Chapter 30: Stock Index Hedging Strategies S49 
Actually he would probably buy 15,100 shares of each stock against the index, 
and on every fourth "round" (100 futures vs. stock) would buy 15,000 shares. This 
would be a very close approximation without dealing in odd lots. 
The trader might also use index options as his hedge instead of futures. The 
striking price of the options does not come into play in this situation. Typically, one 
would fully hedge his position with the index options - that is, if he bought stock, he 
would then sell calls and buy puts against that stock. Both the puts and the calls 
would have the same strike and expiration month. This creates a riskless position. 
This position is a conversion. 
Example: Suppose that cash-based options trade on this index, and that these 
options are worth $100 per point as are normal stock options - that is, an option is 
essentially an option on 100 shares of the index. The trader is going to synthetically 
short the index by buying 100 June 105 puts and selling 100 June 105 calls. Assume 
that the index data is the same as in the previous example, that 0.60298 shares of each 
stock comprise the index. How many shares would one hedge these 100 option syn­
thetics with? 
Number of shares = .60298 x 100 contracts x 100 shares/contract 
= 6029.8 shares 
Note that in the case of a price-weighted index, neither the current index value 
nor the striking price of the options involved (if options are involved) affects the 
number of shares of stock to buy. Both of the above examples demonstrate the fact 
that the number of shares to buy is strictly a function of the divisor of the price­
weighted index and the unit of trading of the option or future. 
Hedging a capitalization-weighted index is more complicated, although the 
technique revolves around determining the makeup of the index in terms of shares 
of stock, just as the price-weighted examples above did. Recall that we could deter­
mine the number of shares of stock in a capitalization-weighted index by dividing the 
float of each stock by the divisor of the index. The general formula for the number of 
shares of each stock to buy is: 
Shares of stock N Shares of N F . Futures unit 
= . . x utures quantity x . to buy m mdex of trading 
We will use the fictional capitalization-weighted index from the previous chap­
ter to illustrate these points. 
Example: The following table identifies the pertinent facts about the fictional index, 
including the important data: number of shares of each stock in the index.