Attempts: 0 Keep the Highest: 0/1 4 Problem 8.07 Problem Walk-Through PORTFOLIO

Question

Attempts: 0 Keep the Highest: 0/1 4 Problem 8.07 Problem Walk-Through PORTFOLIO REQUIRED RETURN Suppose you are the money manager of a $4.91 million investment fund. The fund consists of four stocks with the following investments and betas: Stock s 240,000 640,000 1,180,000 2,850,000 Beta 1.50 (0.50) 1.25 0.75 8 If the market's required rate of return is 12% and the ris free rate is 6% what is the fund's required rate of return? Do not round inter media e ca culations Round your answer to wodeoma places. Contnue wthout saving

Explanation / Answer

Beta of a portfolio is the weighted average of the betas of the stock of the portfolio. The weighted average beta is calculated in the following table

So, the weighted average beta is 0.74

Now, as per capital asset pricing model,

Re = Rf + (Rm – Rf) x Beta

Where,

Re = Required rate of return

Rf = Risk – free rate of return = 6%

Rm = Required return on market = 12%

Beta = Beta of the portfolio = 0.74

So, Re = 6 + (12 – 6) x 0.74

= 6 + 4.44

= 10.44%

Calculations A B = A / 4,910,000 C D = B x C Stock Investment Weights Beta Weighted average beta A         240,000 0.04888 1.5 0.073319756 B         640,000 0.130346         (0.50)    (0.0651731) C     1,180,000 0.240326 1.25 0.300407332 D     2,850,000 0.580448 0.75 0.435336049 Total     4,910,000 Total 0.74

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