Kate recently invested in real estate with the intention of selling the property

Question

Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be -25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.6, 0.2, and 0.2, respectively, then what are the expected return and the standard deviation of the return on Kates investment? (Round expected return to 3 decimal places, e.g. 0.125 and round intermediate calculations and standard deviation to 5 decimal places, e.g. 0.07680.)

Explanation / Answer

x--p(x)
30 .6
10 .2
-25 .2

E(x) = [ (30)(.6)+(10)(.2)+(-25)(.2)] = 15% --- expected retrun

Var(x) = E(x^2) - [E(x)]^2
E(x^2) = [ (30)^2+(10)^2+(-25)^2] =1625

Var(x) = 1625 - (15)^2 =1400

Standard deviation = sqruare root 1400 = 37.41%

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