Investments, tenth edition

 Example  22.8 

Futures Market Arbitrage 

Action

Initial 

Cash Flow

Cash Flow in 

1 Year

Borrow $1,000, repay with interest in 1 year

1

1,000

2

1,000(1.01) 5 2$1,010

Buy stock for $1,000

2

1,000

S

T

 1 $20 dividend

Enter short futures position (F

0

 5 $1,010)

      0

$1,010 2 S

T

             

  TOTAL

0

$20

bod61671_ch22_770-798.indd   786

bod61671_ch22_770-798.indd   786

7/27/13   1:48 AM

7/27/13   1:48 AM

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  C H A P T E R  

2 2

 Futures 

Markets 

787

 The net initial investment of the strategy is zero. But its cash flow in 1 year is $20 regard-

less of the stock price. In other words, it is riskless. This payoff is precisely equal to the 

mispricing of the futures contract relative to its parity value, 1,010  2  990. 

 When parity is violated, the strategy to exploit the mispricing produces an arbitrage 

profit—a riskless profit requiring no initial net investment. If such an opportunity existed, all 

market participants would rush to take advantage of it. The results? The stock price would 

be bid up, and/or the futures price offered down until Equation 22.1 is satisfied. A similar 

analysis applies to the possibility that  F  

0

  is less than $990. In this case, you simply reverse the 

strategy above to earn riskless profits. We conclude, therefore, that in a well- functioning 

market in which arbitrage opportunities are competed away,  F  

0

   5   S  

0

 (1  1   r  

 f 

 )  2   D.  

 The arbitrage strategy of Example 22.8 can be represented more generally as follows: