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The Stock Market Price of Commodity Risk
November 2013
Martijn Boons, Nova School of Business and Economics
Frans de Roon, Tilburg University, CentER
Marta Szymanowska, Rotterdam School of Management
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2
Motivation

Commodity Futures Modernization Act (CFMA)

Dramatic change in size and composition of futures markets
16
TOI in 33 commodities
14
12
10
Energy
Agriculture
8
6
4
2
0
Metals & Fibers
Livestock & Meats
EW Average
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3
Motivation

CFMA: break point in the behavior of (institutional) investors


Pre-CFMA commodity exposure

position limits in futures markets

commodity-related equity, physical commodities (Lewis,
2007)
Post-CFMA commodity exposure

commodity index investment (CII) by institutions from 6% of
total open interest (< 10$ bln) in 1998 to 40% (> 200$ bln) in
2009
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4
Our goal


We want to understand

commodity prices as a source of risk

price of this risk in the stock and commodity futures markets

impact of CFMA / changing investment behavior
This will allow us to shed light on

a link between stock and commodity futures markets

“financialization” of commodities

stock market strategies to hedge or speculate on commodity
prices
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5
Our Approach

A model with investors exposed to commodity price risk



Testable implications



in the spirit of Hirshleifer (1988,1989), Bessembinder and Lemmon
(2002)
Study the effect of position limits on demand and prices
Sort stocks on commodity beta
Sort commodity futures on stock market risk
Main empirical findings
1.
2.
Commodity risk is priced in stock market in the opposite way before
and after CFMA
Stock market risk is priced in the commodity futures market post-CFMA
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6
The model

Agents



Commodity Producers (business exposed to commodity price
risk 𝑟𝑆,𝑡+1 and trade futures contract 𝑟𝐹,𝑡+1 )
Specialized Speculators (e.g. CTA's, trade futures contract)
Investors
 Position limit (pre-CFMA): invest in stocks (𝑟𝑟,𝑡+1 ) only
 No limit (post-CFMA): invest in both stocks and futures contract

Standard, two-date, mean-variance framework

Investors are exposed to commodity price risk: inflation,
state variable

Today: available futures contract is a perfect hedge (𝜌𝑆𝐹 = 1)
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7
The Investor’s problem

Excess portfolio return 𝑟𝑝,𝑡+1 = 𝑤 ′ 𝑟𝑡+1 + 𝜑𝑟𝑆,𝑡+1 , such that
1.
With limit (w = 𝑤 ′ 𝑟 0 ′ )
max w r
2.

γI
w'r μ r  μ S  ( w'r Σ rr w r  2 w'r Σ rS   2 SS )
2
Without limit (𝑤 = 𝑤 ′ 𝑟 𝑤𝐹 ′ )
γI
max w w' μ  μ S  ( w' Σw  2 w' Σ S   2 SS )
2
Optimal portfolios (1) with and (2) without limit
1
1. w r  γ I Σ rr1μ r  Σ rr1Σ rS
1
 w r   γ I Σ rr1μ r  Σ rr1Σ rS w F,spec   0 K 
 
2. 
  ,


w F,spec
 wF  
  
1
where w F,spec  γ I  ee1a using rF,t 1  a  b' rr ,t 1  et 1
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Expected stock returns with
commodity price risk

With limits
E (ri ,t 1 )  γ I im  γ I iS


Cross-hedging demand implies a negative (positive) risk premium
when φ < 0 (φ > 0) and high commodity prices are bad (good) news
Without limits
E (ri ,t 1 )  γ I im  γ I w F,spec iS

Risk premium determined by speculative investment in commodities

If zero  CAPM!
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Risk premiums in the futures
market
1.
With limit: Producers and Speculators only
E (rF ,t 1 ) 
P
P  S
γ P FF (1   )
i  N i / γ i , i  P, S
2.
Without position limits: stock market risk is priced due to
presence of Investors
P γ P (1   )  Iγ I
I γ I
E (rF ,t 1 ) 
 FF 
 FT with
P  S  I
P  S  I
 FF
i  N i / γ i , i  P, S , I and I  I
 ee
 FT  cov(rF ,t 1 , rT ,t 1 ) where w T   rr1  r
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Data and method: stock market

All CRSP stocks, French’s 48 industry portfolios

OIW index of 33 commodities (from CRB and FII)



Sorts on rolling 60 month commodity beta



Robust: EW index, S&P-GSCI index
Variation across commodity sectors
Mean and risk-adjusted returns (CAPM, FF3M and FFCM) of High
minus Low (HLCB) portfolios
Pre- versus Post-CFMA: split around December 2003
Robust





Different break points
Different rebalancing
Fama-MacBeth cross-sectional estimates
Between/within industry sort
Controlling for inflation
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Stock market: pre-CFMA
Stocks
48 Industries
15.00
15.00
10.00
10.00
FFCM
5.00
CAPM
Low
-10.00
FFCM
FF3M
0.00
-5.00
5.00
2
Means
3
4
High
FF3M
0.00
Low
-5.00
-10.00
CAPM
2
3
4
High
Means
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Stock market: post-CFMA
48 Industries
Stocks
15.00
15.00
10.00
10.00
FFCM
5.00
FF3M
CAPM
0.00
Low
-5.00
5.00
2
0.00
Means
3
4
High
-5.00
-10.00
-10.00
FFCM
FF3M
CAPM
Means
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Means and FFCM alphas
Pre-CFMA
Size quintile
Means
One-way
Size quintile
One-way
OIW
OIW
OIW
OIW
OIW
EW
OIW
OIW
OIW
OIW
OIW
EW
S
3
B
Stocks
48 Ind.
Stocks
S
3
B
Stocks
48 Ind.
Stocks
H
5.88
3.55
2.33
1.91
5.00
4.45
12.13 15.29
15.10*
14.85*
14.57
11.93
4
8.88* 6.90*
7.04*
6.58*
8.23*
5.77
12.02
9.97
4.78
5.64
5.97
7.33
3
10.56* 9.44*
6.32*
7.04*
7.84*
8.25*
11.07
8.58
2.08
3.58
6.62
5.16
2
10.55* 11.32*
9.24*
9.53*
10.07*
8.81*
9.25
7.91
3.08
3.87
6.47
5.07
L
8.93* 13.03* 10.01*
10.02*
9.72*
9.33*
1.88
1.98
3.25
2.77
2.35
3.24
-3.04 -9.47*
-7.68*
-8.11*
-4.72*
-4.88
12.08*
12.22*
8.69
H
-1.73 -6.12* -5.52*
-6.67*
-4.75*
-3.52
1.65
6.81
11.30*
9.82*
8.60*
6.23
4
0.69
-3.23*
-0.97
-1.73
-0.92
0.40
2.40
2.46
1.67
1.33
-0.82
1.76
3
2.41
0.43
-0.61
-0.13
-1.99
0.76
1.60
1.66
-1.83
-0.93
1.08
1.16
2
2.82
3.48*
3.22*
3.33*
2.13
1.08
0.77
1.53
-0.47
-0.19
1.23
1.18
L
2.75
5.59*
5.88*
4.99*
2.12
2.77*
-6.66* -4.67*
0.36
-1.08
-2.01
-0.09
-6.87*
-6.30*
8.31* 11.48* 10.94*
10.90*
10.60*
6.32
HLCB
FFCM
Post-CFMA
HLCB -4.48* -11.71* -11.39* -11.66*
* Indicates significance at the 5%-level
10.25* 13.31* 11.85*
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The reversal in the commodity risk
premium I

Recall:
E (ri ,t 1 )  γ I im  γ I iS vs E (ri ,t 1 )  γ I im  γ I wF , spec iS
𝑎

Reversal obtains when (1) 𝜑 < 0 and (2) 𝛾𝐼 𝑤𝐹,𝑠𝑝𝑒𝑐 =
> 0.
𝜎𝑒𝑒
Plausible:
1.
Negative exposure to commodity price risk for Investors
from


Inflation: commodity prices are most volatile components
State-variable risk: Energy and Metals prices predict negative
stock returns (e.g., Driesprong et al. (JFE, 2008), Jacobsen et al.
(2013))
 Results driven by commodities from Energy and Metals sectors
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The reversal in the commodity risk
premium II
A positive speculative investment in commodity futures
𝑎
( > 0) obtains when
2.
𝜎𝑒𝑒


Hedging pressure from Producers is sufficiently large, i.e., the
group of Producers is relatively large and risk averse (“normal
backwardation”)

Indeed, we find that commercial hedger’s short positions are
sufficient to cover non-commercial speculators long positions

Cheng et al. (2011): hedgers short positions increase in
lockstep with CIT’s long positions
Consistent with diversification benefits in Gorton and
Rouwenhorst (FAJ, 2006) and Erb and Harvey (FAJ, 2006)
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Hedgers versus Speculators
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Commodity futures risk premiums

With and without limit: a “classic“ hedging pressure effect


In both sub-periods, sorting on hedging pressure works
Without limits, stock market risk is priced in the futures
market


Using that T=M+H, sort commodities on beta with respect to the
MKT and HLCB portfolio
High stock market beta commodities outperform ONLY postCFMA, as predicted!
Pre-CFMA
Post-CFMA
HLCB
HLCB
MKT
Low
High
MKT
Low
High
Low
1.36%
7.43%
Low
-2.23%
8.09%
High
-2.25%
3.83%
High
9.06%
9.16%
HH-LL
2.48%
HH-LL
11.38%
t(HH-LL)
(0.55)
t(HH-LL)
(1.77)
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Conclusion

Focus on the structural break in investor’s behavior



Study a model with Investors exposed to commodity price risk
Analyze the effect of position limits related to CFMA
We find




Commodity risk is priced in stock market in the opposite way
pre- versus post-CFMA
Stock market risk is priced in the commodity futures market postCFMA
Consistent with Investors seeking commodity exposure in the
stock market pre-CFMA and subsequently in the commodity
futures markets
Stocks to hedge or speculate on commodity prices
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Within-industry sort

“Out-of-sample” test: spreads exist when using only withinindustry variation in commodity beta

Hedge, while keeping industry exposure constant
Within-industry
H
1980-2003 (Pre-CFMA)
2004-2010 (Post-CFMA)
Industries sorted on commodity beta
Industries sorted on commodity beta
4
3
2
L
-6.13* -4.17
-3.34
-4.72
Means
HLCB
-3.39
FFCM
HLCB
-6.92* -7.58* -4.37
Average
-4.35*
-4.86* -9.01* -6.55*
H
4
3
2
L
Average
13.64* 11.01* 5.38
19.05* 9.37
11.69*
13.92* 9.76
14.58* 5.48
9.18*
2.17
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Industry composition of High and
Low portfolio
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
1980-1990
1991-2000
2001-2010
0.25
0.20
0.15
0.10
0.05
1980-1990
0.00
1991-2000
2001-2010