Investments, tenth edition

 Figure 23.3 

Profits as a function of the exchange rate  

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P A R T   V I

  Options, Futures, and Other Derivatives

quarter. Profits generally are lower when the exchange rate is lower, that is, when the 

pound depreciates. To quantify that sensitivity, we might estimate the following regres-

sion  equation:    

Profits 5 a 1 b($/£ exchange rate) 

The slope of the regression, the estimate of  b,  is the sensitivity of quarterly profits to the 

exchange rate. For example, if the estimate of  b  turns out to be 2,000,000, as in  Figure 23.3 , 

then on average, a $1  increase  in the value of the pound results in a $2,000,000  increase   in 

quarterly profits. This, of course, is the sensitivity we posited when we asserted that a $.10 

drop in the dollar/pound exchange rate would decrease profits by $200,000. 

 Of course, one must interpret regression output with care. For example, one would not 

want to extrapolate the historical relationship between profitability and exchange rates 

exhibited in a period when the exchange rate hovered between $1.80 and $2.10 per pound 

to scenarios in which the exchange rate might be forecast at below $1.40 per pound or 

above $2.50 per pound. 

 In addition, extrapolating past relationships into the future can be dangerous. We saw 

in Chapter 8 that regression betas from the index model tend to vary over time; such prob-

lems are not unique to the index model. Moreover, regression estimates are just that—

estimates. Parameters of a regression equation are sometimes measured with considerable 

imprecision. 

 Still, historical relationships are often a good place to start when looking for the average 

sensitivity of one variable to another. These slope coefficients are not perfect, but they are 

still useful indicators of hedge ratios.     

 United Millers purchases corn to make cornflakes. When the price of corn increases, the cost of making 

cereal increases, resulting in lower profits. Historically, profits per quarter have been related to the price of 

corn according to the equation: Profits  5  $8 million  2  1 million  3  price per bushel. How many bushels 

of corn should United Millers purchase in the corn futures market to hedge its corn-price risk? 

 CONCEPT CHECK