Chapter 28: Mathematical Applications 413 
ed an annualized total return (capital gains, dividends, and commissions) of at least 
12%. This would eliminate many potential writes, but would leave him with a fairly 
large number of writing candidates each day. He knows the downside break-even 
point at expiration in each write. Therefore, the probability of the stock being below 
that break-even point at expiration can be computed quickly. His final list would rank 
those writes with the least chance of being below the break-even point at expiration 
as the best writes. Again, this ranking is based on an expected probability and is, of 
course, no guarantee that the stock will not, in reality, fall below the break-even 
point. However, over time, a list of this sort should provide the rrwst conservative cov­
ered writes. 
Example: XYZ is selling for 43 and a 6-month July 40 call is selling for 8 points. After 
including dividends and commission costs for a 500-share position, the downside 
break-even point at expiration is 36. If the annualized volatility of XYZ is 25%, the 
probability of making money at expiration can be computed. The 6-month volatility 
is 17.7% (25% times the square root of½ year). The probability of being below 36 
can be computed by using the formula given earlier in this section: 
The expected probability of XYZ being below 36 in 6 months is 15.8%. Therefore, 
this would be an attractive write on a conservative basis, because it has a large prob­
ability of making money (nearly 85% chance of not being below the break-even point 
at expiration). The return if exercised in this example is approximately 20% annual­
ized, so it should be acceptable from a profit potential viewpoint as well. It is a rela­
tively easy matter to perform a similar calculation, with the aid of a computer, on all 
covered writing candidates. 
The ability to measure downside protection in terms of a common denomina­
tor - volatility - can be useful in other types of covered call writing analyses. The 
writer interested in writing out-of-the-money calls, which generally have higher 
profit potential, is still interested in having an idea of what his downside protection 
is. He might, for example, decide that he wants to invest in situations in which the 
probability of making money is at least 60%. This is not an unusually difficult 
requirement to fulfill, and will leave many attractive covered writes with a high prof­
it potential to choose from. A downside requirement stated in terms of probability 
of success removes the necessity of having to impose arbitrary requirements. Typical