Compute the expected return and standard deviation given these four economic states, their likelihoods, and the potential returns: Economic State
Probability
Return
Fast Growth
0)20
60%
Slow Growth
0)50
13%
Recession
0)15
-15%
Depression
0)15
-45%
A)9.5 percent; 32.43 percent
B)9.5 percent; 21.96 percent
C)9.5 percent; 18.97 percent
D)9.5 percent; 29.18 percent

Question

Quizplus · Accepted Answer

The expected return is the weighted average of the returns, where the weights are the probabilities of each state. The expected return is 0.20 * 60% + 0.50 * 13% + 0.15 * (-15%) + 0.15 * (-45%) = 9.5%. The standard deviation is the square root of the variance, which is the weighted average of the squared deviations from the expected return. The variance is 0.20 * (60% - 9.5%)^2 + 0.50 * (13% - 9.5%)^2 + 0.15 * (-15% - 9.5%)^2 + 0.15 * (-45% - 9.5%)^2 = 828.45. The standard deviation is therefore sqrt(828.45) = 28.78%.

Compute the Expected Return and Standard Deviation Given These Four