810 Part VI: Measuring and Trading Volatility 
Expected profit is computed by calculating the profitability of a position at a 
certain stock price times the probability of the stock being at that price, and summing 
that multiple over all possible stock prices. When the concept was first introduced, 
the "probability of the stock being at that price" was given as what we now know is 
the "endpoint" probability. In reality, a much better measure of the expected profit 
of a position can be obtained by using one of the more advanced probability estima­
tion models presented above. 
In generalized expected return studies done using the fat tails Monte Carlo sim­
ulation, certain general conclusions can be drawn about some strategies. 
• A bull spread is an inferior strategy when the options are fairly priced, no matter 
which distribution is assumed. This more or less agrees with observations that 
have been made previously regarding the disappointments that traders often 
encounter when using vertical spreads. 
• While covered writing might seem superior to stock ownership under the log­
normal distribution, the two are about equal under a fat tail distribution. 
• Most startling, though, is the fact that option buying strategies fare much, much 
better under a fat tail distribution than a lognormal one. This most clearly 
demonstrates the "power" of the fat tail distribution: A limited-risk investment 
with unlimited profit potential can be expected to perform very well if the fat tails 
are allowed for. 
Using the lognormal distribution more or less represents the conventional wisdom 
regarding option strategies - the one that many brokers promote: "Don't buy options, 
don't mess with spreads, either buy stocks or do covered call writes." The fat tail dis­
tribution column stands much of that advice on its head. In real life (as demonstrat­
ed by the fat tail distribution), strategies with limited profit potential and unlimited 
or large risk potential are inferior strategies. 
One should be aware that the phrase "expected return" is used in many quasi­
sophisticated option analyses (and even in analyses not using options). Many 
investors accept these "returns" on blind faith, figuring that if they're generated by a 
computer, they must be correct. In reality, they may be not be representative, even 
for comparisons. 
SUMMARY 
This chapter has demonstrated that probability analysis is an inexact science, because 
markets behave in ways that are very difficult to describe mathematically. However, 
probability analysis is also necessary for the option strategist; without it he would be