B. Empirical analysis on optimal hedging ratio

Hedging Based Price Decline Risk Management of Refined Oil Inventory
Xing Bi1, Yao-long Zhang1, Yan-wei Liu2
College of Management and Economics, University of Tianjin, Tianjin, China
Office of International Cooperation, Peking University Health Science Center, Beijing, China
([email protected])
Abstract - Nowadays oil has become an important
energy source with both political and economic attributes.
Frequent fluctuation of oil demand and price in the
international market confronts enterprises with many
uncertainties in refined oil inventory management. In order
to prevent the risk of oil price decline brought up by those
uncertainties, this article analyzed the inventory methods of
different refined oil, chose hedging as the method to manage
price decline risks of oil inventory, compared the different
optimal hedge ratio models, and made empirical analysis to
gasoline hedging.
Keywords- hedging, risk management, OLS
Uncertainty of demand or price usually causes risk in
inventory management to enterprises. Inventory
management, especially inventory price management of
refined oil, is of great influence on enterprise operations.
Although the rise of inventory value in price-increasing
period can absolutely create extra profit for the enterprises,
the decline of inventory value will bring huge losses when
the oil price goes down if the enterprises cannot
reasonably avoid the risks. Therefore, price decline risk is
an important inventory risk that enterprises are faced with.
In the future, the government is likely to further adjust the
pricing mechanism of refined oil. Therefore, the oil price
may be more frequently regulated, the correlation
between oil prices domestic and abroad strengthened, the
price of refined oil further marketed, and the risk of
inventory price fluctuation increased. For this reason,
study on price decline risk management of refined oil
inventory is of great significance to enhance enterprise
operation efficiency, avoid financial risks, and ensure the
smooth running of daily sales.
A. Methods of Refined Oil Inventory Management
There are already some advanced management ideas
and management tools on an international level about
inventory management and effective inventory risk
control, such as insurance stock quota, lead-time, Activity
Based Classification, VMI (vendor-managed inventory)
theory, JIT (just-in-time) purchasing system, hedging, and
Insurance stock quota is a quantity criterion of the
necessary material reserve for regular production when
the supplier delays the supply for enterprises or when
some other accidents occur [1]. Usually these inventories
will not be used unless the stocks are overused or the
supplies are delayed. For some enterprises, their products
have seasonality or the transportation of their products is
affected by seasons, so seasonal stocks are needed.
Lead-time is the period from the start of ordering to
receiving order quantity [2]. Strictly speaking, lead-time
is random and indeterminate. But it is often regarded as a
determined constant in application. Sometimes enterprises
need to order products to replenish stocks. With the
delivery of cargo from storage, the inventory level will
gradually decrease to a point, and then replenishment is
required, or stockout appears, thus seriously affecting the
regular enterprise operations. This point is called “order
point”. When the inventory level reaches the “order
point”, ordering will start.
Activity Based Classification is a key control method,
which classifies the analyzing objects into three different
categories (A, B, and C) according to their main
technology economic characteristics, in order to
distinguish between important objects and general ones
and to focus on the management of decisive A-category
objects [3]. ABC classification management of inventory
is to classify the inventories of enterprises into A, B, and
C categories in accordance with certain criteria. The most
important inventories belong to A category, general
inventories B category, and the unimportant ones C
category. Commonly, there are two classification criteria:
amount standard and standard number of varieties, among
which amount standard is the most fundamental criterion,
while the other one is only a reference.
VMI means that the upstream enterprises, such as the
suppliers, manage and regulate the inventories of
downstream customers on the basis of the production,
operation and inventory information of their downstream
customers [4]. It is an inventory operation mode in the
supply chain environment. In essence, it is a method that
turns the problem of multi-stage supply chain into that of
single-stage inventory management, compared with the
traditional method of replenishing products according to
the ordering of traditional costumers. VMI is a solution
that utilizes the actual or predicted consumption demand
and inventory as market demand forecast and inventory
replenishment, which means the suppliers can get the
information for consumption demand through sales data,
and more effectively plan and more quickly respond to
market change and consumption demand.
JIT purchase, also called Just In Time purchase, is
evolved from the idea of Just In Time production
management [5]. Its fundamental idea is to provide
appropriate products with appropriate quantity and quality
at the appropriate place and time. JIT purchase includes
the support and collaboration of suppliers, the process of
producing, freight transportation systems, and etc, which
can not only draw down inventories, but also speed up
inventory turnover, shorten lead time, improve shopping
quality, and achieve results of satisfactory delivery.
The above theoretical methods all reduce enterprise
inventories, speed up inventory turnover and reach the
goal of inventory risk control from the perspective of
minimizing inventory cost and maximizing service
standard. However, the common practice for many large
multinational petroleum companies is to hedge against oil
futures, which can help lock the cost and prevent drastic
fluctuation of profit due to the fluctuation of market prices,
thus guaranteeing the smooth operation of enterprises.
Hedging is a trading that insures the price of goods
that is needed to buy in the future or is bought to sell in
the future, making use of futures contract as the
temporary substituent of goods that will be traded in spot
market of the future. In normal market conditions, the
trends of spot market and futures market are similar.
Since the two markets are affected by the identical supply
and demand relation, the prices of the two markets rise
together and fall together; however, the operations of the
two markets are the opposite, so one gains profit when the
other gets a loss, meaning that profit in futures market can
cover the loss in spot market or the otherwise.
B. Optimal hedging ratio model comparison
Modern hedging theory includes three topics: the scale
of hedging, the effectiveness of hedging and the cost of
hedging. The scale of hedging is described by the hedging
ratio; the effectiveness of hedging is measured by the
degree that hedging helps reduce the price risk the
hedgers are faced with; the cost of hedging means the
degree that hedging reduces the expected profit of hedgers.
The effectiveness of hedging and the cost of hedging
combined together decide the efficiency of hedging.
Effective hedging can reduce the maximum amount of
risks relative to each unit cost. The so-called optimal
hedging method is to choose a method from a series of
available efficient hedging methods to reach the
maximum utility. At present, there are mainly two kinds
of hedging ratio calculation methods in domestic and
international literatures: risk minimization based and
revenue maximization based.
1) Optimal hedging ratio model based on risk
minimization: Keynes (1930) [6] indicated that with the
futures price and spot price completely correlated, in
order to get the best hedging effect, the optimal hedging
ratio should be 1, and it is recommended to buy futures
contract in futures market with the equal number and
opposite direction of goods in spot market futures
contract. But the assumption does not coincide with the
actual situation, because the futures price and spot price
interact with each other, but are not completely correlated.
Now scholars focus on risk minimization and regard it as
the optimization objective. Ederington (1973) [7]
measured risks with hedging intraclass variance, and got
the optimal hedging ratio by using the least squares
method with risk minimization as the optimization
objective. Lien and Luo (1993) [8], Viswanath (1993) [9],
Ghosh (1993) [10], Holmes (1996) [11], Sim (2001) [12]
all found that there exists cointegration relationship
between the futures price sequence and spot price
sequence. In view of the above, Ghosh put forward the
VAR model (Vector Autoregression Model) and the ECM
model (Error Correction Model) to calculate optimal
hedging ratio. The characteristic of risk minimization
based static optimal hedging ratio models is that they truly
reflect the hedgers’ desire of avoiding risk in the futures
market while the disadvantages are: ignorance of hedging
profit issue; no consideration for the influence of dynamic
change factors in futures trading on hedging effect.
2) Optimal hedging ratio model based on revenue
maximization: Optimal hedging ratio decision models
based on revenue maximization are rare, mainly because
the primary function of futures market is to avoid price
risk instead of purely pursuing best interests. Cecchetti,
Cumby and Figlewski (1998) [13] calculated the optimal
hedging ratio from data with the hedging portfolio wealth
maximization as the objective function. Chang-Zheng
Huang (2004) [14] got the optimal hedging ratio through
setting up a hedging model with the optimization
objective of maximizing profit. Yu-Chia Hsu and An-Pin
Chen (2008) [15] determined the optimal hedging ratio
with the optimization goal of expected revenue on
condition that negative yields would be normally
distributed. The characteristic of revenue maximization
based static optimal hedging ratio models is that they
reflect the hedgers’ desire of pursing maximum benefit in
futures trading. But their biggest drawback is to ignore
that there also exists great risks in futures trading. Besides,
those models lack consideration for the dynamic changes
of the risk factors.
When people hedge against futures market, the main
problem is to choose a hedging ratio, that is to say the
ratio of futures trading volume to spot transactions. At
present, there are mainly two kinds of hedging ratio
calculation methods in literatures at home and abroad:
risk minimization based and revenue maximization based.
Since the main concern of futures market is avoiding price
risks, which can be completely fulfilled in practical
application by risk-minimization-based ordinary least
squares (OLS), the OLS model is chosen to determine the
optimal hedging ratio in gasoline hedging empirical
The chosen hedging objects are Shanghai fuel oil
futures, WTI futures of NYMEX and Brent futures of ICE;
selected data sample interval is between January 2nd, 2009
and June 1st, 2011; data sources are gasoline factory price
of National Development and Reform Committee, fuel oil
futures price of Shanghai Futures Exchange, WTI futures
price of NYMEX Futures Exchange, and Brent futures
price of ICE Futures Exchange. Since the unit of the first
two prices is Yuan a ton, while the unit of the latter two is
dollar a barrel, dollar a barrel is chosen as the price unit in
empirical analysis, conversion between RMB and US
dollars being done with current exchange rate, 1 ton
gasoline equaling to 8.51 barrel gasoline and 1 ton fuel oil
equaling to 7.25 barrel fuel oil.
Correlation analysis and cointegration test to spot
price and futures price with the introduction of correlation
coefficient index and the use of Eviews software indicates
that gasoline market is highly correlated with Shanghai
fuel oil futures market, WTI futures market and Brent
futures market. Therefore we can hedge against gasoline
with these futures markets.
The essential issue of hedging against gasoline spot
with futures is to establish the optimal hedging ratio. In
order to reduce the inventory risks of refined oil and
minimize the income risk, the risk minimization hedging
model is chosen.
A. Model specification
R refers to the change of hedging value; h(t) refers to
the hedging ratio; S1 and S2 respectively refer to spot
prices at time t1 and t2; F1 and F2 respectively refer to
futures prices at time t1 and t2; S  h(t )F stands for the
h(t )F  S stands for the eventually change of long
hedging. Then:
VAR( R)  VAR(S  h(t )F )   s2  h(t ) 2f  2h(t )  s f
And  s2  VAR(S ), 2f  VAR(F ),   COV (S , F ) /  s f , to
get the optimal hedging ratio which equals to minimizing
the variance of R( VAR ( R ) ), furthermore:
COV (S , F )
h(t )   s 
 2f
Formula (3) gets the optimal hedging ratio.
is the intercept of regression equation;
random error; slope coefficient  is estimated for the
value of the hedging ratio:
  COV ( ln St ,  ln Ft ) / VAR( ln Ft )  h
B. Empirical analysis on optimal hedging ratio
For hedging strategies, we respectively construct the
price change sequences for time interval of 30, 60 and 90
days according to spot price and the corresponding futures
closing price during a certain period, to estimate the
optimal hedging ratio under different hedging deadlines.
Taking the 30-day interval as an example, its statistical
characteristics of trend can be described in Table I.
Table I demonstrates that the average rate of spot price
and futures price changes are all positive, which means
both the spot and futures price have a rising overall trend.
In a point view of price volatility, the prices of WTI
futures and Brent futures have showed stronger volatility
than the spot price of gasoline, and the price of Shanghai
fuel oil futures.
With regard to the price sequences of different time
period, we can get regression results as follows according
to the regression equation formula (4): (see Table II)
Table II shows that different hedging subjects with the
identical hedging time limit would have different optimal
hedging ratios. Taking the 30-day interval as an example,
the hedging ratio is 0.2715 when hedging against fuel oil
futures, while the hedging ratio is just 0.1615 and 0.1737
against the WTI and Brent. Identical hedging subjects
with different hedging time limit would also have
different optimal hedging ratios. Taking the WTI futures
as an example, the hedging ratio of 30-day futures is
0.1615, 0.2116 for 60-day and 0.2623 for 90-day.
30 days
 2h(t ) 2f  2  s f  0
dh(t )
dV 2
 2 2f  0
dh(t ) 2
Build regression equation according to minimum risk
based hedging ratio as follows:
 ln St     ln Ft   t
 lnGAS  ln SHFUEL  lnWTI  ln BRENT
Mean value
Standard deviation
Hedging subject
 lnWTI
30 days
60 days
90 days
 ln BRENT
 lnWTI
 ln BRENT
 lnWTI
 ln BRENT
C. Hedging efficiency comparison and analysis
The calculation of hedging ratio is conducted in risk
minimization principle, and the hedging efficiency is
measured by the decline degree of risk.
According to Johnson (1960) [16] who defined the
hedging performance as the decline degree of variance
after hedging, income variance of hedging and nohedging can be described as:
VAR(U t )  VAR( ln St )
VAR( H t )  VAR( ln St   ln Ft )
Then hedging efficiency index can be calculated:
H e  [VAR(Ut )  VAR( Ht )]/ VAR(Ut )
index reflects the decline degree of risk of
hedging to no-hedging, that is to say the effectiveness of
hedging. After hedging with some contracts, the degree of
risk for spot price change could be reduced; the more the
risk reduction is, the stronger the effectiveness of futures
contract is. Comparing different futures hedging
efficiency through formula (8), we get the results shown
in Table III:
risk management, in order to avoid price decline risk in
gasoline spot market.
I would like to extend my sincere thanks to my
mentor, Associate Professor Xing Bi. I am deeply inspired
by his meticulous scholarship, concentration on academic
studies and visionary guidance to students, from which I
benefited a lot. Meanwhile, I would also like to thank my
girlfriend, who gives me endless energy and great support
to study.
 lnWTI
 ln BRENT
 lnWTI
 ln BRENT
 lnWTI
 ln BRENT
30 days
60 days
Hedging efficiency comparison in Table III shows
that under the measure of risk minimization index and
with the same futures contract time limit, the hedging
effect of Brent futures is the best, WTI futures taking the
second place, and Shanghai fuel oil futures is the least
efficient in hedging. Taking Brent futures as an example,
30-day futures contract will reduce 22.56 percent of risk,
60-day contract reducing 41.52% and 90-day contract
reducing 58.55%. By this token, Brent futures with 90day contract work better than the other Brent futures.
Consequently, it is recommended to buy 90-day Brent
futures contract in futures market in refined oil inventory
Hedging subject matter
90 days
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