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Up53
A portfolio manager has a tight tracking error of 50 basis points. The manager expects to be within this tracking error for a given quarter 85% of the time. If that expectation is correct and each quarter is independent, the probability that the manager is within the tracking error for at least 7 of the next 8 quarters is closest to:
- 35%
- 65%
- 75%
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Up13
We will use a binomial distribution with p = 0.85 and n = 10. We want to calculate:
Pr(X >= 7) = Pr(X = 7) + Pr(X = 8)
Pr(X = 7) = (8 choose 7) * (0.85)^7 * (1 – 0.85)^(8 – 7) = 0.3847
Pr(X = 8) = (8 choose 8) * (0.85)^8 * (1 – 0.85)^(8 – 8) = 0.2725
Pr(X >= 7) = 0.3847 + 0.2725 = 0.6572 -
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