Compute the standard deviation given these four economic states, their likelihoods, and the potential returns: Economic State
Probability
Return
Fast Growth
0)35
40%
Slow Growth
0)45
10%
Recession
0)10
-10%
Depression
0)10
-100%
A)7.5 percent
B)12.65 percent
C)39.48 percent
D)113.69 percent

Question

Quizplus · Accepted Answer

To compute the standard deviation, first calculate the expected return: (0.35*40) + (0.45*10) + (0.10*-10) + (0.10*-100) = 7.5%. Then, calculate the variance: (0.35*(40-7.5)^2) + (0.45*(10-7.5)^2) + (0.10*(-10-7.5)^2) + (0.10*(-100-7.5)^2) = 1559.25. The standard deviation is the square root of the variance, which is approximately 39.48%.

Compute the Standard Deviation Given These Four Economic States, Their