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 0.4, 0.4, and 0.2, respectively, then calculate the coefficient of variation for the investment?

Explanation / Answer

Prbability distribution for returns:

x--p(x)
30 .4
10 .4
-25 .2

E(x) = [ (30)(.4)+(10)(.4)+(-25)(.2)] = 11% --- expected retrun

Var(x) = E(x^2) - [E(x)]^2
E(x^2) = [ (30)^2(.4)+(10)^2(.4)+(-25)^2(.2)] =525

Var(x) = 525 - (11)^2 =404

Standard deviation = sqruare root 404= 20.09%

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