Explore BrainMass
Share

Explore BrainMass

    Expected return and standard deviation

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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?

    © BrainMass Inc. brainmass.com October 9, 2019, 4:20 pm ad1c9bdddf
    https://brainmass.com/business/return-on-equity/expected-return-standard-deviation-29541

    Attachments

    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.

    $2.19