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

Question

7.15 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? I have gotten the answer it just was not gotten use the formula and I have to use the formula I don't know what to do please help. The answer I have gotten is square root 0.128725 = 35.88% Formula to use is below.

Given:
Probability Return
Healthy (h) 0.4 30%
Softens (s) 0.5 10%
Recession ( r ) 0.1 -25%

Required to find: E(R) and standard deviation (s)

E(Rinvestment) = (ph x Rh) + (ps x Rs) + (pr x Rr)

Var ( R) = s2 = (ph x (Rh – E(R))2) + (ps x (Rs – E(R))2) + (pr x (Rr – E(R))2)
Once you solve for s2 in the above equation take the square root of the answer to solve for s.

Explanation / Answer

Probability Return Healthy (h) 0.4 30% Softens (s) 0.5 10% Recession ( r ) 0.1 -25% expected output = (.4 x 30 + .5 x 10 - .1 x 25)/(.4 + .5 + .1) = 14.5 %

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