Investments, tenth edition

 Table 23.3 

 Commodity betas 

Commodity

Beta

Commodity

Beta

Wheat

2

0.370

Orange  juice

     0.117

Corn

2

0.429

Propane

2

3.851

Oats

    0.000

Cocoa

2

0.291

Soybeans

2

0.266

Silver

2

0.272

Soybean oil

2

0.650

Copper

     0.005

Soybean  meal

    0.239

Cattle

     0.365

Broilers

2

1.692

Hogs

2

0.148

Plywood

      0.660

Pork  bellies

2

0.062

Potatoes

2

0.610

Egg

2

0.293

Platinum

    0.221

Lumber

2

0.131

Wool

    0.307

Sugar

2

2.403

Cotton

2

0.015

 Source: Zvi Bodie and Victor Rosansky, “Risk and Return in Commodity Futures,”  Financial Analysts 

Journal  36 (May–June 1980). Copyright 1980, CFA Institute. Reproduced from the  Financial Analysts 

Journal  with permission from the CFA Institute. All rights reserved. 

 Suppose that the systematic risk of orange juice were to increase, holding the expected time  T  price of 

juice constant. If the expected spot price is unchanged, would the futures price change? In what direction? 

What is the intuition behind your answer? 

 CONCEPT CHECK 

23.9 

     1.   Foreign exchange futures trade on several foreign currencies, as well as on a European currency 

index. The interest rate parity relationship for foreign exchange futures is   

F

0

5 E

0

 

¢

1

1 r

US

1

1 r

foreign

≤

T

 

    with exchange rates quoted as dollars per foreign currency. Deviations of the futures price from 

this value imply an arbitrage opportunity. Empirical evidence, however, suggests that generally 

the parity relationship is satisfied.  

   SUMMARY 

where  k  is the required rate of return on the commodity, which may be obtained from 

a model of asset market equilibrium such as the CAPM. 

 Note that Equation 23.4 is perfectly consistent with the spot-futures parity relationship. 

For example, apply Equation 23.4 to the futures price for a stock paying no dividends. 

Because the entire return on the stock is in the form of capital gains, the expected rate 

of capital gains must equal  k,  the required rate of return on the stock. Consequently, the 

expected price of the stock is its current price times (1   1     k ) 

 T 

 , or  E ( P  

 T 

 )   5     P  

0

 (1   1     k ) 

 T 

 . 

Substituting this expression into Equation 23.4 results in  F  

0

   5   P  

0

 (1  1   r  

 f 

   ) 

 T 

 , which is exactly 

the parity relationship. 

 

    

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P A R T   V I

  Options, Futures, and Other Derivatives

    2.   Futures contracts calling for cash settlement are traded on various stock market indexes. 

The contracts may be mixed with Treasury bills to construct artificial equity positions, 

which makes them potentially valuable tools for market timers. Market index contracts are 

used also by arbitrageurs who attempt to profit from violations of the stock-futures parity 

rela tionship.  

    3.   Hedging requires investors to purchase assets that will offset the sensitivity of their portfolios to 

particular sources of risk. A hedged position requires that the hedging vehicle provide profits that 

vary inversely with the value of the position to be protected.  

    4.   The hedge ratio is the number of hedging vehicles such as futures contracts required to offset 

the risk of the unprotected position. The hedge ratio for systematic market risk is proportional 

to the size and beta of the underlying stock portfolio. The hedge ratio for fixed-income portfolios 

is proportional to the price value of a basis point, which in turn is proportional to modified dura-

tion and the size of the portfolio.  

    5.   Many investors such as hedge funds use hedging strategies to create market-neutral bets on per-

ceived instances of relative mispricing between two or more securities. They are not arbitrage 

strategies, but pure plays on a particular perceived profit opportunity.  

    6.   Interest rate futures contracts may be written on the  prices  of debt securities (as in the case 

of Treasury-bond futures contracts) or on interest rates directly (as in the case of Eurodollar 

contracts).  

    7.   Swaps, which call for the exchange of a series of cash flows, may be viewed as portfolios of 

forward contracts. Each transaction may be viewed as a separate forward agreement. However, 

instead of pricing each exchange independently, the swap sets one “forward price” that applies 

to all of the transactions. Therefore, the swap price will be an average of the forward prices that 

would prevail if each exchange were priced separately.  

    8.   Commodity futures pricing is complicated by costs for storage of the underlying commodity. 

When the asset is willingly stored by investors, the storage costs net of convenience yield enter 

the futures pricing equation as follows:   

F

0

 5 P

0 

(1 1 r

f

 1 c)

T