544A COMPleTe gUIde TO THe FUTUreS MArKeT
 Choosing an Optimal Strategy 
 It the previous sections we examined a wide range of alternative trading strategies. Now what? How 
does a trader decide which of these alternatives provides the best trading opportunity? This ques-
tion can be answered only if probability is incorporated into the analysis. The selection of an optimal 
option strategy will depend entirely on the trader’s price and volatility expectations. Insofar as these 
expectations will diff  er from trader to trader, the optimal option strategy will also vary, and the 
success of the selected option strategy will depend on the accuracy of the trader’s expectations. In 
order to select an optimal option strategy, the trader needs to translate his price expectations into 
probabilities. 
 The basic approach requires the trader to assign estimated probability levels for the entire range 
of feasible price intervals. Figure   35.23   illustrates six diff  erent types of probability distributions for 
August gold futures. These distributions can be thought of as representing six diff  erent hypothetical 
expectations. (The charts in Figure   35.23   implicitly assume that the current price of August gold 
futures is $1,200.) Several important points should be made regarding these probability distributions: 
   1.  The indicated probability distributions only represent approximations of traders’ price expec-
tations. In reality, any reasonable probability distribution would be represented by a smooth 
curve. The stair-step charts in Figure   35.23   are only intended as crude models that greatly sim-
plify calculations. (The use of smooth probability distributions would require integral calculus 
in the evaluation process.) 
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
25,000
12,500
−12,500
−25,000
0
1,050 1,100 1,150 1,200 1,250
Breakeven price on long
2 calls = $1,238.80
Long futures
Long 2 calls
1,300 1,350 1,400
37 ,500
+37 ,500
Futures price at time
of position initiation
    FIGURE   35.22    Profi  t/loss Profi  le: Two long Calls vs. long Futures