Replaced with revised version of poster 07/21/10.Risk and Uncertainty,

Bozic, Marin

Fortenbery, T. Randall

English

Research Papers in Economics

Visualizing	Risk	Premiums	in	Commodity	Futures	Markets	
	
	
	
	
	
	
	
	
	
	
Marin	Bozic	
bozic@wisc.edu		
	
T.	Randall	Fortenbery	
tforten@wisc.edu	
	
University	of	Wisconsin‐Madison	
	
	
	
	
	
	
	
	
	
	
	
	
	
Poster	prepared	for	presentation	at	the	Agricultural	&	Applied	Economics	Association	
2010	AAEA,CAES,	&	WAEA	Joint	Annual	Meeting,	Denver,	Colorado,	July	25‐27,	2010	
	
	
	
	
	
Copyright	2010	by	Marin	Bozic	and	T.	Randall	Fortenbery.	All	rights	reserved.	Readers	may	
make	verbatim	copies	of	this	document	for	non‐commercial	purposes	by	any	means,	provided	
that	this	copyright	notice	appears	on	all	such	copies.	Marin	Bozic	and	T.	Randall	Fortenbery,	Department	of	Agricultural	and	Applied	Economics,	University	of	Wisconsin‐Madison
AAEA,	CAES	&	WAEA	2010	Joint	Annual	Meetings	‐ Poster	No:	M16
Holbrook	Working
The American Economic Review, 43(3)
T h er o l eo fr i s k ‐avoidance in most commercial hedging has
been greatly overemphasized in economic discussions.
Most hedging is done largely, and may be done wholly, because information
on which the merchant or processor acts leads logically to hedging. He buys
the spot commodity because the spot price is low relative to the futures price
and he has reason to expect the spot premium to advance; therefore he buys
spot and sells the future.
sweet crude oil class III milk
The series shown above includes only 8 years of data (2002‐
2009), so it may be too short to reveal characteristics of light
crude oil futures prices. What we see thus far is an extreme
a s y m m e t r yi nr e a l i z e dp r e d i c t i o ne r r o r sa n dt h e r es e e m st o
be a nonlinear risk‐premium increasing up to –10% 8 months
to maturity, but vanishing for 12 months to maturity.
Unlike corn, soybeans and wheat, milk futures are cash settled
based on a specified formula. For that reason, we see the
prediction power of futures prices dramatically increasing in
the last 2 months to maturity. Means of realized prediction
errors are remarkably close to zero for up to 6 months to
maturity, declining to ‐4.5% for 12 months to maturity.
Although this market is much thinner than the others
analyzed, we see no clear detrimental impact on the
prediction power of futures prices.
soybeans
Unlike corn and wheat, soybean futures seem to exhibit classical
risk premiums paid to speculators holding long positions, i.e.
over long horizons, futures prices seem to be downward biased
forecasts of terminal spot prices. Interesting, and puzzling, an
additional phenomenon is that in the time‐to‐maturity
dimension, RPE means seem to follow 60‐day cycle. That is a
phenomenon thus far completely unnoticed by the literature
and requires further research.
soft red wheat
The above figure shows strong negative skewness of realized
prediction errors at long horizons. This phenomenon is well
known from the theory of storage: In times when harvest is
abundant, storage can mitigate the downward pressure of
prices. In times when harvest is small, past inventories can
supplement supply only so much. Means of realized prediction
errors are close to zero for the entire time‐to‐maturity horizon.
corn
Although RPE means never reach above 3% when calculated in
the time‐to‐maturity dimension, looking at the seasonal
diagram reveals strong seasonality. In the first part of the year
risk premiums are paid to holders of short futures positions.
That effect vanishes in early July, and futures prices remain on
average unbiased for the rest of the year.
John	Maynard	Keynes
The Treatise on Money
But the existence of a contango does
not mean that a producer can hedge
himself without paying the usual insurance against price
changes. … In other words, the quoted forward price,
though above the present spot price, must fall below the
anticipated future spot price by at least the amount of the
normal backwardation.
Lester	G.	Telser
The Journal of Political Economy, 66(3)
Although hedgers may be willing to
pay speculators to bear the risks of
price changes, they need not do so if
speculators are eager to speculate.
Firms that hedge can reduce their price risks at little at
no cost to themselves. I accepted the hypothesis that
the futures price equals the expected spot price.
Katherine	Dusak
The Journal of Political Economy, 81(6)
…Under [capital asset pricing model] approach the risk
premium required on a futures contract should depend not on
the variability of prices but on the extent to which the
variations in prices are systematically related to variations in
t h er e t u r no nt o t a lw e a l t h .T h es y s t e m a t i cr i s kw a se s t i m a t e df o ras a m p l eo f
wheat, corn, and soybean futures contracts over the period 1952 to 1967 and
found to be close to zero in all three cases.
Paul	H.	Cootner
The Journal of Political Economy, 68(4)
If hedging is always net short, then speculators as a
group must be net long, and they can make money only
if they sell at prices higher than those at which they
bought. ... If commitments to deliver wheat are large,
the hedging interest may be long and speculators short
prior to the harvest. Under these conditions, prices must
fall if speculators are to make money.
1930 1953 1958 1960 1974
1.	Introduction	to	commodity	futures 2.	What	are	risk	premiums? 3.	Can	we	graph	risk	premiums? 4.	Uncovering	seasonality	effects
Does reducing price risk by hedging impose costs on hedgers? If
futures price is lower than the expected spot price at the settlement
date, than sellers of the commodity who take net short positions
incur a cost known as the risk premium.
Foundations of the literature on risk premiums are presented in the
timeline above.
W ed e v e l o pa ne l e g a n tw a yt og a i naf i r s t ‐pass intuition concerning performance of
a futures market for a commodity. Define the realized prediction error as
If there is no risk premium, then the expected value of ƐT‐t, conditional on
information known at T‐t, is zero. A scattergram is drawn with calendar days to
maturity T‐t on the x‐axis, and percentages on the y‐axis. Each ordered pair (T‐t, ƐT‐t )
is the locus of one dot in the graph. Under an assumption of no risk premium, as
n u m b e ro fc o n t r a c t sc h a r t e dg r o w st h em e a no fr e a l i z e dp r e d i c t i o ne r r o r sw i t hs a m e
days‐to‐maturity should go to zero.




 , 100
Tt T
tT
tt
FP
F
A futures contract is an agreement to buy or sell a specific
amount of a commodity or financial instrument at a particular
price on a stipulated future date. Contract obligations can be
offset before the settlement date.
Economic benefits of futures markets include price discovery
and risk transfer. Price discovery means that futures prices
contain information about future cash prices at the settlement
date. Risk transfer means producers or processors of a
commodity can greatly reduce price risk by entering a futures
contract.
If instead of time‐to‐
maturity we chose the x‐
axis to be the day of the
year, we may be able to
uncover any potential
seasonal patterns in risk
premiums. Effects are best
seen when looking at
means instead of the entire
scattergram.
5.	Conclusions
Utilizing realized prediction errors we can graphically show
the forecasting performance of futures prices over an
extended time period. Using this method we can easily
identify time‐to‐maturity and seasonality components of risk
premiums. Figures developed reveal nonlinear behavior of
forecasting bias in the time‐to‐maturity dimension, and the
importance of information revealed at the end of June for
seasonal pattern of bias. In further research we will develop
statistical tests for futures prices unbiasedness based on
correlated realized prediction errors.."
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no risk premium
positive marginal risk premium
negative marginal risk premium
Tt Tt T
Tt Tt T
Tt Tt T
FE P
FE P
FE P

Visualizing Risk Premiums in Commodity Futures Markets

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Research Papers in Economics