Question

Intro Assume that there are only two stocks in the economy, stock A and stock B. The risk-free asset has a return of 3%. The optimal risky portfolio, i.e., the portfolio with the highest Sharpe ratio, is given below: A BC Stock A Stock B Risk-free asset 2 Expected return 0.062 0.075 0.03 3 Variance 0.1521 0.0484 4 Standard deviation 0.39 0.22 5 Covariance 0.02574 D Optimal risky portfolio 8 Weights 9 Expected return 10 Variance 11 Standard deviation 12 Sharpe ratio 0.0609 0.0742 0.04619 0.2149 0.2057 0.939=1-B8 =B8*B2+C8*C2 =B8^2*B3+C8^2*C3+2*B8*C8*B5 =B10^0.5 =(B9-D2)/11 | Attempt 1/10 for 10 pts. Part 1 What is the expected return of a portfolio composed of 20% of the optimal risky portfolio and 80% of the risk-free asset? 4+ de Submit Attempt 1/10 for 10 pts. Part 2 What is the standard deviation of such a portfolio? 4+ de Submit

Answer 1

1. Portfolio consists of 20% of optimal risky portfolio and 80% of risk free asset.

Expected Return of Portfolio = W₁*R₁+W₂*R₂ = 0.20 * 7.42% + 0.80 * 3% = 3.88%

2. Standard Deviation of Risk Free Asset is zero. Thus, Covariance and Correlation between Risk Free Asset and risky portfolio is also zero.

Standard Deviation of Portfolio = V(W202) + (W203) + (2* WaqqW60b* Correlation(a,b))

                                                               

= 0.202 * 0.21492) + (0.802 * 02) + 2 * 0.2 0.2149 * 0.80 * ( * 0)

                                                               

= 0.202 * 0.21492) +0+0

                                                               = 0.04298.