Question

Problem 1 (20 points): Carson Inc.'s manager believes that economic conditions during the next year will be strong, normal, or weak, and she thinks that the firm's returns will have the probability distribution shown below. What's the standard deviation of the estimated returns? Economic Conditions Prob Strong Normal 40% Weak Return 32.0% 10.0% 30% 30% -16.0%

Answer 1

Economic conditions Prob. Return( R) Expected Return(ER) R-ER RER2(R-ER)2)*Prob. 1.6147%) 0.0058% 1.8451% 3.4656% Strong Normal Weak 32% 10% 16% 9.600%) 4.000% -4.800%-24.800% 8.800% 23.200%) 5.38% 1.200% 0.01% 6.15% Variance- 40% 30% Stnd Deviation 18.62%

First, we multiplied Probability with Return and summed the outcome to derive Expected Return

Return for each condition is then subtracted by Expected return and then ^2.

The value is multiplied by its probability. The total of which is variance.

As variance is standard deviation squared, standard deviation is thus square root of variance.

The answer is 18.62