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HKSI PrepStudyingPaper 1
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Mr Lee's portfolio grew from HK$800,000 to HK$1,064,800 over three years, with all income reinvested. What was its annualised return, compounded annually?
The holding period return is 1,064,800 ÷ 800,000 − 1 = 33.10%. Annualised with annual compounding: (1.331)^(1/3) − 1 = 10.00%, since 1.10 × 1.10 × 1.10 = 1.331. Dividing 33.10% by three gives 11.03%, which ignores compounding and overstates the yearly rate. 9.53% is the continuously compounded rate, ln(1.331) ÷ 3, not the annually compounded rate asked for. 33.10% is the three-year return before annualising. Source: Standard investment mathematics: annualised (compound) return (as at October 2026).
Dividing a multi-year holding period return by the number of years instead of taking the nth root.
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