546
A Complete Guide to the Futures mArket
 5. The probability distributions in Figure 35.23 represent sample hypothetical illustrations 
of personal price expectations. The indicated optimal strategy in any given situation will 
depend upon the specific shape of the expected price distribution, an input that will differ from 
trader to trader.
The general nature of the price expectations implied by each of the distributions in Figure 35.23 
can be summarized as follows:
Expected Probability Distribution 1. Higher prices and low volatility. This interpretation follows from 
the fact that there is a greater probability of higher prices and that the probabilities are heavily 
weighted toward intervals close to the current price level.
Expected Probability Distribution 2. Higher prices and high volatility. This distribution reflects the 
same 60/40 probability bias toward higher prices as was the case for 
distribution 1, but the 
assumed probability of a substantially higher or lower price is much greater.
Expected Probability Distribution 3. lower prices and low volatility. This distribution is the bearish 
counterpart of distribution 1.
Expected Probability Distribution 4. lower prices and high volatility. This distribution is the bearish 
counterpart of distribution 2.
Expected Probability Distribution 5. Neutral price assumptions and low volatility. This distribution is 
symmetrical in terms of higher and lower prices, and probability levels are heavily weighted 
toward prices near the current level.
Expected Probability Distribution 6. Neutral price assumptions and high volatility. This distribution is 
also symmetrical in terms of high and low prices, but substantially higher and lower prices have 
a much greater probability of occurrence than in 
distribution 5.
Figure 35.24 combines expected Probability distribution 1 with three alternative bullish strat-
egies. (Since it is assumed that there is a greater probability of higher prices, there is no need to 
consider bearish or neutral trading strategies.) Insofar as the assumed probability distribution is 
very heavily weighted toward prices near the current level, the short put position appears to offer 
the best strategy. Figure 35.25 combines the same three alternative bullish strategies with the bull -
ish/volatile price scenario suggested by 
expected Probability distribution 2. In this case, the long 
call position appears to be the optimal strategy, since it is by far the best performer for large price 
advances and declines—price outcomes that account for a significant portion of the overall prob -
ability distribution.
In analogous fashion, Figure 35.26 suggests the preferability of the short call position given 
the bearish/nonvolatile price scenario assumption, while Figure 35.27 suggests that the long put 
position is the optimal strategy given the bearish/volatile price scenario. Finally, two alternative 
neutral strategies are compared in Figures 35.28 and 35.29 for two neutral price distributions 
that differ in terms of assumed volatility. The short straddle appears to offer the better strategy in 
the low volatility distribution assumption, while the reverse conclusion is suggested in the volatile 
price case.