# Expected return and standard deviation

ROE Distributions (i.e. Calculating Expected Value and Standard Deviation)

Here are the estimated ROE distributions for firms A, B, and C (see attachment)

a. Calculate the expected value and standard deviation for Firm C'c ROE> ROE(A) = 10.0%, o(A) = 5.5%; ROE(B) = 12.0%, o(B) = 7.7%

b. Discuss the relative riskiness of the three firms' returns. (Assume that these distribution are expected to remain constant over time).

c. Now suppose all three firms have the same standard deviation of basic earning power (EBIT/Total assets), o(A) = o(B) = o© = 5.5%. What can we tell about the financial risk of each firm?

Here are the estimated ROE distributions for firms A, B, and C:

Probability

0.1 0.2 0.4 0.2 0.1

Firm A: ROE(A) 0.0% 5.0% 10.0% 15.0% 20.0%

Firm B: ROE(B) (2.0) 5.0 12.0 19.0 26.0

Firm C: ROE(C) (5.0) 5.0 15.0 25.0 35.0

a. Calculate the expected value and standard deviation for Firm C'c ROE>

ROE(A) = 10.0%, o(A) = 5.5%; ROE(B) = 12.0%, o(B) = 7.7%

b. Discuss the relative riskiness of the three firms' returns. (Assume that these distribution are expected to remain constant over time.)

c. Now suppose all three firms have the same standard deviation of basic earning power (EBIT/Total assets), o(A) = o(B) = o( C ) = 5.5%.

What can we tell about the financial risk of each firm?

https://brainmass.com/business/return-on-equity/expected-return-standard-deviation-29541

#### Solution Preview

See attached file for complete answers.

a. Calculate the expected vallue and standard deviation for Firm C'c ROE>

ROE(A) = 10.0%, o(A) = 5.5%; ROE(B) = 12.0%, o(B) = 7.7%

Probability ROE ( C ) Prob x ROE Prob x (ROE - Expected)^2

0.1 -5.00% -0.50% 0.004

0.2 5.00% 1.00% 0.002

0.4 15.00% 6.00% 0

0.2 25.00% 5.00% 0.002

0.1 35.00% 3.50% 0.004

Expected Value= Total= 15.00% Variance= 0.012

Standard deviation =square ...

#### Solution Summary

The expected return and standard deviation (risk) for ROE distribution has been calculated.