Practice quiz · by a Quizcard user

CFA Level I - Quantitative Methods Glossary — quiz

30 multiple-choice questions covering Unbiased Estimator, Confidence Interval, Survivorship Bias, Standardization (z-score), Median. One answer each; you get a score at the end and the explanation for every question. No account needed.

Updated 2026-10-24. Keys 1–4 pick an answer, Enter moves on. Redo it any time, in order or shuffled.

The questions

Answers and explanations are shown after you finish.

1. Unbiased Estimator

   A portfolio manager wants to construct a confidence interval for the expected return of a stock. Which of the following must be true for the sample mean to be an unbiased estimator of the population mean?

   • The sample must come from a normally distributed population
   • The sample standard deviation must be smaller than the population standard deviation
   • The expected value of the sample mean equals the true population parameter
   • The sample size must be at least 30 observations
2. Confidence Interval

   A researcher calculates a 95% confidence interval for bond yields as [4.2%, 4.8%]. What is the most accurate interpretation?

   • If we repeat sampling many times, approximately 95% of such intervals would contain the true population parameter
   • The true population mean is equal to 4.5% with 95% certainty
   • The probability that the true yield lies in this interval is 95%
   • We are 95% confident that the sample mean yield is between 4.2% and 4.8%
3. Survivorship Bias

   An analyst notices that including only mutual funds still trading (excluding closed funds) biases her performance analysis upward. This is an example of which type of bias?

   • Look-ahead bias
   • Data snooping bias
   • Time-period bias
   • Survivorship bias
4. Standardization (z-score)

   A stock's daily returns are normally distributed with mean 0.1% and standard deviation 1.5%. What is the z-score of a return of 2.2%?

   • 1.27
   • 2.00
   • 0.73
   • 1.40
5. Median

   A dataset of equity fund returns is strongly right-skewed with some extreme outliers. Which measure of central tendency is most resistant to these outliers?

   • Harmonic mean
   • Mode
   • Median
   • Arithmetic mean
6. Compound Annual Growth Rate (CAGR)

   A portfolio has annualized returns of 8%, 12%, 5%, and −3% over four years. What is the compound annual growth rate (CAGR)?

   • 5.25%
   • 6.07%
   • 5.50%
   • 6.98%
7. Student's t-Distribution

   Which statement correctly describes the relationship between degrees of freedom and the Student's t-distribution?

   • The t-distribution has heavier tails than the normal distribution only when df < 5
   • As degrees of freedom increase, the t-distribution approaches the normal distribution
   • Degrees of freedom always equal the sample size n, never n−1
   • As degrees of freedom increase, the t-distribution becomes increasingly right-skewed
8. Effective Annual Rate (EAR)

   A loan agreement specifies a nominal annual rate of 8% compounded quarterly. What is the effective annual rate (EAR)?

   • 8.00%
   • 8.24%
   • 8.48%
   • 8.06%
9. p-Value

   A hypothesis test for a mean is conducted at the 5% significance level. The p-value from the test is 0.038. Which conclusion is correct?

   • Reject the null hypothesis and accept the alternative hypothesis
   • Fail to reject the null hypothesis because the p-value is greater than 0.05
   • The null hypothesis is definitely true
   • Fail to reject the null hypothesis because the p-value is less than 0.05
10. Paired t-Test

    A paired t-test is used to compare a stock's returns before and after a market event for 25 observations. What is the appropriate degrees of freedom?

    • 23
    • 24
    • 50
    • 25
11. Type I Error

    An analyst predicts that a fund's return will exceed the risk-free rate, but in reality the fund underperforms the risk-free rate. This is an example of which type of error?

    • Type II error
    • Standard error
    • Sampling error
    • Type I error
12. Skewness

    A distribution exhibits positive (right) skewness of 1.5. Which of the following is most likely true?

    • The mean is less than the median, which is less than the mode
    • The standard deviation is larger than the variance
    • The mean, median, and mode are all equal
    • The mode is less than the median, which is less than the mean
13. Perpetuity

    An investment promises $100 per year forever, with the first payment one year from now, and the discount rate is 5%. What is the present value?

    • $1,000
    • $2,500
    • $5,000
    • $2,000
14. Independent Events

    Which combination of events is possible?

    • All of the above are impossible
    • Two mutually exclusive events that are also independent
    • Two events that are both independent and mutually exclusive unless one has zero probability
    • Two independent events that are also mutually exclusive
15. Combination (nCr)

    How many different ways can a portfolio manager select 3 stocks from a list of 8 stocks when the order of selection does not matter?

    • 336
    • 56
    • 512
    • 24
16. Chi-Square Distribution

    A risk manager uses the chi-square distribution to test whether sample variance differs from a hypothesized population variance. Which property of the chi-square distribution is relevant?

    • It is right-skewed and bounded below by zero
    • It approaches the t-distribution as degrees of freedom increase
    • It is symmetric around zero like the normal distribution
    • It has an undefined mean for df > 2
17. Simple Interest

    An investment of $1,000 earns simple interest at 6% per year for 5 years. What is the future value?

    • $1,300.00
    • $1,300.91
    • $1,190.00
    • $1,338.23
18. Continuous Uniform Distribution

    A continuous uniform distribution is defined on the interval [10, 30]. What is the probability that a randomly selected value lies between 15 and 25?

    • 0.75
    • 0.25
    • 1.00
    • 0.50
19. Binomial Distribution

    A random variable follows a binomial distribution with n = 10 and p = 0.4. What is the expected value?

    • 2.0
    • 4.0
    • 6.0
    • 2.4
20. Sample Variance

    Which statement correctly describes the relationship between sample variance s² and population variance σ²?

    • Sample variance divides by n−1 because there are n−1 independent deviations from the mean
    • Sample variance divides by n−1 to correct for bias and provide an unbiased estimator
    • Sample variance always equals population variance in large samples
    • Sample variance divides by n, making it an unbiased estimator of population variance
21. Bonferroni Correction

    An analyst tests multiple hypotheses (say, 5 independent tests) on the same dataset, each at α = 0.05. Without correction, what is the probability of making at least one Type I error across all tests?

    • 0.05
    • 0.50
    • 0.0025
    • 0.23
22. Standardization (z-score)

    A stock return of −2% occurs when the mean return is 1.5% and the standard deviation is 2%. Using the standard normal table after standardization, would this return be considered unusual?

    • No, because negative returns are common in stocks
    • Yes, because the return is below the mean
    • Yes, because the z-score is negative
    • No, because the z-score of −1.75 falls within ±2 standard deviations, a typical range
23. Two-Tailed Test

    A researcher conducts a two-tailed hypothesis test for the mean at α = 0.05. The critical values for the test statistic are ±1.96 (from a large sample z-test). In which scenario is the null hypothesis rejected?

    • When the calculated test statistic equals 1.90
    • When the calculated test statistic equals −1.80
    • When the calculated test statistic equals 1.50
    • When the calculated test statistic equals 2.10
24. Confidence Interval

    An analyst constructs a confidence interval and observes that increasing the sample size narrows the interval. Which component of the interval is directly reduced?

    • The point estimate
    • The margin of error (reliability factor × standard error)
    • The degrees of freedom
    • The significance level α
25. A Priori Probability

    A multinomial experiment involves drawing cards from a deck with replacement. The event 'draw a heart' has a priori probability 0.25. This method of assigning probability is justified because:

    • It uses subjective expert judgment about card decks
    • It reflects the observed frequency of hearts in a large sample
    • It is based on historical data from past card draws
    • It relies on logical reasoning about the structure of a standard deck
26. Time-Series Data

    A dataset contains quarterly GDP figures for a country over 20 years. This type of data is best classified as:

    • Panel data
    • Time-series data
    • Unstructured data
    • Cross-sectional data
27. Ordinal Data

    A credit analyst uses star ratings (1 to 5 stars) to classify bond funds. This rating system represents which type of data?

    • Ordinal categorical data
    • Discrete numerical data
    • Nominal categorical data
    • Continuous numerical data
28. Rule of 72

    Using the Rule of 72, approximately how long does it take an investment to double at an annual rate of 9%?

    • 72 years
    • 9.0 years
    • 8.0 years
    • 7.2 years
29. Geometric Mean Return

    A portfolio's returns over three years are 10%, −5%, and 15%. The arithmetic mean return is 6.67%, but the geometric mean return is:

    • Equal to 6.67%
    • Greater than 6.67%
    • Undefined for returns with negative values
    • Less than 6.67%
30. Multivariate Normal Distribution

    A multivariate normal distribution describes the joint behavior of three asset returns. Which parameter is NOT required to fully specify this distribution?

    • The variance of each of the three assets
    • The skewness of each asset's marginal distribution
    • The correlation between each pair of assets
    • The mean return of each of the three assets