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FRM Part I · FRM Exam Part I · Fundamentals of Probability

A portfolio manager models the annual return R of a fund with E[R] = 6% and standard deviation 10%. The fund's payoff in dollars on a 2,000,000 investment, after a fixed fee of 20,000, is Y = 2,000,000 x R - 20,000. What is the standard deviation of Y?

The standard deviation of Y is 200,000. Adding or subtracting a constant, such as the fee, leaves dispersion unchanged, while multiplying by 2,000,000 scales the standard deviation by that factor: 2,000,000 x 10% = 200,000.

  1. A200,000Correct
  2. B220,000
  3. C180,000
  4. D40,000,000,000

Explanation

A constant subtracted does not change dispersion, so SD(Y) = 2,000,000 x 0.10 = 200,000. The 220,000 option wrongly adds the fee; 180,000 subtracts it. The 40,000,000,000 figure is the variance (200,000 squared), not the standard deviation.

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