Question

Suppose you are the money manager of a $3.92 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock	Investment	Beta
A	$   200,000	1.50
B	620,000	(0.50)
C	900,000	1.25
D	2,200,000	0.75

If the market's required rate of return is 9% and the risk-free rate is 4%, what is the fund's required rate of return? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Let’s first calculate the portfolio beta on the basis of investments in each stock

Total Portfolio investment = Investment in stock A + Investment in stock B + Investment in stock C + Investment in stock D

= $200,000 + $620,000 + $900,000 + $2,200,000 = $3,920,000 or 3.92 million

Portfolio beta = ∑ (stock’s investment amount/ Portfolio value) * beta of stock

= ($200,000/ $3,920,000) * 1.50 + ($620,000/ $3,920,000) * (-0.50) + ($900,000/ $3,920,000) * 1.25

+ ($2,200,000/ $3,920,000) * 0.75

= 0.7054

Therefore beta of portfolio is 0.7054

Now by using with securities market line (SML), we can calculate required rate of return of portfolio in following manner

Required rate of return of portfolio = risk free rate (rf) + β of portfolio *[Expected market return (Rm) – risk free rate (rf)]

Where,                

Required rate of return of portfolio =?

Risk free rate (rf) = 4%

Beta of portfolio β = 0.7054

The expected return on the market Rm = 9%

Now putting all the values into formula, we get

Required rate of return of portfolio = 4% + 0.7054 * (9% - 4%)

= 4% + 0.7054 * 5%

= 7.53%

Therefore the fund's required rate of return is 7.53%