Question

11.06 Calculating Returns and Standard Deviations Based on the following information, calculate the expected return and standard deviation
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State of Economy	Probability of State of Economy	Rate of Return if State Occurs
Depression	0.150	-10.50%
Recession	0.300	5.90%
Normal	0.450	13.00%
Boom	0.100	21.10%
	Expected Value
	Variance
	Standard Deviation

Answer 1

Expected value = 0.15*-10.5% + 0.3*5.9% + 0.45*13% + 0.1*21.1%

= 8.155%

Variance = (0.15)*(-0.105-0.08155)^2 + (0.3)*(0.059-0.08155)^2 + (0.45)*(0.13-0.08155)^2+(0.1)*(0.211-0.08155)^2

= 0.0081047475

Standard deviation = square root of variance = 0.0081047475^0.5

= 0.0900264 or 9.00264%