Suppose that securities are priced according to the CAPM. You have forecast the

Question

Suppose that securities are priced according to the CAPM. You have forecast the correlation coefficient between the rate of return on the High Value Mutual Fund (HVMF) and the market portfolio (M) at 0.8. Your forecasts of the standard deviations of the rate of return are 0.25 for HVFF and 0.20 for M. How would you combine the HVMF and a risk free security to obtain a portfolio with a beta of 1.6? Suppose that rf = 0.10 and E[rm ]= 0.15. If you were willing to tolerate the same risk as in the above portfolio, how much additional return could you obtain if your portfolio were efficient?

Explanation / Answer

Beta of HVMF = 0.8 * 0.25 / 0.20

= 1.00

Portfolio beta = Weightage of HVMF * beta of HVMF ----------------- [since beta of risk free security us zero]

=> 1.60 = Weightage of HVMF * 1.00

=> Weightage of HVMF = 160%

Weightage of risk free security = 1 - 160%

= -60%

Additional return = rf + beta of portfolio * (E[rm] - rf)

= 10% + 1.6 * (15% - 10%)

= 18%

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