1 ((1 d) + g 1 ) + h p (F S 1 )g]... subject to γ p 2 Var [S 1 ((1 d) + g 1 ) + h p (F S 1 )] 0, where γ p governs the degree of aversion to variance in future earnings. iral Acharya, Lars Lochstoer, and Tarun Ramadorai () 32 / 44

40 Producers Competitive, price-takers. Representative rm: max f,h p g S 0 (g 0 ) + E [Λ fs 1 ((1 d) + g 1 ) + h p (F S 1 )g]... subject to γ p 2 Var [S 1 ((1 d) + g 1 ) + h p (F S 1 )] 0, where γ p governs the degree of aversion to variance in future earnings. nventory FOC: (1 d) + g 1 = hp + E [ΛS 1] (S 0 λ) / (1 d) γ p σ 2, S where λ is Lagrange multiplier in the case of a stock-out. Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 32 / 44

41 Producers Competitive, price-takers. Representative rm: max f,h p g S 0 (g 0 ) + E [Λ fs 1 ((1 d) + g 1 ) + h p (F S 1 )g]... subject to γ p 2 Var [S 1 ((1 d) + g 1 ) + h p (F S 1 )] 0, where γ p governs the degree of aversion to variance in future earnings. nventory FOC: (1 d) + g 1 = hp + E [ΛS 1] (S 0 λ) / (1 d) γ p σ 2, S where λ is Lagrange multiplier in the case of a stock-out. Futures FOC: hp = E [Λ (S (1 d) + g 1 F )] 1 γ p σ 2. S Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 32 / 44

42 The Basis No-Arbitrage futures price (Hull, 2008): F = S r 1 d S 0 y, where y is the convenience yield. The basis is then: S 0 F S 0 = y r + d 1 d, where y = λ 1 + r S 0 1 d. The basis does not re ect time-variation in the futures risk premium if producers hold inventory Common component in spot and futures returns: S 0 F = E (S 1) F F E (S 1 ) S 0. S 0 F S 0 S 0 Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 33 / 44

43 Representative Speculator Objective Function Capital constraints (e.g., due to VaR constraint as in Danielsson, Shin, and Zigrand (2008)) in the form of variance penalty: max h S h s E [Λ (S 1 F )] γ s 2 Var [h s (S 1 F )] =) h s = E [Λ (S 1 F )] γ s σ 2 S 1 f γ s = 0, E [Λ (S 1 F )] = 0. 2 f γ p = 0, E [Λ (S 1 F )] = 0. 3 f γ s, γ p > 0, E [Λ (S 1 F )] > 0. Equilibrium: Futures and spot market clears, producer and speculator FOCs hold (σ f = σ S /F ): S1 F E = Corr (Λ, S 1 ) Std (Λ) σ F f + γ p γ s σ 2 γ p + γ f FQ 1 s Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 34 / 44

44 Model Extension Endogenizing the consumers decision: V = u (C 0, Q 0 ) + βe 0 [u (C 1, Q 1 )], C t consumption of other (numeraire) goods. A t endowment in numeraire (dynamics as before). The intratemporal utility function is: u(x, y) = 1 x (ε 1)/ε + ωy (ε 1)/ε ε/(ε 1) 1 γ c, 1 γ c where ε is the intratemporal elasticity of substitution and γ c is the level of relative risk aversion. ntratemporal FOC: 1/ε Ct S t = ω Q t Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 35 / 44

45 Model Extension (cont d) The pricing kernel is Λ = β 0 γc C1 C ω Q1 C 1 (ε 1 + ω Q0 C 0 (ε 1)/ε 1)/ε 1 C A (1/γ c ε)/((ε 1)/γ c ) Consumers own production rms, manager paid before time 0 and solves mean-variance problem as before (due to unmodeled career concerns). Consumers can invest in futures markets at a cost, however, proportional to risk taken: cost = γ s 2 Var (h s S 1 ) Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 36 / 44

46 Model Extension (cont d) n equilibrium, marginal cost = marginal bene t, so h s = E [Λ (S 1 F )] γ s Var (h s S 1 ). Total cost incurred at time 0 by consumers: C 0 = A 0 1 E [Λ (S 1 F )] 2 2 γ s Var (h s S 1 ) = A 0 1 2γ s γ p γ s γ s + γ p! 2 2(1 1/ε) Q1 k, where k = ω 2 e σ2 1 e 2µ+σ2. Risk-free rate set such that, C1 = A 1: r = 1/E [Λ]. Limits to arbitrage and hedging demand impact standard risk variables (Λ and C ) S1 F E = Corr (Λ, S 1 ) Std (Λ) σ F f + γ p γ s σ 2 γ p + γ f FQ 1 s Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 37 / 44

47 Calibration Parameters: ε = 0.1, d = 0.01, ω = 0.01, A 0 = 1, g 0 = 0.75, g 1 = 0.8, σ = 0.02, µ = 0.004, σ (ln Λ) = 20%, E [ln Λ] = 0.25%. σ (futures return) = 20% per quarter as in the data, E [St Q t /A t ] = 0.1. γs is either 8 (solid) or 40 (dashed), γ p plotted on x axis. Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 38 / 44

48 Model implications Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 39 / 44

49 Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 40 / 44

50 Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 41 / 44

51 Futures Forecasting Regressions: Per commodity () Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 42 / 44

52 Futures Forecasting Regressions: Per commodity () Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 43 / 44

53 Related Literature The old days: Keynes (1930), Hotelling (1931), Kaldor (1940), Hicks (1946), Working (1949), and Brennan (1958). New nventory Models: Deaton and Laroque (1992), Routledge, Seppi and Spatt (2000) Hedging pressure: Hirshleifer (1988, 1990), Bessembinder (1992), Bessembinder and Lemmon (2002), De Roon, Nijman and Veld (2000), Gorton, Hayashi, and Rouwenhorst (2007) Speculative demand: Etula (2009), Tang and Xiong (2009). Some other commodity studies: Sundaresan (1981), Anderson and Danthine (1983), Fama and French (1987), Ng and Pirrong (1994), Cassasus and Collin-Dufresne (2004), Routledge and Collin-Dufresne (2009), Hong and Yogo (2009). Corporate hedging: Stulz (1984), Smith and Stulz (1985), Gilson (1989), Froot, Scharfstein, and Stein (1994), Tufano (1996), Haushalter (2000), Ederington and Lee (2002) Viral Acharya, Lars Lochstoer, and Tarun Ramadorai () 44 / 44