Question

A mutual fund manager has a $20 million portfolio with a beta of 0.75. The risk-free rate is 4.25%, and the market risk premium is 4.5%. 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 16%. 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

SML Equation:

E(R_i) = R_f + b_i (R_m - R_f)

R_f = 4.25% , (R_m - R_f) = 4.5% and E(R_i) = 16% after investing 5 million more.

Therefore, required b_i of the overall portfolio is

16% = 4.25% + b_i(4.5%)

b_i = 2.6111

This the required beta of overall portfolio.

After investing 5 million more,

Total fund invested = 25 million

Percentage invested in new stocks (w) = 20%

b_i = (w)(Beta of new stocks) + (1 - w)(Beta of old stocks)

2.6111 = (.20)(B) + (.80)(0.75)

Beta of new stocks = 10.0555