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