87. Please use theprobability distributions ofexpectedfuturereturnsshownin Probl
ID: 2821105 • Letter: 8
Question
87. Please use theprobability distributions ofexpectedfuturereturnsshownin Problem2for Stock A and Stock B to answer the following questions a. Assume Stocks A and B are in a $50,000 portfolio, consisting of $36,000 in Stock A and $14,000 in Stock B. Calculate the portfolio's expected return. (Hint: You will need your expected return calculations from problem 2 for Stock a and Stock B) mUst noweed etrn b. Assuming the beta for Stock A is 0.40 and the beta for Stock B is 0.90, calculate the portfolio beta. '12 er n C. Assuming the risk free rate of return is 3.50% and the required rate of return for the market portfolio is 10.00%, compute the portfolio's required rate of return. d. Is the portfolio in equilibrium? Why or why not? Suppose you are the money manager of a $4.82 million investment fund. The fund consists of four stocks with the following investments and betas (Note-Beta can be negative): 8-8. Portfolio Stock SInvestment Beta A $460,000 1.50 B $500,000 0.50 C$1,260,000 1.25 D $2,600,000 0.75 If the market's required rate of return is 8.00% and the risk-free rate is 4.00%, what is the fund's required rate of return?Explanation / Answer
8-7
(a )
Wa = weight in stock A = 36000/50000 = 0.72
Wb = weight in stock B = 14000/50000 = 0.28
Let rA and rB be returns of stock A and B respectively
Portfolio return = Wa* rA + Wb * rB
= 0.72 rA + 0.28 rB
Please provide rA and rB from previous calculations and compute
(b)
Portfolio beta = Wa * beta of A + Wb * beta of B
= 0.72 * 0.4 + 0.28 * 0.9
= 0.54
(c)
CAPM equation
rM = return on market = 10%
rF = risk free rate =3.5%
beta = portfolio beta = 0.54
portfolio rate of return, rP
rP = rF + beta * ( rM -rF)
= 3.5% + 0.54 ( 10%-3.5%)
=7.01%
(d)
If the return obtained in (a) is equal to CAPM return of 7.01% , the portfolio is in equilibrium
8-8
Use CAPM Equation
rM = return on market = 8%
rF = risk free rate = 4%
beta = portfolio beta = wA * 1.5 + wB * (-0.5) + wC * 1.25 + wD * 0.75
wA = 460000/4820000 = 0.0954 wC = 1260000/4820000 = 0.2614
wB = 500000/4820000 = 0.1037 wD = 2600000/4820000 = 0.5394
beta = wA * 1.5 + wB * (-0.5) + wC * 1.25 + wD * 0.75
= 0.8226
portfolio rate of return, rP
rP = rF + beta * ( rM -rF)
= 4% + 0.8226 * ( 8% - 4%)
= 7.2905%
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