Question

please answer both parts thankyou !

1)Suppose you are the money manager of a $3.68 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock Investment Beta

A $ 540,000 1.50

B 500,000 (0.50)

C 940,000 1.25

D   1,700,000 0.75

If the market's required rate of return is 8% and the risk-free rate is 4%, what is the fund's required rate of return? Do not round intermediate calculations. Round your answer to two decimal places.

____%

2)

A mutual fund manager has a $20 million portfolio with a beta of 1.8. The risk-free rate is 3.5%, and the market risk premium is 9%. 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 17%. What should be the average beta of the new stocks added to the portfolio? Negative value, if any, should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to one decimal place.

_____

Answer 1

Solution- 1 As per CAPM model, the required rate of return (Ke) is calculated as below: Ke= Rf Beta*(Market's required rate of return Risk free rate) Where, Rf= Risk free rate In the given question, Risk free rate is 4% and market required rate of return is 8% Let's calculate the beta of the portfolio. For this, we must calculate the weighted average beta of all the four stocks with investment size as weights Stock Weight (Investment) Beta*Weight Beta 1.5 5,40,000.0 8,10,000.0 -0.5 5,00,000.0 -2,50,000.0 1.25 C 9,40,000.0 11,75,000.0 17,00,000.0 12,75,000.0 36,80,000.0 30,10,000.0 D 0.75 Beta of the portfolio (weighted avg)= [(Beta*weights)/(sum of weights)] Beta of the portfolio 30,10,000/36,80,000 Beta of the portfolio= 0.817935 Now, using the CAPM model, the fund's required rate of return (Ke) is calculated as follows: Ke= Rf + Beta*(Market return-Risk free rate) Ke= 4% +0.817935*(8%-4%) Ke- 4% 0.817935* (8%-4%) Ke= 4%+3.2717% Ke- 7.27%

Solution- 2 Let the average beta of the new $5 million stocks be X. Therefore, the total beta of portfolio is calculated as follows: Total new size of fund- $20m $5m $25m Existing beta of $20m investment= 1.8 Risk free rate- 3.5% Market risk premium= 9% Beta of total portfolio after new investment= 1.8*(20/25)X*(5/25) Beta of total portfolio after new investment- 1.44 0.2X Now, the required return on total portfolio after new investment is 17%. Therefore, using CAPM the equation (as described in part 1) becomes as follows: 17% =3.5% (Beta of total portfolio*Market risk premium) 17% = 3.5% [(1.44+0.2X) *9%] 13.5%= 12.96% +X*1.8 % X- 0.3 Therefore, the average beta of the new stocks should be 0.3