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