After some study of the economy, your forecast for next year is that a boom econ

Question

After some study of the economy, your forecast for next year is that a boom economy has a 30% chance of occurring, a neutral economy 50%, and a bust economy a 20% chance of occurring. You also estimate that a certain stock would have a return of 34% in a boom economy next year, 15% in a neutral economy , and -14% in a bust economy. The risk-free rate is 4.4%. What is the standard deviation of expected returns for this stock next year?

Risk-Free Rate = 4.4%

Probability Return Boom Economy 30% 34% Neutral Economy 50% 15% Bust Economy 20% -14%

Explanation / Answer

Expected return is probability weighted sum of return in all three conditions:
(0.3*34)+(0.5*15)+(0.2*-14)=14.9% or 0.149

As per caclulation Standard deviation = 16.63% rounded off to two decimals

Probability Return Deviation from Mean Variance Prob*Variance Boom 0.3 34.00% 19.10% 0.036481 0.0109443 Neutral 0.5 15.00% 0.10% 0.000001 0.0000005 Bust 0.2 -14.00% -28.90% 0.083521 0.0167042 Expected return ( mean) 0.149 Variance 0.027649 Standard deviation 16.628%

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