Investments, tenth edition

 Example  22.5 

Hedging with Oil Futures 

Oil Price in February, P

T

$89.86

$91.86

$93.86

  Revenue from oil sale: 100,000 3 P

T

$8,986,000

$9,186,000

$9,386,000

1

 Profit on futures: 100,000 3 (F

0

 2 P

T

)

  

 

200,000

          0

  2200,000

    TOTAL PROCEEDS

$9,186,000

$9,186,000

$9,186,000

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  C H A P T E R  

2 2

 Futures 

Markets

783

  Figure  22.4  illustrates the nature of the hedge in Example 22.5. The upward-sloping 

line is the revenue from the sale of oil. The downward-sloping line is the profit on the 

futures contract. The horizontal line is the sum of sales revenue plus futures profits. This 

line is flat, as the hedged position is independent of oil prices.  

 To generalize Example 22.5, note that oil will sell for  P  

 T 

  per barrel at the maturity of 

the contract. The profit per barrel on the futures will be  F  

0

   2   P  

 T 

 . Therefore, total revenue 

is  P  

 T 

   1  ( F  

0

   2   P  

 T 

 )  5   F  

0

 , which is independent of the eventual oil price. 

 The oil distributor in Example 22.5 engaged in a  short hedge,  taking a short futures 

position to offset risk in the sales price of a particular asset. A  long hedge  is the analogous 

hedge for someone who wishes to eliminate the risk of an uncertain purchase price. For 

example, a power supplier planning to purchase oil may be afraid that prices might rise by 

the time of the purchase. As the following Concept Check illustrates, the supplier might 

buy  oil futures to lock in the net purchase price at the time of the transaction.  

   The revenue from the oil sale plus the proceeds from the contracts equals the current 

futures price, $91.86 per barrel. The variation in the price of the oil is precisely offset by 

the profits or losses on the futures position. For example, if oil falls to $89.86 a barrel, 

the short futures position generates $200,000 profit, just enough to bring total revenues 

to $9,186,000. The total is the same as if one were to arrange today to sell the oil in 

February at the futures price. 

 Suppose as in Example 22.5 that oil will be selling in February for $89.86, $91.86, or $93.86 per barrel. Con-

sider a firm that plans to buy 100,000 barrels of oil in February. Show that if the firm buys 100 oil contracts 

today, its net expenditures in February will be hedged and equal to $9,186,000. 

 CONCEPT CHECK 

22.3 

–20

0

20

40

60

80

100

120

85

90

95

91.86

Hedged revenues are constant at $91.86 per barrel,

equal to the futures price

Sales revenue increases with oil price

Profit on short futures position falls with oil price

Proceeds (per Barrel)

Oil Price

Sales Revenue per Barrel

Futures Profits per Barrel

Total Proceeds

100

105