34 lines
2.4 KiB
Plaintext
34 lines
2.4 KiB
Plaintext
538 Part V: Index Options and Futures
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pared to an equal dollar amount of stock. By selling the futures on an index - say, the
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S&P 500- he removes the "market risk" from his portfolio (assuming the S&P 500
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represents the "market"). What is left over after selling the futures is the "tracking
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error." The discrepancy between the movement of the general stock market and any
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individual portfolio is called "tracking error." This investor will still make money if his
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portfolio outperforms the S&P 500, but he will find that he did not completely elim
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inate his losses if his portfolio underperforms the index. Note that if the market goes
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up, the investor will not make any money except for possible tracking error in his
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favor.
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REMOVING THE MARKET RISK FROM A PORTFOLIO
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Stock portfolios are diverse in nature, not :p.ecessarily reflecting the composition of
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the index underlying the futures contracts. The characteristics of the individual
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stocks must be taken into account, for they may move more quickly or more slowly
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than "the market." Let us spend a moment to define this characteristic of stocks that
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is so important.
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VOLATILITY VERSUS BETA
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Recall that when we originally defined volatility for use in the Black-Scholes model,
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we stated that Beta was not acceptable because it was strictly a measure of the cor
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relation of a stock's performance to that of the stock market and was not a measure
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of how fast the stock changed in price. Now we are concerned with how the stock's
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movement relates to the market's as a whole. This is the Beta.
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Unfortunately, Beta is not as readily available to the option strategist as is
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volatility. Many option traders merely have to punch a button on their quote
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machines and they can receive estimates of volatility. However, Beta estimates are
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more difficult to obtain, and the ones that are available are often for very long time
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periods, such as several years. These long-term Betas cannot be used for the pur
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poses of the index hedging discussed in this chapter. Therefore, if one does not have
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access to shorter-term Beta calculations, then he can approximate Beta by compar
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ing an individual stock's volatility with the market's volatility.
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Example: XYZ is a relatively volatile stock, having both an implied and historical
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volatility of 36%. The overall stock market has a volatility of 15%. Therefore, one
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could approximate the Beta of XYZ as
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Beta approximation = 36/15 = 2.40 |