Chapter 28: Mathematical Applications 475 
A final ranking of all potential call buys can be obtained by performing steps 3 
through 6 on all stocks, and ranking the purchases by their percentage reward. 
RISK 
7. Calculate the stock price that the stock could fall to, when the assumptions in 
steps 1 and 2 are applied. 
8. With a model, price the option after the stock's decline. 
9. Calculate the percentage loss after commissions. 
10. Compute a reward/risk ratio: Divide the percentage profit from step 5 by the 
percentage risk from step 9. 
11. Repeat steps 8 through 10 for each option on the stock. 
A final ranking of less aggressive option purchases can be constructed by performing 
steps 7 through 11 on all stocks, and ranking the purchases by their reward/risk ratio. 
The higher profitability list of option purchases will tend to be at- or slightly 
out-of-the-money calls. The less aggressive list, ranked by reward/risk potential, will 
tend to be in-the-money options. 
Example: Steps 1 and 2: Suppose an investor wants to look at option purchases for a 
90-day holding period, under the assumption that each stock could move up by one 
standard deviation in that time. (There is only about a 16% chance that a stock will 
move more than one standard deviation in one direction in a given time period. 
Therefore, in actual practice, one might want to use a smaller stock movement in his 
ranking calculations.) Furthermore, assume that the following data are known: 
XYZ common, 41; 
XYZ volatility, 30% annually; 
XYZ January 40 call, 4; and 
time to January expiration, 6 months 
Step 3: Calculate upward stock potential. This is accomplished by the following 
formula: 
where 
p = current stock price 
q = potential stock price