If Quant feels like a pile of formulas with no logic behind them, you’re not alone. Almost every candidate feels this way at the start. This guide to CFA Level 1 Quantitative Methods puts every important formula in one place, with a simple note on when to use it. Think of it as a CFA Level 1 cheat sheet you can open before a practice session, not a textbook you have to survive. And since these are CFA Level 1 formulas, we’ll keep the explanations short and the examples simple.

What Is CFA Level 1 Quantitative Methods?

CFA Level 1 Quantitative Methods is the part of the curriculum that teaches the maths and statistics behind investing: time value of money, return and risk measures, probability, hypothesis testing and simple regression. CFA Institute weights it at 6–9% of the 180-question exam, which works out to roughly 11–16 questions.

That looks small, but here’s the catch. CFA quantitative methods skills show up everywhere else. Time value of money powers bond pricing and dividend discount models. Statistics powers portfolio risk. If you’re solid here, Fixed Income, Equity and Portfolio Management all feel easier. You can check the official weights in the CFA Institute Level I topic outline.

How to Use This Formula Sheet for CFA Level 1

Don’t try to memorise everything in one sitting. Read one learning module (LM) at a time, then solve a few questions on it straight away. If you want more material alongside this page, The Capstones Learning free resources are a good place to start. And if you’re still choosing what to study from, our CFA Level 1 study material guide will help.

Formula Sheet CFA Level 1: Module by Module

LM1: Rates and Returns

Geometric mean return = [(1 + R1)(1 + R2)…(1 + Rn)]^(1/n) − 1. Use it for compounded growth over several periods.
Harmonic mean = N ÷ Σ(1/Xi). Think of it as the average price when you invest the same rupee amount each period.
Effective annual rate (EAR) = (1 + periodic rate)^m − 1
Leveraged return = Rp + (VB ÷ VE)(Rp − rD)

For the same dataset, arithmetic mean ≥ geometric mean ≥ harmonic mean. Examiners love this.

LM2: The Time Value of Money in Finance

Future value = PV × (1 + r/m)^(m × N)
PV of an ordinary annuity = PMT × [1 − (1 + r)^−N] ÷ r
PV of a perpetuity = PMT ÷ r
Constant-growth value = D1 ÷ (r − g), valid only when r > g

Calculator tip: clear your TVM registers (2nd + CLR TVM) before every new problem. CFA Institute allows the TI BA II Plus and the HP 12C, so practise on one of them.

LM3: Statistical Measures of Asset Return

Sample variance = Σ(x − x̄)² ÷ (n − 1)
Population variance = Σ(x − μ)² ÷ N
Coefficient of variation = s ÷ x̄ (risk per unit of average return)
Mean absolute deviation = Σ|x − x̄| ÷ n

LM4: Probability Trees and Conditional Expectations

Addition rule: P(A or B) = P(A) + P(B) − P(AB)
Multiplication rule: P(AB) = P(A|B) × P(B)
Expected value: E(X) = ΣP(Xi) × Xi
Bayes’ formula: P(A|B) = [P(B|A) ÷ P(B)] × P(A)

LM5: Portfolio Mathematics

Portfolio return: E(Rp) = Σ wi × E(Ri)
Two-asset variance: wA²σA² + wB²σB² + 2·wA·wB·ρ·σA·σB
Correlation: Cov(A, B) ÷ (σA × σB)
Roy’s safety-first ratio: [E(Rp) − RL] ÷ σp. Pick the portfolio with the higher ratio.

LM6–7: Simulation Methods, Estimation and Inference

Normal distribution: about 68% of values fall within ±1σ, 90% within ±1.65σ, 95% within ±1.96σ and 99% within ±2.58σ.
Lognormal distribution: it can’t go below zero, so it suits asset prices, not returns.
Standard error of the sample mean = s ÷ √n
Central limit theorem: for large samples (n ≥ 30), the sample mean is approximately normal.

LM8–9: Hypothesis Testing and Tests of Independence

Confidence interval = x̄ ± critical value × (s ÷ √n)
t-statistic = (x̄ − μ0) ÷ (s ÷ √n)
Chi-square (single variance) = (n − 1)s² ÷ σ0²
F-statistic = s1² ÷ s2² (larger variance on top)
Test of correlation: t = r√(n − 2) ÷ √(1 − r²)
Spearman rank correlation = 1 − [6Σd² ÷ n(n² − 1)]

LM10: Simple Linear Regression

Model: Y = b0 + b1X + ε
R² = SSR ÷ SST (share of variation explained)
SST = SSR + SSE
Standard error of estimate = √[SSE ÷ (n − 2)]
F-statistic = MSR ÷ MSE

LM11 (Big Data Techniques) is conceptual, so there are no formulas to learn. A clean read-through is enough.

Z-Test or T-Test: Which One Do You Use?

Use a z-test when the population variance is known. When it is unknown, use a t-test, especially for small samples (n < 30). With large samples and an unknown variance, a t-test or a z-test is generally acceptable. The t-distribution has fatter tails, which accounts for the extra uncertainty.

Situation	Test to Use
Mean, variance known	z-test
Mean, variance unknown	t-test
Difference between two means (independent)	Pooled t-test
Difference between two means (paired)	Paired t-test
One variance	Chi-square test
Two variances	F-test
Correlation	t-test for correlation

Which CFA Quantitative Methods Formulas Matter Most?

If your time is short, spend it here first:

Time value of money (PV, FV, annuities)
Sample variance and standard deviation
Expected value and portfolio variance
t-statistic and confidence intervals
R² and the regression F-test

This is where the most practical questions come from, and these formulas feed into other topics too.

Common Formula Mistakes (and How to Avoid Them)

Mixing up n and n − 1. Sample variance uses n − 1. Population variance uses N.
Using the arithmetic mean for multi-year growth. Use the geometric mean.
Forgetting r > g in the constant-growth model. If it isn’t true, the formula doesn’t work.
Confusing Type I and Type II errors. Type I means rejecting a true null. Type II means failing to reject a false one.
Calculator sign errors. Cash outflows are negative, inflows positive. A negative PV when you expect a positive one is a clue.

Don't Just Memorise: Understand Where Formulas Come From

Here’s the honest truth: memorised formulas fade under exam pressure, and understood ones don’t. That’s the approach followed in The Capstone Learnings’ CFA classes, where Prof. Vinit Mehta teaches that formulas are constructed, not memorised. Classes run in both Hinglish and English. You also get thousands of question-bank problems, AI-backed mock tests, and one-to-one doubt-clearing sessions, so every formula gets tested the way the exam tests it. The Capstone Learning app lets you tag important concepts and come back to them before the exam, which is handy for a topic like Quant.

Short on time before the November exam? The CFA Level 1 2026 exam-focused lectures are available at just ₹999.

What Students Say

Devaansh Gupta credits the logical, practical teaching for helping him score above the 90th percentile in CFA Level 1.
Atharva Dixit also passed Level 1 above the 90th percentile and describes Vinit sir as knowledgeable about the logic behind even small details.
Siddhesh Salunke says the focus on the “how” and “why” behind concepts, instead of textbook memorisation, improved his learning.
Pushti Shah says the patient explanations made a complex subject accessible.

Final Thoughts

CFA Level 1 Quantitative Methods feels heavy at first, but once you see why each formula exists, it stops feeling like memory work. Keep this sheet handy, practise a little every day, and check yourself with questions.

If you’d like expert guidance with it, The Capstone Learnings offers live online classes, recorded lectures with two-year access, and an offline batch in Mumbai, plus a free demo session. Visit capstonelearnings.com to book one and start your CFA prep the right way.

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CFA Level 1 Quantitative Methods Cheat Sheet: Key Formulas