C and D 2) In Energy land there are only two risky stocks, energy A and energy B

Question

C and D

2) In Energy land there are only two risky stocks, energy A and energy B, whose details are listed below Number of shares Price Expected Standard deviation Energy A Energy B outstandir 100 150 er share rate of return $1.50 $2.00 15% 12% of return 1 5% 9% Furthermore, the correlation coefficient between the returns of stock A and B is 1/3. There is also a risk-free asset, and Energyland satisfies the CAPM exactly a) What is the expected rate of return of the market portfolio? b) What is the standard deviation of the market portfolio? c) What is the beta of Energy A? d) What is the risk-free rate in Energyland?

Explanation / Answer

Value of market portfolio=100*1.5+150*2=450

Portfolio weights are weight of A=100*1.5/450=1/3 and that of B=150*2/450=2/3

Market return=1/3*15+2/3*12=13%

Cov(a,b)=correl(a,b)*stdeva*stdevb=1/3*15*9=45%^2=0.0045

Cov(a,market)=cov(a,1/3*a+2/3*b)=1/3*var(a)+2/3*covar(a,b)=1/3*0.0225+2/3*0.0045=0.0105

var(market)=1/3^2*var(a)+2^2/3^2*var(b)+2*1/3*2/3*cov(a,b)=0.0225/9+0.0081*4/9+4/9*0.0045=0.0081

Beta=correlation coefficient(stock,market)*standard deviation stock/standard deviation market=cov(a,market)/var(market)

beta of a=0.0105/0.0081=1.296296

Hence, 15=rf+1.296296*(13-rf)=>rf=6.249993%

Market beta=1/3*beta of a + 2/3*beta of b

as market beta is 1

so, 1=1/3*1.296296+2/3*beta of b

hence, beta of b=0.851852

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