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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

Answer :

Shahzaibfaraz

Answer:

Beta of new stock = 6.03333333335 rounded off to 6.03

Explanation:

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

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