You’re on a roll
Create a free account to save your CFA progress, track your accuracy by topic, and pick up right where you left off.
Free Questions › CFA › Quantitative Methods
Free CFA Quantitative Methods Practice Questions & Answers
1,200 exam-style Quantitative Methods questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 961
The geometric mean return is always:
Select an option first.
Correct answer: C — Less than or equal to the arithmetic mean
Explanation: ✔ Why correct: Geometric ≤ arithmetic; equality only when returns have no variability.
Question 962
The difference between arithmetic and geometric means increases when:
Select an option first.
Correct answer: B — Variability in returns increases
Explanation: ✔ Why correct: More variability → larger gap between arithmetic and geometric means.
Question 963
The harmonic mean is most appropriate when averaging:
Select an option first.
Correct answer: B — Ratios such as price per share
Explanation: ✔ Why correct: Harmonic mean is used for averaging ratios like P/E or price per share.
Question 964
The harmonic mean is especially useful when:
Select an option first.
Correct answer: B — A fixed amount of money is invested periodically
Explanation: ✔ Why correct: Harmonic mean applies when a fixed dollar amount buys varying units (cost averaging).
Question 965
Cost averaging involves:
Select an option first.
Correct answer: B — Investing a fixed amount of money periodically
Explanation: ✔ Why correct: Cost averaging = fixed dollar amount invested regularly.
Get the full CFA question bank — free
Drop your email and we'll send you fresh CFA practice questions, fully worked solutions and exam-deadline reminders. No spam — unsubscribe in one click.
Want to save your score and take a full mock exam? Create a free account →
Question 966
When using cost averaging, the appropriate average price per share is:
Select an option first.
Correct answer: C — Harmonic mean
Explanation: ✔ Why correct: Harmonic mean correctly averages prices when a fixed amount buys varying shares.
Question 967
A multi-period return should NOT be calculated using:
Select an option first.
Correct answer: B — Arithmetic mean
Explanation: ✔ Why correct: Arithmetic mean does not reflect compounding over multiple periods.
Question 968
A single-period return is:
Select an option first.
Correct answer: C — Defined for any specified period
Explanation: ✔ Why correct: A single period can be any length.
Question 969
A capital gain occurs when:
Select an option first.
Correct answer: B — The asset price increases
Explanation: ✔ Why correct: Capital gain = price appreciation.
Question 970
A defined benefit pension plan provides returns through:
Select an option first.
Correct answer: B — Periodic income only
Explanation: ✔ Why correct: These plans pay periodic income to beneficiaries.
Question 971
The arithmetic mean return is most appropriate when:
Select an option first.
Correct answer: A — Forecasting future single-period returns
Explanation: ✔ Why correct: Arithmetic mean is best for estimating expected next-period returns.
Question 972
The harmonic mean will always be:
Select an option first.
Correct answer: B — Less than or equal to the geometric mean
Explanation: ✔ Why correct: Harmonic ≤ geometric ≤ arithmetic.
Question 973
The primary reason multiple return measures exist is because:
Select an option first.
Correct answer: B — Different measures apply to different types of data
Explanation: ✔ Why correct: Arithmetic, geometric, and harmonic means each apply to different situations.
Question 974
Which of the following correctly describes the relationship among the arithmetic mean (AM), geometric mean (GM), and harmonic mean (HM) for a set of positive numbers?
Select an option first.
Correct answer: B — AM × HM = (GM)²
Explanation: ✔ Why correct: The identity for positive data values is: Arithmetic Mean × Harmonic Mean = (Geometric Mean)² This relationship holds for any set of positive numbers and reflects the ordering: HM ≤ GM ≤ AM. Why the other options are wrong A — Incorrect rearrangement; GM is squared, not HM. C — No such identity exists; AM is always the largest of the three means. D — The three means are equal only when all observations are identical; otherwise they differ.
Question 975
The primary purpose of using a trimmed mean is to:
Select an option first.
Correct answer: B — Remove a percentage of extreme values before averaging
Explanation: ✔ Why correct: A trimmed mean removes a small percentage of the highest and lowest values before computing the mean. ✘ Why others wrong: A: That describes a winsorized mean. C: Trimmed means reduce outlier influence. D: Compounding relates to geometric mean.
Question 976
A winsorized mean differs from a trimmed mean because it:
Select an option first.
Correct answer: B — Replaces extreme values with the nearest remaining values
Explanation: ✔ Why correct: Winsorizing replaces extreme values rather than removing them. ✘ Why others wrong: A: That is trimming. C: Not necessarily 50%; trimming percentage varies. D: Means differ unless all values are identical.
Question 977
Gross return refers to the return:
Select an option first.
Correct answer: B — Before deducting management and administrative fees
Explanation: ✔ Why correct: Gross return is before management and administrative fees. ✘ Why others wrong: A: That is net return. C: Commissions are deducted in both gross and net returns. D: Taxes are unrelated to gross vs net.
Question 978
Net return refers to the return:
Select an option first.
Correct answer: B — After management and administrative fees
Explanation: ✔ Why correct: Net return = gross return minus management/administrative fees. ✘ Why others wrong: A: That is gross return. C: Taxes are separate from net return. D: Net return does not necessarily include taxes.
Question 979
Pretax nominal return refers to the return:
Select an option first.
Correct answer: B — Before taxes
Explanation: ✔ Why correct: Pretax nominal return is before taxes. ✘ Why others wrong: A: That is after-tax nominal return. C: Inflation adjustment gives real return. D: Fees are unrelated to tax status.
Question 980
After-tax nominal return refers to the return:
Select an option first.
Correct answer: B — After taxes
Explanation: ✔ Why correct: After-tax nominal return deducts tax liabilities. ✘ Why others wrong: A: Opposite of correct. C: Inflation adjustment gives real return. D: Fees are separate.
Question 981
Real return is defined as:
Select an option first.
Correct answer: B — Nominal return minus inflation
Explanation: ✔ Why correct: Real return adjusts nominal return for inflation. ✘ Why others wrong: A: Taxes are unrelated to real return. C: Fees relate to gross/net return. D: Taxes are not part of real return.
Question 982
The money-weighted return is most similar to:
Select an option first.
Correct answer: B — Internal rate of return (IRR)
Explanation: ✔ Why correct: Money-weighted return = IRR of cash flows. ✘ Why others wrong: A: Arithmetic mean ignores cash flows. C: Geometric mean ignores timing of cash flows. D: Harmonic mean applies to ratios.
Question 983
Money-weighted return accounts for:
Select an option first.
Correct answer: C — The timing and amount of cash flows
Explanation: ✔ Why correct: Money-weighted return incorporates cash inflows/outflows and their timing. ✘ Why others wrong: A & B: Both values matter, but not exclusively. D: Ignores cash flows.
Question 984
In the money-weighted return calculation, cash invested by the investor is treated as:
Select an option first.
Correct answer: B — A cash outflow
Explanation: ✔ Why correct: From the investor’s perspective, investing money is an outflow. ✘ Why others wrong: A: Inflows are withdrawals or ending value. C: Cash flows must be classified. D: Investment is not a return.
Question 985
A leveraged return occurs when:
Select an option first.
Correct answer: B — The investor’s return is a multiple of the underlying asset’s return
Explanation: ✔ Why correct: Leverage magnifies gains and losses relative to the underlying asset. ✘ Why others wrong: A: That is unleveraged return. C: Fees are irrelevant. D: Leverage increases risk.
Question 986
Leveraged returns arise in futures contracts because:
Select an option first.
Correct answer: B — Only a fraction of the underlying asset’s value is deposited
Explanation: ✔ Why correct: Margin requirements are small relative to underlying value → leverage. ✘ Why others wrong: A: Opposite of true. C: Futures involve significant risk. D: Futures do not pay interest.
Question 987
A winsorized mean is most useful when:
Select an option first.
Correct answer: B — You want to reduce outlier impact without removing data
Explanation: ✔ Why correct: Winsorizing keeps all data but caps extreme values. ✘ Why others wrong: A: That is trimming. C: Geometric mean handles compounding. D: Harmonic mean is used for cost averaging.
Question 988
A trimmed mean is most useful when:
Select an option first.
Correct answer: B — You want to remove extreme values
Explanation: ✔ Why correct: Trimmed mean removes extreme values before averaging. ✘ Why others wrong: A: That is winsorizing. C: Harmonic mean averages ratios. D: IRR relates to money-weighted return.
Question 989
Which return measure is most affected by the timing of cash flows?
Select an option first.
Correct answer: C — Money-weighted return
Explanation: ✔ Why correct: Money-weighted return incorporates timing of cash flows. ✘ Why others wrong: A & B: Ignore timing. D: Gross return is before fees, not timing-based.
Question 990
Which return measure is most appropriate for evaluating manager skill?
Select an option first.
Correct answer: B — Time-weighted return
Explanation: ✔ Why correct: Time-weighted return removes the effect of investor cash flows. ✘ Why others wrong: A: Influenced by investor timing. C: Fees irrelevant to skill. D: Leverage distorts skill measurement.
More free CFA topics
Economics2,066
Portfolio Management1,079
Fixed Income908
Financial Statement Analysis904
Corporate Issuers884
Portfolio Construction605
Alternative Investments540
Specialized Pathway - Private Markets500
Asset Allocation499
Derivatives498
Equity390
Performance Measurement295
Specialized Pathway - Portfolio Management253
Derivatives and Risk Management131
Ten questions in
- The ones you miss are saved as a drill you can repeat
- Your place is kept, on this device and any other
- A streak, if that is the thing that gets you back tomorrow
Every question on this page stays free and open either way.