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+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.