## Figure 134

The Security Market Line (SML)

Asset expected return (E(R/))

Asset expected return (E(R/))

The slope of the security market line is equal to the market risk premium; i.e., the reward for bearing an average amount of systematic risk. The equation describing the SML can be written:

The slope of the security market line is equal to the market risk premium; i.e., the reward for bearing an average amount of systematic risk. The equation describing the SML can be written:

which is the capital asset pricing model (CAPM).

3Our discussion leading up to the CAPM is actually much more closely related to a more recently developed theory known as the arbitrage pricing theory (APT). The theory underlying the CAPM is a great deal more complex than we have indicated here, and the CAPM has a number of other implications that go beyond the scope of this discussion. As we present it here, the CAPM has essentially identical implications to those of the APT, so we don't distinguish between them.

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

CHAPTER 13 Return, Risk, and the Security Market Line

This concludes our presentation of concepts related to the risk-return trade-off. For future reference, Table 13.9 summarizes the various concepts in the order in which we discussed them.

### Risk and Return

Suppose the risk-free rate is 4 percent, the market risk premium is 8.6 percent, and a particular stock has a beta of 1.3. Based on the CAPM, what is the expected return on this stock? What would the expected return be if the beta were to double?

With a beta of 1.3, the risk premium for the stock is 1.3 x 8.6%, or 11.18 percent. The risk-free rate is 4 percent, so the expected return is 15.18 percent. If the beta were to double to 2.6, the risk premium would double to 22.36 percent, so the expected return would be 26.36 percent.

I. Total risk

The total risk of an investment is measured by the variance or, more commonly, the standard deviation of its return.

### II. Total return

The total return on an investment has two components: the expected return and the unexpected return. The unexpected return comes about because of unanticipated events. The risk from investing stems from the possibility of an unanticipated event.

### III. Systematic and unsystematic risks

Systematic risks (also called market risks) are unanticipated events that affect almost all assets to some degree because the effects are economywide. Unsystematic risks are unanticipated events that affect single assets or small groups of assets. Unsystematic risks are also called unique or asset-specific risks.

### IV. The effect of diversification

Some, but not all, of the risk associated with a risky investment can be eliminated by diversification. The reason is that unsystematic risks, which are unique to individual assets, tend to wash out in a large portfolio, but systematic risks, which affect all of the assets in a portfolio to some extent, do not.

### V. The systematic risk principle and beta

Because unsystematic risk can be freely eliminated by diversification, the systematic risk principle states that the reward for bearing risk depends only on the level of systematic risk. The level of systematic risk in a particular asset, relative to the average, is given by the beta of that asset.

VI. The reward-to-risk ratio and the security market line

The reward-to-risk ratio for Asset i is the ratio of its risk premium, E(R) - Rf, to its beta, ft:

In a well-functioning market, this ratio is the same for every asset. As a result, when asset expected returns are plotted against asset betas, all assets plot on the same straight line, called the security market line (SML).

VII. The capital asset pricing model

From the SML, the expected return on Asset i can be written:

This is the capital asset pricing model (CAPM). The expected return on a risky asset thus has three components. The first is the pure time value of money (Rf), the second is the market risk premium [E(RM) - Rf], and the third is the beta for that asset, (ft).

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