Securities D, E and F have the following characteristics with respect to expected return, standard deviation and correlation coefficients.
Security Expected Return Standard Deviation Correlation Coefficient D - E D - F E - F
D 0.08 0.02 0.4 0.6
E 0.15 0.16 0.4 0.8
F 0.12 0.08 0.6 0.8
Com pute the expected rate of return and standard deviation of a portfolio comprised of equal investment in each security.
The risk free rate is 10% and the expected return on the market portfolio is 15%. The expected returns for 4 securities are listed below together with their expected betas
SECURITY EXPECTED RETURN EXPECTED BETA
A 17.0% 1.3
B 14.5% 0.8
C 15.5% 1.1
D 18.0% 1.7
a. On the basis of these expectations, which securities are overvalued? Which are undervalued?
b. If the risk-free rate were to rise to 12% and the expected return on the market portfolio rose to 16%, which securities would be overvalued? which would be under-valued? (Assume the expected returns and the betas remain the same).
XYZ ltd. is considering three possible capital projects for next year. Each project has a 1 year life, and project returns depend on next years state of the economy. The estimated rates of return are shown below.
STATE OF THE PROBABILITY RATE OF RETURN
ECONOMY OF OCCURRENCE A B C
Recession 0.25 10% 9% 14%
Average 0.50 14 13 12
BOOM 0.25 16 18 10
a. Find each project expected rate of return, variance, standard deviation and coefficient of variation.
b. Compute the correlation coefficient between
i. A and B
ii. A and C
iii. B and C
c. Compute the expected return on a portfolio if the firm invests equal wealth on each asset.
d. Compute the standard deviation of the portfolio.