A stock will have a loss of 11.5% in a bad economy, a return of 11.3% in a normal economy, and a return of 31% in a hot economy. There is a 29% probability of a bad economy, a 32% probability of a normal economy and a 39% probability of a hot economy. What is the variance of the stock's returns

Variance = 0.030096 or 3.0096% rounded off to 3.01%

Explanation:

To calculate the variance of the stock's returns, we first need to calculate the expected return on the stock. The expected return on the stock can be calculated by multiplying the stock return in each scenario by the probability of that scenario and taking a sum of the answers for each scenario.

Expected return of stock rE=  pA * rA  +  pB * rB  + ... + pN * rN

Where,

Expected return of stock rE = 0.29 * -0.115  +  0.32 * 0.113  +  0.39 * 0.31

Expected return of stock rE = 0.12371 or 12.371%

Variance = ∑ p * (r - rE)²

Variance = 0.29 * (-0.115 - 0.12371)^2  +  0.32 * (0.113 - 0.12371)^2  +  

0.39 * (0.31 - 0.12371)^2

Variance = 0.030096 or 3.0096% rounded off to 3.01%

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