31 lines
1.6 KiB
Plaintext
31 lines
1.6 KiB
Plaintext
470
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where
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v = annual volatility
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t = time, in years
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vt = volatility for time, t.
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Part IV: Additional Considerations
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As an example, a 3-month volatility would be equal to one-half of the annual
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volatility. In this case, t would equal .25 (one fourth of a year), so v_25 = v65 = .5v.
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The necessary groundwork has been laid for the computation of the probabili
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ty necessary in the expected return calculation. The following formula gives the prob
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ability of a stock that is currently at price p being below some other price, q, at the
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end of the time period. The lognormal distribution is assumed.
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Probability of stock being below price q at end of time period t:
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P (below) = N (In~))
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where
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N = cumulative normal distribution
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p = current price of the stock
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q = price in question
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In = natural logarithm for the time period in question.
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If one is interested in computing the probability of the stock being above the
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given price, the formula is
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P (above)= 1- P (below)
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With this formula, the computation of expected return is quickly accomplished
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with a computer. One merely has to start at some price - the lower strike in a bull
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spread, for example - and work his way up to a higher price - the high strike for a
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bull spread. At each price point in between, the outcome of the spread is multiplied
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by the probability of being at that price, and a running sum is kept.
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Simplistically, the following iterative equation would be used.
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P ( of being at price x) = P (below x) - P (below y)
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where y is close to but less than x in price. As an example:
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P (of being at 32.4) = P (below 32.4) - P (below 32.3) |