An investment has the following return distribution. How much is its expected return and standard deviation? State of Economy Probability Return Peak 0.1 10% Contraction 0.5 0% trough 0.2 2% Expansion 0.2 15% 4.4% and 6.04% 5.4% and 7.85% 4.4% and 3.64% 6.75% and 6.71%

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An investment has the following return distribution

Finance Dec 24, 2020

An investment has the following return distribution. How much is its expected return and standard deviation?

State of Economy	Probability	Return
Peak	0.1	10%
Contraction	0.5	0%
trough	0.2	2%
Expansion	0.2	15%

4.4% and 6.04%

5.4% and 7.85%

4.4% and 3.64%

6.75% and 6.71%

Expert Solution

Expected return = 0.1*0.1 + 0.5*0 + 0.2*0.02 + 0.2*0.15

Expected return = 0.01 + 0 + 0.004 + 0.03

Expected return = 0.044 or 4.4%

Standard deviation = [0.1(0.1 - 0.044)^2 + 0.5(0 - 0.044)^2 + 0.2(0.02 - 0.044)^2 + 0.2(0.15 - 0.044)^2]^1/2

Standard deviation = [0.00031 + 0.00097 + 0.00012 + 0.00225]^1/2

Standard deviation = 0.0604 or 6.04%

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