Question

What is the standard deviation of the returns on a stock given the following information?

State of Economy	Probability of State of Economy	Rate of Return if State Occurs
Boom	.28	.175
Normal	.67	.128
Recession	.05	.026

Group of answer choices

3.42 percent

4.01 percent

3.89 percent

3.28 percent

3.57 percent

Answer 1

State of Economy	Probability of state of Economy	Rate of return if state occurs
Boom	0.28	0.175
Normal	0.67	0.128
Recession	0.05	0.026

Expected rate of return when the probabilities (p_i) of state of Economies are given is calculated using the formula:

Expected Return = E[R] = p₁*R₁ + p₂*R₂ + p₃*R₃ = 0.28*0.175 + 0.67*0.128 + 0.05*0.026 = 0.049 + 0.08576 + 0.0013 = 0.13606

Expected Return = E[R] = 0.13606

Now, Varicance is calculated using the formula:

Variance = σ² = p₁*(R₁-E[R])² + p₂*(R₂-E[R])² + p₃*(R₃-E[R])²

Varince = σ² = 0.28*(0.175-0.13606)² + 0.67*(0.128-0.13606)² + 0.05*(0.026-0.13606)² = 0.000424570608 + 0.0000435256119999998 + 0.00060566018 = 0.0010737564

Standard Deviation is square-root of variance

Standard Deviation = σ = (0.0010737564)^1/2 = 0.0327682224113546 = 3.27682224113546% ~ 3.28% (Rounded to two-decimals)

Answer -> 3.28 percent