FRM Part II · FRM Exam Part II · Portfolio Performance Evaluation
A fund has a value of 100 at the start of Year 1. It earns 20% in Year 1 and loses 10% in Year 2, with no cash flows. What is the time-weighted (geometric) annualized return over the two years?
The geometric annualized return is 3.92%. Compounding 20% and -10% gives 1.08 over two years, and the square root of 1.08 minus one is about 3.92%. The 5% arithmetic average overstates growth because it ignores volatility drag.
- A5.00%
- B3.92%Correct
- C4.00%
- D8.00%
Explanation
Growth factor = 1.20 x 0.90 = 1.08. Annualized = sqrt(1.08) - 1 = 3.92%. The arithmetic mean of 5% ignores compounding and overstates the realized annual growth.
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