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Question

Kay invested in real estate with the intention of selling the property 1 yr from today. She has modeled on that investment based on 3 economic scenarios. She believes that if the economy stays healthy, then her will generate a 30% return. However, if the economy softens, as predicted, the return will be 10%, while the return will be -25% if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.5, 0.3, and 0.2, respectively, then what are the expected return and the standard deviation of the return on her investment?

Answer 1

If we weight the investment returns by multiplying the percentage returns by their respective probabilities we get:

15%, 3%, -5%.

The expected return is the mean of these: 13/3%=4.33% approx.

The variance is ((15-13/3)²+(3-13/3)²+(-5-13/3)²)/3=608/9.

The square root of the variance is the standard deviation 8.22% approx.