Question

You consider investing in two mutual funds with the following parameters:

	Fund 1	Fund 2
Beta	0.8	1.2
Standard Deviation	20%	32%

The funds are valued in a market where investors can borrow and lend, using T-bills, at the risk free rate of 5% and require a risk premium above this risk free rate of 8% for holding the market portfolio.

Suppose you can borrow and lend at the risk free rate of interest. Which of the two funds do you prefer?

What is the lowest risk portfolio that gives you an expected return of 14.6%? What is its standard deviation? Construct this portfolio using one of the funds and T-bills.

Suppose you can invest at the risk free rate of 5% but you can only borrow at the higher rate of 7%. What is the lowest risk portfolio with an expected return of 14.6% now?

Answer 1

(a) The expected return of fund 1 = rf +beta * market risk premium = 5 + 0.8*8 = 11.4%

The expected return of fund 2 = 5+1.2*8 = 14.6%

Since fund 2 has a higher expected return, I would prefer fund 2

(b) The lowest risk portfolio would be to invest 100% in fund 2 since it is the only fund that gives 14.6% return. The standard deviation of this would be 32% which is the standard deviation of fund 2

(c) Let us invest say x is t bill and (1-x) in fund 2

SInce the borrowal rate is 7%, the return of fund 2 becomes, 7+1.2*8 = 16.6%

x*5 +(1-x)*16.6 = 14.6

5x +16.6 -16.6x = 14.6

11.6x = 2

x = 0.1724

So, invest 17.24% in T-bills and 82.76% in fund 2