Question

Problem 8-7 Portfolio required return

Suppose you are the money manager of a $4.09 million investment fund. The fund consists of 4 stocks with the following investments and betas: Stock Investment Beta A $ 380,000 1.50 B 500,000 - 0.50 C 1,060,000 1.25 D 2,150,000 0.75 If the market's required rate of return is 10% and the risk-free rate is 7%, what is the fund's required rate of return? Round your answer to two decimal places.

Answer 1

The required rate of return is computed as shown below:

= Risk free rate + Beta ( return on market - risk free rate)

Beta is computed as follows:

= Beta of A x Investment in A / (Investment in A + Investment in B +  Investment in C + Investment in D ) + Beta of B x Investment in B / (Investment in A + Investment in B +  Investment in C + Investment in D ) + Beta of C x Investment in C / (Investment in A + Investment in B +  Investment in C + Investment in D ) + Beta of D x Investment in D / (Investment in A + Investment in B +  Investment in C + Investment in D )

= 1.50 x $ 380,000 / $ 4,090,000 - 0.50 x $ 500,000 / $ 4,090,000 + 1.25 x $ 1,060,000 / $ 4,090,000 + 0.75 x $ 2,150,000 / $ 4,090,000

= 0.139364303 - 0.061124694 + 0.32396088 + 0.394254279

= 0.796454768

So, the required rate of return will be:

= 0.07 + 0.796454768 x ( 0.10 - 0.07)

= 9.39% Approximately

Feel free to ask in case of any query relating to this question