Suppose the riskfree rate is 47 and the market portfolio has

Suppose the risk-free rate is 4.7% and the market portfolio has an expected return of 11.4%. The market portfolio has variance of 0.0432, and Portfolio Z has a correlation coefficient with the market portfolio of 0.33 and has variance of 0.3335. According to the CAPM, the expected return on Portfolio Z is ______________%.

Solution

Standard deviation of the market = 0.0432^0.5 = 0.2078 or 20.78%

Standard deviation of the portfolio = 0.3335^0.5 = 0.5775 or 57.75%

Th next step is to find the beta of the portfolio. Beta = correlation coefficient*standard deviation of portfolio/standard deviation of market

= 0.33*0.5775/0.2078

= 0.9169

Now, per CAPM, expected return = risk free rate + beta*(return of market portfolio - risk free rate)

= 0.047+0.9169*(0.114-0.047)

= 0.1084

or 10.84%