Investments, tenth edition

  SOLUTIONS TO CONCEPT CHECKS 

Payoff, Profit

Short Futures

F

0

P

T

Payoff

Buy (Long) Put

X

P

T

Payoff

Write (Sell) Call

X

P

T

    1.        

 

 

 

2.  The clearinghouse has a zero net position in all contracts. Its long and short positions are 

offsetting, so that net cash flow from marking to market must be zero.  

bod61671_ch22_770-798.indd   797

bod61671_ch22_770-798.indd   797

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7/27/13   1:48 AM

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798 

P A R T   V I

  Options, Futures, and Other Derivatives

   3.      

Oil Price in February, P

T

$89.86

$91.86

$93.86

  Cash flow to purchase oil: 2100,000 3 P

T

2

$8,986,000

2

$9,186,000

2

$9,386,000

1

 Profit on long futures: 100,000 3 (P

T

 2 F

0

)

  

 

2

200,000

           0

  

 

1

200,000

    TOTAL CASH FLOW

2

$9,186,000

2

$9,186,000

2

$9,186,000

   4.  The risk would be that the index and the portfolio do not move perfectly together. Thus basis 

risk involving the spread between the futures price and the portfolio value could persist even 

if the index futures price were set perfectly relative to the index itself. You can measure this 

risk using the index model. If you regress the return of the active portfolio on the return of the 

index portfolio, the regression R-square will equal the proportion of the variance of the active 

portfolio’s return that could have been hedged using the index futures contract. You can also 

measure the risk of the imperfectly hedged position using the standard error of the regression, 

which tells you the standard deviation of the residuals in the index model. Because these are the 

components of the risky returns that are independent of the market index, this standard deviation 

measures the variability of the portion of the active portfolio’s return that  cannot  be hedged using 

the index futures contract.  

   5.  The futures price, $980, is $10 below the parity value of $990. The cash flow to the following 

strategy is riskless and equal to this mispricing.    

Action

Initial Cash Flow

Cash Flow in 1 Year

Lend S

0

 dollars

2

1,000

1,000(1.01) 5 1,010

Sell stock short

1

1,000

2

S

T

 2 20

Long futures

      0

S

T

 2 980      

  TOTAL

0

$10 risklessly

   6.  It must have zero beta. If the futures price is an unbiased estimator, then we infer that it has a zero 

risk premium, which means that beta must be zero.             

 

bod61671_ch22_770-798.indd   798

bod61671_ch22_770-798.indd   798

7/27/13   1:48 AM

7/27/13   1:48 AM

Final PDF to printer

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