Question

question/ A mutual fund manager expects her portfolio to earn a rate of return of 11% this year. The beta of her portfolio is 0.9.

If the rate of return available on risk-free assets is 4% and you expect the rate of return of the market portfolio to be 14%.

#1A- What expected rate of return would you demand before you would be willing to invest in this mutual fund?

#2A- Is this fund attractive? Why?

#3A- How could you mix mutual fund with a risk-free position in Treasury bills to create a portfolio with the same managers but with a higher expected rate of return? what is the rate of the return of the portfolio?

Answer 1

1A

The expected rate of return that investors will demand of the portfolio is:

According to Capital Asset Pricing Model (CAPM)

Re=Rf+ Beta(Rm−Rf)

Return on T-Bills(Rf) = 4%

Return on Market (Rm)= 14%

Beta = 0.9

By putting values we get,

Re = 4% +0.9*(14% − 4%) = 4% + 9% = 13%

2A

This is an unattractive investment as the portfolio is expected to provide only 11% rate of return which is less than the required rate of return at the given level of risk.

3A

A portfolio that is invested 90% in a stock index mutual fund (with a beta of 1.0) and 10% in a T-Bill (with a beta of zero) would have the same beta as this manager’s portfolio:

Beta of portfolio = Weight * B + Weight * B

=(0.9*1.0) + (0.1 * 0) = 0.9 + 0 = 0.9

Expected return of portfolio is

Return on T-Bills = 4%

Return on Market = 14%

Expected return of portfolio = 0.9 * 14% + 0.1 * 4% = 12.6% + 0.4% = 13%

This expected return is better than the portfolio manager’s expected return i.e 11%.