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CFA Level I · Study Guide

Quantitative Methods

6-9% of exam11 modulesChallenging
Overview

Quantitative Methods covers the mathematical and statistical toolkit used across all CFA disciplines. At Level I the focus is time value of money (TVM), descriptive statistics, probability theory, and an introduction to hypothesis testing and simple linear regression. Questions tend to be calculation-heavy but formula-driven, making this one of the most reliably learnable topics once the formulas are memorised.

Key Formulas

The formulas that appear most often

Future Value (lump sum)
FV = PV × (1 + r)ⁿ
r = periodic rate; n = number of compounding periods
Present Value (lump sum)
PV = FV / (1 + r)ⁿ
Present Value of Perpetuity
PV = CF / r
Growing perpetuity: PV = CF₁ / (r − g)
Effective Annual Rate (EAR)
EAR = (1 + r_stated/m)^m − 1
m = compounding periods per year; continuous: EAR = e^r_stated − 1
Variance of a two-asset portfolio
σ²_p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov(R₁,R₂)
Cov(R₁,R₂) = ρ₁₂ × σ₁ × σ₂
Confidence interval for the mean
x̄ ± z_(α/2) × (σ/√n)
Use t-distribution when σ unknown and/or n < 30; z = 1.645 (90%), 1.96 (95%), 2.576 (99%)
Coefficient of Variation (CV)
CV = σ / μ
Relative dispersion measure; useful for comparing investments with different means
Bayes' Theorem
P(A|B) = [P(B|A) × P(A)] / P(B)
High-Yield Exam Areas

What actually gets tested

1

TVM with the financial calculator: set P/Y and C/Y correctly for every problem. The most common errors are sign errors (PV and FV must have opposite signs) and failing to clear the calculator between problems.

2

Hypothesis testing: know the four steps (state hypothesis, select significance level, identify test statistic, decision rule). Type I error = rejecting a true null (α); Type II error = failing to reject a false null (β).

3

Normal distribution properties: 68-95-99.7 rule. Know the z-scores for the four most common confidence intervals.

4

Sampling distributions: the central limit theorem states that sample means are approximately normally distributed for n ≥ 30 regardless of the population distribution.

Common Mistakes

Where candidates lose marks

Using nominal rates when periodic rates are required — always convert: r_periodic = r_annual / m before entering into TVM formulas.

Confusing the Roy's Safety-First ratio (SFR = [E(R_p) − R_T] / σ_p) with the Sharpe ratio — SFR uses a threshold return, not the risk-free rate.

Treating kurtosis of 3 as "excess kurtosis of 3" — excess kurtosis is kurtosis minus 3, so a normal distribution has excess kurtosis of zero.

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