CFA Quantitative Methods
Past Questions
20+ verified Quantitative Methods past questions for CFA. Step-by-step worked answers in 5 Nigerian languages.
Quantitative Methods topics (2)
Sample Quantitative Methods past questions
1. Time value of money implies:
- A. Money grows over time at interest
- B. Money loses utility
- C. Time = money is false
- D. Cash is worthless
Answer: A
2. Standard deviation measures:
- A. Mean
- B. Dispersion
- C. Skew only
- D. Mode
Answer: B
AI Explanation
**The reasoning** Standard deviation tells you **how spread out** your data is from the average (mean). That's what "dispersion" means—the scatter or variability in your dataset. Imagine two classes both scored an average of 60% in a test. In Class A, most students got between 55-65%. In Class B, scores ranged from 20-95%. Both have the same mean, but Class B has much **higher dispersion**—the scores are scattered far from the average. Standard deviation would be small for Class A and large for Class B. The formula √[Σ(x - x̄)²/n] literally measures how far each value (x) deviates from the mean (x̄), then averages those deviations. It's a **dispersion measure**, pure and simple. **Why the wrong options tempt you** - **A (Mean)**: You might confuse this because standard deviation *uses* the mean in its calculation, but it doesn't measure the mean itself. - **C (Skew only)**: Skewness is different—it measures asymmetry, not spread. - **D (Mode)**: Mode is the most frequent value; totally unrelated. **Quick takeaway** Standard deviation = how scattered your data is around the average—always remember: **dispersion = spread**.
3. The present value of money decreases as the discount rate:
- A. Decreases
- B. Increases
- C. Stays constant
- D. Becomes zero
Answer: B
4. The future value of money increases with a higher:
- A. Time only
- B. Interest rate
- C. Inflation only
- D. Risk-free of zero
Answer: B
5. A higher correlation coefficient (closer to 1) means a ___ linear relationship.
- A. weaker
- B. stronger
- C. negative
- D. random
Answer: B
6. Compounding more frequently ___ the effective annual rate.
- A. lowers
- B. raises
- C. removes
- D. fixes
Answer: B
7. The time-value-of-money concept states that:
- A. Future money is worth more than present money
- B. Money received now is worth more than the same amount in the future
- C. Money is constant in value
- D. Inflation does not matter
Answer: B
AI Explanation
TVM core principle: $1 today > $1 tomorrow due to earning potential and inflation.
8. PV of $100 received in 1 year at 10% discount rate:
- A. $110.00
- B. $90.91
- C. $100.00
- D. $95.00
Answer: B
AI Explanation
PV = FV/(1+r)^n = 100/1.10 ≈ $90.91.
9. Effective annual rate of 12% compounded monthly is approximately:
- A. 12.00%
- B. 12.68%
- C. 13.00%
- D. 10.00%
Answer: B
AI Explanation
EAR = (1 + 0.12/12)^12 − 1 ≈ 12.68%.
10. Correlation coefficient ranges from:
- A. 0 to 1
- B. −1 to +1
- C. −10 to 10
- D. 0 to 100
Answer: B
AI Explanation
Correlation: −1 (perfect inverse), 0 (no relationship), +1 (perfect positive).
11. A null hypothesis (H₀) is typically:
- A. What the researcher is trying to prove
- B. The default assumption to be tested (no effect/no difference)
- C. Always false
- D. Always true
Answer: B
AI Explanation
H₀ states the no-effect/no-difference baseline; analyst tries to find evidence to reject it.
12. If p-value is 0.03 and significance level α = 0.05, we should:
- A. Fail to reject H₀
- B. Reject H₀ (significant at the 5% level)
- C. Accept H₀ definitively
- D. Test again
Answer: B
AI Explanation
p-value (0.03) < α (0.05) → reject H₀. Note: 'reject' doesn't mean 'prove false', just statistically significant.
13. Skewness in a return distribution measures:
- A. Sample size
- B. Asymmetry — left or right tail extension
- C. Mean
- D. Variance
Answer: B
AI Explanation
Positive skew = long right tail; negative skew = long left tail. Affects risk perception.
14. Kurtosis measures:
- A. Symmetry
- B. Tail thickness / extreme-value frequency
- C. Average
- D. Median
Answer: B
AI Explanation
Kurtosis describes tail risk. High kurtosis (leptokurtic) = fatter tails = more extreme outcomes.
15. A 95% confidence interval means:
- A. The estimate is 95% accurate
- B. If we repeated sampling many times, ~95% of CIs would contain the true parameter
- C. There's 95% chance of error
- D. 5% of the data is included
Answer: B
AI Explanation
Strict CI interpretation — relates to repeated-sampling coverage rate, not the probability the parameter lies in any single CI.
16. Annualised return of 1% per month is approximately:
- A. 12%
- B. 12.68%
- C. 14%
- D. 10%
Answer: B
AI Explanation
Compounded: (1.01)^12 − 1 ≈ 12.68%.
17. NPV decision rule:
- A. Reject if NPV > 0
- B. Accept if NPV > 0
- C. Reject if NPV = 0
- D. Always accept
Answer: B
AI Explanation
Positive NPV adds value to shareholders → accept the project.
18. IRR is the discount rate at which:
- A. NPV = 1
- B. NPV = 0
- C. PV = FV
- D. Profit = revenue
Answer: B
AI Explanation
IRR is the rate making NPV exactly zero. Accept if IRR > required rate of return.
19. Geometric mean is preferred over arithmetic mean for:
- A. One-period return
- B. Multi-period (compounding) return calculations
- C. Cross-section data only
- D. Forecasting
Answer: B
AI Explanation
Geometric mean accurately captures compounded growth over multiple periods; arithmetic mean overstates true CAGR.
20. The Sharpe ratio measures:
- A. Tax efficiency
- B. Excess return per unit of total risk (standard deviation)
- C. Beta
- D. Tracking error
Answer: B
AI Explanation
Sharpe Ratio = (Rp − Rf) / σp. Higher = better risk-adjusted return.
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