Calculating the variance and standard deviation: Kate recently invested in real

Question

Calculating the variance and standard deviation: 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, 0.5, and 0.1, respectively, then what are the expected return and the standard deviation for Kate’s investment?

Explanation / Answer

E(x) = [ (0.30)(0.40)+(0.10)(0.50)+(-0.25)(0.10)] = 14.5% --- expected retrun Var(x) = E(x^2) - [E(x)]^2 E(x^2) = [ (0.30)^2(0.40)+(0.10)^2(0.50)+(-0.25)^2(.10)] =0.15075 Var(x) = 0.15075 - (0.145)^2 =0.128725 Standard deviation = sqruare root 0.128725 = 35.88%

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