= of the security beta β Thus the expected return on a security increases with increases in its beta. Fore stance, assume a security with a of 1.2 is being considered, while the Treasury bill rate beta (Rf) is 4% and the market (GSE Composite index) return is 12%. The security’s expected rate of return will be: R = Rf + Rf) β(Rm – Where Rf = 4% = 1.2 β Rm = 12% Therefore R = 4% + [1.2 (12% - 4%)] = 4% + [1.2 x 8%] = 4% + 9.6% = 13.60% The investor should therefore require a return of 13.60% on the security as compensation for the non-diversifiable risk assumed. Now if the were lower, say 1.00, the R will be; 4% + [1.00 (12% - 4%)] = 12% beta And if the had been higher, say 1.50, R will be; 4% + [1.50 (12% - 4%)] = 16% beta The Security Market Line When the CAPM is depicted graphically, the resulting straight line is called the Security Market Lime (SML). The security market line provides a benchmark for evaluating investment performance. Given the risk of an investment as measured by its beta, the SML indicates the required rate of return that will compensate investors for the risk of that investment. Risk-Free Return
β = beta of the security Thus the expected return on a security increases with increases in its beta. Fore stance, assume a security with a beta of 1.2 is being considered, while the Treasury bill rate (Rf) is 4% and the market (GSE Composite index) return is 12%. The security’s expected rate of return will be: R = Rf + β(Rm – Rf) Where Rf = 4% β = 1.2 Rm = 12% Therefore R = 4% + [1.2 (12% - 4%)] = 4% + [1.2 x 8%] = 4% + 9.6% = 13.60% The investor should therefore require a return of 13.60% on the security as compensation for the non-diversifiable risk assumed. Now if the beta were lower, say 1.00, the R will be; 4% + [1.00 (12% - 4%)] = 12% And if the beta had been higher, say 1.50, R will be; 4% + [1.50 (12% - 4%)] = 16% The Security Market Line When the CAPM is depicted graphically, the resulting straight line is called the Security Market Lime (SML). The security market line provides a benchmark for evaluating investment performance. Given the risk of an investment as measured by its beta, the SML indicates the required rate of return that will compensate investors for the risk of that investment. Risk-Free Return
pbbf306-chapter-three.docx