Compute the standard deviation given these four economic states, their likelihoods, and the potential returns: Economic State
Probability
Return
Fast Growth
0)40
50%
Slow Growth
0)40
10%
Recession
0)10
-10%
Depression
0)10
-5%
A)6.71 percent
B)22.5 percent
C)23.37 percent
D)52.20 percent

Question

Quizplus · Accepted Answer

To compute the standard deviation, we first need to calculate the expected return for each state by multiplying the probability and return. Then, we can use these expected returns to find the variance and take the square root to get the standard deviation.

Expected Return:
Fast Growth: 0.5 * 40 = 20
Slow Growth: 0.1 * 40 = 4
Recession: 0.1 * (-10) = -1
Depression: 0.1 * (-5) = -0.5

Variance:
[(50-20)^2*0.4 + (10-4)^2*0.4 + (-10+1)^2*0.1 + (-5+0.5)^2*0.1] = 482.9

Standard Deviation:
sqrt(482.9) = 23.37%

Therefore, the best choice is C.

Compute the Standard Deviation Given These Four Economic States, Their