Question

PLEASE SHOW WORK

The following annual returns for Stock E are projected over the next year for three possible states of the economy. What is the stock’s standard deviation, variance, and mean of returns?E(R) = 8.5% ; σ = 22.70%; mean = $7.50; standard deviation = $2.50

State	Prob	E(R)
Boom	10%	40%
Normal	60%	20%
Recession	30%	- 25%

Answer 1

State	Actual return (AR)	Probability	Expected Return(ER)
Boom	40	0.1	4.00
Normal	20	0.6	12.00
Recession	-25	0.3	-7.50
		TOTAL	8.50

Expected return = 8.5%

State	AR	ER	AR-ER	(AR-ER)^2	Probability	{(AE-EE)^2}*Prob.
Boom	40	8.50	31.50	992.25	0.1	99.23
Normal	20	8.50	11.50	132.25	0.6	79.35
Recession	-25	8.50	-33.50	1122.25	0.3	336.68
					TOTAL	515.25

Standard deviation = square root of sum of {(AE-EE)^2}*Prob. = (515.25)^1/2 = 22.70%