Calculate the expected return and standard deviation for the returns of each asset. Which portfolios are efficient? Calculate the expected return and the standard deviation of the minimum-variance portfolio, G. 

Calculations and Analysis

You are given the following distributions of returns for two assets, X and Y:
Probability Returns
X
%
Y
%
0.2 11 –3
0.2 9 15
0.2 25 2
0.2 7 20
0.2 –2 6
A . Calculate the expected return and standard deviation for the returns of each asset.  (2 marks)
B . Calculate the covariance between the returns of asset X and asset Y.  (2 marks)
C . Complete the table below for the mean and standard deviation of the given portfolios.  (3 marks)
Hint: Use the weights in decimals in the calculations and then covert your answers into percentages. A few results are calculated for you in the table.
Percentage in X Percentage in Y E(rP)
(%)
σP
(%)
125 –25
100 0
75 25 9.50 6.18
50 50
25 75 8.50 5.96
0 100
–25 125 7.50 11.42

D . Discuss your results. (2 marks)
E . Next, sketch the following relationships:
a. Between the expected return on the portfolios and the weight, w, invested in asset X.
b. Between the standard deviation of the portfolios and the weight in X.
c. Between the mean and standard deviation of the portfolios in a single graph (the mean–standard deviation plane).
(3 marks)
F . Discuss your plots. (2 marks)

G . Which portfolios are efficient? (2 marks)
H . The minimum–variance portfolio weight in X, w*, is given by: YXXY22 YXXY2

The minimum–variance portfolio is also called the global minimum–variance portfolio. Find w* using this formula.
(2 marks)
I . Calculate the expected return and the standard deviation of the minimum–variance portfolio, G.  (2 marks