- Crude oil inventories in the US have been rising steadily since 2003 and are nearing 1985-86 levels, with more prominent seasonal variations in 2004-2009. - Rolling returns on crude oil futures contracts were slightly left-skewed but non-commercial traders increasingly held equal long and short positions from 2004-2009. - A statistical analysis found a causal and negative relationship between lags in inventory levels and current returns, supporting the theory that inventory levels influence risk premiums. However, as inventories have risen but futures returns remain volatile without sustained growth or decline, the relationship presents a conundrum.

1. International P
Petroleum Week
15 – 17 Feb
February 2010
Risk Adjusted Theo of Storage and
ory
the “Crude
th “C d Oil Futures C
F t Conundrum”
d ”
Jyoti Prasad Deka†, GradEI
d
Oil and Gas Consulting Mott MacDonald Limited
g,
g
OBJECTIVE Notations
To study the crude oil futures market based on commodity storage theory and F1t = Nearest front month (M) futures contract price at time t
draw conclusions by analysing the 1985-2009 data of NYMEX traded light crude
1985 2009 e F2t = Second nearest front month (M+1) f t
S d tf t th (M 1) futures contract price at time t
t t i t ti
oil futures contract prices1, traders positions2 and US stock levels3.
traders’
St = Spot Price t ti
S t P i at time t
THEORIES AND CONVENTIONS In = Crude oil inventory levels at time t
The
Th modern th
d theory of commodity storage posits, i absence of stock-out
f dit t i in b f k E (St+1) = Expected future spot price at t+1, at time t (note that there is no
t+1
way to measure E(St+1); however in theory, E(St+1) establishes an
risk at any time t, St < F1t < F2t < F3t …and so on; in order to compensate
risk, t and t 1 t 1
equilibrium with F1t+1.
inventory holders for their storage cost.
y g
Normal backwardation theory posits, at time t, F1t < E(St+1), F2t < E(St+2),
yp ( t 1) ( t 2) Fig 1: Illustration of futures market mechanism
…and so on; it describes futures market as a risk transfer mechanism where
‘speculators’ go long and earn a premium from hedgers for bearing future
‘ l t ’ l d i f h d f b i f t F1t+1 “Speculator may ‘roll into’ the
F1 t
price risk
risk. next nearest front month
GHR (2008) extend the storage theory to show that this risk premium (or F2 t
{E(St+1)} ⇔F 1
t+1
F2t+1
t 1 contract”
futures return) are determined by commodity’s inventory levels.
Note that, both theories combined, futures market can be in ‘contango’ and {E(St+2 )} ⇔ F 2
t+1
‘backwardation’ at the same time. It may lead to simple arbitrage of futures
M1
M-1 M M+1
contracts and rolling returns without obligation of storage for delivery (Fig1)
delivery. t t+1
t 1 t+2
t 2
METHODOLOGY I Excess futures return, ER = (F1t+1 - F2t)/ F2t
I. E cess f t res ret rn
Inventories: We de-trend the stock data1 (In) and record the ‘cyclic’ II. Spot Return, SR = (F1t+1 – F1t)/ F1t
deviations about ‘normalised’ levels (‘N-In’). W th run a li
d i ti b t‘ li d’ l l (‘N I ’) We then linear regression
i
(I – II) = Rolling return, RR
on monthly dummies to investigate the seasonal variation of these deviations.
deviations.
(Fig 3.1 – 3.4)
Fig 2: F1, F2, In/ ‘N-In’ (NYMEX traded and US data-1985:2009)
N-In
Futures returns: We investigate futures returns – spot, excess and rolling,
and compare results with snapshots of ‘non-commercial4’ trading positions in n
the light crude oil market at NYMEX. (Fig 4 1 – 4 2)
NYMEX 4.1 4.2)
F1 F2 In
Causal relationship: Finally we develop a multivariate vector auto-regression
auto regressionn
(
(VAR) model on lagged variables of (In/N-In), returns (
) gg ( ), (both taken as
endogenous) and historic US treasury bill rates (taken as exogenous) and
discuss its structural inferences. (Table 5.1 – Fig 5.2)
RES
SULTS
Fig 3.1: In, 1985:2009 Fig 4.1 Distribution of ER, SR and RR, during 1985:2009
n Table 5.1 Granger Causality Test
Null hypothesis: all lags of a particular
Hodrick – endogenous variable can be excluded as
d i bl b l d d
Deviation
D i ti
Prescott trend ER SR explanator for the other.
from trend
filter
Variables P-values
P values Rejected?
∆ d SR
d_SR 0.1223
0 1223 No
Fig 3.2: ‘N-In’ Fig 3.3: In/‘N-In’
∆In/N In
∆In/N-In 0.0052
0 0052 Yes
RR
Fig 5 2 Impulse R
Fi 5.2 I l Response
d_SR response to d_SR response to
shock in d (In/N-In)
d_(In/N In) shock in d SR
d_SR
Fig 4.2 ‘Non-commer
rcial’ spread as a % of all open interest
Fig 3.4: Seasonal Variation in ‘de-trended’ inventories
N o n C o m m S p re a d a s %
35.00%
o f a lll o p e n in tte r e s t
30.00% 2004 - 2009
8 4
P e rc e n t D e v ia t n
P e rc e n t D e v ia t n
25.00%
5 00%
tio
tio
6 1985 - 2003 2004 - 2009
20.00%
4 2 15.00%
15 00%
d_(In/N-In) response to
2 0 10.00% d_(In/N-In) response
to shock in d_SR
d SR shock in d_(In/N-In)
_( )
0 5.00%
-2
2 -2
2 0.00%
0 00%
J ul
Nov
J an
J un
M ar
A pr
Oct
F eb
A ug
S ep
15 January 1986 15 January 1996 15 January 2006
M ay
Jul
Apr
Aug
M ar
Jun
Oct
M ay
Nov
Jan
Feb
Sep
CO C US O S
CONCLUSIONS REFERENCES
Crude oil inventories show a rising ‘trend’ in 2003-09, and are nearing the
trend 2003 09, Accomazzo, D. & Frankfurter M. M. (2007). “Is Managed Futures an Asset
Is
levels of 1985-86 (Fig 3.2). Seasonal variations in stocks are more Class? The Search for the Beta of Commodity Futures - Working Paper”,
prominent during 2004-2009 than previous years. (Fig 3.4) Cervino Capital Management LLC, California, United States.
Rolling
R lli returns on crude oil futures were found slightly l f k
d il f f d li h l left-skewed.d Deaton, A & L
D A. Laroque G. (1992) “On the B h i of C
G (1992). “O h Behavior f Commodity P i di Prices,”
”
However,
However there is a strong upward surge of non commercial ‘spread’
non-commercial spread Review of Economic Studies 59: 1-23
1 23
during 2004-09 (‘spread’ is an extent to which non-commercial traders hold
g ( p Gorton G. B., Hayashi F & Rouwenhorst K G (GHR 2008) “The
G B F. K. G. (GHR, 2008). The
equal ‘long’ and ‘short’ positions in futures contracts). (Fig 4.1- 4.2) Fundamentals of Commodity Futures Returns”, Yale ICF Working Paper
y g p
VAR results show causal and negative relationship between lags of No 07-08. Yale University, United States.
inventories and returns on their current l
i t i d t th i t levels. Th
l Thus, GHR’ (2008)
GHR’s
assertion on stock levels and risk premium is found empirically sound sound. ACKNOWLEDGEMENT & CONTACT
(
(Table 5.1 – Fig 5.2)
g )
The conundrum: as discussed, inventories of crude oil have steadily built Author would like to thank Mr Azfar Shaukat, Director, Oil and Gas
up since 2004 and non-commercial traders now hold more equal long and Consulting at Mott MacDonald Limited and colleagues for their support.
short positions th any other ti
h t iti than th time i th hi t
in the history. F t
Futures returns all thi
t ll this †
jyoti.deka@mottmac.com
j ti d k @ tt
while,
while albeit volatile show little sustained growth or decline.
volatile, decline
Title image courtesy: www.flickr.com; www.liveoilprices.co.uk. 1,3 Published by the Energy Info
ormation Administration, Department of Energy, United States. 2 Published by the US Commodity
Futures Trading Commission. 4 Trading positions are classified as ‘commercial’ if traders use fu
utures for hedging, otherwise they are ‘non-commercial’.