Investments, tenth edition

 Example  23.4 

Hedging Market Risk 

 We also could approach the hedging problem in Example 23.4 using a similar regres-

sion procedure as that illustrated in  Figure 23.3  for foreign exchange risk. The predicted 

value of the portfolio is graphed in  Figure 23.4  as a function of the value of the S&P 500 

index. With a beta of .8, the slope of the relationship is 24,000: A 2.5% increase in the 

index, from 1,000 to 1,025, results in a capital gain of 2% of $30 million, or $600,000. 

Therefore, your portfolio will increase in value by $24,000 for each increase of one point 

in the index. As a result, you should enter a short position on 24,000 units of the S&P 500 

index to fully offset your exposure to marketwide movements. Because the contract multi-

plier is $250 times the index, you need to sell 24,000/250  5  96 contracts.  

 Notice that when the slope of the regression line relating your unprotected position to 

the value of an asset is positive, your hedge strategy calls for a  short  position in that asset. 

The hedge ratio is the negative of the regression slope. This is because the hedge position 

should offset your initial exposure. If you do poorly when the asset value falls, you need 

a hedge vehicle that will do well when the asset value falls. This calls for a short position 

in the asset. 

 Active managers sometimes believe that a particular asset is underpriced, but that the 

market as a whole is about to fall. Even if the asset is a good buy relative to other stocks 

in the market, it still might perform poorly in a broad market downturn. To solve this 

problem, the manager would like to separate the bet on the firm from the bet on the 

market: The bet on the company must be offset with a hedge against the market exposure 

that normally would accompany a purchase of the stock. In other words, the manager 

seeks a    market-neutral  bet    on the stock, by which we mean that a position on the stock 

bod61671_ch23_799-834.indd   811

bod61671_ch23_799-834.indd   811

7/25/13   2:01 AM

7/25/13   2:01 AM

Final PDF to printer

---

812

P A R T   V I

  Options, Futures, and Other Derivatives

is taken to capture its alpha (its abnormal risk-adjusted expected return), but that market 

exposure is fully hedged, resulting in a position beta of zero. 

 By allowing investors to hedge market performance, the futures contract allows the port-

folio manager to make stock picks without concern for the market exposure of the stocks 

chosen. After the stocks are chosen, the resulting market risk of the portfolio can be modu-

lated to any degree using the stock futures contracts. Here again, the stock’s beta is the key 

to the hedging strategy. We discuss market-neutral strategies in more detail in Chapter 26. 

 

   

Predicted Value

of Portfolio

Slope 

= 24,000

S&P 500

Index

$30.6 million

$30 million

1,000

1,025