Principles of Corporate Finance_ 12th Edition

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200 Part Two Risk

In the mid-1960s three economists—William Sharpe, John Lintner, and Jack Treynor—

produced an answer to this question.^8 Their answer is known as the capital asset pricing

model, or CAPM. The model’s message is both startling and simple. In a competitive market,

the expected risk premium varies in direct proportion to beta. This means that in Figure 8.6

all investments must plot along the sloping line, known as the security market line. The

expected risk premium on an investment with a beta of .5 is, therefore, half the expected risk

premium on the market; the expected risk premium on an investment with a beta of 2 is twice

the expected risk premium on the market. We can write this relationship as

Expected risk premium on stock = beta × expected risk premium on market

r − rf = β(rm − rf)

Some Estimates of Expected Returns

Before we tell you where the formula comes from, let us use it to figure out what returns

investors are looking for from particular stocks. To do this, we need three numbers: β, rf, and

rm – rf. We gave you estimates of the betas of 10 stocks in Table 7.5. We will suppose that the

interest rate on Treasury bills is about 2%.

How about the market risk premium? As we pointed out in the last chapter, we can’t mea-

sure rm – rf with precision. From past evidence it appears to be 7.7%, although many econo-

mists and financial managers would forecast a somewhat lower figure. Let us use 7% in this

example.

Table  8.2 puts these numbers together to give an estimate of the expected return on

each stock. The stock with the highest beta in our sample is Caterpillar. Our estimate of

the expected return from Caterpillar is 13.6%. The stock with the lowest beta is Newmont.

Our estimate of its expected return is just 2%. Notice that these expected returns are not the

same as the hypothetical forecasts of return that we assumed in Table 8.1 to generate the

efficient frontier.

You can also use the capital asset pricing model to find the discount rate for a new capital

investment. For example, suppose that you are analyzing a proposal by Walmart to expand its

business. At what rate should you discount the forecasted cash flows? According to Table 8.2,

(^8) W. F. Sharpe, “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,” Journal of Finance 19 (September
1964), pp. 425–442; and J. Lintner, “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and
Capital Budgets,” Review of Economics and Statistics 47 (February 1965), pp. 13–37. Treynor’s article has not been published.
Stock Beta (β)
Expected Return
rf = β(rm – rf)
Caterpillar 1.66 13.6
Dow Chemical 1.65 13.5
Ford 1.44 12.1
Microsoft 0.98 8.9
Apple 0.91 8.4
Johnson & Johnson 0.53 5.7
Walmart 0.45 5.2
Campbell Soup 0.39 4.7
Consolidated Edison 0.17 3.2
Newmont 0 2.0
❱ TABLE 8.2
These estimates of the returns
expected by investors in November
2014 were based on the capital asset
pricing model. We assumed 2% for
the interest rate rf and 7% for the
expected risk premium rm – rf.