In this problem we will use Figure to estimate the expected return on the stock market. To estimate the expected return, we will create a list of possible returns and we will assign a probability to each outcome. To find the expected return, you simply multiply each possible return by the probability that it will occur, and then add up across outcomes. Notice that Figure 6.5 divides the range of possible returns into intervals of 10 percent (except for very low or very high outcomes). Let us create a list of potential future stock returns by taking the midpoint of the various ranges as follows:

Figure shows that four out of 111 years had returns of between ˆ’20% and ˆ’30%. So let us capture this fact by assuming that if returns do occur inside that interval that the typical return would be ˆ’25% (in the middle of the interval). The probability associated with this outcome is 4/111 or about 3.6%. Fill in the missing values in the table and then fill in the missing parts of the equation to calculate the expected return.

Possible Stock Returns (%) 25 -35 -25 15 -5 15 35 45 Expected retum-(3/111 -35)+(4/111)(-25) +..+(3/111)(45) +(2/111)55)