Answer: The fund's performance has been consistently improving year over year

## Explanation Let's analyze each statement: **Given returns:** +7.0%, +15.0%, +20.0%, +5.0%, +18.0% ### Statement A: Arithmetic average return is 13.0% - Calculation: (7 + 15 + 20 + 5 + 18) / 5 = 65 / 5 = 13.0% - **TRUE** ### Statement B: Geometric average return is 12.9% - Calculation: [(1.07 × 1.15 × 1.20 × 1.05 × 1.18)^(1/5) - 1] × 100 - (1.07 × 1.15) = 1.2305 - (1.2305 × 1.20) = 1.4766 - (1.4766 × 1.05) = 1.55043 - (1.55043 × 1.18) = 1.8295 - (1.8295)^(1/5) = 1.129 - Geometric return = (1.129 - 1) × 100 = 12.9% - **TRUE** ### Statement C: Volatility (standard deviation) is 6.5% - Mean = 13% - Deviations: (7-13)=-6, (15-13)=2, (20-13)=7, (5-13)=-8, (18-13)=5 - Squared deviations: 36, 4, 49, 64, 25 - Sum of squared deviations = 178 - Variance = 178 / (5-1) = 44.5 - Standard deviation = √44.5 ≈ 6.67% ≈ 6.5% - **TRUE** ### Statement D: The fund's performance has been consistently improving year over year - Returns: 7% → 15% → 20% → 5% → 18% - The sequence shows: 15% > 7% (improvement), 20% > 15% (improvement), but 5% < 20% (decline), then 18% > 5% (improvement) - There is a decline from 20% to 5% in year 4 - **FALSE** - Performance did not consistently improve ### Statement E: The fund has achieved positive returns in all five years - All returns are positive: 7%, 15%, 20%, 5%, 18% - **TRUE** ### Statement F: Cumulative return over five years is approximately 83.2% - Cumulative return = (1.07 × 1.15 × 1.20 × 1.05 × 1.18 - 1) × 100 - = (1.8295 - 1) × 100 = 82.95% ≈ 83.2% - **TRUE** **Therefore, Statement D is the false statement.**

Author: LeetQuiz .