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training_data/relevant/text/07ad210be30cf4ea0b67ea4e5d3ba5b2c40734f2b1048ec23f2566444b638b81.txt

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+Chapter 28: Mathematical Applications 
+TABLE 28-5. 
+Calculation of expected returns. 
+Price of XYZ in 6 Months 
+Below 30 
+31 
+32 
+33 
+34 
+Above 35 
+467 
+Chance of XYZ Being at That Price · 
+20% 
+10% 
+10% 
+10% 
+10% 
+40% 
+100% 
+Since the percentages total 100%, all the outcomes have theoretically been 
+allowed for. Now suppose a February 30 call is trading at 4 and a February 35 call is 
+trading at 2 points. A bull spread could be established by buying the February 30 and 
+selling the February 35. This position would cost 2 points - that is, it is a 2-point 
+debit. The spreader could make 3 points if XYZ were above 35 at expiration for a 
+return of 150%, or he could lose 100% if XYZ were below 30 at expiration. The 
+expected return for this spread can be computed by multiplying the outcome at expi­
+ration for each price by the probability of being at that price, and then summing the 
+results. For example, if XYZ is below 30 at expiration, the spreader loses $200. It was 
+assumed that there is a 20% chance of XYZ being below 30 at expiration, so the 
+expected loss is 20% times $200, or $40. Table 28-6 shows the computation of the 
+expected results at all the prices. The total expected profit is $100. This means that 
+the expected return (profit divided by investment) is 50% ($100/$200). This appears 
+to be an attractive spread, because the spreader could "expect" to make 50% of his 
+money, less commissions. 
+What has really been calculated in this example is merely the return that one 
+would expect to make in the long run if he invested in the same position many times 
+throughout history. Saying that a particular position has an expected return of 8 or 
+9% is no different from saying that common stocks return 8 or 9% in the long run. 
+Of course, in bull markets stock would do much better, and in bear markets much 
+worse. In a similar manner, this example bull spread with an expected return of 50% 
+may do as well as the maximum profit or as poorly as losing 100% in any one case. It 
+is the total return on many cases that has the expected return of 50%. Mathematical 
+theory holds that, if one constantly invests in positions with positive expected returns, 
+he should have a better chance of making rrwney.