Investments, tenth edition

 Figure 21.9 

Call option value and hedge ratio  

 Consider two portfolios, one holding 750 FinCorp calls and 200 shares of FinCorp and 

the other holding 800 shares of FinCorp. Which portfolio has greater dollar exposure to 

FinCorp price movements? You can answer this question easily by using the hedge ratio. 

 Each option changes in value by  H  dollars for each dollar change in stock price, 

where  H  stands for the hedge ratio. Thus, if  H  equals .6, the 750 options are equivalent 

to .6   3   750   5   450 shares in terms of the response of their market value to FinCorp 

stock price movements. The first portfolio has less dollar sensitivity to stock price change 

because the 450 share-equivalents of the options plus the 200 shares actually held are 

less than the 800 shares held in the second portfolio. 

 This is not to say, however, that the first portfolio is less sensitive to the stock’s rate of 

return. As we noted in discussing option elasticities, the first portfolio may have lower 

total value than the second, so despite its lower sensitivity in terms of total market 

value, it might have greater rate of return sensitivity. Because a call option has a lower 

market value than the stock, its price changes more than proportionally with stock price 

changes, even though its hedge ratio is less than 1.0. 

 Example  21.6 

Hedge Ratios 

bod61671_ch21_722-769.indd   747

bod61671_ch21_722-769.indd   747

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