HKSI Paper 12 Basic theoretical aspects of portfolio management question: geometric (compound) average annual return

Answer: C. 7.49%

Geometric average = [(1 + r1)(1 + r2)(1 + r3)]^(1/3) − 1 = (1.20 × 0.90 × 1.15)^(1/3) − 1 = 1.242^(1/3) − 1 = 7.49%. It is the constant yearly rate that turns HK$1 into the same HK$1.242 over three years. The arithmetic average, (20 − 10 + 15) ÷ 3 = 8.33%, ignores compounding and overstates the growth achieved. 24.20% is the cumulative three-year return, and dividing it by three (8.07%) still ignores compounding. Source: Standard investment mathematics: arithmetic and geometric average returns (as at October 2026).