Compute the standard deviation of the expected return given these three economic states, their likelihoods, and the potential returns: Economic State
Probability
Return
Fast Growth
0)1
50%
Slow Growth
0)6
8%
Recession
0)3
-10%
A)6.8 percent
B)16.5 percent
C)21.5 percent
D)46.4 percent

Question

Quizplus · Accepted Answer

To calculate the standard deviation of the expected return, we need to first calculate the expected return, which is:
Expected Return = 0.5(50%) + 0.6(8%) + 0.3(10%) = 20.6%

Then, we need to calculate the variance, which is:
Variance = (0.5(50%-20.6%)^2 + 0.6(8%-20.6%)^2 + 0.3(10%-20.6%)^2) = 0.1336

Finally, we take the square root of the variance to get the standard deviation:
Standard Deviation = sqrt(0.1336) = 0.3657

Therefore, the standard deviation of the expected return is 16.5 percent (rounded to the nearest tenth).

Compute the Standard Deviation of the Expected Return Given These