CFA Drill · Original study notes · Educational only, not advice · Updated 31 August 2026

Quantitative Methods: timing is the whole question

Most Level I quantitative misses are not “forgot the formula.” They are a wrong clock: end-of-period versus beginning, nominal versus effective, sample versus population, one-sided versus two-sided. CFA Drill items are original. They reuse standard identities so you can rebuild the number after you pick A/B/C.

1. Time value of money checklist

1. Draw the cash-flow timeline before touching a calculator.
2. Label whether payments are ordinary (end) or due (beginning).
3. Convert nominal rates to the rate that matches the payment frequency.
4. Confirm n counts periods, not “years” when compounding is monthly.

Ordinary annuity present value (payments at end of each period, first payment one period from now):

PV = C × [1 − (1+r)⁻ⁿ] / r

Annuity due: multiply that PV by (1+r), or treat as one cash flow today plus an ordinary annuity of n−1 payments.

2. Effective rates without hand-waving

If a bank quotes 12% compounded monthly, the monthly rate is 1%, and the effective annual rate is (1.01)¹² − 1, not 12%. Mixing EAR and APR is one of the most common Quant traps in our bank. When a stem gives you two quotes, convert both to the same basis before comparing.

3. Descriptive statistics: which average?

Means are pulled by outliers; medians are not. Geometric means matter for multi-period growth. Variance and standard deviation answer “how spread out,” not “how high.” If an item asks which measure is least sensitive to extreme observations, think median or trimmed approaches—not the arithmetic mean of a skewed sample.

4. Probability and expected value

Write events before numbers. Mutually exclusive versus independent changes how you combine probabilities. Expected value is a probability-weighted average of outcomes—not the “most likely” outcome alone. Covariance and correlation describe co-movement; correlation is scaled, covariance is not.

5. Hypothesis testing without theater

State H₀, choose a statistic, compare to a critical value or p-value. “Fail to reject” is not “prove true.” If a stem gives a t-stat and a two-sided 5% critical value, do not invent a one-sided story to save a favorite conclusion. Type I error is rejecting a true null; Type II is failing to reject a false null—know which the examiner is asking about.

6. Regression basics for Level I

Slope is the typical change in Y for a one-unit change in X in the estimated linear model. Intercept is the fitted Y when X = 0—which may or may not be economically meaningful. R² measures in-sample fit, not permission to forecast. Omitting a variable that belongs in the model can bias coefficients; adding irrelevant variables can dilute precision.

7. Sampling and estimation (Level I intuition)

A sample statistic estimates a population parameter. Confidence intervals widen when samples are small or volatility is high. Do not confuse a 95% confidence interval with “95% probability the next observation falls inside.” Read the claim the stem is actually making before picking a letter.

Central limit theorem intuition: averages of many independent draws become more normal-looking under broad conditions. That does not mean every raw dataset is Gaussian, and it does not excuse ignoring dependence in returns.

8. Common calculator discipline

• Clear TVM registers between problems.
• Match P/Y and compounding to the stem.
• Watch sign conventions on PV/PMT/FV—pick one convention and stick to it for the item.
• If the answer is exactly the undiscounted sum, you probably forgot discounting.

9. Practice rhythm

Attempt first (method), then open the reverse panel for the identity that was actually used—TVM clock, test type, or regression interpretation. Open the app. Related: study guide, Ethics, FSA.