The key Quantitative Methods formulas and decision rules for 2026, module by module. Quantitative Methods is 6-9% of the Level I exam.
Free to read, no sign-up. A revision companion to use alongside your curriculum or prep provider. The full sheet (60 concepts, 43 formulas, 14 decision rules) is in the study dashboard.
The ones to know cold before exam day.
Where: r = interest rate per period, n = number of periods
Open the lessonWhere: X̄ = sample mean, n-1 for Bessel correction
Open the lessonWhere: zα/2 = critical value for confidence level
Open the lessonKey concepts and formulas from each of the 11 Quantitative Methods modules. Open a module for its lesson page, or the dashboard for the full sheet.
Nominal rate = Real risk-free rate + Inflation premium + Default risk premium + Liquidity premium + Maturity premium.
Total return earned from holding an asset over a single period, including price change and income.
Arithmetic mean is the simple average of returns; geometric mean accounts for compounding. Geometric ≤ Arithmetic always.
Used for averaging ratios like P/E or dollar-cost averaging. Always ≤ Geometric mean ≤ Arithmetic mean.
IRR of all cash flows; sensitive to timing and size of external cash flows. Reflects investor experience.
Geometric mean of sub-period returns; not affected by external cash flows. Reflects manager performance.
r<sub>cc</sub> = ln(1 + HPR). Allows additive compounding across time periods.
Gross = before management fees; Net = after all fees. Pre-tax vs after-tax returns also critical.
Where: P0 = beginning price, P1 = ending price, D1 = income/dividend
Where: Ri = return in period i, n = number of periods
Where: n = number of observations, Xi = individual values
Where: c = number of periods per year
Where: ln = natural logarithm
Where: π = inflation rate
Use when:
Avoid when:
Use when:
Avoid when:
The current worth of a future cash flow discounted at the appropriate rate. Foundation of all valuation.
The value of a current amount after earning interest over a specified period.
Where: r = interest rate per period, n = number of periods
Where: r = discount rate, n = periods
Full sheet: 7 concepts · 7 formulas · 2 decision rules
Mean (arithmetic, geometric, harmonic), median (middle value, robust to outliers), mode (most frequent).
Quartiles divide data into 4 parts, quintiles into 5, deciles into 10, percentiles into 100.
Where: μ = population mean, N = population size
Where: X̄ = sample mean, n-1 for Bessel correction
Full sheet: 7 concepts · 6 formulas · 2 decision rules
E(X) = Σ P(x<sub>i</sub>) × x<sub>i</sub>. The probability-weighted average of all possible outcomes.
P(A|B) = P(AB) / P(B). The probability of A given that B has occurred.
Where: P(xi) = probability of outcome i
Where: P(B) = prior, P(B|A) = posterior
Full sheet: 6 concepts · 4 formulas · 1 decision rules
E(R<sub>p</sub>) = Σ w<sub>i</sub> E(R<sub>i</sub>). Weighted average of individual expected returns.
σ²<sub>p</sub> = w²<sub>1</sub>σ²<sub>1</sub> + w²<sub>2</sub>σ²<sub>2</sub> + 2w<sub>1</sub>w<sub>2</sub>Cov(1,2). Key: correlation drives diversification benefit.
Where: w = weights, ρ = correlation, σ = standard deviation
Where: ρ = correlation coefficient
Full sheet: 5 concepts · 4 formulas · 1 decision rules
If ln(X) is normally distributed, X follows a lognormal distribution. Bounded below by 0 — natural for asset prices.
If r<sub>cc</sub> is normally distributed, then the price relative (1+R) is lognormally distributed.
Where: rcc = continuously compounded return, T = time
Where: ln = natural logarithm
Full sheet: 4 concepts · 2 formulas · 1 decision rules
Every member of the population has an equal probability of being selected. Foundation of statistical inference.
Divide population into subgroups (strata), then sample from each. Ensures representation of all groups.
Where: σ = population SD, n = sample size
Where: zα/2 = critical value for confidence level
Full sheet: 5 concepts · 3 formulas · 1 decision rules
H<sub>0</sub>: status quo (what we try to reject). H<sub>a</sub>: what we want to prove. We never "accept" H<sub>0</sub>, only fail to reject.
Type I (α): reject true H<sub>0</sub> (false positive). Type II (β): fail to reject false H<sub>0</sub> (false negative). Power = 1 - β.
Where: μ0 = hypothesized mean
Where: For independent samples
Full sheet: 5 concepts · 3 formulas · 1 decision rules
Tests whether population correlation ρ = 0. t = r√(n-2) / √(1-r²) with df = n-2.
Non-parametric alternative. Ranks data, then calculates correlation of ranks. Robust to outliers and non-linearity.
Where: r = sample correlation, df = n-2
Where: O = observed frequency, E = expected frequency
Full sheet: 3 concepts · 3 formulas · 1 decision rules
Ŷ = b<sub>0</sub> + b<sub>1</sub>X. b<sub>0</sub> = intercept, b<sub>1</sub> = slope (change in Y per unit change in X).
Coefficient of determination = proportion of Y's variation explained by X. R² = correlation². Range: 0 to 1.
Where: OLS estimator
Where: Regression line passes through (X̄, Ȳ)
Full sheet: 5 concepts · 5 formulas · 1 decision rules
Volume (large amount), Velocity (speed of generation), Variety (structured/unstructured), Veracity (reliability).
Supervised: labeled data (classification, regression). Unsupervised: no labels (clustering, dimensionality reduction). Reinforcement: reward-based learning.
Full sheet: 5 concepts · 1 decision rules
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