Question

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	-0.02
Normal	0.5	0.09
Expansion	0.2	0.14

1. What is the expected return for the stock?

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

Answer 1

1. Expected return = Respective probabilities of states * expected return of states

= (0.3*-0.02)+(0.5*0.09)+(0.2*0.14)

= 6.70%

Answer = 6.70%

2. Variance = Product of Deviation Squared and Probability

State of Economy	Probability	Probable Return	Deviation ( Probable Return- Expected Return)	Deviation Squared	Product ( Deviation Squared* Probability)
Recession	0.30	-2.00	-8.700	75.690000	22.7070
Normal	0.50	9.00	2.300	5.290000	2.6450
Expansion	0.20	14.00	7.300	53.290000	10.6580
			Variance ( Sum of Product)		36.01

Standard Deviation = Square root of Variance

= 36.01^(1/2)

= 6.00%

Answer = 6.00%