The slope of the SML in an economy is 8.9%. The risk-free rate prevailing in the economy is 4.9%. A security has a correlation coefficient of 0.23 with the market. The market's standard deviation is 15% while that of the security is 19%. The expected return on the portfolio equals ________.
Correct Answer: B
The Security Market Line (SML) is a plot of the expected returns on securities against their betas. CAPM implies that the slope of the SML equals the market risk premium and the intercept equals the risk-free rate. Hence, the data given in the problem imply that the market premium is 8.9%.
To calculate the expected return on the security using CAPM, we must first find its beta. The beta of the security equals the covariance between the security and the market divided by the market variance. Also, the covariance equals the product of the correlation coefficient and the individual standard deviations.
Hence, the covariance between the security and the market equals 0.23 * 0.15 * 0.19 = 0.0066. Therefore, the beta of the security equals 0.0066/(0.152) = 0.29. Therefore, the CAPM expected return on the security equals 4.9% + 0.29 * 8.9% = 7.49%.