## The Security Market Line

We can view the expected return-beta relationship as a reward-risk equation. The beta of a security is the appropriate measure of its risk because beta is proportional to the risk that the security contributes to the optimal risky portfolio.

Risk-averse investors measure the risk of the optimal risky portfolio by its variance. In this world we would expect the reward, or the risk premium on individual assets, to depend on the contribution of the individual asset to the risk of the portfolio. The beta of a stock measures the stock's contribution to the variance of the market portfolio. Hence we expect, for any asset or portfolio, the required risk premium to be a function of beta. The CAPM confirms this intuition, stating further that the security's risk premium is directly proportional to both the beta and the risk premium of the market portfolio; that is, the risk premium equals (3[E(rM) - rf].

The expected return-beta relationship can be portrayed graphically as the security market line (SML) in Figure 9.5. Because the market beta is 1, the slope is the risk premium of the market portfolio. At the point on the horizontal axis where (3 = 1 (which is the market portfolio's beta) we can read off the vertical axis the expected return on the market portfolio.

It is useful to compare the security market line to the capital market line. The CML graphs the risk premiums of efficient portfolios (i.e., portfolios composed of the market and the risk-free asset) as a function of portfolio standard deviation. This is appropriate because standard deviation is a valid measure of risk for efficiently diversified portfolios that are candidates for an investor's overall portfolio. The SML, in contrast, graphs individual asset risk premiums as a function of asset risk. The relevant measure of risk for individual assets held as parts of well-diversified portfolios is not the asset's standard deviation or variance; it is, instead, the contribution of the asset to the portfolio variance, which we measure by the asset's beta. The SML is valid for both efficient portfolios and individual assets.

The security market line provides a benchmark for the evaluation of investment performance. Given the risk of an investment, as measured by its beta, the SML provides the required rate of return necessary to compensate investors for both risk as well as the time value of money.

CHAPTER 9 The Capital Asset Pricing Model 273

Figure 9.5 The security market line.

Because the security market line is the graphic representation of the expected return-beta relationship, "fairly priced" assets plot exactly on the SML; that is, their expected returns are commensurate with their risk. Given the assumptions we made at the start of this section, all securities must lie on the SML in market equilibrium. Nevertheless, we see here how the CAPM may be of use in the money-management industry. Suppose that the SML relation is used as a benchmark to assess the fair expected return on a risky asset. Then security analysis is performed to calculate the return actually expected. (Notice that we depart here from the simple CAPM world in that some investors now apply their own unique analysis to derive an "input list" that may differ from their competitors'.) If a stock is perceived to be a good buy, or underpriced, it will provide an expected return in excess of the fair return stipulated by the SML. Underpriced stocks therefore plot above the SML: Given their betas, their expected returns are greater than dictated by the CAPM. Overpriced stocks plot below the SML.

The difference between the fair and actually expected rates of return on a stock is called the stock's alpha, denoted a. For example, if the market return is expected to be 14%, a stock has a beta of 1.2, and the T-bill rate is 6%, the SML would predict an expected return on the stock of 6 + 1.2(14 - 6) = 15.6%. If one believed the stock would provide an expected return of 17%, the implied alpha would be 1.4% (see Figure 9.6).

One might say that security analysis (which we treat in Part V) is about uncovering securities with nonzero alphas. This analysis suggests that the starting point of portfolio management can be a passive market-index portfolio. The portfolio manager will then increase the weights of securities with positive alphas and decrease the weights of securities with negative alphas. We show one strategy for adjusting the portfolio weights in such a manner in Chapter 27.

The CAPM is also useful in capital budgeting decisions. For a firm considering a new project, the CAPM can provide the required rate of return that the project needs to yield, based on its beta, to be acceptable to investors. Managers can use the CAPM to obtain this cutoff internal rate of return (IRR), or "hurdle rate" for the project.

The nearby box describes how the CAPM can be used in capital budgeting. It also discusses some empirical anomalies concerning the model, which we address in detail in

PART III Equilibrium in Capital Markets

Figure 9.6 The SML and a positive-alpha stock.

PART III Equilibrium in Capital Markets

Figure 9.6 The SML and a positive-alpha stock.

Chapters 12 and 13. The article asks whether the CAPM is useful for capital budgeting in light of these shortcomings; it concludes that even given the anomalies cited, the model still can be useful to managers who wish to increase the fundamental value of their firms.

Yet another use of the CAPM is in utility rate-making cases.11 In this case the issue is the rate of return that a regulated utility should be allowed to earn on its investment in plant and equipment. Suppose that the equityholders have invested $100 million in the firm and that the beta of the equity is .6. If the T-bill rate is 6% and the market risk premium is 8%, then the fair profits to the firm would be assessed as 6 + .6(8) = 10.8% of the $100 million investment, or $10.8 million. The firm would be allowed to set prices at a level expected to generate these profits.

Stock XYZ has an expected return of 12% and risk of p = 1. Stock ABC has expected return of 13% and p = 1.5. The market's expected return is 11%, and rf = 5%.

a. According to the CAPM, which stock is a better buy?

b. What is the alpha of each stock? Plot the SML and each stock's risk-return point on one graph. Show the alphas graphically.

The risk-free rate is 8% and the expected return on the market portfolio is 16%. A firm considers a project that is expected to have a beta of 1.3.

a. What is the required rate of return on the project?

b. If the expected IRR of the project is 19%, should it be accepted?

CONCEPT CHECK ^ QUESTION 4 and

### QUESTION 5

11 This application is fast disappearing, as many states are in the process of deregulating their public utilities and allowing a far greater degree of free market pricing. Nevertheless, a considerable amount of rate setting still takes place.

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