CFA CFA Level 1 Quantitative Methods

Quantitative Methods

  • This topic has 1 reply, 2 voices, and was last updated Dec-20 by fp92.
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    • pcunniff
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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

    • fp92
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      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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