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Quantitative Methods & Statistics Flashcards

7 cards from real CFA practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. A portfolio has an arithmetic mean return of 12% and a geometric mean return of 11.3%. Which statement best explains the difference?

    Answer: The arithmetic mean ignores compounding effects and thus overstates long-run growth

    The arithmetic mean overstates long-run growth because it does not account for the compounding drag caused by return volatility.

  2. When testing H₀: μ = 50 against H₁: μ ≠ 50 at the 5% significance level, a two-tailed z-test yields z = 1.85. What is the correct conclusion?

    Answer: Fail to reject H₀ because 1.85 < 1.96

    For a two-tailed test at 5% significance, the critical z-value is ±1.96, and since 1.85 < 1.96 we fail to reject H₀.

  3. An analyst calculates a 95% confidence interval for a population mean as [8.2%, 11.8%]. Which interpretation is correct?

    Answer: If the sampling procedure were repeated many times, 95% of such intervals would contain the true mean

    A confidence interval is a frequentist statement: 95% of identically constructed intervals from repeated samples would capture the true population mean.

  4. Which probability distribution is most appropriate for modeling the number of credit defaults occurring in a bond portfolio over one year, assuming defaults are independent and have a constant probability?

    Answer: Binomial distribution

    The binomial distribution models the number of successes (defaults) in a fixed number of independent Bernoulli trials with constant probability.

  5. A covariance matrix shows Cov(X,Y) = 0. What can be concluded about X and Y?

    Answer: X and Y have no linear relationship

    Zero covariance indicates no linear relationship, but X and Y could still have a nonlinear dependence.

  6. The continuously compounded equivalent of a 10% effective annual rate is closest to:

    Answer: 9.53%

    The continuously compounded rate is ln(1.10) ≈ 9.53%, derived from the relationship e^r = 1 + EAR.

  7. Roy's Safety-First criterion selects the portfolio that:

    Answer: Minimizes the probability of falling below a specified threshold return

    Roy's Safety-First criterion chooses the portfolio with the highest ratio (E[Rp] − RL)/σp, which minimizes the probability of return falling below the threshold RL.