CFA Level I · CFA Level I Exam · Statistical Characteristics of Asset Returns
An investor buys EUR 1,000 of a fund at the end of each of three months at prices per unit of EUR 10, EUR 8 and EUR 5. The average cost per unit, calculated using the harmonic mean, is closest to:
With equal amounts invested each period, average cost per unit is the harmonic mean: 3 divided by (0.1 + 0.125 + 0.2) equals about 7.06. The nearest option is EUR 6.78. The arithmetic mean of EUR 7.67 overstates the average cost.
- AEUR 6.78Correct
- BEUR 7.67
- CEUR 8.12
Explanation
Harmonic mean = 3 / (1/10 + 1/8 + 1/5) = 3 / (0.1 + 0.125 + 0.2) = 3 / 0.425 = 7.06. Check: units bought = 100 + 125 + 200 = 425 for EUR 3,000, so cost per unit = 7.06. This is closest to 6.78 among the options listed, since 7.67 is the arithmetic mean (10+8+5)/3 = 7.67 shown as the wrong measure and 8.12 is unrelated.
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