Cbapter 30: Stock Index Hedging Strategies 547 
paid out and, if the market stabilizes, the time value decay will cause a loss on the 
puts. If one actually suspects that such a stabilization might occur, he should use 
futures against his position instead of puts or calls. 
INDEX ARBITRAGE 
As previously stated, index arbitrage consists of buying virtually all of the stocks in an 
index and selling futures against them, or vice versa. Whenever the futures on an 
index are mispriced, as determined by comparing their actual value with their fair 
value, there may be opportunities for arbitrage if the mispricing is large enough. 
When futures are extremely overpriced: buy stocks, sell futures; or when futures are 
underpriced: sell stocks, buy futures. In either case, the arbitrageur is attempting to 
capture the differential between the fair value price of the futures contract and the 
price at which he actually buys or sells the index. First, we will examine fully hedged 
situations - ones in which the entire index is bought or sold. After that, we will exam­
ine smaller sets of stocks that are designed to simulate the performance of the entire 
index. 
Hedging indices which contain fewer stocks is easier than hedging larger 
indices. Hedging a price-weighted index is probably the simplest type of hedge. As 
examples, the same sample indices that were constructed in the previous chapter will 
be used. 
Whenever futures or index options trade on an index, it is possible to set up 
market baskets for arbitrage. The trader should determine, in advance, how many 
shares of each stock he will buy or sell in order to duplicate the index. In a price­
weighted index, of course, he will buy the same number of shares of each stock. In a 
capitalization-weighted index, he will be buying different numbers of shares of each 
stock. Let us first look at how the number of shares to buy is determined. Then we 
will discuss some of the nuances, such as monitoring bids and offers of the indices, 
order execution, and others. 
HOW MANY SHARES TO BUY 
In advance of actually trading the stocks and futures or options, one should deter­
mine exactly how many shares of each stock he will be buying in each index he plans 
to arbitrage. Normally, one would decide in advance how many futures contracts or 
option contracts he will trade at one time. Then the number of shares of stock to be 
bought as a hedge can be determined as well. Essentially, one is going to hedge equal 
dollar amounts - that is, he will buy enough stocks to offset the total dollar amount 
represented by the index.