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CFA Level 1 Formula Sheet: Every Key Formula You Need (2026)
How to use this page: This is a consolidated reference of the most important formulas across all 10 CFA Level 1 topics. Review it daily in the final two weeks before your exam. Don’t just memorize — make sure you understand what each formula measures and when to apply it. For context on any formula, follow the links to the relevant topic page.
Quantitative Methods
Rates and Returns
Holding Period Return
HPR = (P₁ − P₀ + D₁) / P₀
Geometric Mean Return
RG = [(1 + R₁)(1 + R₂)…(1 + Rn)]1/n − 1
Money-Weighted Return (IRR)
Solve for r: Σ [CFt / (1 + r)t] = 0
Money-weighted reflects the investor’s actual experience (affected by cash flow timing). Time-weighted reflects the manager’s skill (unaffected by cash flow timing). See Quantitative Methods.
Time Value of Money
Future Value
FV = PV × (1 + r)N
Present Value of a Perpetuity
PV = PMT / r
Present Value of a Growing Perpetuity
PV = PMT / (r − g)
Effective Annual Rate
EAR = (1 + r/m)m − 1
See Time Value of Money for full treatment.
Statistics and Probability
Coefficient of Variation
CV = σ / μ
Sharpe Ratio
S = (Rp − Rf) / σp
Bayes’ Formula
P(A|B) = [P(B|A) × P(A)] / P(B)
Standard Error of the Sample Mean
SE = σ / √n
Confidence Interval (z)
CI = x̄ ± zα/2 × (σ / √n)
Test Statistic (z-test)
z = (x̄ − μ₀) / (σ / √n)
See Probability Concepts and Hypothesis Testing.
Economics
Fiscal Multiplier
Multiplier = 1 / (1 − MPC × (1 − t))
Covered Interest Rate Parity
F / S = (1 + rprice) / (1 + rbase)
Forward Premium/Discount
Forward premium = (F − S) / S
See Economics for context on exchange rate calculations.
Financial Reporting & Analysis
Income Statement
Basic EPS
Basic EPS = (Net Income − Preferred Dividends) / Weighted Average Shares Outstanding
Diluted EPS (Treasury Stock Method for Options)
Additional shares = [(Market Price − Exercise Price) / Market Price] × Options Outstanding
Cash Flows
Free Cash Flow to the Firm (FCFF)
FCFF = CFO + Int(1 − t) − CapEx
Free Cash Flow to Equity (FCFE)
FCFE = CFO − CapEx + Net Borrowing
Ratios and Analysis
DuPont Analysis (3-Part)
ROE = Net Profit Margin × Asset Turnover × Financial Leverage
DuPont Analysis (5-Part)
ROE = (NI/EBT) × (EBT/EBIT) × (EBIT/Revenue) × (Revenue/Assets) × (Assets/Equity)
Current Ratio
Current Ratio = Current Assets / Current Liabilities
Quick Ratio
Quick Ratio = (Cash + Receivables + Short-term Investments) / Current Liabilities
Inventory Turnover
Inventory Turnover = COGS / Average Inventory
Receivables Turnover
Receivables Turnover = Revenue / Average Receivables
Interest Coverage
Interest Coverage = EBIT / Interest Expense
See Financial Reporting, Inventory Analysis, and Reporting Quality.
Corporate Issuers
Cash Conversion Cycle
CCC = DOH + DSO − DPO
Net Present Value
NPV = Σ [CFt / (1 + r)t] − Initial Investment
Weighted Average Cost of Capital
WACC = (E/V) × re + (D/V) × rd × (1 − t)
Cost of Equity (CAPM)
re = Rf + β × (E(Rm) − Rf)
Value of Levered Firm (MM with Taxes)
VL = VU + (t × D)
See Corporate Issuers, Cost of Capital, and Working Capital Management.
Equity Investments
Gordon Growth Model (Constant DDM)
V₀ = D₁ / (r − g)
Justified Trailing P/E
P₀/E₀ = (1 − b)(1 + g) / (r − g)
Justified Leading P/E
P₀/E₁ = (1 − b) / (r − g)
Sustainable Growth Rate
g = ROE × b (retention ratio)
Enterprise Value
EV = Market Cap + Total Debt − Cash
Preferred Stock Valuation (Perpetuity)
V₀ = D / r
See Equity Investments for DDM, multiples, and EV context.
Fixed Income
Bond Valuation
Bond Price (Flat)
P = Σ [C / (1 + r)t] + FV / (1 + r)N
Full (Dirty) Price
Full Price = Flat Price + Accrued Interest
Bond Pricing with Spot Rates
P = C/(1+s₁) + C/(1+s₂)² + … + (C+FV)/(1+sN)N
Yield Conversions
Semi-Annual to Annual Effective
EAY = (1 + semi-annual yield)² − 1
Forward Rate from Spot Rates
(1 + s2)² = (1 + s₁)(1 + f1,1)
Duration and Convexity
Modified Duration
ModDur = MacDur / (1 + YTM per period)
Price Change (Duration Only)
%ΔP ≈ −ModDur × ΔYield
Price Change (Duration + Convexity)
%ΔP ≈ −ModDur × ΔYield + ½ × Convexity × (ΔYield)²
Approximate Modified Duration
ApproxModDur = (P− − P+) / (2 × P₀ × ΔYield)
Price Value of a Basis Point
PVBP = ModDur × Price × 0.0001
Credit Risk
Expected Loss
Expected Loss = PD × LGD × EAD
Loss Given Default
LGD = 1 − Recovery Rate
See Fixed Income for full treatment of all bond math.
Derivatives
Forward Price (Cost of Carry)
F₀ = S₀ × (1 + r)T − FV(Benefits) + FV(Costs)
Value of Long Forward (During Life)
Vt = St − F₀ / (1 + r)(T−t)
Put–Call Parity
c + PV(X) = p + S
Put–Call Forward Parity
c + PV(X) = p + PV(F)
One-Period Binomial Call Value
c = [π × cu + (1 − π) × cd] / (1 + r)
Risk-Neutral Probability (Up Move)
π = (1 + r − d) / (u − d)
Call Option Payoff
cT = max(ST − X, 0)
Put Option Payoff
pT = max(X − ST, 0)
See Derivatives for arbitrage, replication, and pricing context.
Portfolio Management
Two-Asset Portfolio Variance
σ²p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρ₁₂σ₁σ₂
Capital Market Line
E(Rp) = Rf + [(E(Rm) − Rf) / σm] × σp
CAPM / Security Market Line
E(Ri) = Rf + βi × [E(Rm) − Rf]
Beta
βi = Cov(Ri, Rm) / σ²m
Utility Function
U = E(r) − ½ × A × σ²
Treynor Ratio
Treynor = (Rp − Rf) / βp
Jensen’s Alpha
α = Rp − [Rf + βp(Rm − Rf)]
See Portfolio Management for CAPM, efficient frontier, and performance appraisal.
Study Approach
Don’t try to memorize this page in one sitting. Instead, review one section per day during your final two weeks. Use active recall: cover the formula, try to write it from memory, then check. Focus extra time on formulas you keep getting wrong. The highest-ROI formulas to master: Gordon Growth Model, CAPM, modified duration, put–call parity, WACC, portfolio variance, and DuPont analysis.
Top 10 Must-Know Formulas
- Gordon Growth Model: V₀ = D₁ / (r − g) — the foundation of equity valuation.
- CAPM: E(Ri) = Rf + β[E(Rm) − Rf] — the foundation of portfolio theory and cost of equity.
- WACC: (E/V)re + (D/V)rd(1−t) — the bridge between corporate finance and valuation.
- Modified Duration: %ΔP ≈ −ModDur × ΔYield — the key fixed income risk measure.
- Put–Call Parity: c + PV(X) = p + S — the core derivatives relationship.
- Portfolio Variance (2-asset): w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂ — the math of diversification.
- DuPont (3-part): ROE = Margin × Turnover × Leverage — decomposes FRA analysis.
- Forward Price: F₀ = S₀(1+r)T − FV(benefits) + FV(costs) — prices any forward contract.
- NPV: Σ[CFt/(1+r)t] − Investment — the gold standard for capital allocation.
- EAR: (1 + r/m)m − 1 — converts between compounding frequencies.
Frequently Asked Questions
Do I need to memorize all these formulas?
Yes — the CFA Level 1 exam does not provide a formula sheet. Every formula on this page could appear on the exam. However, the Top 10 list above covers the formulas that appear most frequently. Start there and build outward.
How should I practice formula memorization?
Use active recall daily: cover the formula, write it from memory, then check. Spaced repetition works best — review all formulas on Day 1, then test yourself on the ones you missed on Day 2, and so on. By exam day, every formula should be accessible without hesitation. Many candidates also find it helpful to write all formulas at the start of the exam session as a “brain dump.”
Which formulas are most likely to appear?
Based on exam weight and question frequency: CAPM, Gordon Growth Model, WACC, modified duration (both the formula and the price approximation), put–call parity, portfolio variance, DuPont analysis, NPV/IRR, and the cash conversion cycle. These span the highest-weight topics and appear on virtually every exam administration.
What if I forget a formula during the exam?
First, don’t panic — try to derive it from first principles. Most CFA formulas are logical: the Gordon Growth Model is just a growing perpetuity, CAPM is just risk-free rate plus a risk premium, and duration is just a sensitivity measure. Understanding the intuition behind each formula makes reconstruction possible even under pressure.