568 Part V: Index Options and Futures 
Recall how these items are calculated: The number of shares of a stock in the 
index is that stock's float divided by the divisor of the index. Also, the percent of the 
index is the stock's capitalization (float times price) divided by the total capitalization 
of the index (this is step 1 above). Finally, the index value is the index's total capital­
ization divided by the index divisor. 
With this information, we can now construct a mini-index that could be used to 
hedge the UVX itself. Notice that these four stocks alone comprise 28.4% of the 
entire UVX index. We would want each of these four stocks to have the same relative 
weight within our mini-index as they do within the UVX itself. The sum of the capi­
talizations of the four stocks in the above table as well as their relative percentages 
are given in the following table. 
Pct of Pct of 
Index Mini-Index 
Stock Copitolizotion (Step 1) (Step 2) 
IBM 78,000,000 13.1% 46.2% 
XON 34,000,000 5.7% 20.1% 
GE 31,500,000 5.3% 18.6% 
GM 25,500,000 4.3% 15.1% 
Total: 169,000,000 28.4% 100.0% 
The percent of the mini-index is each of the four stocks' capitalizations as a per­
cent of the sum of their capitalizations (step 2 from above). There are two ways to 
compute step 2. First, for IBM one would divide 78 million (its capitalization) by 169 
million (the total capitalization). Second, using the percentages from step 1, divide 
IBM's percent, 13.1, by 28.4, the total percent. Either method gives the answer of 
46.2 percent. We have now constructed the relative percentages of the mini-index 
that each stock comprises. Note that they are in the same relationship to each other 
as they are in the UVX itself. Now it is a simple matter to convert that percent into 
shares of stock, once we decide how many futures contracts to trade against our mini­
index. 
When we know the total dollar amount of futures to hedge and we know the 
percent of the mini-index that each stock comprises, we can compute each stock's 
capitalization within the mini-index. Finally, we divide by that stock's price to see how 
many shares of each stock to buy. Assume that we are going to use UVX options, 
which are worth $100 per point, in lots of 50 options. The total dollar amount of the 
index with the UVX at 170.25 would then be $851,250 (170.25 x 100 x 50). This 
accomplishes step 3. The following table shows the calculations necessary to deter­
mine how many shares of stock to buy against these 50 option contracts.