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IAI Actuarial Core Principles · Economic Modelling · Measures of investment risk

Returns on a fund have mean 8% and standard deviation 12% and are assumed normally distributed. A new fund has returns equal to 2 + 1.5 times the old fund's return (in percent), with no other randomness. What are the new fund's mean and variance (percent squared)?

The mean becomes 2 + 1.5 × 8 = 14%. Variance becomes 1.5 squared times 144, which is 324, since a constant shift does not alter variance but a multiplier scales it by its square. The standard deviation is 18%.

  1. AMean 14%, variance 324Correct
  2. BMean 14%, variance 216
  3. CMean 10%, variance 324
  4. DMean 14%, variance 144
  5. Mean 10%, variance 216

Explanation

Mean = 2+1.5*8 = 14. Variance scales by the square of the multiplier and ignores the constant: 1.5^2*144 = 324. Using 1.5*144 = 216 is the mistake of not squaring the multiplier. Adding the constant does not change variance.

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