A mutual fund manager has a $20 million portfolio with a beta of 1.20. The risk-free rate is 7.00%, and the market risk premium is 6.0%. 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 20%. What should be the average beta of the new stocks added to the portfolio

We first need to calculate the required rate of return of the current portfolio of $20 million. We can calculate the required rate of return using the CAPM.

r = rRF + Beta * rpM

Where,

rRF is the risk free rate
rpM is the market risk premium

r of existing portfolio = 7% + 1.2 * 6%

r of existing portfolio = 14.2%

Using the CAPM, we need to determine the overall Beta of a portfolio whose required rate of return should be 20%. Plugging in the value for required rate of return, risk free rate and market risk premium in the CAPM equation, we calculate the overall beta to be,

20% = 7% + Beta * 6%

20% - 7% = Beta * 6%

13% / 6% = Beta

Beta = 2.16666666667 rounded off to 2.17

So the new portfolio should have a beta of 2.16666666667 n order to earn a required return of 20%.

Using the formula for portfolio beta, we can calculate the beta of the new stocks to be,

Portfolio Beta = wA * Beta of A + wB * Beta of B + ... + wN * Beta of N

Where,

w represents the weight of each stock in the portfolio as a proportion of the overall portfolio investment

Total investment in new portfolio = 20 + 5 = $25 million

2.16666666667 = 20/25 * 1.2 + 5/25 * Beta of new stocks

2.16666666667 = 0.96 + 0.2 * Beta of new stocks

2.16666666667 - 0.96 = 0.2 * Beta of new stocks

1.20666666667 / 0.2 = Beta of new stocks

Beta of new stock = 6.03333333335 rounded off to 6.03