Question

Consider the following information on three stocks:

a-1 If your portfolio is invested 40 percent each in A and B and 20 percent in C, what is the portfolio expected return?

Portfolio expected return = _________ %

a-2 What is the variance?

Variance= _________            

a-3 What is the standard deviation?

Standard deviation= _________   %

b. If the expected T-bill rate is 4.00 percent, what is the expected risk premium on the portfolio?

Expected risk premium= _________   %

c-1 If the expected inflation rate is 3.60 percent, what are the approximate and exact expected real returns on the portfolio?

Approximate expected real return =	%
Exact expected real return -	%

c-2 What are the approximate and exact expected real risk premiums on the portfolio?

Approximate expected real risk premium=_________ %

Exact expected real 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 * 0.24 + 0.40 * 0.36 + 0.20 * 0.58
Expected Return = 0.3560

Normal:

Expected Return = 0.40 * 0.20 + 0.40 * 0.18 + 0.20 * 0.16
Expected Return = 0.1840

Bust:

Expected Return = 0.40 * 0.04 + 0.40 * (-0.36) + 0.20 * (-0.45)
Expected Return = -0.2180

Expected Return of Portfolio = 0.20 * 0.3560 + 0.50 * 0.1840 + 0.30 * (-0.2180)
Expected Return of Portfolio = 0.0978 or 9.78%

Variance of Portfolio = 0.20 * (0.3560 - 0.0978)^2 + 0.50 * (0.1840 - 0.0978)^2 + 0.30 * (-0.2180 - 0.0978)^2
Variance of Portfolio = 0.04697

Standard Deviation of Portfolio = (0.04697)^(1/2)
Standard Deviation of Portfolio = 0.2167 or 21.67%

Answer b.

Expected Risk Premium = Expected Return of Portfolio - Risk-free Rate
Expected Risk Premium = 9.78% - 4.00%
Expected Risk Premium = 5.78%

Answer c.

Approximate Expected Real Return = Expected Return - Inflation Rate
Approximate Expected Real Return = 9.78% - 3.60%
Approximate Expected Real Return = 6.18%

Exact Expected Real Return = (Expected Return - Inflation Rate) / (1 + Inflation Rate)
Exact Expected Real Return = (0.0978 - 0.0360) / (1 + 0.0360)
Exact Expected Real Return = 0.0597 or 5.97%

Answer d.

Approximate Expected Real Risk Premium = Expected Risk Premium - Inflation Rate
Approximate Expected Real Risk Premium = 5.78% - 3.60%
Approximate Expected Real Risk Premium = 2.18%

Exact Expected Real Risk Premium = (Expected Risk Premium - Inflation Rate) / (1 + Inflation Rate)
Exact Expected Real Risk Premium = (0.0578 - 0.0360) / (1 + 0.0360)
Exact Expected Real Risk Premium = 0.0210 or 2.10%