3.
45 points We have two stocks. The random variables of return for those two stocks are X1 and
X2, respectively. Suppose the random vector (X1, X2) follows the 2-dimensional normal
[0.2 -0.05] distribution N(μ,Σ) with μ=(0.04,0.04) and Σ = [0.05 0.1
We have two portfolios as follows:
Portfolio 1 (P1): capital allocation weight is Wp1=(w1, w2)=(0.6,0.4)
Portfolio return for P1 is rp1 = 0.6X1 + 0.4X2
Portfolio 2 (P2): capital allocation weight is Wp2=(w1, w2)=(0.2,0.8).
Portfolio return for P2 is rp2 = 0.2X1 + 0.8X2
Suppose that the risk-free rate of return is rf=0.01
a. Calculate mean for the return of Portfolio 1.
b. Calculate mean for the return of Portfolio 2
c. Calculate standard deviation for the return of Portfolio 1
d. Calculate standard deviation for the return of Portfolio 2
e. Calculate Sharpe Ratio of Portfolio 1
f. Calculate Sharpe Ratio of Portfolio 2
g. Calculate 99%-Value at Risk (VaR1%(rp)) of Portfolio 1.
h. Calculate 99%-Value at Risk (VaR1%(rp2)) of Portfolio 2.
Note that 99% quantile value of the standard normal distribution is q99% = 2.326.
Which portfolio is more efficient? Explain the reason for your selection in the sense of Mean.
Variance Optimization.