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The CAPM developed by William F Sharpe, John Linter and Jan Mossin is one of the major developments in financial theory. The CAPM establishes a linear relationship between the required rate of return of a security and its systematic or undiversifiable risk or beta.

 

This relationship as defined by CAPM can be used to value an equity share. Mathematically the relationship between the share's return and the market return can be depicted by the following formula:

                                               

Here

R_s stands for return expected on the security,

R_f stands for risk-free return,

R_m stands for return from the market portfolio and

b stands for beta.

 

This relationship means that if the market goes up by 10 % and the security price also goes up by 10 %, and vice versa, the beta is said to be 1.00, i.e., there is a perfect correlation between return from the security and return from the market. If the beta is 2.00 the security price would up or down by twice the %age of change of the market. If the beta is 0.00 then no correlation exists between the market movement and the security price movement.

It is easy to see that the required return for a given security increases with increases in its beta.

 

Assumptions

 

The CAPM is based on a list of critical assumptions, some of which are as follows:

• Investors are risk-averse and use the expected rate of return and standard deviation of return as appropriate measures of risk and return for their portfolio.  In other words, the greater the perceived risk of a portfolio, the risk-averse investor expects a higher return to compensate the risk.
• Investors make their investment decisions based on a single-period horizon, i.e., the next immediate time period.
• Transaction costs in financial markets are low enough to ignore and assets can be bought and sold in any unit desired.  The investor is limited only by his wealth and the price of the asset.
• Taxes do not affect the choice of buying assets.
• All individuals assume that they can buy assets at the going market price and they all agree on the nature of the return and risk associated with each investment.

 

In the CAPM, the expected rate of return can also be thought of as a required rate of return because the market is assumed to be in equilibrium. The expected return is the return from an asset that investors anticipate or expect to earn over some future period. The required rate of return for a security is defined as the minimum expected rate of return needed to induce an investor to purchase it.

 

Investors can earn a risk less rate of return by investing in risk less assets like treasury bills. This risk free rate of return is designated R_f and the minimum return expected by the investors.  In addition to this, because investors are risk-averse, they will expect a risk premium to compensate them for the additional risk assumed in investing in a risky asset.

          Required Rate of Return = Risk-free rate + Risk premium

The CAPM provides an explicit measure of the risk premium. It is the product of the Beta for a particular security j and the market risk premium K_m - R_f.

Risk premium =         b_j (K_m-R_f)

 

This Beta coefficient 'b_j' is the nondiversifiable risk of the asset relative to the risk of the market. If the risk of the asset is greater than the market risk, i.e., b exceeds 1.0, the investor assigns a higher risk premium to asset j, than to the market.

 

The Security Market Line

 

The plot of relationship between the required rate of return (kj) and nondiversifiable risk (beta) as expressed in CAPM will produce a graph of the Security Market Line. As per the CAPM assumptions any individual security's expected return and beta statistics should lie on the SML. The SML intersects the vertical axis at the risk-free rate of return R_f and k_m - R_f is the slope of the SML. Since all securities are expected to plot along the SML, the line provides a direct and convenient way of determining the expected/required return of a security if we know the Beta of the securities. The SML can also be used to classify securities. Those with betas greater than 1.00 and plotting on the upper part of the SML are classified as aggressive securities while those with betas less than 1.00 and plotting on the lower part of the SML can be classified as defensive securities, which earn below-average returns.

 

Asset pricing implications of the SML

 

One of the major assumptions of the CAPM is that the market is in equilibrium and that the expected rate of return is equal to the required rate of return for a given level of market risk or beta. In other words, the SML provides a framework for evaluating whether high-risk stocks are offering returns more or less in proportion to their risk and vice versa.

 

Once a security's expected rate of return and beta have been computed they may be plotted with reference to the SML. If the security's required rate of return, the security may be over or under priced and may fall below or above the SML.

 

                                                                                X    

                           25                                                                                                                                                                                                      SML

                                                            

Rate     K_m  12                                                             

 of                                                                                                     

Return                                                     Y   

              R_f    6

 

                                                                                                      Beta                                                                          1.0    1.2     1.7

From the figure we see that R_f = 6% and k_m = 12%.

Two securities X and Y have been shown in the figure. Both X and Y should have been on the SML but obviously are not.  Taking the case of X first, the expected rate of return from X is around 25%. But at a beta of around 1.2, using the SML we see that the required rate of return need be only around 13%.  This tells us that security X is undervalued or priced too low because its average rate of return is inappropriately high for the level of risk it bears.

 

On the other hand, Security Y with a beta of around 1.7 requires a rate of return of around 16% but its expected return is only about 7%. This tells us that the asset is overvalued or overpriced and hence unattractive because it is expected to produce a return lower than stocks with similar betas.  These two assets should move toward their equilibrium - required return positions on the SML (i.e., expected rate of return should be equal to required rate of return and correspond to their respective betas).

 

To reach equilibrium and their required rate of return positions on the SML both stocks have to go through a temporary price adjustment.  In order to reach equilibrium, assuming betas remain the same, the expected return of X has to be brought down to be equal to the required rate of return and be plotted on the SML.  To accomplish this, the purchase price has to be sufficiently increased.  Similarly, for security Y, the purchase price has to be sufficiently reduced so that the expected return rises to be the same level as the required rate of return.

 

In practice, investors will be interested in purchasing security X because it offers more than proportionate returns in comparison to the risk.  This demand will push up the price of X as more of it is purchased and correspondingly bring down the returns.  This process will continue till it reaches the equilibrium price and the expected returns are the same as the required returns.

 

In the case of security Y, investors will be tempted to sell as it offers less than the required rate of return.  This increase in the supply of Y will drive down its price and correspondingly increase the return until the expected return rises enough to reach the SML and the security is once again in equilibrium.

 

Thus, the CAPM provides many useful insights for the finance manager to maximize the value of the firm.  It shows the type of risk for which shareholders require compensation in the form of higher risk premium, and hence higher returns.  Because finance managers also perform the investment function on behalf of shareholders, they must keep sight of the returns shareholders expect for taking risks.

 

Now let us look at another part of the investment decision, i.e., what cash flows to include and what cash flows to exclude.