Limits to Arbitrage and Hedging: Evidence from Commodity ... · "limits-to-hedging"-argument I...

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

Motivation: Limits-to-arbitrage and hedging pressure

A measure of arbitrage capital employed in the Crude Oil futures marketversus the component of the futures risk premium due to producer hedgingpressure (from one of our measures)

I data annual, overlapping at quarterly frequency, variables normalized


Managers maximize �rm value (no role for futures market)


Managers maximize �rm value BUT also wants to minimize varianceI a role for futures marketI hedging decisions have no impact on commodity spot or futures prices


Real-world markets have frictions. An important one: Limits to Arbitrage.I Shleifer and Vishny, 1997; Gromb and Vayanos, 2002; Brunnermeier andPedersen, 2009.


Paper summary

Propose simple equilibrium model that formalizes the"limits-to-hedging"-argument

I Managers of commodity producing �rms aim to maximize share value, but alsoaverse to price risk

I Financial intermediaries in commodity futures market capital constrainedI These features a¤ect producers�desire and economic cost of inventoryhedging, which in turn a¤ects spot and futures prices

Novel empirical analysisI Propose measures of producers�default risk as proxies for managers�desire tohedge price risk:

"The amount of production we hedge is driven by the amount of debt on ourconsolidated balance sheet and the level of capital commitments we have inplace." - St. Mary Land & Exploration Co., in their 10-K �ling for 2006.

(Average market value of equity in 2006 was $2.5 billion.)


Paper summary (II)

We con�rm model predictions in U.S. Crude Oil, Heating Oil, Gasoline, andNatural 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 demandand speculator capital constraints

4 Interaction between arbitrage capital and hedging demand on futures riskpremium and inventory levels


Outline of Talk

1 The Model

2 Evidence of producer hedging

3 Price impact of producer hedging

4 Interaction of producer hedging and speculative demand


The model

Two periods (empirical analysis focuses on short-term futures):

1 Supply of commodity, gt , pre-determined

2 r = 1/E [Λ]� 1; d 2 [0, 1)

Consumers�inverse demand function:

St = ω

�AtQt

�1/ε

,

where: Qt = gt � It + (1� d) It�1lnAt � lnAt�1 � N

�µ, σ2

�is demand shock

St is the commodity spot price

ω and ε are positive constants.


Producers

Competitive, price-takers. Representative �rm:

maxfI ,hpg

S0 (g0 � I ) + E [Λ fS1 ((1� d) I + g1) + hp (F � S1)g] ...

�γp2Var [S1 ((1� d) I + g1) + hp (F � S1)]

subject toI � 0,

where γp governs the degree of aversion to variance in future earnings.

Note: if E [Λ (S1 � F )] > 0, costly in terms of �rm value to hedge by going short


Representative Speculator Objective Function

Capital constraints (e.g., due to VaR constraint as in Danielsson, Shin, andZigrand (2008)) in the form of variance penalty:

maxhShsE [Λ (S1 � F )]�

γs2Var [hs (S1 � F )]

Equilibrium: Futures and spot market clears, producer and speculator FOCshold (σf = σS/F ):

E�S1 � FF

�= �Corr (Λ,S1) Std (Λ) σf| {z }

usual risk term

+γpγs

γp + γsσ2f FQ1| {z }

price pressure


Comparative Statics and Empirical Predictions

1 Increasing producer risk aversion (fundamental hedging demand), γp :

1 Increases optimal number of short futures contracts (hedging)2 Increases futures risk premium3 Decreases inventory4 Decreases current spot price and increases expected future spot price

2 Increasing speculator risk tolerance, γs :

1 Decreases futures risk premium2 Increases inventory3 Increases current spot price

3 Interaction between speculator risk tolerance and e¤ect of hedging demandon risk premium, spot price, and inventory.


Overview of Empirical Approach

1 Measures of Default Risk proxy for time-varying fundamental hedgingdemand (γp) (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 activityindeed is related to default risk measures

3 Construct commodity sector average default risk measures from �rm-leveldata and test model�s pricing implications

4 Control for other possible omitted determinants of futures risk premium

1 Controls: Standard predictive variables2 Volatility Interaction (implied by model)3 Hedgers versus non-hedgers4 Producers versus re�ners


Controls

Aggregate:

1 Slope of the Treasury bond term structure (5yr - 1yr yields)2 The quarterly T-bill rate3 Aggregate default spread (Baa - Aaa spread on corporate bonds)4 Analyst GDP growth forecasts

Commodity speci�c:

1 Basis2 Inventory level3 Lagged futures return


Proxies for Hedging DemandVery poor data for most �rms in terms of actual hedging positions

I E.g., do not report direction, only notional, only VaR, etc.

1 Zmijewski-score (Zmijewski, 1984):

Zmijewski-score = �4.3� 4.5 �NetInc/TotAssets + 5.7 � TotDebt/TotAssets

�0.004 � CurrentAssets/CurrentLiabilities.

2 Naive EDF (Bharath and Shumway, 2004):

EDF = Φ

� ln(V/F ) + (µ� 0.5σ2V )T

σvpT

!!

3 3-year average stock return (Gilson, 1989):

ThreeYearAvg i ,t=136

35

∑k=0

ln (1+ R i ,t�k )


Data Sample

Main analysis (maximum) sample period: 1980Q1 - 2006Q4.I Varies across commodities given data availability (DataStream; NYMEX)I Quarterly, commodity producer balance sheet data (Compustat and Edgar)I Aggregate U.S. inventory data from Energy Information Administration.I Aggregate "hedger" positions per commodity from CFTC.

In the following, often show regression results only from regressions that arepooled across the four commodities

I Rogers (1993) standard errors; HAC, 3 lags

1 "ControlVariables": The controls listed before as well as quarterly dummiesto control for seasonalities

2 "HedgeVar": One of the three measures of default risk as proxies forfundamental hedging demand


Macro Evidence of Producer Hedging and Default Risk

CFTC data on aggregate short "hedger" positions

NetShortHedgerst = βHedgeVart + ControlVariablest + εt

CFTC Hedger Positions: Pooled

HedgeVar: Zmscore Naïve EDF avg3yr

HedgeVar 0.140** 0.147** 0.090**(0.062) (0.072) (0.045)

R2 18.3% 20.2% 17.4%# obs 305 261 305

Controls? yes yes yes


Commodity Futures Return (NYMEX contracts)

Excess return from the end of month t to t + 1 is calculated as:

Ft+1,T � Ft ,TFt ,T

,

where Ft ,T is nearest contract that matures after time t + 1.I Quarterly return is constructed from monthly data (Hayashi, Gorton, andRouwenhorst, 2008)

I These are most liquid contracts + avoid issues related to delivery.


Futures Forecasting Regressions

FuturesReturnst+1 = βHedgeVart + ControlVariablest + εt+1

Futures return: Pooled


HedgeVar 0.038** 0.036*** 0.040**(0.016) (0.009) (0.016)

R2 11.4% 9.8% 12.8%# obs 343 287 343



Futures Forecasting Regressions - Volatility InteractionModel predicts interaction between futures return volatility and producers�fundamental hedging demand (γp)

E�S � FF

�= �Rf Cov (Λ,S/F ) + Rf

γpγsγp + γs

σ2S/F FQ

Futures return: Pooled


Realized Variance (RV) 0.025 0.054*** 0.005(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)

R2 13.3% 17.2% 13.1%# obs 332 276 332



Futures Forecasting Regressions - Producers vs. Re�ners

Classi�cation based on information from annual/quarterly reports

Futures return: Crude OilZmscore Naïve EDF avg3yr

All firms 0.107*** 0.055* 0.153***(0.026) (0.033) (0.049)

Refiners 0.051*** 0.006 0.105*(0.018) (0.024) (0.054)

R2 18.8% 19.0% 19.1%

# obs 90 76 90



Futures Forecasting Reg�s - Hedgers vs. Non-Hedgers

Classi�cation based on information from annual/quarterly reportsI Use sum of three proxies for each �rm as hedging measure (each proxynormalized to have unit variance)

FutRett+1 = b1 (Hedgert +NonHedgert ) + b2NonHedgert + ContVarst + εt+1

b1 (Hedger + b2

NonHedger) (NonHedger) Controls? R2# obs

(1) Hedger measure constructed 0.055*** 0.057** yes 13.0% 343using all hedgers (0.016) (0.026)

(2) Hedger measure constructed 0.054*** 0.045** yes 12.2% 343using 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


Spot Forecasting RegressionsModel predicts common component in spot and futures return

I Hedging measures should predict changes in spot price as well:

Spot "return": Pooled


HedgeVar 0.037** 0.033*** 0.037**(0.016) (0.011) (0.016)

R2 15.2% 16.7% 15.3%# obs 351 294 351


Magnitudes cannot explain crude prices going from $40 to $147 to $40I Not suprising, since argument is one of risk-sharing (second order e¤ects)I Still, highlights a channel that is not based on information about futuresupply/demand where speculator activity in the futures market a¤ects spotprices


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 $250billion in commodities compared to their $10 billion holding in 2000."- Financial Times, July 8 2008.

"Non-fundamental price pressure in futures market responsible forspot price increase." - Michael Masters, George Soros


Measures of Speculator Risk Tolerance

Adrian and Shin (2008), Etula (2009): growth in Broker-Dealer assetsrelative to Household Assets

I Scaled by ratio of Broker-Dealer assets to Household assets (Flow of Fundsdata)

Growth in CTA assets relative to household assetsI CTA = Commodity Trading Advisors (Commodity hedge funds; TASS, HFRand CISDM consolidated database)

I Measure scaled by ratio of CTA assets to household assets


Futures return, Spot, and Inventory

Testing model implications including the measures of speculator capitalconstraints:

BD measure CTA measure

Pooled Futures Spot Annual Futures Spot Annualforecasting regs: return %change Inventory return %change Inventory

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)

R2 15.6% 22.6% 76.9% 22.8% 18.1% 81.0%# obs 287 294 287 144 144 144

Controls? yes yes yes yes yes yes


Hedging Pressure vs. Arbitrage Activity (94Q1-06Q4)Both speculator and hedger measures orthogonalized wrt controls; extractnon-systematic component

I Create hedging component of FRP as an R2:

ln��

βHedgeVar orthogonalt

�2 /�

β0AllControls�2�

I Rolling annual, overlapping quarterly

Hedging pressure is high when arbitrage activity is low... Stronger relationlater in sample


Updated analysis: Crude Oil 1994Q2 - 2009Q3

Lots of variation in hedging demand and speculator capital

More precise measure of speculator capital �owsI Energy CTA�s onlyI Controlling for spot price movements important


Updated regressions: 1994:Q2 - 2009:Q3Crude oil only:

quarterly crude futures return Quarterly crude inventory level

Zmscore(1) 0.058*** RP(1) 0.294***(0.022) (0.073)

CTA_Energy(1) 0.012 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 low2 Estimated crude oil risk premium (RP) negatively related to aggregateinventory holdings


Conclusion

Asset pricing implications of corporate hedging demand hard to uncoverI Commodity markets: natural hedgers, low basis risk

Find that corporate hedging policy a¤ects asset prices and vice versaI economically signi�cant e¤ect: predictability in commodity futures and spotreturns, inventory

Support for limits-to-arbitrage / market segmentationI interaction with producer hedging demandI speculator capital supply in the futures market has real e¤ectsI recent debate: increased risk appetite of speculators decreases cost of hedging,which increases inventory, which increases spot prices.


Data: Inventory vs. spot and basis (Crude Oil)


ProducersCompetitive, price-takers. Representative �rm:

maxfI ,hpg

S0 (g0 � I ) + E [Λ fS1 ((1� d) I + g1) + hp (F � S1)g] ...

�γp2Var [S1 ((1� d) I + g1) + hp (F � S1)]

subject toI � 0,

where γp governs the degree of aversion to variance in future earnings.

Inventory FOC:

I � (1� d) + g1 = h�p +E [ΛS1 ]� (S0 � λ) / (1� d)

γpσ2S,

where λ is Lagrange multiplier in the case of a stock-out.

Futures FOC:

h�p = I� (1� d) + g1 �

E [Λ (S1 � F )]γpσ2S

.


The Basis

No-Arbitrage futures price (Hull, 2008):

F = S01+ r1� d � S0y ,

where y is the convenience yield.

The basis is then:

S0 � FS0

= y � r + d1� d , where y =

λ

S0

1+ r1� d .

The basis does not re�ect time-variation in the futures risk premium ifproducers hold inventory

I Common component in spot and futures returns:

S0 � FS0

=E (S1)� F

FFS0� E (S1)� S0

S0.


Representative Speculator Objective Function

Capital constraints (e.g., due to VaR constraint as in Danielsson, Shin, andZigrand (2008)) in the form of variance penalty:

maxhShsE [Λ (S1 � F )]�

γs2Var [hs (S1 � F )] =) h�s =

E [Λ (S1 � F )]γsσ

2S

1 If γs = 0, E [Λ (S1 � F )] = 0.2 If γp = 0, E [Λ (S1 � F )] = 0.3 If γs ,γp > 0, E [Λ (S1 � F )] > 0.

Equilibrium: Futures and spot market clears, producer and speculator FOCshold (σf = σS/F ):

E�S1 � FF

�= �Corr (Λ,S1) Std (Λ) σf +

γpγsγp + γs

σ2f FQ1


Model Extension

Endogenizing the consumers�decision:

V = u (C0,Q0) + βE0 [u (C1,Q1)] ,

Ct consumption of other (numeraire) goods. At endowment in numeraire(dynamics as before).

The intratemporal utility function is:

u(x , y) =1

1� γc

��x (ε�1)/ε +ωy (ε�1)/ε

�ε/(ε�1)�1�γc

,

where ε is the intratemporal elasticity of substitution and γc is the level ofrelative risk aversion.

Intratemporal FOC:

St = ω

�CtQt

�1/ε


Model Extension (cont�d)

The pricing kernel is

Λ = β

�C1C0

��γc

0B@1+ω�Q1C1

�(ε�1)/ε

1+ω�Q0C0

�(ε�1)/ε

1CA(1/γc�ε)/((ε�1)/γc )

Consumers own production �rms, manager paid before time 0 and solvesmean-variance problem as before (due to unmodeled career concerns).

Consumers can invest in futures markets at a cost, however, proportional torisk taken:

cost =γs2Var (hsS1)


Model Extension (cont�d)In equilibrium, marginal cost = marginal bene�t, so

h�s =E [Λ (S1 � F )]γsVar (hsS1)

.

Total cost incurred at time 0 by consumers:

C �0 = A0 �12E [Λ (S1 � F )]2

γsVar (hsS1)= A0 �

12γs

γpγs

γs + γp

!2Q2(1�1/ε)1 k,

where k = ω2�eσ2 � 1

�e2µ+σ2 . Risk-free rate set such that, C �1 = A1:

r = 1/E [Λ].

Limits to arbitrage and hedging demand impact standard risk variables (Λ and C )

E�S1 � FF

�= �Corr (Λ,S1) Std (Λ) σf +

γpγsγp + γs

σ2f FQ1


Calibration

Parameters: ε = 0.1, d = 0.01, ω = 0.01, A0 = 1, g0 = 0.75, g1 = 0.8,σ = 0.02, µ = 0.004, σ (lnΛ) = 20%, E [lnΛ] = �0.25%.

I σ (futures return) = 20% per quarter as in the data, E [StQt/At ] = 0.1.I γs is either 8 (solid) or 40 (dashed), γp plotted on x � axis .


Model implications


Futures Forecasting Regressions: Per commodity (I)


Futures Forecasting Regressions: Per commodity (II)


Related Literature

The old days: Keynes (1930), Hotelling (1931), Kaldor (1940), Hicks (1946),Working (1949), and Brennan (1958).

New Inventory Models: Deaton and Laroque (1992), Routledge, Seppi and Spatt(2000)

Hedging pressure: Hirshleifer (1988, 1990), Bessembinder (1992), Bessembinderand Lemmon (2002), De Roon, Nijman and Veld (2000), Gorton, Hayashi, andRouwenhorst (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 andLee (2002)


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