Question

Consider the following information on a portfolio of three stocks:

State of Economy	Probability of State of Economy	Stock A Rate of Return	Stock B Rate of Return	Stock C Rate of Return
Boom	.12	.07	.32	.45
Normal	.55	.15	.27	.25
Bust	.33	.16	–.26	–.35

a.	If your portfolio is invested 40 percent each in A and B and 20 percent in C, what is the portfolio’s expected return, the variance, and the standard deviation? (Do not round intermediate calculations. Round your variance answer to 5 decimal places, e.g., 32.16161. Enter your other answers as a percent rounded to 2 decimal places, e.g., 32.16.)
b.	If the expected T-bill rate is 4.5 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

  

A) Expected return -------

variance ------

standard division -----

B)Expected risk premium ------

Answer 1

Answer a.

Weight of Stock A = 0.40
Weight of Stock B = 0.40
Weight of Stock C = 0.20

Boom:

Expected Return = 0.40 * 0.07 + 0.40 * 0.32 + 0.20 * 0.45
Expected Return = 0.2460

Normal:

Expected Return = 0.40 * 0.15 + 0.40 * 0.27 + 0.20 * 0.25
Expected Return = 0.2180

Bust:

Expected Return = 0.40 * 0.16 + 0.40 * (-0.26) + 0.20 * (-0.35)
Expected Return = -0.1100

Expected Return of Portfolio = 0.12 * 0.2460 + 0.55 * 0.2180 + 0.33 * (-0.1100)
Expected Return of Portfolio = 0.1131 or 11.31%

Variance of Portfolio = 0.12 * (0.2460 - 0.1131)^2 + 0.55 * (0.2180 - 0.1131)^2 + 0.33 * (-0.1100 - 0.1131)^2
Variance of Portfolio = 0.02460

Standard Deviation = (0.02460)^(1/2)
Standard Deviation = 0.1568 or 15.68%

Answer b.

Expected Risk Premium = Expected Return - Risk-free Rate
Expected Risk Premium = 11.31% - 4.50%
Expected Risk Premium = 6.81%