The risk or variation in return of a security is caused by two types of factors. The first type of factors will affect the return of almost all securities in the market. Examples of such sources of risks are changes in the interest rates and inflation of the economy, movement of stock market index and exchange rate movement. The risk caused by such factors is known as systematic risk. Apart from systematic risk, the variation in return of a security is also caused by some other factors which are specific to a security, like strike in a company or caliber of the management of a company. The risk caused by such factors is known as unsystematic or specific risk. The unsystematic risk of a security can be diversified away by combining different securities into a portfolio. But systematic risk cannot be diversified away by construction of a portfolio. So the real risk of a security is the systematic risk as the investors can diversify the unsystematic risk by construction of a portfolio. The systematic risk of a security is measured by a statistic known as beta. The beta of a security measures the sensitivity of a security’s return to changes in the return of the market portfolio or stock market index.
Capital Asset Pricing Model (CAPM)
The Capital Asset Pricing Model (CAPM) is a general equilibrium market model developed to analyze the relationship between risk and required rates of return on assets when they are held in well-diversified portfolios. The Capital Asset Pricing Model (CAPM) provides a linear relationship between the required rate of return (Ri) of a security and its Systematic or undiversifiable risk as measured by the security’s beta. The systematic risk of a security, which is measured by the beta coefficient of the security, is the market risk that cannot be eliminated through diversification.
The CAPM requires an extensive set of assumptions:
- All investors are single-period expected utility of terminal wealth maximizers, who choose among alternative portfolios on the basis of each portfolio’s expected return and standard deviation.
- All investors can borrow or lend an unlimited amount at a given risk-free rate of interest.
- Investors have homogeneous expectations (that is, investors have identical estimates of the expected values, variances, and covariances of returns among all assets).
- All assets are perfectly divisible and perfectly marketable at the going price, and there are no transactions costs.
- There are no taxes.
- All investors are price takers (that is, all investors assume that their own buying and selling activity will not affect stock prices).
- The quantities of all assets are given and fixed.
According to Capital Asset Pricing Model approach, the required return on a security is given by the equation:
Ri = Rf + βi ( Rm – Rf )
- Ri = Required rate of return on security i or cost of equity.
- Rf = Risk-free rate of return.
- βi = Beta of security i.
- Rm = Rate of return on market portfolio.
Security Market Line (SML) Analysis
The graphical plot of the relationship between the required rate of return (ke) and the nondiversifiable risk (beta) of security is known as Security Market Line (SML).
The CAPM model uses the Security Market Line (SML), which is a tradeoff between expected return and security’s risk (beta risk) relative to the market portfolio. Under equilibrium conditions, any individual securities expected return and beta should lie on the SML. Since all securities are expected to plot along the SML, the line provides a direct way of determining the expected (required) return of a security once the beta of the security is known.
It is useful to compare the security market line (SML) to the capital market line (CML). 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 both for 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. Because the SML 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 chapter, all securities must lie on the SML in market equilibrium.
If a stock is perceived to be a good buy, or under-priced, it will provide an expected return in excess of the fair return stipulated by the SML. Under-priced 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.
Empirical Tests for Capital Asset Pricing Model (CAPM)
Since the Capital Asset Pricing Model (CAPM) was developed on the basis of a set of unrealistic assumptions, empirical tests should be used to verify the CAPM.
The first test looks for stability in historical betas. If betas have been stable in the past for a particular stock, then its historical beta would probably be a good proxy for its ex-ante, or expected beta. Empirical work concludes that the betas of individual securities are not good estimators of their future risk, but that betas of portfolios of ten or more randomly selected stocks are reasonably stable, hence that past portfolio betas are good estimators of future portfolio volatility.
The second type of test is based on the slope of the SML. As we have seen, the CAPM states that a linear relationship exists between a security’s required rate of return and its beta. Further, when the SML is graphed, the vertical axis intercept should be RF, and the required rate of return for a stock (or portfolio) with beta = 1.0 should be Rm, the required rate of return on the market. Various researchers have attempted to test the validity of the CAPM model by calculating betas and realized rates of return, plotting these values in graphs, and then observing whether or not (1) the intercept is equal to RF, (2) the regression line is linear, and (3) the SML passes through the point b = 1.0, Rm. Evidence shows a more-or-less linear relationship between realized returns and market risk, but the slope is less than predicted. Tests that attempt to assess the relative importance of market and company-specific risk do not yield definitive results, so the irrelevance of diversifiable risk specified in the CAPM model can be questioned.
In general, evidence seems to support the CAPM model when it is applied to portfolios, but the evidence is less convincing when the CAPM is applied to individual stocks.
Nevertheless, the CAPM provides a rational way to think about risk and return as long as one recognizes the limitations of the CAPM when using it in practice.