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CFA Level I · CFA Level I Exam · Returns of Financial Assets and Instruments

An investor buys a share at 50 at time 0. At the end of Year 1 the price is 60 and she buys one more share. At the end of Year 2 the price is 54 and she sells both shares. No dividends are paid. The annual time-weighted return is closest to:

The time-weighted return is about 3.9% per year, so 4.5% is the closest option. Link the yearly returns of 20% and -10% geometrically to get 1.08 over two years, then take the square root. Cash flows do not alter the yearly sub-period returns.

  1. A-1.0%
  2. B4.5%Correct
  3. C9.5%

Explanation

Year 1 return = 60/50 - 1 = 20%. Year 2 return = 54/60 - 1 = -10%. Geometric linking: 1.20 x 0.90 = 1.08, and 1.08^0.5 - 1 = 3.92%, which is closest to 4.5% among the options. The 9.5% figure comes from the arithmetic mean (5%) adjusted incorrectly, and -1.0% ignores the first year's gain.

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