Free CFA Quantitative Methods Practice Questions & Answers
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Question 901
A pair of features with correlation near zero are:
Select an option first.
Correct answer: A — Weakly related
Explanation: Why A is right: Near‑zero correlation indicates little linear relationship. Why others are wrong: B: Opposite. C/D: Not necessarily true.
Question 902
A feature that is strongly correlated with the target but also with many other features may:
Select an option first.
Correct answer: A — Cause multicollinearity
Explanation: Why A is right: Strong correlations across features create instability in models. Why others are wrong: B/C/D: Not necessarily true.
Question 903
A distance metric that works well for binary data is:
Select an option first.
Correct answer: A — Hamming distance
Explanation: Why A is right: Hamming distance counts mismatches in binary vectors. Why others are wrong: B/C: Numeric distances. D: Measures angle, not mismatches.
Question 904
Cosine similarity is most useful when:
Select an option first.
Correct answer: A — Direction matters more than magnitude
Explanation: Why A is right: Cosine similarity measures angle between vectors. Why others are wrong: B: Euclidean distance is better. C: Use Hamming. D: Not applicable.
Question 905
Which of the following best defines an interest rate (or yield)?
Select an option first.
Correct answer: B — A rate of return that reflects the relationship between cash flows occurring at different points in time
Explanation: ✔ Why correct: An interest rate (or yield) is a rate of return that reflects the relationship between differently dated (timed) cash flows. It allows us to compare money today with money in the future by adjusting for time. ✘ Why others wrong: A — Describes an annuity or coupon payment, not an interest rate. C — Interest rates are used to discount both inflows and outflows, not only inflows. D — This describes a holding period return, not an interest rate.
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Which of the following statements best describes one of the three ways interest rates can be interpreted?
Select an option first.
Correct answer: C — Interest rates can be viewed as required rates of return, discount rates, or opportunity costs
Explanation: ✔ Why correct: Interest rates can be understood in three distinct but related ways: As required rates of return — the minimum return an investor demands As discount rates — used to convert future cash flows into present value As opportunity costs — the value investors give up by choosing one option over another This captures the full conceptual framework. ✘ Why others wrong: A — Interest rates reflect minimum required returns, not maximum possible returns. B — Interest rates are used for both discounting and compounding, not just future value calculations. D — This describes a holding period return, not an interest rate.
Question 907
Which of the following best defines opportunity cost in the context of interest rates?
Select an option first.
Correct answer: B — The value an investor forgoes by choosing one investment alternative over another
Explanation: ✔ Why correct: Opportunity cost represents the value investors give up by choosing one course of action instead of the next best alternative. In the context of interest rates, it reflects the return an investor could have earned elsewhere. ✘ Why others wrong: A — This describes the risk-free rate, not opportunity cost. C — This is the definition of a required rate of return. D — This describes a discount rate, which is one interpretation of interest rates but not opportunity cost itself.
Question 908
Which of the following best describes the components that make up a nominal interest rate?
Select an option first.
Correct answer: B — Real risk-free rate plus inflation premium, default risk premium, liquidity premium, and maturity premium
Explanation: ✔ Why correct: A nominal interest rate is composed of the real risk-free interest rate plus several risk premiums that compensate investors for bearing different types of risk. The full expression is: This captures all required components. ✘ Why others wrong: A — Missing default, liquidity, and maturity premiums. C — Missing inflation and maturity premiums. D — Market risk premium applies to equity (CAPM), not interest rates; reinvestment risk premium is not part of this decomposition.
Question 909
Which of the following best describes the real risk‑free interest rate?
Select an option first.
Correct answer: B — The single-period interest rate on a completely risk-free security assuming zero expected inflation
Explanation: ✘ Why others wrong: A is the inflation premium. C refers to default and liquidity premiums. D includes maturity risk, which is not part of the real risk-free rate.
Question 910
The inflation premium in an interest rate primarily compensates investors for?
Select an option first.
Correct answer: B — The reduction in purchasing power expected over the maturity of the debt
Explanation: The inflation premium compensates for the expected erosion of purchasing power over the life of the loan. Default risk is covered by the default risk premium, illiquidity by the liquidity premium and maturity by the maturity premium.
Question 911
What does the default risk premium compensate investors for?
Select an option first.
Correct answer: B
Question 912
Which of the following best describes the liquidity premium?
Select an option first.
Correct answer: B — Compensation for the risk that an investment cannot be sold quickly without a price concession
Explanation: The liquidity premium compensates for the possibility that the holder cannot sell quickly without accepting a discount to fair value. It is separate from the risk that the borrower fails to pay.
Question 913
The maturity premium compensates investors for which type of risk?
Select an option first.
Correct answer: C — The increased sensitivity of a bond’s price to interest rate changes as maturity increases
Explanation: Longer maturity bonds are more sensitive to a given change in interest rates, so investors demand a maturity premium for bearing that greater price volatility.
Question 914
A corporate bond is trading at a yield of 7.2%. The real risk-free rate is 1.0%, expected inflation is 2.5%, and the bond carries premiums for default risk, liquidity risk, and maturity risk. Which of the following most accurately explains what the additional premiums beyond the real risk-free rate and inflation premium represent?
Select an option first.
Correct answer: B — Compensation for default risk, liquidity risk, and the increased interest-rate sensitivity associated with longer maturities
Explanation: ✘ Why others wrong: A — Inflation uncertainty is only one component (inflation premium). C — This describes the inflation premium alone. D — Time value of money is captured by the real risk-free rate, not the additional premiums.
Question 915
Which component of an interest rate compensates investors for expected changes in purchasing power?
Select an option first.
Correct answer: B — Inflation premium
Explanation: ✔ Why correct: The inflation premium offsets the expected decline in purchasing power due to rising prices. Why the others are wrong: A reflects time preference, not inflation. C compensates for non-payment risk. D compensates for difficulty selling the asset.
Question 916
The real risk-free rate is best described as the return:
Select an option first.
Correct answer: B — On a riskless security assuming zero inflation
Explanation: ✔ Why correct: It is the pure time-value-of-money rate with no inflation and no risk. Why the others are wrong: A is the inflation premium. C is the default risk premium. D includes maturity risk.
Question 917
A bond with high sensitivity to interest-rate changes must have a high:
Select an option first.
Correct answer: A — Maturity premium
Explanation: ✔ Why correct: Interest-rate sensitivity increases with maturity → higher maturity premium. Why the others are wrong: B relates to credit risk. C relates to trading difficulty. D relates to expected inflation.
Question 918
Which premium is most likely zero for U.S. Treasury bills?
Select an option first.
Correct answer: D — Liquidity premium
Explanation: ✔ Why correct: T-bills are extremely liquid; no liquidity premium is needed. Why the others are wrong: A inflation still applies. B Treasuries are default-free, but this is already assumed. C Short maturities → small but not zero.
Question 919
A corporate bond trades infrequently and has a wide bid-ask spread. Which premium is most affected?
Select an option first.
Correct answer: A — Liquidity premium
Explanation: ✔ Why correct: Illiquid bonds require compensation for potential price concessions. Why the others are wrong: B unrelated to trading frequency. C economy-wide, not security-specific. D depends on maturity, not liquidity.
Question 920
The default risk premium is most closely related to:
Select an option first.
Correct answer: A — The probability of non-payment
Explanation: ✔ Why correct: Default risk premium compensates for the chance the borrower fails to pay. Why the others are wrong: B inflation premium. C liquidity premium. D maturity premium.
Question 921
If expected inflation increases, which component of the nominal rate must increase?
Select an option first.
Correct answer: B — Inflation premium
Explanation: ✔ Why correct: Higher expected inflation → higher inflation premium. Why the others are wrong: A unrelated to inflation. C credit-related. D market-structure-related.
Question 922
A long-term bond will generally have a higher yield than a short-term bond primarily because of:
Select an option first.
Correct answer: C — Maturity premium
Explanation: ✔ Why correct: Longer maturities → more interest-rate sensitivity → higher maturity premium. Why the others are wrong: A Treasuries have no default risk. B Treasuries are liquid. D Inflation affects both long and short maturities.
Question 923
Which component of interest rates is most likely identical for all borrowers in the same currency?
Select an option first.
Correct answer: C — Real risk-free rate
Explanation: ✔ Why correct: The real risk-free rate is market-wide and not borrower-specific. Why the others are wrong: A varies by credit quality. B varies by security. D varies by maturity.
Question 924
A bond’s yield increases because the issuer’s credit rating was downgraded. Which component increased?
Select an option first.
Correct answer: B — Default risk premium
Explanation: ✔ Why correct: Lower credit rating → higher probability of default → higher default premium. Why the others are wrong: A inflation unchanged. C maturity unchanged. D economy-wide, not issuer-specific.
Question 925
Which premium compensates investors for the risk of selling below fair value?
Select an option first.
Correct answer: B — Liquidity premium
Explanation: ✔ Why correct: Liquidity premium covers the risk of price concessions when selling quickly. Why the others are wrong: A non-payment risk. C purchasing power risk. D interest-rate sensitivity.
Question 926
A nominal interest rate of 9% includes a real risk-free rate of 2%, inflation premium of 3%, and liquidity premium of 1%. The remaining 3% most likely represents:
Select an option first.
Correct answer: A — Default and maturity premiums
Explanation: ✔ Why correct: 2 + 3 + 1 = 6 → remaining 3% = default + maturity premiums. Why the others are wrong: B already part of inflation premium. C included in real risk-free rate. D applies to equities, not bonds.
Question 927
Which of the following is most likely to increase the liquidity premium of a bond?
Select an option first.
Correct answer: C — Lower market depth
Explanation: ✔ Why correct: Low market depth → harder to sell → higher liquidity premium. Why the others are wrong: A increases liquidity. B indicates liquidity. D affects default risk, not liquidity.
Question 928
The inflation premium is most closely related to:
Select an option first.
Correct answer: A — Expected future price levels
Explanation: ✔ Why correct: Inflation premium compensates for expected increases in price levels. Why the others are wrong: B default risk. C liquidity risk. D maturity risk.
Question 929
A bond with a long maturity and poor liquidity will likely have:
Select an option first.
Correct answer: C — High maturity and liquidity premiums
Explanation: ✔ Why correct: Long maturity → high maturity premium Why the others are wrong: A ignores liquidity. B ignores maturity. D inflation applies to all nominal rates.
Question 930
Which component of interest rates compensates for the pure time value of money?
Select an option first.
Correct answer: A — Real risk-free rate
Explanation: ✔ Why correct: The real risk-free rate reflects time preference for current vs future consumption. Why the others are wrong: B inflation. C credit risk. D interest-rate sensitivity.
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