PORTFOLIO REQUIRED RETURN Suppose you are the money manager of a $4.47 million i

Question

PORTFOLIO REQUIRED RETURN

Suppose you are the money manager of a $4.47 million investment fund. The fund consists of four stocks with the following investments and betas:

If the market's required rate of return is 9% 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.

Stock Investment Beta A $   440,000                                 1.50 B 760,000                                 (0.50) C 1,420,000                                 1.25 D 1,850,000                                 0.75

Explanation / Answer

STEP 1 : Calculation of Beta of the portfolio

Beta (B) of portfolio = {(440,000*1.5) + (760,000*-0.5) + (1,420,000*1.25) + (1,850,000*0.75)}/ 4,470,000

Beta (B) of portfolio = 3,442,500 / 4,470,000

Beta (B) of portfolio = 0.77

STEP 2: Calculation of Fund required rate of return

As per CAPM model Required rate of return = Rf + B(Rm - Rf)

where Rf = Risk free rate

B = Beta

Rm = Market required rate of return

So, putting the value in equation we get,

Required rate of return = 4% + 0.77(9%-4%)

Required rate of return = 4% + 3.85%

Required rate of return = 7.85%.

Extra Explanation

1) It is noted that the Stock B is having negetive beta. The theory says it is not possible in practical life to have a negetive beta in a individual stock. But the question may have its own opinion. So please check it wetehr the beta is in actual negetive or not. Also it is worth noted that in few sums when there is a negetive beta the sums also assume it to be 0. It depends upon the sums assumution in that case all the calculation will remauin same expecept in clculation of beta we use (760,000 * 0 ) instead of (760,000 * -0.5).

2)Beta denotes the risk of portfolio w.r.t Market. If the Beta is 1 the risk of portfolio is equal to risk of market. As in the given case the beta is lower then 1 and so the protfolio return will be ofcoursee lower then market return.

Please hit the thumps up if its hit your conceptual understanding. feel free to comment for any doubt. Thank you.

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