Free CFA Level I Formula Sheet (2026)

Every CFA Level I formula you need on the test, grouped by topic, rendered with full math notation. 58 formulas across 9 topics, calibrated to the 2026 syllabus. Free forever, no signup required.

58 Formulas
9 Topics
2026 Syllabus
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All CFA Level I Formulas

Quantitative Methods 10 items
Correlation coefficient
ρXY=Cov(X,Y)σXσY\rho_{XY} = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y}
Ranges from −1 to +1; unitless measure of linear association
Holding Period Return (HPR)
HPR=P1−P0+D1P0HPR = \frac{P_1 - P_0 + D_1}{P_0}
P_1 = ending price, P_0 = beginning price, D_1 = cash distributions received
Population variance
σ2=∑i=1N(Xi−μ)2N\sigma^2 = \frac{\sum_{i=1}^{N}(X_i - \mu)^2}{N}
μ\mu = population mean, N = population size
Future Value of ordinary annuity
FV=PMT×(1+r)n−1rFV = PMT \times \frac{(1+r)^n - 1}{r}
PMT = periodic payment, r = periodic rate, n = periods
Present Value (single sum)
PV=FV(1+r)nPV = \frac{FV}{(1 + r)^n}
FV = future value, r = periodic rate, n = number of periods
Sharpe ratio
Sp=Rp−RfσpS_p = \frac{R_p - R_f}{\sigma_p}
R_p = portfolio return, R_f = risk-free rate, σp\sigma_p = portfolio std dev
Excess return per unit of total risk
Present Value of perpetuity
PV=PMTrPV = \frac{PMT}{r}
PMT = periodic payment, r = discount rate
Sample variance
s2=∑i=1n(Xi−Xˉ)2n−1s^2 = \frac{\sum_{i=1}^{n}(X_i - \bar{X})^2}{n-1}
Xˉ\bar{X} = sample mean, n = sample size (uses n−1 for unbiasedness)
Present Value of ordinary annuity
PV=PMT×1−(1+r)−nrPV = PMT \times \frac{1 - (1+r)^{-n}}{r}
PMT = periodic payment, r = periodic rate, n = periods
Bayes' Theorem
P(A∣B)=P(B∣A)⋅P(A)P(B)P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}
Updates prior probability P(A) given new information B
P(B)=P(B∣A)P(A)+P(B∣Ac)P(Ac)P(B) = P(B|A)P(A) + P(B|A^c)P(A^c)
Economics 6 items
GDP expenditure approach
GDP=C+I+G+(X−M)GDP = C + I + G + (X - M)
C = consumption, I = investment, G = government spending
X = exports, M = imports, (X−M) = net exports
Fisher effect
(1+rnom)=(1+rreal)(1+π)(1 + r_{nom}) = (1 + r_{real})(1 + \pi)
Approx: rnom≈rreal+πr_{nom} \approx r_{real} + \pi
r_nom = nominal rate, r_real = real rate, π\pi = expected inflation
Money multiplier
m=1reserve requirementm = \frac{1}{\text{reserve requirement}}
Maximum deposit expansion from a given reserve base
ΔMoney supply=m×ΔReserves\Delta\text{Money supply} = m \times \Delta\text{Reserves}
Price elasticity of demand
Ed=%ΔQd%ΔPE_d = \frac{\%\Delta Q_d}{\%\Delta P}
∣Ed∣>1|E_d| > 1: elastic (revenue rises when P falls). ∣Ed∣<1|E_d| < 1: inelastic. =1= 1: unit-elastic (revenue maximized).
Breakeven and shutdown points
Breakeven: P=ATCP = ATC (price covers all costs).
Shutdown (short run): P<AVCP < AVC. If AVC<P<ATCAVC < P < ATC, keep operating short-run because contribution covers some fixed cost.
Cross-rate calculation
AC=AB×BC\frac{A}{C} = \frac{A}{B} \times \frac{B}{C}
Multiply or divide quoted rates to derive a cross-rate. Bid-ask: use bid for one leg and ask for the other to be conservative.
Corporate Issuers 6 items
WACC
WACC=wdrd(1−t)+wprp+wereWACC = w_d r_d (1-t) + w_p r_p + w_e r_e
w = weights (market value), r = required returns
d = debt, p = preferred, e = equity, t = tax rate
FCFF
FCFF=NI+NCC+Int(1−t)−ΔWC−CapExFCFF = NI + NCC + Int(1-t) - \Delta WC - CapEx
NI = net income, NCC = non-cash charges, Int = interest expense
ΔWC\Delta WC = change in working capital, t = tax rate
Free Cash Flow to Equity (FCFE)
FCFE=FCFF−Int(1−t)+ΔDebtFCFE = FCFF - \text{Int}(1-t) + \Delta\text{Debt}
Cash available to equity holders after all obligations and reinvestment
Degree of Total Leverage (DTL)
DTL=DOL×DFL=Q(P−V)Q(P−V)−F−IDTL = DOL \times DFL = \frac{Q(P - V)}{Q(P - V) - F - I}
% change in EPS per 1% change in sales
Degree of Financial Leverage (DFL)
DFL=EBITEBIT−IDFL = \frac{EBIT}{EBIT - I}
I = interest expense
% change in EPS per 1% change in EBIT
Degree of Operating Leverage (DOL)
DOL=Q(P−V)Q(P−V)−F=Contribution marginEBITDOL = \frac{Q(P - V)}{Q(P - V) - F} = \frac{\text{Contribution margin}}{\text{EBIT}}
Q = units, P = price, V = variable cost/unit, F = fixed costs
Financial Statement Analysis 6 items
Receivables turnover and DSO
Receivables turnover=RevenueAvg Accounts Receivable\text{Receivables turnover} = \frac{\text{Revenue}}{\text{Avg Accounts Receivable}}
DSO=365Receivables turnover\text{DSO} = \frac{365}{\text{Receivables turnover}}
Days Sales Outstanding — average collection period
Current ratio
Current ratio=Current assetsCurrent liabilities\text{Current ratio} = \frac{\text{Current assets}}{\text{Current liabilities}}
Measures short-term liquidity; higher = more liquid
Inventory turnover
Inventory turnover=COGSAverage inventory\text{Inventory turnover} = \frac{\text{COGS}}{\text{Average inventory}}
Days on hand (DOH): DOH=365Inventory turnoverDOH = \frac{365}{\text{Inventory turnover}}
Return on Equity (ROE)
ROE=Net incomeAvg total equityROE = \frac{\text{Net income}}{\text{Avg total equity}}
DuPont: ROE = Net margin × Asset turnover × Leverage. Drives sustainable growth: g=b×ROEg = b \times ROE.
Return on Assets (ROA)
ROA=Net incomeAverage total assetsROA = \frac{\text{Net income}}{\text{Average total assets}}
Alternative: ROA=Net profit margin×Asset turnoverROA = \text{Net profit margin} \times \text{Asset turnover}
2-factor DuPont decomposition
3-factor DuPont decomposition
ROE=NISales×SalesAssets×AssetsEquityROE = \frac{NI}{\text{Sales}} \times \frac{\text{Sales}}{\text{Assets}} \times \frac{\text{Assets}}{\text{Equity}}
Net profit margin × Asset turnover × Financial leverage
Equity Investments 6 items
Justified P/E (leading)
P0E1=1−br−g\frac{P_0}{E_1} = \frac{1 - b}{r - g}
b = retention ratio (1−b = payout ratio), r = required return, g = ROE × b
Gordon Growth Model (DDM)
V0=D1r−g=D0(1+g)r−gV_0 = \frac{D_1}{r - g} = \frac{D_0(1+g)}{r - g}
D_1 = next dividend, r = required return, g = constant growth rate
Requires r > g
Enterprise Value (EV)
EV=Market cap+Debt+Preferred−CashEV = \text{Market cap} + \text{Debt} + \text{Preferred} - \text{Cash}
EV/EBITDAEV/EBITDA = enterprise value multiple
Capital-structure-neutral valuation metric
Price-to-Book ratio
P/B=Market price per shareBook value per share\text{P/B} = \frac{\text{Market price per share}}{\text{Book value per share}}
Justified P/B: ROE−gr−g\frac{ROE - g}{r - g}
P/B > 1 implies market values assets above book
Sustainable growth rate
g=b×ROEg = b \times ROE
b = retention rate (1 − dividend payout). Maximum growth a firm can sustain without external financing.
P/E ratio (trailing & leading)
Trailing: P0EPS0\frac{P_0}{EPS_{0}} — uses last 12 months EPS.
Leading: P0EPS1\frac{P_0}{EPS_{1}} — uses next 12 months / forecast EPS. Forward-looking variant.
Fixed Income 6 items
Forward rate from spot rates
(1+z2)2=(1+z1)(1+1f1)(1 + z_2)^2 = (1 + z_1)(1 + {_1f_1})
General: (1+zn)n=(1+zn−1)n−1(1+n−1f1)(1+z_n)^n = (1+z_{n-1})^{n-1}(1 + {_{n-1}f_1})
z = spot rate, f = implied forward rate
Bond price
P=∑t=1nC(1+r)t+FV(1+r)nP = \sum_{t=1}^{n} \frac{C}{(1+r)^t} + \frac{FV}{(1+r)^n}
C = coupon payment, r = periodic YTM, n = periods, FV = face value
Macaulay duration
DMac=∑t=1nt⋅CFt(1+r)tPD_{Mac} = \frac{\sum_{t=1}^{n} t \cdot \frac{CF_t}{(1+r)^t}}{P}
Weighted average time to receive cash flows; measured in years
Modified duration
DMod=DMac1+rD_{Mod} = \frac{D_{Mac}}{1 + r}
%ΔP≈−DMod×Δy\%\Delta P \approx -D_{Mod} \times \Delta y
r = periodic YTM, Δy\Delta y = change in yield
Current yield
Current yield=Annual couponPrice\text{Current yield} = \frac{\text{Annual coupon}}{\text{Price}}
Simplest yield measure; ignores capital gains/losses and time value
Price value of a basis point (PVBP)
PVBP=∣Py+0.01%−Py∣PVBP = |P_{y+0.01\%} - P_y|
Alternative: PVBP=Dmod×P×0.0001PVBP = D_{\text{mod}} \times P \times 0.0001
Dollar price change for a 1 bp yield move
Derivatives 6 items
Forward contract price
F0=S0(1+r)TF_0 = S_0(1+r)^T
With continuous dividends: F0=S0e(r−q)TF_0 = S_0 e^{(r-q)T}
S_0 = spot, r = risk-free rate, T = time, q = dividend yield
Put-call parity
C+X(1+r)T=P+S0C + \frac{X}{(1+r)^T} = P + S_0
C = call price, P = put price, S_0 = spot price, X = exercise price
r = risk-free rate, T = time to expiration
Intrinsic value and time value
Call intrinsic: max⁡(S−X,0)\max(S - X, 0); Put intrinsic: max⁡(X−S,0)\max(X - S, 0)
Time value = Option price − intrinsic. ATM/OTM intrinsic = 0; deep ITM time value → 0 near expiry.
Lower bound on European options (no dividends)
Call: c≥max⁡(S0−X(1+r)−T,0)c \geq \max(S_0 - X(1+r)^{-T}, 0)
Put: p≥max⁡(X(1+r)−T−S0,0)p \geq \max(X(1+r)^{-T} - S_0, 0)
Enforces no-arbitrage. Below these, the option is mispriced relative to the synthetic.
Option payoff at expiration
Long call: max⁡(ST−X,0)\max(S_T - X, 0); Long put: max⁡(X−ST,0)\max(X - S_T, 0)
STS_T = price at expiry, X = strike. Short positions are the negative of long. Subtract premium paid for profit.
Forward price with discrete income or cost
F0(T)=(S0−PV(I)+PV(C))(1+r)TF_0(T) = (S_0 - PV(I) + PV(C))(1 + r)^T
I = discrete income (dividends, coupons) over T; C = carrying cost (storage). PV at risk-free rate. Income reduces the forward; cost raises it.
Alternative Investments 6 items
Capitalization rate (Cap rate)
V=NOIrcapV = \frac{NOI}{r_{cap}}
NOI = net operating income (stabilized), r_cap = cap rate
Cap rate = NOI / Value (inverse: value = NOI / cap rate)
NAV per share
NAV=Total assets−Total liabilitiesShares outstandingNAV = \frac{\text{Total assets} - \text{Total liabilities}}{\text{Shares outstanding}}
Used for mutual funds, ETFs, private equity fund valuation
Hedge fund fee structure (2-and-20)
Mgmt fee =m×AUM= m \times AUM (e.g. 2%). Incentive fee =p×max⁡(0,Profit above hurdle)= p \times \max(0, \text{Profit above hurdle}) (e.g. 20%).
Net investor return = gross − both fees.
Debt Service Coverage Ratio (DSCR)
DSCR=NOIDebt serviceDSCR = \frac{NOI}{\text{Debt service}}
Debt service = annual principal + interest. DSCR > 1 means cash flow covers debt; CRE lenders typically require ≥ 1.20–1.30.
Loan-to-Value (LTV)
LTV=Loan amountProperty valueLTV = \frac{\text{Loan amount}}{\text{Property value}}
Higher LTV = more leverage and credit risk. Typical max ≈ 80% commercial; 95%+ residential with mortgage insurance.
Net Operating Income (NOI)
NOI=Effective Gross Income−Operating ExpensesNOI = \text{Effective Gross Income} - \text{Operating Expenses}
Excludes financing (interest), income tax, depreciation, and amortization. Foundation of cap-rate valuation.
Portfolio Management 6 items
Information ratio
IR=Rp−RBσRp−RB=αTracking errorIR = \frac{R_p - R_B}{\sigma_{R_p - R_B}} = \frac{\alpha}{\text{Tracking error}}
R_B = benchmark return, α\alpha = active return, TE = active risk
Jensen's alpha
αp=Rp−[Rf+βp(Rm−Rf)]\alpha_p = R_p - [R_f + \beta_p(R_m - R_f)]
Actual return minus CAPM-expected return
α>0\alpha > 0 means manager added value beyond compensation for risk
Two-asset portfolio variance
σp2=w12σ12+w22σ22+2w1w2σ1σ2ρ12\sigma_p^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 w_1 w_2 \sigma_1 \sigma_2 \rho_{12}
w = weights, σ\sigma = std devs, ρ12\rho_{12} = correlation coefficient
Capital Market Line (CML)
E(Rp)=Rf+E(Rm)−Rfσm⋅σpE(R_p) = R_f + \frac{E(R_m) - R_f}{\sigma_m} \cdot \sigma_p
Sharpe ratio of market is slope; uses total risk σp\sigma_p (not beta)
Treynor ratio
Tp=Rp−RfβpT_p = \frac{R_p - R_f}{\beta_p}
Excess return per unit of systematic risk (beta)
Compare with Sharpe (uses total risk σp\sigma_p)
CAPM / Security Market Line (SML)
E(Ri)=Rf+βi[E(Rm)−Rf]E(R_i) = R_f + \beta_i [E(R_m) - R_f]
βi=Cov(Ri,Rm)σm2\beta_i = \frac{\text{Cov}(R_i, R_m)}{\sigma_m^2}
Uses systematic risk only; SML plots expected return vs beta

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