CAPITAL ASSET PRICING MODEL   (CAPM)

A classic model showing the relationship between the historic risk of a security and the expected return of that security is the Capital Asset Pricing Model (CAPM).  Introduced by William Sharpe in 1964, the model incorporates the concept of beta, or the volatility of a security's return relative to the volatility of the returns of the market (as measured, for example, by the S&P 500).

When historic return data for a particular security (Ke) are regressed against historic return data for the market (Kmkt), the resulting regression line illustrates graphically how much the of the changes in the returns of the security are "caused by" the changes in the returns of the market.  Remember, in it's general form, regression analysis compares a dependent variable, "y", to an independent variable, "x", and yields a "regression line" of the form y = mx + b.  In this particular application to financial returns, the dependent variables are the returns on the security (Ke) and the independent variables are the returns of the market (Kmkt), where the market is usually defined as the S&P 500 .  Thus, when the returns of an individual security are regressed against the returns of the market, the resulting slope of the regression line (the line of best fit, or the line of least squares) is defined as "beta" (or the volatility of a security's return relative to the volatility of the returns of the market).  Obviously, when the returns of the market are regressed against the returns of the market, the slope of the line will be 1.000.  Therefore, by definition, the beta of the market is 1.00.

The CAPM model estimates the return on a security as being the return on a risk free security (as exemplified by a 3-month US T-Bill), plus a "risk premium".  In CAPM the risk premium is estimated to be β(Kmkt-Krf), or beta times the difference between the expected return of the market and the risk free rate. 

Thus the CAPM model:   Ke=Krf+β(Kmkt-Krf).

Sample problem:  Use CAPM to find the expected returns of a security, given that a 3-month Treasury bill yields .93 %, that the expected returns on the S&P500 are 17 %  and the beta of the security is 1.50.  Draw the related Security Market Line (SML) on the graph provided.
Solution:  The CAPM set up would be Ke=.0093 + 1.5(.17-.0093) for an expected yield of 25.035%.   The graph should have points (X,Y)=(βeta, K) at (0, .93%) for the Risk Free instrument (the US T-Bill); (1.0,17%) for the market; and (1.5,25%) for the security in question.