34 lines
2.0 KiB
Plaintext
34 lines
2.0 KiB
Plaintext
476 Part IV: Additional Considerations
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vt == volatility for the time period, t
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a == a constant (see below).
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The constants, a and t, are fixed under the assumptions in steps 1 and 2. The first
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constant, a, is the number of standard deviations of movement to be allowed. In our
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example, a == I. That is, the analysis is being made under the assumption that the
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stock could move up by one standard deviation. The second constant, t, is .25, since
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the analysis is for a 90-day holding period, which is 25% of a year. In this example:
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Vt == v-ft == .30 {is== .30 X .50 == .15
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so
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q == 4le· 15 == 41 X 1.16 == 47.64
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Thus, this stock would move up to approximately 475/s if it moved one standard devi
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ation in exactly 90 days.
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Step 4: Using the Black-Scholes model, the XYZ January 40 call can be priced.
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It would be worth approximately 81/s if XYZ were at 475/s and there were 90 days' less
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life in the call.
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Step 5: Calculate the profit potential. For this example, commissions will be
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ignored, but they should be included in a real-life situation.
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81/s-4 41/s Percent profit == --- == - == 103% 4 4
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Thus, if XYZ stock moves up by one standard deviation over the next 90 days, this call
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would yield a projected profit of 103%. Recall again that there is only about a 16%
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chance of the stock actually moving at least this far. If all options on all stocks are
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ranked under this same assumption, however, a fair comparison of profitable options
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will be obtained.
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Step 6 is omitted from this example. It would consist of performing a similar
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profit analysis (steps 4 and 5) on all other XYZ options, with the assumption that XYZ
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is at 475/s after 90 days.
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Step 7: Calculate the downside potential of XYZ. The formula for the downside
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potential of the stock is nearly the same as that used in step 3 for the upside poten
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tial:
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q = pe-avt
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== 4lc· 15 = 41 x .86 = 35.39
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XYZ would fall to approximately 35¼ in 90 days if it fell by one standard deviation.
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Note that the actual distances that XYZ could rise and fall are not the same. The |