CFA Level 1 Formula Sheet (2026)

Use when. Operating-efficiency comparisons across firms or across periods; a primary lever for working-capital management.

How many days a firm's cash is locked up between paying suppliers and collecting from customers. A shorter cycle means less working capital tied up — better.

Use when. First-pass liquidity check during credit analysis or fundamental screening. Industry-dependent — compare to peers, not to a universal benchmark.

Can the company cover its next-12-month obligations using assets it expects to turn into cash within the next 12 months? Higher is safer but extremely high may indicate idle capital.

Use when. When inventory is large or hard to liquidate — common in retail, manufacturing, real estate development.

Also called the acid-test ratio. Removes inventory (and prepaids) from the numerator — measures liquidity using only what can be turned into cash quickly. A stricter test than the current ratio.

Use when. Investment decisions, M&A valuation, project ranking.

Present-value-weighted profit from a project. Accept if NPV > 0 (project adds value). Strongest capital-budgeting criterion.

Use when. Discount rate for DCF valuations, hurdle rate for accept/reject decisions on projects with the same risk as the firm, and as a proxy for the firm's marginal cost of capital.

A firm finances assets with a mix of debt, preferred stock, and equity. WACC is the blended after-tax cost of that mix — the minimum return the firm must earn to satisfy all capital providers.

Use when. Estimating how a change in capital structure (e.g. a leveraged buyout, share buyback funded by debt) will move the cost of equity.

MM Proposition II with taxes: adding debt makes equity riskier (financial leverage) so the required return on equity rises linearly with D/E. The (1−t) factor reflects the tax shield on interest payments.

Use when. Capital structure theory; quantifying the tax-shield benefit of debt.

MM Proposition I with taxes: debt creates value via the tax shield (interest is tax-deductible). Levered firm worth more than unlevered by t × D.

Use when. FX hedging, carry-trade analysis, valuing currency forwards.

Covered interest-rate parity, continuous form. High-rate currency depreciates in forward; low-rate currency appreciates.

Use when. Mark-to-market of an existing forward position.

At initiation, no money changes hands so V_0 = 0 if priced correctly. Between initiation and maturity, value changes as spot moves vs locked-in forward price.

Use when. Yield-curve analysis; valuing forward rate agreements (FRAs).

The rate the market implies for a future borrowing period, derived from current spot rates. Investing for A years and then rolling at IFR should equal investing for B years today.

Use when. Hedging short-term interest rate exposure; trading expectations of future short rates.

Eurodollar/SOFR futures are quoted as 100 minus the rate. Higher rate → lower price. A 0.25% rate move = 25 bps × $25 per bp = $2,500 per contract.

Use when. Valuing periodic cash flows of plain-vanilla interest-rate swaps.

In an interest-rate swap, fixed and floating payments are netted each period. Sign depends on whether MRR > or < swap rate.

Use when. Computing terminal payoffs of long call positions.

Exercise only if S_T > X (otherwise let it expire worthless). The 'hockey-stick' payoff diagram.

Use when. Terminal payoff of long puts; hedging downside; portfolio insurance.

Exercise only if S_T < X. Mirror of the call payoff. Max value capped at X (when stock goes to zero).

Use when. Identifying arbitrage opportunities in mispriced options; setting upper/lower bounds for option pricing models.

A call must be worth at least its intrinsic value (S − X) discounted, otherwise arbitrage. Time value sits above this floor.

Use when. Pricing one option given the other plus the underlying; constructing synthetic positions (synthetic call, synthetic put, synthetic stock, synthetic risk-free bond); checking for arbitrage.

Two portfolios with identical payoffs at expiry must cost the same today, or arbitrage exists. Long call + PV of strike ("fiduciary call") has the same expiry payoff as long stock + long put ("protective put").

Use when. Constructing a riskless hedge in a binomial tree (delta-hedging the option). Forms the basis of no-arbitrage option pricing.

The fraction of a share you need to hold for every option written so the combined position is risk-free over the next period. The delta of the option in a one-step world.

Use when. Pricing options on a binomial tree (one or multi-step). The same logic underlies Black-Scholes in continuous time.

Under risk-neutral pricing we pretend everyone is indifferent to risk and discount expected payoffs at the risk-free rate. π is the synthetic probability that makes that pricing consistent — it is NOT the real-world probability.

Use when. Estimating GDP impact of fiscal stimulus (or austerity).

A government spending boost circulates through the economy as recipients spend their new income. Multiplier > 1 because each round of spending creates more income.

Use when. Assessing currency competitiveness; PPP analysis.

Strips out inflation differentials to show how many real (purchasing-power) units of A you get per unit of B.

Use when. Macro framing of current-account deficits and surpluses.

A country's trade balance equals private net savings plus government surplus. Trade deficits = excess domestic investment over savings.

Use when. FX hedging, carry-trade analysis, valuing currency forwards.

Interest-rate parity: forward rate equals spot times the ratio of interest factors. Otherwise arbitrage. Higher-rate currency trades at forward discount.

Use when. INR/EUR via USD; any pair that has no direct quote.

Triangulate the exchange rate between A and B through a third currency C. Used heavily when one currency lacks a direct quote.

Use when. Valuing perpetual preferred stock.

Preferred shares pay a fixed dividend forever. Value = perpetuity of that dividend.

Use when. Estimating intrinsic value for stable, mature dividend payers (utilities, large banks, FMCG). Also for terminal-value calculations in two-stage DDMs.

Values a mature, dividend-paying stock by treating it as a constantly growing perpetuity. The second equation gives g from fundamentals: the firm grows by retaining a fraction of earnings and reinvesting at its ROE.

Use when. Cross-check market P/E against fundamentals; relative valuation.

Justified P/E derived from Gordon Growth. Higher payout, lower required return, higher growth → higher justified multiple.

Use when. EV/EBITDA, EV/Sales multiples; M&A pricing.

What it would cost to acquire the entire business — pay off all capital providers, then keep the cash on hand. EV is capital-structure neutral.

Use when. Reporting period-over-period price moves.

Price-only return (ignores dividends). Most stock indices reported in media (Sensex headline) are price-return indices.

Use when. Performance measurement, fund returns, true long-term equity returns.

Total return = price change + income, expressed as % of starting price. Reflects the full investor experience including dividends.

Use when. Margin investing, derivatives, hedge fund risk analysis.

How many rupees of exposure per rupee of own money. Margin trading with 50% initial margin gives 2× leverage.

Use when. Enterprise-value DCF; valuing a firm independent of its capital structure.

Cash flow available to ALL capital providers (debt + equity) after operating needs and capex. The cash the business actually generates for investors.

Use when. Equity DCF valuation; computing intrinsic share value.

Cash flow available to equity holders only — after debt service and after reinvestment.

Use when. Most non-tax financial reporting; standard accounting practice.

Spreads the depreciable amount evenly over the asset's useful life. Simplest method, most commonly used for financial reporting.

Use when. Accelerated depreciation for tax purposes; assets that lose value disproportionately early.

Accelerated method: charges more depreciation in early years (book value × 2/life), less later. Matches assets that lose value faster up front (cars, IT equipment).

Use when. Efficiency analysis; one of the three DuPont components.

How efficiently the firm generates sales from its assets. Higher = each rupee of assets produces more revenue.

Use when. Activity / operating-efficiency analysis, particularly for retailers, manufacturers, and consumer-goods firms. Pair with days-of-inventory-on-hand for the time interpretation.

How many times in a year a company sells through its inventory. Higher means inventory is moving fast (good); too high may indicate stockouts.

Use when. Estimating working-capital requirements; an input to the Cash Conversion Cycle.

The time interpretation of inventory turnover: roughly how many days of selling activity the firm has tied up in inventory at any moment.

Use when. Working-capital and credit-policy analysis.

How many times per year the firm collects its outstanding credit sales. Higher = better credit control.

Use when. Time-based working-capital analysis.

Average number of days it takes to collect on credit sales. Component of Cash Conversion Cycle.

Use when. Solvency / leverage analysis; credit risk assessment.

How much debt the company carries per rupee of equity. Higher = more leverage = more financial risk.

Use when. Credit analysis, bond covenants, default risk screening.

How many times the firm could pay its interest from its operating earnings. Higher = safer for bondholders.

Use when. When two companies have the same ROE but you want to know whether it's driven by margins, efficiency, or leverage. Also useful for tracking changes in a single company's ROE over time.

Decomposes return on equity into three drivers: how much profit per rupee of sales, how much sales per rupee of assets, and how much the firm has levered its equity. Lets you trace ROE changes back to the underlying business lever.

Use when. Breakeven analysis, sensitivity analysis, what-if questions on volume / pricing.

Contribution margin per unit (P − VC) × units, minus fixed costs. The mechanical link between sales volume and operating profit.

Use when. Cyclicality analysis; identifying companies that will swing hard with the economy.

Sensitivity of operating income to a change in sales. Driven by fixed cost — high fixed cost → high DOL → operating leverage.

Use when. Capital structure analysis; understanding earnings volatility.

Sensitivity of net income to operating income changes. Driven by debt (fixed interest). More debt → higher DFL.

Use when. Equity-risk assessment for highly cyclical and leveraged firms.

Combined sensitivity of net income to sales. DTL = 5 means a 10% sales rise becomes a 50% net income rise.

Use when. Pricing bonds traded between coupon dates; settlement calculations.

Bonds trade between coupon dates. The buyer pays the seller for interest accrued so far — that's the accrued interest, added to the quoted clean price.

Use when. Quick income comparisons; sales-pitch yield.

Simple income yield. Like a dividend yield for bonds, but ignores capital gains/losses to maturity.

Use when. Valuing callable bonds; conservative yield reporting.

For callable bonds, the issuer will redeem when it benefits them — bad for investors. YTW captures the worst-case outcome.

Use when. Credit spread analysis for option-free bonds.

The constant spread you add to every spot rate so the discounted cash flows equal the bond's market price. Captures credit + liquidity premium over the risk-free curve.

Use when. Relative-value analysis of bonds with embedded options (callables, putables, MBS).

Strips the embedded-option value out of the Z-spread, leaving pure credit + liquidity compensation. The right spread to compare a callable bond against an option-free benchmark.

Use when. Comparing the interest-rate sensitivity timeline of bonds. Almost always a stepping-stone to Modified Duration for hedging and price-change estimation.

The weighted-average time (in years or periods) until the bondholder receives back the present-value-weighted cash flows. Acts as the 'effective maturity' of the bond's cash flows.

Use when. Estimating bond price change for small yield moves, immunising a portfolio, computing dollar duration for hedging.

The slope: for a 1% change in yield, a bond's price changes by roughly Modified Duration percent (in the opposite direction). Direct measure of interest-rate sensitivity.

Use when. Whenever the yield change is larger than ~50 bps, or whenever you want a more accurate hedge calculation.

Duration assumes the price–yield relationship is a straight line; in reality it is curved (convex). Convexity adds the second-order correction so the estimate works for larger yield changes.

Use when. Mortgage-backed securities, callable bonds, any bond whose cash flows are interest-rate-dependent.

Numerical (shock-based) duration. Captures price sensitivity for bonds where cash flows depend on yields (callable, MBS).

Use when. Money-market funding, short-term financing for bond dealers.

Repo = sell now and buy back later. Repo price = purchase price plus interest at the repo rate over the term. Day-count uses 360.

Use when. Pricing credit risk, computing credit spreads, loan-loss provisioning.

Probability of default × loss when it happens. Foundation of credit-risk modelling.

Use when. Commercial mortgage credit analysis; underwriting CRE loans.

How many times the property's operating income covers its debt service. DSC > 1.2 = adequate margin of safety.

Use when. Comparing portfolios that are already components of a larger, well-diversified portfolio. There, only beta matters because idiosyncratic risk has been diversified away.

Excess return per unit of systematic (non-diversifiable) risk. Same idea as Sharpe but uses beta instead of standard deviation.

Use when. Mean-variance optimisation; portfolio selection from the efficient frontier.

Quadratic utility: investors like return but dislike variance. Higher A means risk hurts more. The utility-maximising portfolio depends on A.

Use when. Asset-allocation lectures; understanding how cash + risky portfolio combine.

Straight line of return-risk combinations available by mixing the risk-free asset with a chosen risky portfolio i. Slope = Sharpe ratio of i.

Use when. Defining the efficient frontier with a risk-free asset; foundation of CAPM.

The CAL that dominates all others: when everyone holds the market portfolio. Slope is the Sharpe ratio of the market itself.

Use when. Estimating the cost of equity for a public company, finding the discount rate for DCF, or producing a benchmark return for performance evaluation (Jensen alpha).

Investors expect compensation only for systematic (market) risk because they can diversify away the rest. CAPM prices an asset's required return as the risk-free rate plus its share of the market risk premium.

Use when. Ranking portfolios when total risk (not just systematic risk) matters — e.g. comparing standalone investment options that are not already diversified.

Excess return per unit of total risk. Higher is better. Lets you compare portfolios with different risk levels on an apples-to-apples basis.

Use when. Evaluating active manager skill. Use when you have a benchmark and a CAPM beta estimate.

Actual return minus what CAPM said the portfolio should have earned given its beta. Positive alpha = manager added value beyond the market. Negative = manager underperformed risk-adjusted expectation.

Use when. Performance comparison; communicating Sharpe-equivalent returns to a non-technical audience.

Sharpe ratio reinterpreted as a return: 'what return would I have earned if the portfolio had market-level risk?' Allows ranking portfolios on a common-risk basis.

Use when. Robust spread measure when standard deviation is overly punished by outliers.

Average distance from the mean, without squaring. Easier to interpret than standard deviation.

Use when. Forecasting next-period expected return.

Simple average of period returns. Best estimate of return for a single future period (unbiased estimator).

Use when. Converting between nominal and real rates; comparing rates across high- and low-inflation regimes.

Fisher relation: the nominal rate compensates lenders for both real time-value-of-money and expected inflation.

Use when. Single-period return calculations; chaining sub-period returns into a cumulative figure.

Total return = capital gain + income, expressed as a fraction of starting price. For multi-period returns, chain-link (compound) each sub-period.

Use when. Measuring actual realised performance of an investment over multiple periods.

The constant per-period rate that, compounded over n periods, would produce the same total ending value. The 'true' historical return for a buy-and-hold investor.

Use when. Average cost per share under SIP / dollar-cost averaging; averaging P/E ratios.

Used when averaging rates over a constant cost (dollar-cost averaging). Buying a fixed rupee amount each period averages purchase price at the harmonic mean.

Use when. Any single-cash-flow time value of money question with annual (or matched-period) compounding.

Money grows by a factor of (1+r) each period. Present value just runs that forward equation in reverse to discount a future amount back to today.

Use when. TVM problem where the compounding frequency differs from once-a-year (e.g. quarterly, monthly, semi-annual bonds).

When interest is compounded more often than once a year, the effective return on the investment rises slightly. The formula adjusts the rate down to per-period (r/m) and the exponent up to total periods (m×T).

Use when. Option pricing, log returns, theoretical finance models.

The limit of periodic compounding as the number of periods per year goes to infinity. Used heavily in derivatives pricing (Black-Scholes).

Use when. Cross-country comparisons, long-horizon retirement planning where inflation matters.

Strip out inflation from the nominal return to see real purchasing-power growth.

Use when. Margin investing, real-estate analyses, LBO modelling.

Borrowing amplifies returns: if asset returns > cost of debt, equity holders earn the spread, scaled by leverage.

Use when. Valuing any fixed-coupon bond given its yield, or solving for yield given price.

A bond is a portfolio of cash flows: an annuity of coupons plus a final principal repayment. Discount each at the YTM and sum.

Use when. A cash flow stream that is (i) constant, (ii) infinite, and (iii) starts one period from now (ordinary perpetuity). Example: a perpetual preferred share or a British consol bond.

A stream of identical cash flows that never ends is worth the single-period payment divided by the discount rate. Higher rates make the perpetuity less valuable today.

Use when. Equal-payment streams that last for a fixed term: mortgage payments, retirement withdrawals, equipment leases, fixed-coupon bonds (ignoring face value).

A finite stream of equal payments is just the difference between two perpetuities: one starting now, minus one starting after n periods. The bracketed term is the annuity factor.

Use when. Valuing perpetual preferred shares or any cash flow expected to stay flat indefinitely.

Identical to a perpetuity. Used to value perpetual preferred stock paying a fixed dividend forever.

Use when. Mature companies expected to grow dividends at a stable rate forever (e.g. blue-chip utilities). Requires r > g.

Same idea as a perpetuity, but the cash flow grows. The denominator (r − g) is the "net" discount rate after subtracting the growth tailwind.

Use when. T-bills, commercial paper, zero-coupon bonds where only purchase price and final amount matter.

Solves for the yield on a zero-coupon (or discount) bond, given price and maturity.

Use when. Backing out the market's implied return on a stock given its price and dividend trajectory.

Solves Gordon Growth for r. Required return = dividend yield + growth (sometimes called the 'implied return' from current price).

Use when. Sanity-checking market P/E ratios against fundamentals; relative valuation.

Justified P/E from Gordon Growth. Higher payout, lower r, higher g → higher justified P/E.

Use when. Central tendency of a sample; an unbiased estimator of population mean.

Best single-number summary of a sample's center.

Use when. Describing dispersion when distribution is skewed or has outliers.

Spread of the middle 50% of data, ignoring extreme tails. Robust to outliers.

Use when. Computing quartiles, deciles, VaR cut-offs from raw data.

Finds the position of a percentile in sorted data; interpolate between neighbouring observations if not integer.

Use when. Building up a required return from fundamentals, especially for fixed-income securities.

A nominal interest rate is a stack of premiums on top of the real risk-free rate — each premium compensates investors for a specific risk they bear.

Use when. Foundation for standard deviation, hypothesis testing, regression diagnostics.

Squared deviations from the mean, averaged. The square forces them positive and penalises large deviations more than small.

Use when. Computing Sortino ratio, downside-focused portfolio construction.

A one-sided risk measure: only counts deviations below a target. Captures 'downside risk' rather than total volatility.

Use when. Comparing risk of investments with very different means (e.g. growth stock vs treasury).

Risk per unit of expected return. Lower CV = more return per unit of variability.

Use when. Distribution diagnostics; risk analysis (downside-heavy returns have negative skew).

Asymmetry of a distribution. Positive skew = long right tail (mean > median); negative skew = long left tail (mean < median).

Use when. Risk analysis, VaR adjustments; understanding tail events.

"Tailedness" relative to a normal distribution. Positive = fat tails (leptokurtic) — extreme events more likely than normal predicts.

Use when. Portfolio variance, regression slope, beta calculation.

How two variables move together. Positive = same direction; negative = opposite directions; zero = no linear relationship.

Use when. Diversification analysis; relationship strength assessment.

Standardised covariance, bounded between -1 and +1. ±1 = perfect linear relationship; 0 = no linear relationship.

Use when. Decision-making under uncertainty; valuing probabilistic cash flows.

Probability-weighted average of all possible outcomes. The mean of a random variable.

Use when. Risk measurement for discrete probability distributions.

Probability-weighted average of squared deviations from the mean. The shortcut form E(X²) − [E(X)]² is faster when you have raw moments.

Use when. Scenario analysis: e.g., expected portfolio return weighted by recession / normal / boom probabilities.

Unconditional expectation = weighted sum of conditional expectations across mutually exclusive scenarios.

Use when. Credit analysis, hypothesis testing intuition, classifier intuition. Beloved by question writers because candidates frequently confuse P(A|B) with P(B|A).

Updates a prior belief about an event after receiving new information. The multiplier (likelihood/marginal) tells you how strongly the info shifts the prior.