Question

Ted, a mutual fund manager, has a $40 million portfolio with a beta of 1.00. The risk-free rate is 4.25%, and the market risk premium is 7.00%. Ted expects to receive an additional $60 million, which she plans to invest in additional stocks. After investing the additional funds, she wants the fund's required and expected return to be 13.00%. What must the average beta of the new stocks be to achieve the target required rate of return?

*Show the formula you used and formula inputs.

Answer 1

The current portfolio consists of $40 million with a beta of 1.00. Ted is going to invest $60 million in new stocks.

As per CAPM,

Expected return = R_f + [Beta * Market risk premium]

Where R_f is the risk free return and Market risk premium is the difference between market rate and risk-free rate of return, Beta is the measure of volatility of the stock.

we have to achieve a Target return of 13.00%. Substituting the target return in the equation, we get the target beta of the overall portfolio.

13.00% = 4.25% + Target beta * 7%

=> Target beta = [13.00% - 4.25%] / 7%

=> Target beta = 1.25

The combined portfolio's (old stocks + new stocks) beta should be 1.25. Combined portfolio is worth $100 million at the time of investment.

Weight of old stocks in the combined portfolio = 40 / 100 => 0.4

Weight of new stocks in the combined portfolio = 60 / 100 => 0.6

Beta of the portfolio = Beta of each stock * Weight of each stock in the portfolio

1.25 = 1.00 * 0.4 + Beta of new stocks * 0.6

=> 1.25 = 0.4 + Beta of new stocks * 0.6

=> Beta of new stocks = [1.25 - 0.4] / 0.6

=> 1.416666666666667

=> Average beta of the new stocks should be 1.42 (rounded off).