Overview
Quantitative Methods provides the mathematical and statistical foundations used throughout the CFA curriculum. Concepts introduced here — time value of money, probability, regression — recur in Fixed Income, Equity, and Portfolio Management. Mastering this section pays dividends across the entire exam.
Time Value of Money
The time value of money (TVM) is the core principle that a dollar today is worth more than a dollar in the future because of its earning potential. Key calculations include:
- Future Value (FV): FV = PV × (1 + r)^n
- Present Value (PV): PV = FV / (1 + r)^n
- Annuities: A series of equal cash flows at regular intervals — both ordinary annuities (end of period) and annuities due (beginning of period)
- Perpetuities: PV = PMT / r
Exam questions frequently test your ability to solve for any one of the five TVM variables: N, I/Y, PV, PMT, FV.
Statistical Concepts
Measures of Central Tendency
- Mean (arithmetic): Simple average of observations
- Median: Middle value in a sorted dataset; preferred when data contains outliers
- Mode: Most frequently occurring value
- Geometric mean: Used for compounding returns: G = [(1+R₁)(1+R₂)···(1+Rₙ)]^(1/n) − 1
Measures of Dispersion
- Variance: Average of squared deviations from the mean
- Standard deviation: Square root of variance; same units as the data
- Coefficient of variation (CV): σ / μ — relative risk per unit of return
Probability
Probability theory covers:
- Joint probability: P(A and B) = P(A|B) × P(B) for dependent events
- Total probability rule: P(A) = Σ P(A|Bᵢ)P(Bᵢ)
- Bayes’ formula: Updates a prior probability given new information
Understand the distinction between unconditional, conditional, and joint probabilities. Venn diagrams and probability trees are useful visualization tools.
Common Distributions
- Uniform distribution: All outcomes equally likely
- Normal distribution: Symmetric, bell-shaped; fully described by μ and σ
- Lognormal distribution: Used for asset prices (cannot be negative)
- Student’s t-distribution: Used when population variance is unknown; heavier tails than normal
Hypothesis Testing
A hypothesis test evaluates whether a sample provides enough evidence to reject a null hypothesis (H₀) at a chosen significance level (α). Key concepts:
- Type I error: Rejecting a true null (probability = α)
- Type II error: Failing to reject a false null (probability = β)
- p-value: Smallest α at which H₀ would be rejected
- Test statistics: z-statistic (known variance), t-statistic (unknown variance)