CFA CFA Level 1 Quantitative Methods

# Quantitative Methods

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Anyone know how to solve this on a calc for NcR?

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:

(A) 35 % ✘

(B) 65 %

(C) 75 %

Explanation:

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

• Hi @pcunniff – there’s the nCr function in BA II Plus calculators on top of the “+” sign.

So for “8 choose 7”, i.e. 8C7, here are the keystrokes which should get you the answer 8: 8 [2ND] [+] 7 =

For “8 choose 8”, i.e. 8C8, the answer is 1 (without the need to do the calculations), because there is only 1 way to choose 8 items out of 8. But just in case the keystrokes here follow the same principle (which should give you 1): 8 [2ND] [+] 8 =

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