Question

Elizabeth 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. Assume the probabilities of the healthy, soft, and recessionary states are 0.3, 0.5, and 0.2, respectively.

1.Calculate the coefficient of variation for the investment.

Answer 1

Let the probability for a state of economy be denoted by P_i and Return by R_i

Hence, μ = mean = ΣP_iR_i = 0.3*0.30 + 0.5*0.10 + 0.2*(-0.25)  = 0.09

standard deviation = σ = sqrt ΣP_i(R_i - μ)² = sqrt [ 0.3(0.30 - 0.09)² + 0.5(0.10 - 0.09)² + 0.2(-0.25 - 0.09)² ] = 0.19079

Coefficient of variation =   σ/μ = 0.19079/0.09 = 2.11989