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CFA® Program Level I formula sheet: printable, with checks

A printable formula sheet for Level I of the CFA® Program: time value of money, statistics, ratios, NPV and WACC, dividend discount models, bond duration, forwards and options, portfolio risk and CAPM – each formula with a worked check value and a link to a guide.

CFA® Program Level I guideBy High Performer CertsPublished 9 min read

Key facts

  • The sheet lists 48 formulas for seven of the ten Level I topic areas, grouped by area.
  • Each formula has a check value – inputs and result – so you can test your recall and your calculator.
  • The print layout keeps only the title and the formula tables.
  • The formulas are our own selection from finance textbooks and lecture notes, not CFA Institute material.
  • Rates are decimals inside the formulas: 5% is 0.05.

This printable sheet collects 48 core formulas for seven of the ten topic areas of Level I of the CFA® Program, each with a check value you can rework on your calculator and a link to a worked guide or calculator. It is our own selection from finance textbooks and lecture notes, as of 30 October 2026.

The CFA® Program is run by CFA Institute (CFA Institute, Level I exam). This sheet is not CFA Institute material and not a list of what your exam will test: it gathers the standard formulas behind the topic areas, written in our own notation. Our questions and guides complement CFA Institute's curriculum; they do not replace it.

How do you use this formula sheet?

  1. Print it. Use your browser's print command (Ctrl+P or ⌘P). The print layout keeps the title and the formula tables and leaves out the rest of the page.
  2. Recall before you read. Cover the formula column, say or write the formula, then check. Testing yourself this way beats rereading (Roediger and Karpicke, 2006) (Dunlosky et al., 2013).
  3. Rework the check. Enter the inputs on your calculator and compare with the result. If they differ, look for a timing, rate or sign error before you look for a wrong formula.
  4. Go deeper where you stumble. Most areas link to a guide or calculator that works the formulas through step by step.

Rates are decimals inside the formulas: 5% is 0.05. Results are rounded at the end, not in between. Ethical and Professional Standards has no formulas, and for Economics and Alternative Investments this sheet lists none – the currency forward sits under Derivatives. Which calculators you may use in the exam is explained on calculators allowed in the CFA® Program and the FRM® Exam.

High Performer Certs · https://highperformer-certs.com/blog/level-1-formula-sheet · as of 30 October 2026 · our own selection, not CFA Institute material

Quantitative Methods: which formulas do you need?

Go deeper with the time value of money guide and the time value of money calculator. Sources: (NYU Stern, time value of money (secondary source))(NYU Stern, covariance and correlation (secondary source))(Chen, probability moments (secondary source))(NIST, confidence limits for the mean (secondary source))(NIST, skewness and kurtosis (secondary source))

Quantitative Methods: formulas and check values
FormulaWhat it givesCheck: inputs → result
Future valueFV=PV(1+r)nFV = PV(1+r)^nA single amount after n periodsPV 1,000, r 5%, n 3 → 1,157.63
Present valuePV=FV(1+r)nPV = \dfrac{FV}{(1+r)^n}Today's value of a single future amountFV 1,000, r 5%, n 3 → 863.84
Ordinary annuityPV=PMT 1−(1+r)−nrPV = PMT\,\dfrac{1-(1+r)^{-n}}{r}Equal payments at the end of each periodPMT 100, r 6%, n 5 → 421.24
Annuity duePVdue=PVordinary (1+r)PV_{\text{due}} = PV_{\text{ordinary}}\,(1+r)Equal payments at the start of each periodPMT 100, r 6%, n 5 → 446.51
PerpetuityPV=PMTrPV = \dfrac{PMT}{r}Level payments for ever, the first one period from nowPMT 50, r 4% → 1,250.00
Effective annual rateEAR=(1+jm)m−1EAR = \left(1+\dfrac{j}{m}\right)^{m} - 1Nominal rate j compounded m times a yearj 6%, m 12 → 6.1678%
Continuous compoundingEAR=ej−1EAR = e^{j} - 1Nominal rate j compounded continuouslyj 6% → 6.1837%
Sample variances2=∑i(xi−xˉ)2n−1s^2 = \dfrac{\sum_i (x_i-\bar x)^2}{n-1}Spread of a sample; s is its square root2, 4, 6, 8 → 6.6667
Correlationρ=Cov⁡(X,Y)σXσY\rho = \dfrac{\operatorname{Cov}(X,Y)}{\sigma_X\sigma_Y}Strength of a linear relationship, from −1 to +1Cov 0.0036, σ 0.12 and 0.15 → 0.20
Bayes' formulaP(A∣B)=P(B∣A) P(A)P(B)P(A\mid B) = \dfrac{P(B\mid A)\,P(A)}{P(B)}Updating a probability after new informationP(A) 0.30, P(B | A) 0.60, P(B | not A) 0.20 → 0.5625
t-statistic for a meant=xˉ−μ0s/nt = \dfrac{\bar x - \mu_0}{s/\sqrt{n}}Tests a sample mean against μ₀x̄ 8, μ₀ 6, s 4, n 25 → 2.50
Confidence interval for a meanxˉ±t sn\bar x \pm t\,\dfrac{s}{\sqrt{n}}Range for the population mean; t depends on the level and n − 1x̄ 8, s 4, n 25, t 2.064 → 6.35 to 9.65
Simple regressionb^=Cov⁡(X,Y)Var⁡(X),a^=Yˉ−b^ Xˉ\hat b = \dfrac{\operatorname{Cov}(X,Y)}{\operatorname{Var}(X)},\quad \hat a = \bar Y - \hat b\,\bar XSlope and intercept of Y = a + bXCov 0.0012, Var(X) 0.0016, X̄ 4%, Ȳ 5% → b 0.75, a 2.00%
Skewness and kurtosisg1=∑i(xi−xˉ)3/ns3,K=∑i(xi−xˉ)4/ns4g_1 = \dfrac{\sum_i (x_i-\bar x)^3/n}{s^3},\quad K = \dfrac{\sum_i (x_i-\bar x)^4/n}{s^4}Asymmetry and tail weight; here s divides by n, not n − 1, and excess kurtosis is K − 3A normal distribution has skewness 0 and kurtosis 3

Financial Statement Analysis: which formulas do you need?

Go deeper with the ratio analysis and DuPont guide. Sources: (ACCA, ratio interpretation (secondary source))(BDC, quick ratio (secondary source))(CFI, cash conversion cycle (secondary source))(Damodaran, financial ratios (secondary source))(AAII, DuPont analysis (secondary source))

Financial Statement Analysis: formulas and check values
FormulaWhat it givesCheck: inputs → result
Current ratioCurrent assetsCurrent liabilities\dfrac{\text{Current assets}}{\text{Current liabilities}}Short-term liquidity300 and 200 → 1.50
Quick ratioCurrent assets−InventoriesCurrent liabilities\dfrac{\text{Current assets} - \text{Inventories}}{\text{Current liabilities}}Liquidity without inventories; a stricter version, used in the ratio guide, counts only cash, liquid investments and receivables300, 120 and 200 → 0.90
Receivable daysTrade receivablesCredit sales×365\dfrac{\text{Trade receivables}}{\text{Credit sales}}\times 365How long customers take to pay125 and 900 → 50.7 days
Inventory daysInventoriesCost of sales×365\dfrac{\text{Inventories}}{\text{Cost of sales}}\times 365How long stock is held120 and 600 → 73.0 days
Payable daysTrade payablesCredit purchases×365\dfrac{\text{Trade payables}}{\text{Credit purchases}}\times 365How long the company takes to pay suppliers80 and 600 → 48.7 days
Cash conversion cycleInventory days+Receivable days−Payable days\text{Inventory days} + \text{Receivable days} - \text{Payable days}Days cash is tied up in working capitalThe three examples above → 75.0 days
Debt to equityDebtEquity\dfrac{\text{Debt}}{\text{Equity}}Financial leverage400 and 500 → 0.80
Interest coverageEBITInterest expense\dfrac{\text{EBIT}}{\text{Interest expense}}How many times operating profit covers interest120 and 30 → 4.0×
ROE, three-step DuPontROE=NIS×SA×AEROE = \dfrac{NI}{S}\times\dfrac{S}{A}\times\dfrac{A}{E}Net margin × asset turnover × equity multiplierNI 90, sales 1,200, assets 1,500, equity 600 → 7.50% × 0.80 × 2.50 = 15.00%
ROE, five-step DuPontROE=NIEBT×EBTEBIT×EBITS×SA×AEROE = \dfrac{NI}{EBT}\times\dfrac{EBT}{EBIT}\times\dfrac{EBIT}{S}\times\dfrac{S}{A}\times\dfrac{A}{E}Adds the tax burden and the interest burden–

Corporate Issuers: which formulas do you need?

Go deeper with the online financial calculator. Sources: (NYU Stern, time value of money (secondary source))(Texas Instruments, NPV definition and calculation)(Damodaran, discount rates (secondary source))

Corporate Issuers: formulas and check values
FormulaWhat it givesCheck: inputs → result
Net present valueNPV=∑t=0nCFt(1+r)tNPV = \sum_{t=0}^{n}\dfrac{CF_t}{(1+r)^t}Value a project adds at the cost of capital rCF −1,000, 400, 500, 300; r 8% → 37.19
Internal rate of return∑t=0nCFt(1+IRR)t=0\sum_{t=0}^{n}\dfrac{CF_t}{(1+IRR)^t} = 0The rate at which NPV is zeroSame cash flows → 10.13%
Weighted average cost of capitalWACC=wd rd(1−t)+we reWACC = w_d\,r_d(1-t) + w_e\,r_eCost of capital, with debt after taxDebt 40% at 6%, tax 25%, equity at 11% → 8.40%

Equity Investments: which formulas do you need?

Sources: (Damodaran, dividend discount model (secondary source))

Equity Investments: formulas and check values
FormulaWhat it givesCheck: inputs → result
Gordon growth modelV0=D1r−gV_0 = \dfrac{D_1}{r-g}Value with dividends growing at g for ever (r > g)D₁ 2.00, r 9%, g 4% → 40.00
Implied required returnr=D1P0+gr = \dfrac{D_1}{P_0} + gDividend yield plus growthD₁ 2.00, P₀ 40, g 4% → 9.00%
Justified forward P/EP0E1=D1/E1r−g\dfrac{P_0}{E_1} = \dfrac{D_1/E_1}{r-g}The Gordon model divided by next year's earningsPayout 40%, r 9%, g 4% → 8.0
Sustainable growthg=b×ROEg = b\times ROEGrowth from retained earnings; b = 1 − payoutb 60%, ROE 12% → 7.20%

Fixed Income: which formulas do you need?

Go deeper with the duration and convexity guide and the online financial calculator. Sources: (IMF, duration definitions (secondary source))(RBI, bond sensitivity (secondary source))(CME Group, basis-point value (secondary source))(IMF, convexity and curve assumptions)

Fixed Income: formulas and check values
FormulaWhat it givesCheck: inputs → result
Bond priceP=∑t=1NC(1+y)t+F(1+y)NP = \sum_{t=1}^{N}\dfrac{C}{(1+y)^t} + \dfrac{F}{(1+y)^N}Price on a coupon date from the yield to maturityCoupon 5% a year, 3 years, y 4%, face 100 → 102.78
Macaulay durationDMac=∑tt PV(CFt)PD_{\text{Mac}} = \dfrac{\sum_t t\,PV(CF_t)}{P}Weighted average time to the cash flows, in yearsSame bond → 2.861
Modified durationDmod=DMac1+y/mD_{\text{mod}} = \dfrac{D_{\text{Mac}}}{1+y/m}Percentage price change per unit change in yieldSame bond → 2.751
Convexity (annual coupons)C=1P∑tt(t+1) CFt(1+y)t+2C = \dfrac{1}{P}\sum_t \dfrac{t(t+1)\,CF_t}{(1+y)^{t+2}}Curvature of the price–yield lineSame bond → 10.41
Price change from duration and convexityΔPP≈−Dmod Δy+12 C (Δy)2\dfrac{\Delta P}{P} \approx -D_{\text{mod}}\,\Delta y + \tfrac12\,C\,(\Delta y)^2Estimate for a parallel yield changeSame bond, +100 basis points → −2.699% (repriced: −2.700%)
Price value of a basis pointPVBP≈Dmod×P×0.0001PVBP \approx D_{\text{mod}}\times P\times 0.0001Price change for one basis pointSame bond → 0.0283 per 100 face

Derivatives: which formulas do you need?

Go deeper with the forwards and put–call parity guide and the binomial option pricing guide. Sources: (Naranjo, forward pricing (secondary source))(Back, Liu and Loewenstein, carry (secondary source))(Naranjo, European parity (secondary source))(Back, Liu and Loewenstein, binomial trees (secondary source))

Derivatives: formulas and check values
FormulaWhat it givesCheck: inputs → result
Forward price, no incomeF0=S0 erTF_0 = S_0\,e^{rT}Spot financed to delivery, continuous compoundingS₀ 100, r 5%, T 0.5 → 102.53
Forward price with a yieldF0=S0 e(r−q)TF_0 = S_0\,e^{(r-q)T}q is an income yield, or the foreign interest rate for a currencyS₀ 1.2500, r 5%, q 3%, T 1 → 1.2753
Value of a long forwardVt=(Ft−K) e−r(T−t)V_t = (F_t - K)\,e^{-r(T-t)}Value before delivery of a contract at price KForward price now 104, K 102, r 5%, 0.5 years left → 1.95
Put–call parityc0+Ke−rT=p0+S0c_0 + K e^{-rT} = p_0 + S_0European options on an asset without incomec 8, S₀ 100, K 100, r 5%, T 1 → p 3.12
One-step binomial treep=R−du−d,V0=p Vu+(1−p) VdRp = \dfrac{R-d}{u-d},\quad V_0 = \dfrac{p\,V_u + (1-p)\,V_d}{R}Risk-neutral value of an option on a tree; R is one plus the rate per stepS₀ 100, u 1.2, d 0.8, R 1.03, call with K 100 → p 0.575, value 11.17

Portfolio Management: which formulas do you need?

Go deeper with the CAPM and beta guide and the portfolio risk and Sharpe ratio calculator. Sources: (Naranjo, portfolio risk (secondary source))(Naranjo, CAPM (secondary source))(Sharpe, equilibrium and the SML (secondary source))(Sharpe, The Sharpe Ratio (1994))

Portfolio Management: formulas and check values
FormulaWhat it givesCheck: inputs → result
Portfolio returnE(Rp)=∑iwi E(Ri)E(R_p) = \sum_i w_i\,E(R_i)Weighted average of expected returnsw 60% and 40%, E(R) 9% and 4% → 7.00%
Two-asset portfolio riskσp2=wA2σA2+wB2σB2+2wAwB ρ σAσB\sigma_p^2 = w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_Aw_B\,\rho\,\sigma_A\sigma_BVariance of a two-asset portfoliow 60% and 40%, σ 20% and 10%, ρ 0.3 → portfolio σ 13.74%
Betaβi=Cov⁡(Ri,Rm)σm2=ρim σiσm\beta_i = \dfrac{\operatorname{Cov}(R_i,R_m)}{\sigma_m^2} = \rho_{im}\,\dfrac{\sigma_i}{\sigma_m}Sensitivity to the marketρ 0.6, σ 25%, market σ 15% → 1.00
CAPME(Ri)=Rf+βi [E(Rm)−Rf]E(R_i) = R_f + \beta_i\,[E(R_m) - R_f]Required return for systematic riskRisk-free 3%, β 1.2, market 8% → 9.00%
Sharpe ratioS=Rp−RfσpS = \dfrac{R_p - R_f}{\sigma_p}Excess return per unit of total riskReturn 10%, risk-free 3%, σ 14% → 0.50
Treynor ratioT=Rp−RfβpT = \dfrac{R_p - R_f}{\beta_p}Excess return per unit of betaReturn 10%, risk-free 3%, β 1.4 → 5.00%

Which formula mistakes are common?

  • Mixing periods. A monthly payment needs a monthly rate and a number of months; an annual rate divided by 12 is only right for a nominal rate quoted with monthly compounding.
  • Annuity timing. Payments at the start of each period are an annuity due: one extra factor of (1 + r).
  • Sample or population. A sample variance divides by n − 1.
  • Yield changes in the wrong unit. 100 basis points is 0.01 in the duration formula, not 1.
  • Before-tax debt in WACC. The cost of debt enters after tax.
  • Gordon model with g ≥ r. The formula only works when the required return exceeds growth.

What this means for you

A formula sheet helps you check what you know; it does not teach you when to use a formula. Work through one area a week, rework every check value until it comes out right, then move on to mixed questions. Our CFA® Program Level I course gives you practice questions with worked explanations and formulas, and the FRM® Exam Part I formula sheet covers the risk side.

Frequently asked questions

Which formulas belong on a CFA® Program Level I formula sheet?

The core ones for time value of money and statistics, financial ratios and DuPont, NPV, IRR and WACC, dividend discount models, bond prices and duration, forwards, put–call parity and binomial trees, and portfolio risk with beta, CAPM and the Sharpe and Treynor ratios. Our sheet lists 48 of them.

Can I print this formula sheet?

Yes. Use your browser's print command (Ctrl+P or ⌘P). The print layout keeps the title and the formula tables and leaves out the rest of the page.

Does this formula sheet come from CFA Institute?

No. It is our own selection of standard formulas from finance textbooks and lecture notes, in our own notation. It is not CFA Institute material and not a list of what your exam will test.

What are the check values for?

Each formula comes with inputs and a result. Cover the formula, recall it, then rework the check on your calculator: if your answer differs, look for a timing, rate or sign error first.

Which topic areas does the sheet leave out?

Ethical and Professional Standards, which has no formulas, and Economics and Alternative Investments, for which the sheet lists none. The currency forward formula sits under Derivatives.

Sources

  1. Aswath Damodaran, NYU Stern School of Business (secondary source): A Primer on the Time Value of Money. Accessed 29 October 2026.
  2. Aswath Damodaran, NYU Stern School of Business (secondary source): A Primer on Statistics — covariance and correlation. Accessed 29 October 2026.
  3. Yen-Chi Chen, University of Washington (lecture notes, secondary source): STAT 535, Lecture 1: Review on Probability and Statistics — expectation, covariance and total expectation. Accessed 29 October 2026.
  4. National Institute of Standards and Technology (statistical handbook, secondary source): NIST/SEMATECH e-Handbook §1.3.5.2 — Confidence limits for the mean and the t test statistic. Accessed 30 October 2026.
  5. National Institute of Standards and Technology (statistical handbook, secondary source): NIST/SEMATECH e-Handbook §1.3.5.11 — Measures of skewness and kurtosis. Accessed 30 October 2026.
  6. Association of Chartered Certified Accountants (technical article, secondary source): Financial statements interpretation — profitability, liquidity, activity and gearing. Accessed 29 October 2026.
  7. Business Development Bank of Canada (financial education, secondary source): Quick ratio calculator — eligible quick assets and current liabilities. Accessed 29 October 2026.
  8. Corporate Finance Institute (financial education, secondary source): Cash Conversion Cycle — days inventory outstanding + days sales outstanding − days payables outstanding (11 September 2019). Accessed 30 October 2026.
  9. Aswath Damodaran, NYU Stern School of Business (academic primer, secondary source): A Primer on Financial Statements — profitability, book equity, leverage and interest coverage. Accessed 29 October 2026.
  10. American Association of Individual Investors (analytical article, secondary source): Deconstructing ROE: DuPont Analysis — three-step and five-step decompositions. Accessed 29 October 2026.
  11. Texas Instruments: Solution 11241: Computing Net Present Value (NPV) and Internal Rate of Return (IRR) Using the BA II PLUS and the BA II PLUS PROFESSIONAL. Accessed 29 October 2026.
  12. Aswath Damodaran, NYU Stern School of Business (secondary source): The Little Book of Valuation — Discount rates: cost of capital as a weighted average, after-tax cost of debt. Accessed 30 October 2026.
  13. Aswath Damodaran, NYU Stern School of Business (lecture notes, secondary source): Discounted cashflow models — I. The stable growth DDM: Gordon growth model; stable-period payout ratio 1 − g/ROE. Accessed 30 October 2026.
  14. International Monetary Fund (methods overview, secondary source): A Primer on Managing Sovereign Debt-Portfolio Risks — Macaulay and modified duration (Working Paper 2018/074). Accessed 29 October 2026.
  15. Reserve Bank of India (educational primer, secondary source): Government Securities Market in India — A Primer: full price; §27, duration, PV01 and convexity. Accessed 29 October 2026.
  16. CME Group (market education, secondary source): How Can You Measure Risk in Treasuries? — Value of a basis point and modified duration. Accessed 29 October 2026.
  17. International Monetary Fund: Financial Soundness Indicators: Compilation Guide — Appendix VI, §§50–55: convexity and the term structure. Accessed 29 October 2026.
  18. Lorenzo Naranjo, Washington University in St. Louis (lecture notes, secondary source): Forward and Futures Prices — no-arbitrage replication, income, contract value and settlement timing. Accessed 29 October 2026.
  19. Kerry Back, Hong Liu and Mark Loewenstein (academic textbook, secondary source): Pricing and Hedging Derivative Securities — Chapter 3, §§3.2–3.3: expectations, cost of carry and convenience yield. Accessed 29 October 2026.
  20. Lorenzo Naranjo, Washington University in St. Louis (lecture notes, secondary source): Properties of European Options — put-call parity and matching terminal payoffs. Accessed 29 October 2026.
  21. Kerry Back, Hong Liu and Mark Loewenstein (academic textbook, secondary source): Pricing and Hedging Derivative Securities — Chapter 4, §§4.1–4.4 and Exercise 4.8: replication, risk-neutral pricing, backward induction, tree calibration and convergence. Accessed 29 October 2026.
  22. Lorenzo Naranjo, Washington University in St. Louis (lecture notes, secondary source): Portfolios of Risky Assets — expected return, covariance, portfolio variance and the minimum-variance frontier. Accessed 29 October 2026.
  23. Lorenzo Naranjo, Washington University in St. Louis (lecture notes, secondary source): The Capital Asset Pricing Model — assumptions, beta, systematic risk and model limitations. Accessed 29 October 2026.
  24. William F. Sharpe, Stanford University (academic notes, secondary source): Macro-Investment Analysis: Equilibrium (preliminary) — Expected Return and Beta Values; The Market Portfolio and the Security Market Line. Accessed 29 October 2026.
  25. William F. Sharpe, The Journal of Portfolio Management (author's Stanford reprint): The Sharpe Ratio — The Ratio, Time Dependence, Correlations and Related Measures (1994). Accessed 29 October 2026.
  26. CFA Institute: CFA Program Level I exam: format and topic weights. Accessed 26 October 2026.
  27. Roediger, H. L. & Karpicke, J. D., Psychological Science 17(3), 249–255: Test-enhanced learning: Taking memory tests improves long-term retention (2006).
  28. Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J. & Willingham, D. T., Psychological Science in the Public Interest 14(1), 4–58: Improving students’ learning with effective learning techniques (2013).

High Performer Certs is an independent study platform. It is not affiliated with, endorsed by, or sponsored by CFA Institute or the Global Association of Risk Professionals (GARP). We are not a CFA Institute Prep Provider and not a GARP Exam Preparation Provider. CFA Institute does not endorse, promote, review or warrant the accuracy or quality of our products and services. GARP does not endorse, promote, review or warrant the accuracy of our products or services. All questions and explanations are our own original material and contain no CFA Institute or GARP exam, curriculum or practice questions. CFA®, Chartered Financial Analyst®, CIPM® and GIPS® are registered trademarks owned by CFA Institute. FRM® and GARP® are trademarks owned by the Global Association of Risk Professionals.

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