Compute the expected return and standard deviation given these four economic states,their likelihoods,and the potential returns:

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

Compute the expected return and standard deviation given these four economic states,their likelihoods,and the potential returns:

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

Quizplus · Accepted Answer

To compute the expected return, we multiply the potential return of each state by its likelihood and sum up the products:

Expected Return = (0.25 x 7%) + (0.35 x 9%) + (0.30 x 12%) + (0.10 x 18%)
                = 1.75% + 3.15% + 3.60% + 1.80%
                = 9.3%

To compute the standard deviation, we first need to find the variance of the returns. To do this, we square each potential return, multiply it by its likelihood, subtract the squared expected return, and sum up the products:

Variance = (0.25 x (7% - 9.3%)^2) + (0.35 x (9% - 9.3%)^2) 
         + (0.30 x (12% - 9.3%)^2) + (0.10 x (18% - 9.3%)^2)
         = 0.008975

The standard deviation is the square root of the variance:

Standard Deviation = sqrt(0.008975)
                   = 0.0948

Therefore, the answer is A) 9.5 percent; 32.43 percent, as it has the highest expected return and a moderate level of risk.

Compute the Expected Return and Standard Deviation Given These Four