36 lines
2.7 KiB
Plaintext
36 lines
2.7 KiB
Plaintext
466 Part IV: Additional Considerations
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taking a moving average of the last 20 or 30 days' implied volatilities. An alternative
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that does not require the saving of many previous days' worth of data is to use a
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momentum calculation on the implied volatility. For example, today's final volatility
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might be computed by adding 5% of today's implied volatility to 95% of yesterday's
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final volatility. This method requires saving only one previous piece of data - yester
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day's final volatility - and still preserves a "smoothing" effect.
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Once this implied volatility has been computed, it can then be used in the
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Black-Scholes model ( or any other model) as the volatility variable. Thus one could
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compute the theoretical value of each option according to the Black-Scholes formu
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la, utilizing the implied volatility for the stock. Since the implied volatility for the
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stock will most likely be somewhat different from the implied volatility of this par
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ticular option, there will be a discrepancy between the option's actual closing price
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and the theoretical price as computed by the model. This differential represents the
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amount by which the option is theoretically overpriced or underpriced, compared to
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other options on that same stock.
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EXPECTED RETURN
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Certain investors will enter positions only when the historical percentages are on
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their side. When one enters into a transaction, he normally has a belief as to the pos
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sibility of making a profit. For example, when he buys stock he may think that there
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is a "good chance" that there will be a rally or that earnings will increase. The investor
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may consciously or unconsciously evaluate the probabilities, but invariably, an invest
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ment is made based on a positive expectation of profit. Since options have fixed
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terms, they lend themselves to a more rigorous computation of expected profit than
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the aforementioned intuitive appraisal. This more rigorous approach consists of com
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puting the expected return. The expected retum is nothing more than the retum that
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the position should yield over a large number of cases.
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A simple example may help to explain the concept. The crucial variable in com
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puting expected return is to outline what the chances are of the stock being at a cer
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tain price at some future time.
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Example: XYZ is selling at 33, and an investor is interested in determining where
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XYZ will be in 6 months. Assume that there is a 20% chance of XYZ being below 30
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in 6 months, and that there is a 40% chance that XYZ will be above 35 in 6 months.
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Finally, assume that XYZ has an equal 10% chance of being at 31, 32, 33, or 34 in 6
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months. All other prices are ignored for simplification. Table 28-5 summarizes these
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assumptions. |