Question

PORTFOLIO BETA

A mutual fund manager has a $20 million portfolio with a beta of 1.50. The risk-free rate is 6.00%, and the market risk premium is 5.0%. The manager expects to receive an additional $5 million, which she plans to invest in a number of stocks. After investing the additional funds, she wants the fund's required return to be 12%. What should be the average beta of the new stocks added to the portfolio? Do not round intermediate calculations. Round your answer to two decimal places. Enter a negative answer with a minus sign.

Answer 1

Compute the return on existing investment, using the equation as shown below:

Return = Risk-free rate + (Beta*Market premium)

            = 6% + (1.50*5%)

            = 6% + 7.5%

            = 13.5%

Hence, the return on existing investment is 13.5%.

Compute the expected return of new funds, using the equation as shown below:

Expected portfolio return = (Existing investment*Return/ Total investment) + (New investment*Return/ Total investment)

                                     12% = ($20 million*13.5%/ $25 million) + ($5 million*Return/ $25 million)

                                      12% = 10.8% + (0.20*Return)

Rearrange the above-mentioned equation to determine the return on new investment as follows:

Return = (12% - 10.8%)/ 0.20

            = 6%

Hence, the return on new investment is 6%.

Compute the beta of new stock, using the equation as shown below:

Return = Risk-free rate + (Beta*Market premium)

   6% = 6% + (Beta*5%)

After rearranging the above-mentioned equation the beta on new stock is 0.