IAI Actuarial Core Principles · Economic Modelling · Measures of investment risk
Over 5 years a portfolio's annual active returns relative to its benchmark were: +2%, -1%, +3%, 0% and +1%. Using the sample standard deviation (divisor n-1), what is the tracking error, to two decimal places?
The tracking error is 1.58%. The mean active return is 1%, the sum of squared deviations is 10, the sample variance is 10/4 = 2.5, and its square root is about 1.58%. Dividing by n instead would wrongly give 1.41%.
- A1.00%
- B1.58%Correct
- C1.41%
- D1.79%
- 2.00%
Explanation
Mean = (2-1+3+0+1)/5 = 1. Deviations: 1, -2, 2, -1, 0; squares: 1+4+4+1+0 = 10. Sample variance = 10/4 = 2.5, so the standard deviation = 1.58%. Using divisor n gives variance 2, i.e. 1.41%, which is the wrong divisor.
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