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	.15	.04	.33	.55
Normal	.60	.09	.13	.19
Bust	.25	.15	–.14	–.28

  

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? The standard deviation? (Do not round intermediate calculations. Round your variance answer to 5 decimal places, e.g., .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 3.75 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.)

  

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 * 0.04 + 0.40 * 0.33 + 0.20 * 0.55
Expected Return = 0.2580

Normal:

Expected Return = 0.40 * 0.09 + 0.40 * 0.13 + 0.20 * 0.19
Expected Return = 0.1260

Bust:

Expected Return = 0.40 * 0.15 + 0.40 * (-0.14) + 0.20 * (-0.28)
Expected Return = -0.0520

Expected Return of Portfolio = 0.15 * 0.2580 + 0.60 * 0.1260 + 0.25 * (-0.0520)
Expected Return of Portfolio = 0.1013 or 10.13%

Variance of Portfolio = 0.15 * (0.2580 - 0.1013)^2 + 0.60 * (0.1260 - 0.1013)^2 + 0.25 * (-0.0520 - 0.1013)^2
Variance of Portfolio = 0.00992

Standard Deviation of Portfolio = (0.00992)^(1/2)
Standard Deviation of Portfolio = 0.0996 or 9.96%

Answer b.

Expected Risk Premium on Portfolio = Expected Return of Portfolio - Risk-free Rate
Expected Risk Premium on Portfolio = 10.13% - 3.75%
Expected Risk Premium on Portfolio = 6.38%