Free CFA Quantitative Methods Practice Questions & Answers
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Question 1111
Spurious correlation can arise when:
Select an option first.
Correct answer: A — Two variables are unrelated but both depend on a third variable
Explanation: ✔ Why correct: Shared dependence on a third variable can create false correlation.
Question 1112
Dividing two unrelated variables by a common variable may:
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Correct answer: B — Induce spurious correlation
Explanation: ✔ Why correct: Dividing by a common variable can artificially increase correlation.
Question 1113
Correlation of 1 means:
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Correct answer: A — Perfect positive linear relationship
Explanation: ✔ Why correct: Correlation of +1 means variables move together perfectly.
Question 1114
Correlation of −1 means:
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Correct answer: B — Perfect inverse relationship
Explanation: ✔ Why correct: −1 means perfect negative linear relationship.
Question 1115
A correlation of 0.85 between two sectors suggests:
Select an option first.
Correct answer: A — Strong positive linear relationship
Explanation: ✔ Why correct: 0.85 is close to +1, indicating strong positive linear movement.
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A scatter plot showing no visible pattern indicates:
Select an option first.
Correct answer: C — No linear correlation
Explanation: ✔ Why correct: Random scatter suggests no linear relationship.
Question 1119
Investment strategies based solely on high correlations may fail because:
Select an option first.
Correct answer: B — Correlation may be spurious
Explanation: ✔ Why correct: Spurious correlations can mislead investors into false conclusions.
Question 1120
Variance of a random variable is best described as:
Select an option first.
Correct answer: B — The probability-weighted average of squared deviations from the mean
Explanation: ✔ Why correct: Variance = Σ p(x)·(x − E[x])², the probability-weighted squared deviations from the expected value.
Question 1121
Standard deviation is defined as:
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Correct answer: B — The square root of the variance
Explanation: ✔ Why correct: Standard deviation = √variance, providing dispersion in the same units as the original variable.
Question 1122
Bayes’ formula is primarily used to:
Select an option first.
Correct answer: B — Update prior probabilities when new information arrives
Explanation: ✔ Why correct: Bayes’ formula revises prior probabilities into posterior probabilities after observing new evidence.
Question 1123
In a probability tree, conditional probabilities are used to:
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Correct answer: B — Represent outcomes that depend on previous events
Explanation: ✔ Why correct: Conditional probabilities show how the probability of an event changes given that another event has occurred.
Question 1124
If the variance of returns is expressed in percent squared, the standard deviation of returns will be expressed in:
Select an option first.
Correct answer: A — Percent
Explanation: ✔ Why correct: Standard deviation is the square root of variance, so the units return to the original units — here, percent.
Question 1125
Mean–variance analysis holds exactly when:
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Correct answer: B — Investors are risk averse and returns are normally distributed or utility is quadratic
Explanation: ✔ Why correct: MPT’s mean–variance framework is exact when investors are risk averse and either returns are normally distributed or investors have quadratic utility.
Question 1126
Mean–variance analysis treats risk as:
Select an option first.
Correct answer: C — Symmetric deviations above and below the mean
Explanation: ✔ Why correct: Standard deviation treats upside and downside variability equally.
Question 1127
Shortfall risk refers to:
Select an option first.
Correct answer: B — The probability that returns fall below a minimum acceptable level
Explanation: ✔ Why correct: Shortfall risk measures the chance that portfolio value or return falls below a specified threshold.
Question 1128
Roy’s safety-first criterion selects the portfolio that:
Select an option first.
Correct answer: C — Minimizes the probability of falling below a threshold return
Explanation: ✔ Why correct: Roy’s rule chooses the portfolio with the lowest probability of breaching the minimum acceptable return.
Question 1129
Value at Risk (VaR) is best described as:
Select an option first.
Correct answer: B — The minimum expected loss at a given probability level over a time horizon
Explanation: ✔ Why correct: VaR gives the minimum loss expected at a specified confidence level (e.g., 5%) over a defined period.
Question 1130
A lognormal distribution is appropriate for modeling asset prices because:
Select an option first.
Correct answer: C — Asset prices are bounded below by zero and skewed right
Explanation: ✔ Why correct: Lognormal distributions cannot take negative values and have a long right tail, matching real-world asset price behavior.
Question 1131
A random variable is lognormally distributed if:
Select an option first.
Correct answer: B — The natural logarithm of the variable is normally distributed
Explanation: ✔ Why correct: By definition, a variable is lognormal when its natural log is normal.
Question 1132
A key property of the lognormal distribution is that it:
Select an option first.
Correct answer: C — Is bounded below by zero
Explanation: ✔ Why correct: Lognormal variables cannot fall below zero.
Question 1133
The assumption that returns are independently and identically distributed (i.i.d.) implies:
Select an option first.
Correct answer: C — Returns are unpredictable and have constant distributional properties
Explanation: ✔ Why correct: Independence means past returns do not predict future returns; identical distribution means constant mean and variance.
Question 1134
Volatility in finance typically refers to:
Select an option first.
Correct answer: B — The standard deviation of continuously compounded returns
Explanation: ✔ Why correct: Volatility is conventionally defined as the standard deviation of continuously compounded returns.
Question 1135
Volatility is usually expressed as:
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Correct answer: C — An annualized standard deviation
Explanation: ✔ Why correct: By convention, volatility is annualized.
Question 1136
Bootstrap resampling treats the observed sample as:
Select an option first.
Correct answer: B — The true population for simulation purposes
Explanation: ✔ Why correct: Bootstrap assumes the sample approximates the population and resamples from it with replacement.
Question 1137
Bootstrap resampling differs from Monte Carlo simulation because bootstrap:
Select an option first.
Correct answer: B — Uses the observed sample as the basis for resampling
Explanation: ✔ Why correct: Bootstrap draws repeated samples from the observed dataset.
Question 1138
Monte Carlo simulation requires the analyst to:
Select an option first.
Correct answer: B — Specify the probability distribution of each risk factor
Explanation: ✔ Why correct: Monte Carlo generates random values from assumed distributions.
Question 1139
Monte Carlo simulation is best described as:
Select an option first.
Correct answer: B — Generating random outcomes from specified probability distributions
Explanation: ✔ Why correct: Monte Carlo simulates outcomes by drawing from assumed distributions.
Question 1140
Resampling methods are used when:
Select an option first.
Correct answer: B — Only a sample is available and the population is unknown
Explanation: ✔ Why correct: Resampling approximates the population using the available sample.
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