Question 3
- i) Calculate the standard deviation of the market portfolio
The market portfolio is (5/16, 3/16, 2/16, 6/16), so
RM = (5RA + 3RB + 2RC+6RD) / 16
Thus,
Cov (Ri, RM) = [ 5Cov(Ri, RA) + 3Cov(Ri, RB) + 2 Cov(Ri, RC)+ 6 Cov( Ri,RD)] / 16
Cov (RA, RM) = (5×1+3×0+2×0+6×0)/16
=5/16
Cov (RB, RM) = (5×0+3×1+2×0+6×0)/16
=3/16
Cov (RC, RM) = (5×0+3×0+2×1+6×0)/16
=2/16
Cov (RD, RM) = (5×0+3×0+2×0+6×1)/16
=6/16
Hence, the variance will be:
Cov (RM, RM) = [5Cov (RM, RA) + 3 Cov (RM, RB) + 2 Cov (RM, RC) + 6 Cov (RM, RD)] / 16
= [5(5/16) +3(3/16) +2(2/16) +6(6/16)]/16
=0.2890625
The standard deviation is given as = 0.537645
- ii) Relevant Capital Market Line
Risk free interest rates= 5%
Expected rate of return on the market=10%
The expected return on any efficient portfolio P can be written as:
Eᵨ =r+ ((EM – r)/ɗm) ɗᵨ (Baker and Filbeck 52)
Eᵨ is the expected return of any portfolio on the efficient frontier
R is the risk-free rate of return
ɗᵨ is the standard deviation of the return on portfolio P
Hence r=5
= (EM – r)/ɗm
= (0.1-0.05)/0.537645
=0.092998
=0.093
Hence our equation of capital market line
Eᵨ = 0.05+0.093 ɗᵨ
Capital market line
iii) Investment strategy
You have to advice someone seeking to obtain an expected rate of return of 15%. What investment strategy do you advise them to achieve and what standard deviation can they expect?
Recall that the slope of the above graph is given by 0.093
= (EM – r)/ɗm
I would advise the investor to invest in a security with higher standard deviation; that is, a security with a higher risk.
He can also invest in a security with higher risk free interest rate
2) Calculating the standard deviation given expected rate of return is 15% or 0.15 and r=0.05
0.093= (EM – r)/ɗm
0.093= (0.15-0.05) ɗm
ɗm=0.093/ (0.1)
=0.93
Work Cited
Baker, H Kent, and Greg Filbeck. Portfolio Theory and Management. New York: Oxford University Press, 2013. Print.
