Question

A mutual fund manager expects her portfolio to earn a rate of return of 9% this year. The beta of her portfolio is 0.8. If the rate of return available on risk free assets is 4% and you expect the rate of return on the market portfolio to be 11%.

1. Should you invest in this mutual fund? Show your work.
2. Suppose you want to create a portfolio with the same risk as the fund manager’s portfolio above, however you only want to invest in T-Bills and a stock index mutual fund (with the same risk as the market portfolio). How much of your portfolio must be invested in each security?
3. What is the rate of return on this new portfolio (from part b)?

Answer 1

As per CAPM model: Require rate of return= Risk Free Rate+Beta* Market Risk Premium

Hence, required rate return for the above fund= 4%+0.8*(11%-4%)=9.6%

a. As the required rate of return 9.6% is less than the expected return (i.e. 9%) for the fund. You should not invest in this mutual fund.

b. Say, x% need to be invested in T-bill and (100-x)% in stock index mutual fund

Hence, Beta of portfolio= x%*0+(100-x)%*1=0.8

or, 1-x/100=0.8

or, x=20%

Hence, you need to invest 20% into T-bill and 80% into the stock index mutual fund.

c. Rate of return of the new portfolio= 20%*4%+80%*11%=9.6%