Beta coefficients and the capital asset pricing modelKatherine Wilson is wonderi

Question

Beta coefficients and the capital asset pricing modelKatherine Wilson is wondering how much risk she must undertake to generate an acceptable return on her portfolio. The risk-free return currently is 5%. The return on the overall stock market is 16%. Use the CAPM to calculate how high the beta coefficient of Katherine’s portfolio would have to be to achieve each of the following expected portfolio returns. 10% 15% 18% 20% Katherine is risk averse. What is the highest return she can expect if she is unwilling to take more than an average risk?

Explanation / Answer

risk-free rate   (rf) 5% return on overalll stock market   (rm) 16% Expected return on stock   (re) = riskfree rate + beta (return on market - riskfree rate) rearranging the equation beta *(return on market - riskfree rate) = Expected return on stock - riskfree rate beta = (expected return on stock - riskfree rate)/(return on market - riskfree rate) that is Beta = (re - rf)/(rm-rf) re rf rm beta 10% 5% 16% 0.45 15% 5% 16% 0.91 18% 5% 16% 1.18 20% 5% 16% 1.36 Given that the investor is risk averse, then she will be looking at a return equal to market which is 16% and a beta equal to 1.0. then the maximum return she will be looking at will be equal to that of market viz., 16%

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