## Table 132

Calculation of Expected Return

In other words, you should expect to earn 20 percent from this stock, on average.

For Stock L, the probabilities are the same, but the possible returns are different. Here, we lose 20 percent half the time, and we gain 70 percent the other half. The expected return on L, E(RL), is thus 25 percent:

Table 13.2 illustrates these calculations.

In our previous chapter, we defined the risk premium as the difference between the return on a risky investment and that on a risk-free investment, and we calculated the historical risk premiums on some different investments. Using our projected returns, we can calculate the projected, or expected, risk premium as the difference between the expected return on a risky investment and the certain return on a risk-free investment.

For example, suppose risk-free investments are currently offering 8 percent. We will say that the risk-free rate, which we label as Rf, is 8 percent. Given this, what is the projected risk premium on Stock U? On Stock L? Because the expected return on Stock U, ER), is 20 percent, the projected risk premium is:

Risk premium = Expected return — Risk-free rate [13.1]

Similarly, the risk premium on Stock L is 25% — 8 = 17%.

In general, the expected return on a security or other asset is simply equal to the sum of the possible returns multiplied by their probabilities. So, if we had 100 possible returns, we would multiply each one by its probability and then add up the results. The result would be the expected return. The risk premium would then be the difference between this expected return and the risk-free rate.

### Unequal Probabilities

Look again at Tables 13.1 and 13.2. Suppose you think a boom will only occur 20 percent of the time instead of 50 percent. What are the expected returns on Stocks U and L in this case? If the risk-free rate is 10 percent, what are the risk premiums?

The first thing to notice is that a recession must occur 80 percent of the time (1 — .20 = .80) because there are only two possibilities. With this in mind, we see that Stock U has a 30

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

V. Risk and Return

13. Return, Risk, and the Security Market Line

© The McGraw-Hill Companies, 2002

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