Question

1. You've estimated the following expected returns for a stock, depending on the strength of the economy:

State (s)	Probability	Expected return
Recession	0.3	-0.06
Normal	0.5	0.06
Expansion	0.2	0.12

a. What is the expected return for the stock?

b. What is the standard deviation of returns for the stock?

2. You observed the following returns for a stock and Treasury bills:

Year	Stock A	T-bills
2016	18%	4%
2015	8%	5%
2014	19%	2%

a. What was the excess return for the stock in 2016?

b. What was the (arithmetic) average return for the stock?

c. What was the (arithmetic) average return for T-bills?

d. What was the average excess return?

2. Below are the returns for different asset classes for a particular year:

Asset class	Return
T-bills	1.3%
Corporate bonds	4.9%
Small company stocks	17%
Large company stocks	9.5%

a. What was the excess return for corporate bonds?

b. What was the excess return for small company stocks?

c. What was the excess return for large company stocks?

Answer 1

Answer to Question 1:

Answer a.

Expected Return = 0.30 * (-0.06) + 0.50 * 0.06 + 0.20 * 0.12
Expected Return = 0.036 or 3.60%

Answer b.

Variance = 0.30 * (-0.06 - 0.036)^2 + 0.50 * (0.06 - 0.036)^2 + 0.020 * (0.12 - 0.036)^2
Variance = 0.003194

Standard Deviation = (0.003194)^(1/2)
Standard Deviation = 0.0565 or 5.65%

Answer to Question 2:

Answer a.

Excess Return = Return for Stock A - Return for T-bills
Excess Return = 18% - 4%
Excess Return = 14%

Answer b.

Average Return for Stock A = [0.18 + 0.08 + 0.19] / 3
Average Return for Stock A = 0.45 / 3
Average Return for Stock A = 0.15 or 15%

Answer c.

Average Return for T-bills = [0.04 + 0.05 + 0.02] / 3
Average Return for T-bills = 0.11 / 3
Average Return for T-bills = 0.0367 or 3.67%

Answer d.

Average Excess Return = Average Return for Stock A - Average Return for T-bills
Average Excess Return = 15.00% - 3.67%
Average Excess Return = 11.33%