CFA Level 1 Formula Sheet

All 83 essential formulas across 9 subjects, organized by topic. Searchable and free — no signup required.

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Quantitative Methods(14)Economics(7)Financial Statement Analysis(14)Corporate Issuers(9)Equity Investments(9)Fixed Income(10)Derivatives(7)Alternative Investments(5)Portfolio Management(8)

Quantitative Methods

14 formulas

Future Value

FV = PV × (1 + r)n

Single lump sum compounding

Present Value

PV = FV / (1 + r)n

Discounting future cash flows

Annuity PV

PV = PMT × [1 - (1+r)-n] / r

Equal periodic payments

Effective Annual Rate

EAR = (1 + r/m)m - 1

m = compounding periods per year

Holding Period Return

HPR = (P₁ - P₀ + D) / P₀

Total return including income

Population Variance

σ² = Σ(Xᵢ - μ)² / N

Divide by N for population

Sample Variance

s² = Σ(Xᵢ - X̄)² / (n-1)

Divide by n-1 for sample (Bessel's correction)

Coefficient of Variation

CV = σ / μ

Risk per unit of return

Sharpe Ratio

Sharpe = (R̄ₚ - Rᶠ) / σₚ

Excess return per unit of total risk

Bayes' Formula

P(A|B) = P(B|A) × P(A) / P(B)

Updating probabilities with new info

Correlation

ρ = Cov(X,Y) / (σₓ × σᵧ)

Standardized covariance, -1 to +1

Linear Regression

Y = b₀ + b₁X + ε

b₁ = Cov(X,Y)/Var(X)

Confidence Interval

X̄ ± z(α/2) × (σ/√n)

z = 1.96 for 95% CI

Test Statistic

t = (X̄ - μ₀) / (s/√n)

Compare to critical value

Economics

7 formulas

GDP (Expenditure)

GDP = C + I + G + (X - M)

Consumption + Investment + Government + Net Exports

Fiscal Multiplier

Multiplier = 1 / (1 - MPC)

MPC = marginal propensity to consume

Quantity Theory of Money

M × V = P × Y

Money supply × Velocity = Price level × Real output

Fisher Equation

Nominal rate ≈ Real rate + Inflation

Exact: (1+nom) = (1+real)(1+inf)

Elasticity of Demand

E = %ΔQ / %ΔP

|E| > 1: elastic, |E| < 1: inelastic

No-Arbitrage Forward Rate

F = S × (1 + rₐ)/(1 + r_b)

Interest rate parity

Real Exchange Rate

Real FX = Nominal FX × (P_foreign / P_domestic)

Adjusting for price levels

Financial Statement Analysis

14 formulas

Basic EPS

EPS = (NI - Pref Div) / Wtd Avg Shares

Earnings per common share

Diluted EPS

Diluted EPS = (NI - Pref Div + Convertible Interest) / (Shares + Dilutive Securities)

Treasury stock method for options

Current Ratio

Current Ratio = Current Assets / Current Liabilities

>1 indicates short-term solvency

Quick Ratio

Quick = (Cash + Receivables + ST Investments) / Current Liabilities

Excludes inventory

ROE

ROE = Net Income / Average Equity

Return to shareholders

DuPont (3-way)

ROE = (NI/Rev) × (Rev/Assets) × (Assets/Equity)

Profit margin × Turnover × Leverage

DuPont (5-way)

ROE = Tax Burden × Interest Burden × EBIT Margin × Turnover × Leverage

Extended decomposition

Inventory Turnover

Inv Turnover = COGS / Avg Inventory

Days = 365 / Turnover

DSO

DSO = 365 / Receivables Turnover

Receivables Turnover = Revenue / Avg AR

Debt-to-Equity

D/E = Total Debt / Total Equity

Financial leverage measure

Interest Coverage

Interest Coverage = EBIT / Interest Expense

Ability to service debt

CFO (Indirect)

CFO = NI + Non-cash charges ± WC changes

Start from net income, adjust

Free Cash Flow to Firm

FCFF = NI + NCC + Int(1-t) - FCInv - WCInv

Cash available to all capital providers

Free Cash Flow to Equity

FCFE = FCFF - Int(1-t) + Net Borrowing

Cash available to equity holders

Corporate Issuers

9 formulas

NPV

NPV = Σ[CFₜ / (1+r)ᵗ] - Initial Investment

Accept if NPV > 0

IRR

Rate where NPV = 0

Accept if IRR > required return

Payback Period

Time to recover initial investment

Ignores TVM and post-payback CFs

WACC

WACC = w_d × r_d(1-t) + w_e × r_e

After-tax weighted average cost

Cost of Equity (CAPM)

r_e = Rᶠ + β(R_m - Rᶠ)

Risk-free + equity risk premium

DOL

DOL = %ΔOI / %ΔREV = (Rev - VC) / (Rev - VC - FC)

Operating leverage sensitivity

DFL

DFL = %ΔEPS / %ΔOI = OI / (OI - Interest)

Financial leverage sensitivity

DTL

DTL = DOL × DFL

Total leverage effect

Breakeven

Q = FC / (P - VC)

Units to cover fixed costs

Equity Investments

9 formulas

DDM (Gordon Growth)

V₀ = D₁ / (r - g)

Constant growth dividend model

Required Return (DDM)

r = (D₁/P₀) + g

Dividend yield + growth rate

Price-to-Earnings

P/E = Price / EPS

Leading P/E uses forecasted EPS

Justified P/E (Leading)

P/E = (1-b) / (r-g)

b = retention ratio, g = b × ROE

Sustainable Growth

g = ROE × b

b = retention ratio = 1 - payout

PEG Ratio

PEG = (P/E) / g

P/E relative to growth rate

Price-to-Book

P/B = Price / Book Value per Share

P/B < 1 may signal undervaluation

Enterprise Value

EV = Market Cap + Debt - Cash

Total value of the firm

EV/EBITDA

EV / EBITDA

Cross-capital structure comparison

Fixed Income

10 formulas

Bond Price

P = Σ[C/(1+r)ᵗ] + FV/(1+r)ⁿ

PV of coupons + PV of par

Current Yield

CY = Annual Coupon / Price

Income return only

YTM

Rate that equates PV of all CFs to price

Total return if held to maturity

Macaulay Duration

MacD = Σ[t × PV(CFₜ)] / Price

Weighted average time to receive CFs

Modified Duration

ModD = MacD / (1 + YTM/m)

Price sensitivity to yield change

Price Change (Duration)

ΔP/P ≈ -ModD × Δy

First-order approximation

Price Change (with Convexity)

ΔP/P ≈ -ModD × Δy + ½ × Convexity × (Δy)²

More accurate for large yield changes

Effective Duration

EffD = (P₋ - P₊) / (2 × P₀ × Δy)

For bonds with embedded options

Credit Spread

Spread = YTM_corporate - YTM_benchmark

Compensation for credit risk

Expected Loss

EL = PD × LGD × EAD

PD=prob default, LGD=loss given default

Derivatives

7 formulas

Forward Price

F₀ = S₀ × (1 + r)T

No-arbitrage forward (no income)

Forward Payoff (Long)

Payoff = S_T - F₀

Gain if spot > forward

Call Payoff

max(0, S_T - X)

Right to buy at strike X

Put Payoff

max(0, X - S_T)

Right to sell at strike X

Put-Call Parity

c + PV(X) = p + S

European options only

Risk-Neutral Probability

πᵤ = (1 + r - d) / (u - d)

Binomial model probability

Binomial Option Value

C = [πᵤCᵤ + (1-πᵤ)C_d] / (1+r)

Discounted expected payoff

Alternative Investments

5 formulas

Cap Rate

Cap Rate = NOI / Property Value

Real estate income yield

Property Value

Value = NOI / Cap Rate

Income approach to RE valuation

Management Fee

Fee = Rate × AUM (or Committed Capital)

Typically 1-2% annually

Performance Fee

Incentive Rate × max(0, Return - Hurdle)

Typically 20% above hurdle

Net Return to LP

Net = Gross - Mgmt Fee - Perf Fee

What investor actually earns

Portfolio Management

8 formulas

Utility Function

U = E(R) - ½ × A × σ²

A = risk aversion (A>0: risk-averse)

CAL Equation

E(Rᶜ) = Rᶠ + [E(Rₚ)-Rᶠ]/σₚ × σᶜ

Slope = Sharpe ratio

Portfolio Variance (2 assets)

σ²ₚ = w²ₐσ²ₐ + w²_bσ²_b + 2wₐw_bρσₐσ_b

Diversification when ρ < 1

CAPM

E(Rᵢ) = Rᶠ + βᵢ[E(R_m) - Rᶠ]

Only systematic risk rewarded

Beta

β = Cov(Rᵢ, R_m) / σ²_m

Systematic risk measure

Treynor Ratio

Treynor = (Rₚ - Rᶠ) / βₚ

Return per unit of beta risk

Jensen's Alpha

α = Rₚ - [Rᶠ + β(R_m - Rᶠ)]

Excess return above CAPM

M-squared

M² = (Sharpeₚ - Sharpe_m) × σ_m

Risk-adjusted in return units

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