Quantitative Methods - Quantitative Methods Section 1

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46. An analyst computes the geometric mean of a portfolio that has yearly returns of: -8%, 2%, -4%, 7%, and 12%. The geometric mean computed by the analyst is closest to:

  • Option : A
  • Explanation : Geometric mean= RG=[(1 + R1)(1 + R2)…(1 + Rn)] /n – 1
    Geometric Mean=[(1-0.08)*(1+0.02*(1-0.04)*(1+0.07)*(1+.12)]/15-1=1.5%
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47. Considering the following set of numbers (which have been arranged in ascending order)

39    40414141
43    48535555

  • Option : B
  • Explanation : The mode is the most frequent value in the set of items and thus is equal to 41. The mean is the average value from the set of items and is computed as follows: Mean = Sum of observations / Number of observations = 456 / 10 = 45.6 The median is the value of the middle item of a set of items. For even number of observations, the median is equal to the average of the middle two values. The median is thus the average of 41 and 43. Median = 42. Therefore, the median is smaller than the mean but larger than the mode.
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48. The following ten observations are a sample drawn from a normal population: 24, 5, 12, 6, -3, 11, 18, 15, -4, and 29. The mean of the sample is closest to:

  • Option : A
  • Explanation : The sum of the ten numbers is 113. Dividing by 10 gives the mean of 11.30.
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49. Over the past five years, a portfolio gave returns of 18%, 12% -5%, -10% and 7%. The geometric mean return of the portfolio over the five year period is closest to:

  • Option : A
  • Explanation : Add one to each of the given returns, then multiply them together, then take the fifth root of the resulting product. 1.18 × 1.12 × 0.95 × 0.90 × 1.07 = 1.209066. 1.209066 raised to the 0.20 power is 1.0387. Subtracting one and multiplying by 100 gives the correct geometric mean return of 3.87%.
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50. A portfolio has the following annual returns: 5%, 11%, -6%, 0%. The geometric mean across the four-year period is closest to:

  • Option : A
  • Explanation : The geometric mean return is calculated as = [(1 + 0.05) × (1 + 0.11) × (1 − 0.06) × (1 + 0.00)]0.25 − 1 = 0.0231 ~ 2.3%
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