Question

Suppose you are a money manager of a $4 million investment fund. The fund consists of 4 stocks:

Stock	Investment	Beta
A	400,000	1.50
B	600,000	-0.5
C	1,000,000	1.25
D	2,000,000	0.75

If the market return is 14% and the risk free rate is 6%,

a) What is the fund's required rate of return?

b)What is the reward/risk ratio for each stock?

c)Is this a good investment?

Answer 1

Part a. Required Return For Fund

In order to calculate the required rate of return on fund, we need to use the CAPM Equation.

According to CAPM Equation,

Reqd rate of return on stock = Risk free rate + Beta * (Expected market return – Risk free rate)

But, in order to apply this equation, we first need to calculate Beta of the fund. Beta of a portfolio is a weighted average of Beta of all the constituents.

Weight of Stock A = 400,000/4,000,000 = 10%

Weight of Stock B = 600,000/4,000,000 = 15%

Weight of Stock C = 1,000,000/4,000,000 = 25%

Weight of Stock D = 2,000,000/4,000,000 = 50%

Beta (Portfolio) = (1.5 * 10%) + (-0.5 * 15%) + (1.25 * 25%) + (0.75 * 50%) = 0.7625

Now, substituting values in question,

Reqd return on fund = 6% + 0.7625 * (14% - 6%) = 12.1%

Part b. Reward to Risk Ratio for each stock

Reward to Volatility Ratio = (Required Return – Risk free rate)/Beta

Now, in this question, we will apply the CAPM equation for each stock first.

For Stock A, Reqd return = 6% + 1.5 * (14% - 6%) = 18%

Reward to Volatility Ratio for Stock A = (18% - 6%)/1.5 = 0.08

For Stock B, Reqd return = 6% + -0.5 * (14% - 6%) = 2%

Reward to Volatility Ratio for Stock A = (2% - 6%)/-0.5 = 0.08

For Stock C, Reqd return = 6% + 1.25 * (14% - 6%) = 16%

Reward to Volatility Ratio for Stock A = (16% - 6%)/1.25 = 0.08

For Stock D, Reqd return = 6% + 0.75 * (14% - 6%) = 12%

Reward to Volatility Ratio for Stock A = (12% - 6%)/0.75 = 0.08

Part c.

In order to assess if this is a good investment or not, let us first calculate the reward to risk ratio for the fund.

Reward to risk ratio = (12.1% - 6%)/0.7625 = 0.08

So the investment is no better than the individual stock investments. (If the reward to risk ratio for the fund was higher, we would have said the fund to be better than the stock investments)