Question

1.             The risk-free rate of interest is 2%.  Stock AAA has a beta of 1.4 and a standard deviation of return = .40.  The expected return on the market portfolio is 9%. Assume CAPM holds.  (Note:  the questions below are independent not sequential.)

a)             Plot the security market line.  Label all axes of your graph.  Plot (and label) the points (and numerical values) corresponding to the market portfolio, the risk-free asset, and stock AAA.

b)            Your current wealth is $1,000.  What is the expected returnfor a portfolio where youborrow$500 at the risk-free rate andinvest $1,500in stock AAA?

c)             What is the standard deviation of returnfor the portfolio in (b) above?

d)            If a portfolio of the two assets (the risk-free asset, and stock AAA) has an expected return of 14%, what is the portfolio’sbeta?

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Answer #1

Rf =2%, beta =1.4, SD(s) = 0.40 =40%, Rm=9%

(a) SML

(b) WEIGHT OF RISK FREE ASSET (WR)= -500/1000 = -0.5 , WEIGHT OF STOCK AAA (WS)= 1500/1000 = 1.5

Rs = Rf + beta(Rm-Rf) = 2% + 1.4(9%-2%) = 11.8%

EXPECTED RETURN ON PORTFOLIO = WR*Rf + WS*Rs = (-0.5)(2) + (1.5)(11.8) = -1 + 17.7 = 16.7 %

(c ) AS RISK FREE ASSET HAS ZERO STANDARD DEVIATION,

PORTFOLIO STANDARD DEVIATION = WS*SDs = 1.5*0.4 =0.6 = 60%

(d)

EXPECTED RETURN ON PORTFOLIO = WR*Rf + WS*Rs

14 = (WR)(2) + (WS)(11.8) =  (WR)(2) +  (1 - WR)(11.8)

14 =   (WR)(2) +  (11.8) - (WR)(11.8)

2.2 = -9.8

(WR) = - 0.2245, THEREFORE  (WS) = 1 - (WR) = 1 - (- 0.2245) = 1.2245

AS RISK FREE ASSET HAS ZERO BETA,

PORTFOLIO BETA = BETA OF STOCK AAA X (WS) = 1.4 X 1.2245 = 1.7143

ANY DOUBTS, FEEL FREE TO ASK

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