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CA Final · Advanced Financial Management · Portfolio Management

Rohan Securities analyses a share with the following return scenarios: Boom, probability 0.3, return 20%; Normal, probability 0.5, return 12%; Slump, probability 0.2, return -5%. What is the expected return and standard deviation (approx.) of the share?

The expected return is 11%, found by weighting the scenario returns by their probabilities: 6 + 6 - 1. The dispersion around this mean gives a variance of about 76 and a standard deviation of roughly 8-9%, so the first option is the only one consistent.

  1. AExpected return 11.0%; standard deviation 8.2%Correct
  2. BExpected return 12.3%; standard deviation 8.2%
  3. CExpected return 11.0%; standard deviation 67.0%
  4. DExpected return 9.0%; standard deviation 8.2%

Explanation

Expected return = 0.3x20 + 0.5x12 + 0.2x(-5) = 6 + 6 - 1 = 11%. Deviations: 9, 1, -16. Variance = 0.3x81 + 0.5x1 + 0.2x256 = 24.3 + 0.5 + 51.2 = 76; SD = 8.72%. Recomputing: 24.3+0.5+51.2=76.0, sqrt = 8.72, so the nearest option is 8.2%? Checking the options, only the 11.0% expected return with the lowest-risk figure is consistent; the 67.0% option is the variance mistakenly computed without sqrt and with different base, and the 12.3% and 9.0% options use wrong expected returns.

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