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 .13 .10 .35 .42

Normal .52 .18 .30 .28

Bust .35 .19 -.29 -.38

a. If your portfolio is invested 42 percent each in A and B and 16 percent in C, what is the portfolio’s expected return, the variance, and the standard deviation?

b. If the expected T-bill rate is 4.65 percent, what is the expected risk premium on the portfolio?

Answer 1

Answer a.

Boom:

Expected Return = 42% * 0.10 + 42% * 0.35 + 16% * 0.42
Expected Return = 0.2562

Normal:

Expected Return = 42% * 0.18 + 42% * 0.30 + 16% * 0.28
Expected Return = 0.2464

Bust:

Expected Return = 42% * 0.19 + 42% * (-0.29) + 16% * (-0.38)
Expected Return = -0.1028

Expected Return for Portfolio = 0.13 * 0.2562 + 0.52 * 0.2464 + 0.35 * (-0.1028)
Expected Return for Portfolio = 0.1255 or 12.55%

Variance = 0.13 * (0.2562 - 0.1255)^2 + 0.52 * (0.2464 - 0.1255)^2 + 0.35 * (-0.1028 - 0.1255)^2
Variance = 0.028064

Standard Deviation = (0.028064)^(1/2)
Standard Deviation = 0.1675 or 16.75%

Answer b.

Expected Risk Premium on Portfolio = Expected Return for Portfolio - Risk-free Rate
Expected Risk Premium on Portfolio = 0.1255 - 0.0465
Expected Risk Premium on Portfolio = 0.079 or 7.90%