Problem 1) Consider the following three investments:
Security Expected return Standard deviation
J 0.12 0.4
K 0.14 0.4
L 0.13 0.5
M 0.12 0.3
Using the mean-variance criteria, identify whether one security dominates or whether there is no dominance for each pssible pair of securities
Problem 2) Tor Johnson has identified the following securities for a portfolio:
Security Amount invested Expected Return Beta
A $1,000 0.10 0.75
B 5000 0.15 1.20
C 1500 0.12 0.90
D 2500 0.16 1.30
Compute the expected return of the portfolio. Compute the beta of the portfolio.
Problem 3) Stock X has a standard deviation of return of 0.6 and stock Y has a standard deviation of 0.4. The correlation of the two stocks is 0.5. Compute the standard deviation of a portfolio invested half in X and half in Y.
Problem 4) The expected standard deviation of market returns is 0.20. Maria Houseman has the following four stocks:
Standard deviation of market returns = 0.20
Security Standard deviation Correlation with market
A 0.30 0.70
B 0.75 0.30
C 0.45 0.50
D 0.50 0.16
Compute the beta of each stock
Problem 5) The rate of treasury bills is 4% and the equity risk premium is 10%. Use the SML to estimate the return on each of the stocks in problem 4.
Problem 6) Maria has decided to invest $5,000 in each of the stocks in 4). Compute the expected return on the portfolio and the portfolio beta.