Expected Rate of Return
by MaestriIf we multiply each possible outcome by its probability of occurrence and then sum these products, as in Table 3-2, we have a weighted average of outcomes. The weights are the probabilities, and the weighted average is the expected rate of return, ˆr, called “r-hat.”3 The expected rates of return for both Martin Products and U.S. Water are shown in Table 3-2 to be 15 percent. This type of table is known as a payoff matrix.
We can graph the rates of return to obtain a picture of the variability of possible outcomes; this is shown in the Figure 3-1 bar charts. The height of each bar signifies the probability that a given outcome will occur. The range of probable returns for Martin Products is from 70 to 100 percent, with an expected return of 15 percent. The expected return for U.S. Water is also 15 percent, but its range is much narrower.
Thus far, we have assumed that only three situations can exist: strong, normal, and weak demand. Actually, of course, demand could range from a deep depression to a fantastic boom, and there are an unlimited number of possibilities in between. Suppose we had the time and patience to assign a probability to each possible level of demand (with the sum of the probabilities still equaling 1.0) and to assign a rate of return
to each stock for each level of demand. We would have a table similar to Table 3-1, except that it would have many more entries in each column. This table could be used to calculate expected rates of return as shown previously, and the probabilities and outcomes could be approximated by continuous curves such as those presented in Figure 3-2. Here we have changed the assumptions so that there is essentially a zero probability that Martin Products’ return will be less than 70 percent or more than 100 percent, or that U.S. Water’s return will be less than 10 percent or more than 20 percent, but virtually any return within these limits is possible.
The tighter, or more peaked, the probability distribution, the more likely it is that the actual outcome will be close to the expected value, and, consequently, the less likely it is that the actual return will end up far below the expected return. Thus, the tighter the probability distribution, the lower the risk assigned to a stock. Since U.S. Water has a relatively tight probability distribution, its actual return is likely to be closer to its 15 percent expected return than is that of Martin Products.
Taken From : Five-Minute MBA – Corporate Finance
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