566 Part V: Index Options and Futures 
SIMULATING AN INDEX 
The discussion in the previous section assumed that one bought enough stocks to 
duplicate the entire index. This is unfeasible for many investors for a variety of rea­
sons, the most prominent being that the execution capability and capital required 
prevent one from being able to duplicate the indices. Still, these traders obviously 
would like to take advantage of theoretical pricing discrepancies in the futures con­
tracts. The way to do this, in a hedged manner, would be to set up a market basket 
of a small number of stocks, in order to have some sort of hedge against the futures 
position. 
In this section, we will demonstrate approaches that can be taken to hedge the 
futures position with a small number of stocks. This is different from when we looked 
at how to hedge individualized portfolios with index futures or options, because we 
are now going to try to duplicate the performance of the entire index, but do it with 
a subset of stocks in the index. In either of these cases, a mathematical technique 
called regression analysis can be used to measure the performance of these portfo­
lios or small market baskets. However, we will take a simpler approach that does not 
require such sophisticated calculations, but will produce the desired results. 
USING THE HIGH-CAPITALIZATION STOCKS 
Recall that in a capitalization-weighted index, the stocks with the largest capitaliza­
tions (price times float) have the most weight. In many such indices, there are a 
handful of stocks that carry much more weight than the other stocks. Therefore, it is 
often possible to try to create a market basket of just those stocks as a hedge against 
a futures position. While this type of basket will certainly not track the index exactly, 
it will have a definite positive correlation to the index. 
What one essentially tries to accomplish with the smaller market basket is to 
hedge dollars represented by the index with the same dollar amount of stocks. No 
hedge works in which the total dollars involved are not nearly equal. Listed below are 
the steps necessary to compute how many shares of each stock to buy in order to cre­
ate a "mini-index" to hedge futures or options on a larger index: 
1. Determine the percent of the large index to be hedged (OEX, NYSE, S&P 500, 
etc.) that each stock comprises. This information is readily available from the 
exchange on which the futures or options trade or can be calculated by the meth­
ods shown in Chapter 29. 
2. Determine the percent of the mini-index to be constructed that each stock com­
prises, by inflating their relative percentages to total 100%.