Question

1. We know the following expected returns for stocks A and B, given different states of the economy:

State (s)	Probability	E(rA,s)	E(rB,s)
Recession	0.1	-0.04	0.02
Normal	0.5	0.11	0.05
Expansion	0.4	0.19	0.09

a. What is the expected return for stock A?

b. What is the expected return for stock B?

c. What is the standard deviation of returns for stock A?

d. What is the standard deviation of returns for stock B?

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

State (s)	Probability	Expected return
Recession	0.1	-0.05
Normal	0.5	0.06
Expansion	0.4	0.11

a. What is the expected return for the stock?

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

Answer 1

Probability (P)	E(rA,s) (X)	E(rB,s) (Y)	PX	PY	X-PX	P(X-PX)^2	Y-PY	P(Y-PY)^2
0.1	-4	2	-0.4	0.2	-16.7	27.889	-4.3	1.849
0.5	11	5	5.5	2.5	-1.7	1.445	-1.3	0.845
0.4	19	9	7.6	3.6	6.3	15.876	2.7	2.916
Total			12.7	6.3		45.21		5.61

Expected return on stock A = Sum of PX = 12.7%

Expected return on stock B = Sum of PY = 6.3%

Standard deviation of returns for stock A = 45.21^0.5 = 6.72%

Standard deviation of returns for stock B = 5.61^0.5 = 2.37%

Probability (P)	Expected return X	PX	X-PX	P(X-PX)^2
0.1	-5	-0.5	-11.9	14.161
0.5	6	3.0	-0.9	0.405
0.4	11	4.4	4.1	6.724
Total		6.90		21.29

Expected return on the stock = 6.90%

standard deviation of returns for the stock = 21.29^0.5 = 4.61%