Is this CFA Level 1 formula sheet updated for 2026?

Yes. This formula sheet is aligned with the 2026 CFA Level I curriculum and is updated whenever CFA Institute publishes curriculum changes.

Is the OneQuest CFA Level 1 formula sheet free?

Yes. The OneQuest CFA Level 1 formula sheet is 100% free to view online. No sign-up, no email, and no payment is required to use it.

Can I use this formula sheet during the actual CFA exam?

No. The CFA exam is closed-book. You may not bring formula sheets, notes, or printed materials into the testing centre. Use this sheet for study and revision only.

How many formulas do I need to know for CFA Level 1?

Most candidates need to memorise roughly 50–70 core formulas across all 10 topic areas. This sheet covers every key formula from the curriculum so you can review them in one place.

What topics are covered in this formula sheet?

All 10 CFA Level I topic areas: Quantitative Methods, Economics, Financial Statement Analysis, Corporate Issuers, Equity Investments, Fixed Income, Derivatives, Alternative Investments, Portfolio Management, and Ethical & Professional Standards.

How should I use this formula sheet in my study plan?

Keep the relevant topic section open while you study, use it as a quick reference during practice questions, and run fast formula-review passes in your final weeks before the exam.

Which CFA Level 1 formulas are most important to memorise?

High-yield formulas include time value of money (PV/FV/annuities), DuPont decomposition, ratio analysis, CAPM, WACC, bond duration and convexity, put-call parity, and the Sharpe ratio. They appear repeatedly across topics and exam questions.

Does the CFA Level 1 exam provide a formula sheet?

No. CFA Institute does not provide a formula sheet during the exam. Candidates are expected to memorise all formulas, though common financial calculator functions (BA II Plus or HP 12C) may be used.

How is this formula sheet different from a CFA cheat sheet?

Most cheat sheets are just LaTeX dumps. This sheet pairs every formula with its 'use when' trigger, plain-language intuition, and variable definitions — designed for actual revision, not just decoration.

CFA Level 1 Formula Sheet (2026)

Last updated 10 June 2026

Topic

Alternative Investments

Alternative Investments formulas cover real estate valuation (cap rate, NOI), private equity (DPI, RVPI, TVPI), hedge fund fee structures, and commodity index returns.

Multiple of Invested Capital
$M O I C = \frac{Realized value + Unrealized value}{Total investment}$ MOIC = (Realized + Unrealized) / Total investment
Use when. Private equity / venture fund performance reporting.
Total value / paid-in (TVPI). Tells you the headline "X times your money" of a PE fund.
Variables
$Realized value$
Distributions / cash returned to LPs
$Unrealized value$
NAV of remaining investments
$Total investment$
Capital invested to date
Performance Fee (Hard Hurdle)
$Fee = max [0, p \times (r - r_{0})]$ Fee = max(0, p*(r - r0)) for hard hurdle
Use when. Hedge fund / PE fee modelling.
Hedge funds charge a performance fee on returns ABOVE the hurdle (hard hurdle only). Below the hurdle: no incentive fee.
Variables
$p$
Performance fee rate (e.g. 20%)
$r$
Realised return
$r_{0}$
Hurdle rate

Topic

Corporate Issuers

Corporate Issuers formulas include WACC, cost of equity (CAPM and DDM approaches), operating and financial leverage, and breakeven analysis.

Return on Invested Capital
$R O I C = \frac{After-tax net profit}{Avg. BV of invested capital} = \frac{( 1 - t ) \times Operating profit}{Avg. (LT liabilities + Equity)}$ ROIC = After-tax profit / Avg invested capital
Use when. Assessing whether management is creating value, not just generating accounting profit.
Return earned on all capital deployed in the business, debt and equity alike. Compare to WACC: ROIC > WACC = creating value.
Variables
$Invested capital$
Long-term debt + equity (avg)
$t$
Tax rate
Cash Conversion Cycle
$CCC = DOH + DSO - DPO$ Cash conversion cycle = DOH + DSO - DPO
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.
Variables
$DOH$
Days of inventory on hand
$DSO$
Days of sales outstanding (receivables)
$DPO$
Days of payables outstanding
Current Ratio
$Current ratio = \frac{Current assets}{Current liabilities}$ Current ratio = Current assets / Current liabilities
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.
Variables
$Current assets$
Cash, receivables, inventory, prepaids, etc.
$Current liabilities$
Obligations due within 12 months
Quick Ratio
$Quick ratio = \frac{Cash + Marketable securities + Receivables}{Current liabilities}$ Quick ratio = (Cash + Marketable securities + Receivables) / Current liabilities
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.
Variables
$Cash$
Cash and cash equivalents
$Marketable securities$
Short-term liquid investments
$Receivables$
Trade and other current receivables
$Current liabilities$
Obligations due within 12 months
Net Present Value
$N P V = t = 1 \sum n \frac{C F _{t}}{( 1 + r ) ^{t}} - Outlay$ NPV = Sum CF_t/(1+r)^t - Outlay; accept if NPV > 0
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.
Variables
$C F_{t}$
Cash flow in period t
$r$
Discount rate (cost of capital)
$Outlay$
Initial investment (t = 0)
Weighted Average Cost of Capital
$W A C C = w_{d} r_{d} (1 - t) + w_{p} r_{p} + w_{e} r_{e}$ WACC = wd*rd*(1-t) + wp*rp + we*re
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.
Variables
$w_{d}, w_{p}, w_{e}$
Weights of debt / preferred / equity— sum to 1
$r_{d}$
Pre-tax cost of debt
$r_{p}$
Cost of preferred stock
$r_{e}$
Cost of equity— typically from CAPM
$t$
Marginal corporate tax rate
Cost of Equity (Modigliani-Miller)
$r_{e} = r_{0} + (r_{0} - r_{d}) (1 - t) \frac{D}{E}$ re = r0 + (r0 - rd)(1-t)(D/E) with taxes
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.
Variables
$r_{e}$
Cost of equity (levered)
$r_{0}$
Cost of equity if unlevered (all-equity firm)
$r_{d}$
Cost of debt
$t$
Tax rate
$D/E$
Debt-to-equity ratio
Firm Value with Taxes
$V_{L} = V_{U} + t D$ V_L = V_U + t*D
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.
Variables
$V_{L}$
Levered firm value
$V_{U}$
Unlevered firm value
$t$
Corporate tax rate
$D$
Market value of debt

Topic

Derivatives

Derivatives formulas include put-call parity, binomial option pricing, Black-Scholes-Merton inputs, and forward/futures pricing relationships.

Forward Price (Benefits/Income and Costs)
$F_{0} (T) = [S_{0} + P V_{0} (C) - P V_{0} (I)] (1 + r)^{T} or F_{0} (T) = S_{0} e^{(r - c) T}$ F0(T) = [S0 + PV(C) - PV(I)](1+r)^T or continuous: S0*e^((r-c)T)
Use when. Pricing forwards on stocks, bonds, commodities, currencies.
No-arbitrage forward price = spot, grown at the risk-free rate, with carry costs added and income subtracted.
Variables
$S_{0}$
Spot price
$P V_{0} (C)$
PV of carry costs (storage etc.)
$P V_{0} (I)$
PV of income (dividends, coupons)
$r$
Risk-free rate
$c$
Continuous convenience / cost-of-carry yield
Currency Forward Price
$F_{0, A / B} (T) = S_{0, A / B} e^{(r_{A} - r_{B}) T}$ F_A/B(T) = S_A/B * e^((rA - rB)*T)
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.
Variables
$S_{0, A / B}$
Spot rate, A per B
$r_{A}, r_{B}$
Risk-free rates in currencies A and B
$T$
Time to forward delivery
Forward Valuation
$V_{0} (T) = S_{0} - \frac{F _{0} ( T )}{( 1 + r ) ^{T}}, V_{t} (T) = S_{t} - \frac{F _{0} ( T )}{( 1 + r ) ^{T - t}}$ V0 = S0 - F0/(1+r)^T; Vt = St - F0/(1+r)^(T-t)
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.
Variables
$V_{0} (T)$
Value of forward at initiation
$V_{t} (T)$
Value of forward at time t between initiation and maturity
$S_{t}$
Spot at time t
$F_{0} (T)$
Locked-in forward price
Implied Forward Rate
$I F R_{A, B - A} = (\frac{( 1 + z _{B} ) ^{B}}{( 1 + z _{A} ) ^{A}})^{1/ (B - A)} - 1$ IFR = ((1+z_B)^B/(1+z_A)^A)^(1/(B-A)) - 1
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.
Variables
$z_{A}, z_{B}$
Spot rates for A and B years
$IFR$
Implied forward rate from A to B
Interest Rate Futures Price
$f_{A, B - A} = 100 - (100 \times M R R_{A, B - A})$ Futures price = 100 - 100*MRR
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.
Variables
$MRR$
Market reference rate (e.g. SOFR)
$f_{A, B - A}$
Futures price
Swap Periodic Settlement
$Settlement = (M R R - Swap rate) \times Notional \times Period$ Settlement = (MRR - Swap rate)*Notional*Period
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.
Variables
$MRR$
Market reference rate at reset
$Swap rate$
Fixed rate of the swap
$Notional$
Notional principal
$Period$
Day-count fraction
Call Value at Expiry
$c_{T} = max [0, S_{T} - X]$ Call at expiry: cT = max(0, ST - X)
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.
Variables
$c_{T}$
Call value at expiry
$S_{T}$
Underlying price at expiry
$X$
Strike price
Put Value at Expiry
$p_{T} = max [0, X - S_{T}]$ Put at expiry: pT = max(0, X - ST)
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).
Variables
$p_{T}$
Put value at expiry
$X$
Strike price
$S_{T}$
Underlying price at expiry
Call Lower Bound
$c_{t} \geq max [0, S_{t} - X / (1 + r)^{T - t}]$ ct >= max(0, St - X/(1+r)^(T-t))
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.
Variables
$c_{t}$
European call value at time t
$S_{t}$
Spot at t
$X$
Strike
$r$
Risk-free rate
$T - t$
Time remaining to expiry
Put-Call Parity
$c_{0} + \frac{X}{( 1 + r ) ^{T}} = S_{0} + p_{0}$ c0 + X/(1+r)^T = S0 + p0
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").
Variables
$c_{0}$
Call option premium today
$p_{0}$
Put option premium today
$S_{0}$
Underlying spot price today
$X$
Strike price
$r$
Risk-free rate
$T$
Time to expiration
Binomial Hedge Ratio
$h = \frac{c _{u} - c _{d}}{S _{u} - S _{d}}$ h = (cu - cd)/(Su - Sd)
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.
Variables
$h$
Hedge ratio (shares per option)
$c_{u}, c_{d}$
Option value at up / down node
$S_{u}, S_{d}$
Stock price at up / down node
Risk-Neutral Probability
$π = \frac{1 + r - d}{u - d}, c_{0} = \frac{π c _{u} + ( 1 - π ) c _{d}}{1 + r}$ pi = (1+r-d)/(u-d); c0 = (pi*cu + (1-pi)*cd)/(1+r)
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.
Variables
$π$
Risk-neutral probability of up-move
$u, d$
Up-move and down-move factors— d < 1 < u
$r$
Risk-free rate per period
$c_{u}, c_{d}$
Call value at up / down node

Topic

Economics

Economics formulas span micro and macroeconomics, including supply-demand analysis, GDP calculations, exchange rate parity conditions, and monetary/fiscal policy models.

Profit Maximization
$M R = M C$ Marginal Revenue = Marginal Cost
Use when. Output decisions for firms in any market structure (perfect competition, monopoly, oligopoly).
Produce one more unit as long as it adds more revenue than cost. Stop when they're equal — that's the profit-maximising quantity.
Variables
$MR$
Marginal revenue (Δ revenue from one more unit)
$MC$
Marginal cost (Δ cost from one more unit)
Fiscal Multiplier
$Multiplier = \frac{1}{1 - M P C ( 1 - t )}$ Fiscal multiplier = 1 / (1 - MPC(1-t))
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.
Variables
$MPC$
Marginal propensity to consume
$t$
Tax rate
Real Exchange Rate
$Real ex. rate_{A / B} = Nominal ex. rate_{A / B} \times \frac{C P I _{B}}{C P I _{A}}$ Real exchange rate = Nominal rate * (CPI_B/CPI_A)
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.
Variables
$N o mina l r a t e_{A / B}$
Units of A per unit of B
$C P I_{A}, C P I_{B}$
Consumer price indices
Trade Balance
$X - M = (S - I) + (T - G)$ Trade balance: X - M = (S - I) + (T - G)
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.
Variables
$X - M$
Net exports (trade balance)
$S - I$
Private savings minus investment
$T - G$
Government surplus (taxes minus spending)
Forward Exchange Rate
$\frac{F _{A / B} ( T )}{S _{A / B}} = \frac{1 + i _{A}}{1 + i _{B}}$ Forward/Spot = (1+i_A)/(1+i_B)
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.
Variables
$F_{A / B} (T)$
Forward rate at horizon T
$S_{A / B}$
Spot rate
$i_{A}, i_{B}$
Risk-free rates in currencies A and B
Cross-Rate
$S_{A / B} = S_{A / C} \times S_{C / B}$ S_A/B = S_A/C * S_C/B
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.
Variables
$S_{A / B}$
Implied rate of A per B
$C$
Bridge / vehicle currency (often USD)

Topic

Equity Investments

Equity valuation formulas cover the Dividend Discount Model (DDM), Free Cash Flow models, and relative valuation multiples like P/E, P/B, and EV/EBITDA.

Dividend Discount Model
$V_{0} = t = 1 \sum \infty \frac{D _{t}}{( 1 + r ) ^{t}} = t = 1 \sum n \frac{D _{t}}{( 1 + r ) ^{t}} + \frac{P _{n}}{( 1 + r ) ^{n}}$ V0 = Sum Dt/(1+r)^t; or finite + terminal Pn/(1+r)^n
Use when. General DDM framework; building block for Gordon, two-stage, and H-models.
A stock is worth the PV of all future dividends. For finite horizons, add a terminal value at the end.
Variables
$V_{0}$
Intrinsic value today
$D_{t}$
Dividend in period t
$P_{n}$
Terminal stock price at horizon n
$r$
Required return on equity
Perpetual Preferred Stock
$V_{0} = \frac{D _{0}}{r}$ V0 = D0 / r
Use when. Valuing perpetual preferred stock.
Preferred shares pay a fixed dividend forever. Value = perpetuity of that dividend.
Variables
$D_{0}$
Constant preferred dividend
$r$
Required return on the preferred
Gordon Growth Model
$V_{0} = \frac{D _{0} ( 1 + g )}{r - g} = \frac{D _{1}}{r - g}, g = (1 - D / E) \times R O E$ V0 = D1/(r-g); g = (1 - D/E)*ROE
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.
Variables
$V_{0}$
Intrinsic value of the equity today
$D_{0}, D_{1}$
Most recent / next-year dividend
$r$
Required return on equity
$g$
Sustainable growth rate
$1 - D/E$
Retention ratio— = 1 − payout ratio
$ROE$
Return on equity
Forward P/E (Gordon)
$\frac{P _{0}}{E _{1}} = \frac{D _{1} / E _{1}}{r - g}$ P0/E1 = (D1/E1)/(r-g)
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.
Variables
$D_{1} / E_{1}$
Forward payout ratio
$r$
Required return on equity
$g$
Constant growth rate
Enterprise Value
$E V = M V (Equity) + M V (Preferred) + M V (Debt) - (Cash + ST investments)$ EV = MV(Equity) + MV(Pref) + MV(Debt) - Cash - ST investments
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.
Variables
$MV(Equity)$
Market cap = price × shares
$MV(Debt)$
Market value of debt
$Cash$
Cash and short-term liquid investments
Price Return (Single Period)
$P R_{i} = \frac{P _{i, 1} - P _{i, 0}}{P _{i, 0}}, P R_{I} = i = 1 \sum n w_{i} P R_{i}$ PR_i = (P_i,1 - P_i,0)/P_i,0; Index PR = Sum wi*PRi
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.
Variables
$P R_{i}$
Price return of constituent i
$P_{i, 0}, P_{i, 1}$
Start / end prices
$w_{i}$
Constituent weight in index
Total Return (Single Period)
$T R_{i} = \frac{P _{i, 1} - P _{i, 0} + I n c _{i}}{P _{i, 0}}, T R_{I} = i = 1 \sum n w_{i} T R_{i}$ TR_i = (P_i,1 - P_i,0 + Inc_i)/P_i,0
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.
Variables
$T R_{i}$
Total return of constituent i
$I n c_{i}$
Dividend / income received in period
Leverage Ratio
$Leverage ratio = \frac{Position}{Equity}, Max initial = \frac{1}{Initial margin}$ Leverage = Position/Equity; Max initial = 1/Initial margin
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.
Variables
$Position$
Total value of position
$Equity$
Own capital invested
$Initial margin$
Fraction of position funded by investor

Topic

Financial Statement Analysis

Financial Statement Analysis (FSA) carries one of the highest topic weights. Key formulas include profitability, liquidity, solvency, and activity ratios, plus LIFO-FIFO adjustments and DuPont decomposition.

Basic EPS
$Basic EPS = \frac{Net income - Preferred dividends}{Weighted avg. shares outstanding}$ Basic EPS = (NI - Preferred dividends) / Weighted avg shares
Use when. Earnings per share reporting; per-share comparisons over time and across companies.
Earnings per common share available to common stockholders. Strip out preferred dividends (which belong to preferred holders).
Variables
$NI$
Net income
$Preferred dividends$
Cumulative preferred dividends
$WAvg shares$
Weighted-average common shares outstanding
Free Cash Flow to Firm
$F C F F = N I + N C C + I (1 - t) - F C I - W C I or F C F F = C F O + I (1 - t) - F C I$ FCFF = NI + NCC + I(1-t) - FCI - WCI
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.
Variables
$NI$
Net income
$NCC$
Non-cash charges (depreciation, amortisation)
$I$
Interest expense
$t$
Tax rate
$FCI$
Fixed capital investment (capex)
$WCI$
Working capital investment
$CFO$
Cash flow from operations
Free Cash Flow to Equity
$F C F E = C F O - F C I + Net borrowing$ FCFE = CFO - FCI + Net borrowing
Use when. Equity DCF valuation; computing intrinsic share value.
Cash flow available to equity holders only — after debt service and after reinvestment.
Variables
$CFO$
Cash from operations
$FCI$
Fixed capital investment
$Net borrowing$
New debt − repayments
Straight-Line Depreciation
$Depreciation = \frac{Cost - Salvage}{Useful life}$ Depreciation = (Cost - Salvage) / Useful life
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.
Variables
$Cost$
Acquisition cost
$Salvage$
Estimated residual value
$Useful life$
Years over which asset is depreciated
Double-Declining Balance
$Depreciation_{t} = \frac{Book value _{t}}{Depreciable life} \times 2$ DDB: Depreciation = (Book value / Life) * 2
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).
Variables
$B oo k v a l u e_{t}$
Beginning-of-period book value
$Life$
Useful life in years
Total Asset Turnover
$\frac{Revenue}{Average total assets}$ Total asset turnover = Revenue / Avg total assets
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.
Variables
$Revenue$
Net sales
$Avg total assets$
Average of beginning and ending total assets
Inventory Turnover
$\frac{COGS}{Average inventory}$ Inventory turnover = COGS / Avg inventory
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.
Variables
$COGS$
Cost of goods sold
$Average inventory$
Average of beginning and ending inventory
Days of Inventory on Hand
$\frac{365}{Inventory turnover}$ Days inventory = 365 / Inventory turnover
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.
Variables
$365$
Days in a year
$Inventory turnover$
COGS / Avg inventory
Receivables Turnover
$\frac{Annual sales}{Average receivables}$ Receivables turnover = Annual sales / Avg receivables
Use when. Working-capital and credit-policy analysis.
How many times per year the firm collects its outstanding credit sales. Higher = better credit control.
Variables
$Sales$
Annual credit sales (or net sales)
$Avg receivables$
Average accounts receivable
Days of Sales Outstanding
$\frac{365}{Receivables turnover}$ DSO = 365 / Receivables turnover
Use when. Time-based working-capital analysis.
Average number of days it takes to collect on credit sales. Component of Cash Conversion Cycle.
Variables
$365$
Days in a year
$Receivables turnover$
Sales / Avg receivables
Debt-to-Equity
$\frac{Total debt}{Total shareholders’ equity}$ Debt-to-equity = Total debt / Total equity
Use when. Solvency / leverage analysis; credit risk assessment.
How much debt the company carries per rupee of equity. Higher = more leverage = more financial risk.
Variables
$Total debt$
Long-term + short-term debt
$Total equity$
Common + preferred + retained earnings
Interest Coverage
$\frac{E B I T}{Interest payments}$ Interest coverage = EBIT / Interest payments
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.
Variables
$EBIT$
Earnings before interest and taxes
$Interest payments$
Periodic interest expense
ROE (DuPont)
$R O E = \frac{N I}{Assets} \times \frac{Assets}{Equity} = ROA \times Leverage$ ROE = ROA * Leverage = (NI/Revenue)*(Revenue/Assets)*(Assets/Equity)
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.
Variables
$NI$
Net income
$NI / Revenue$
Net profit margin— profitability
$Revenue / Assets$
Asset turnover— efficiency
$Assets / Equity$
Financial leverage
Operating Income
$Operating income = [Q \times (P - V C)] - F C$ Operating income = Q*(P - VC) - FC
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.
Variables
$Q$
Units sold
$P$
Price per unit
$VC$
Variable cost per unit
$FC$
Fixed cost (total)
Degree of Operating Leverage
$D O L = \frac{%Δ Operating income}{%Δ Sales}$ DOL = % change Operating income / % change Sales
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.
Variables
$% Δ Operating income$
Percent change in operating income
$% Δ Sales$
Percent change in sales
Degree of Financial Leverage
$D F L = \frac{%Δ Net income}{%Δ Operating income}$ DFL = % change NI / % change Operating income
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.
Variables
$% Δ NI$
Percent change in net income
$% Δ Operating income$
Percent change in operating income (EBIT)
Degree of Total Leverage
$D T L = D F L \times D O L$ DTL = DFL * DOL
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.
Variables
$DOL$
Degree of operating leverage
$DFL$
Degree of financial leverage

Topic

Fixed Income

Fixed Income formulas address bond pricing, yield measures (YTM, current yield, spread), duration, convexity, and term-structure models essential for the CFA exam.

Bond PV (Market Discount Rate)
$P V = \frac{P M T}{( 1 + r ) ^{1}} + \dots + \frac{P M T + F V}{( 1 + r ) ^{n}}$ PV = Sum PMT/(1+r)^t + FV/(1+r)^n
Use when. Bond pricing given YTM; calculating clean prices.
A bond is the sum of present values of all coupon payments plus the final principal repayment.
Variables
$PMT$
Periodic coupon payment
$FV$
Face value (paid at maturity)
$r$
Periodic discount rate (YTM)
$n$
Periods to maturity
Full Price and Accrued Interest
$P V_{f u l l} = P V_{f l a t} + A I = P V (1 + r)^{t / T}, A I = (t / T) \times P M T$ Full price = Flat + AI; AI = (t/T)*PMT
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.
Variables
$P V_{f} u l l$
Dirty price (what you pay)
$P V_{f} l a t$
Clean price (quoted)
$AI$
Accrued interest
$t/T$
Fraction of period since last coupon
Current Yield
$\frac{Annual coupon}{Flat price}$ Current yield = Annual coupon / Flat 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.
Variables
$Annual coupon$
Total coupon income per year
$Flat price$
Clean / quoted price
Yield to Worst
$Y T W = min [Y T C, Y T M]$ Yield to worst = min(YTC, YTM)
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.
Variables
$YTC$
Yield to call (computed for each call date)
$YTM$
Yield to maturity
Z-Spread
$P V = \sum \frac{P M T}{( 1 + z _{t} + Z ) ^{t}} + \frac{F V}{( 1 + z _{n} + Z ) ^{n}}$ PV = Sum PMT/(1+zt+Z)^t + FV/(1+zn+Z)^n (trial and error for Z)
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.
Variables
$z_{t}$
Spot rate at maturity t
$Z$
Z-spread (constant additive)
$PMT, FV$
Coupon and face value
Option-Adjusted Spread
$O A S = Z -spread - Option value (bps)$ OAS = Z-spread - Option value in bps
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.
Variables
$Z-spread$
Constant spread over spot curve
$Option value$
Value of embedded option in bps
Macaulay Duration
$D_{M a c} = \frac{1 + r}{r} - \frac{1 + r + n ( c - r )}{c [( 1 + r ) ^{n} - 1 ] + r} - \frac{t}{T}$ Macaulay duration formula (r=YTM, c=coupon rate, n=periods, t/T=accrued)
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.
Variables
$r$
Yield to maturity per period· decimal
$c$
Periodic coupon rate· decimal
$n$
Periods to maturity
$t/T$
Fraction of period since last coupon
Modified Duration
$M o d D u r = \frac{D _{M a c}}{1 + r}, %Δ P V_{f u l l} \approx - M o d D u r \times Δ Y i e l d$ ModDur = MacDur/(1+r); % change PV ≈ -ModDur * delta Yield
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.
Variables
$D_{M} a c$
Macaulay duration
$r$
Yield per period
$ΔYield$
Change in yield· decimal
$%ΔPV$
Approximate % change in bond price
Convexity Adjustment
$%Δ P V \approx - D_{M o d} \times Δ Y T M + \frac{1}{2} \times C o n v \times (Δ Y T M)^{2}$ % delta PV ≈ -ModDur*delta YTM + (1/2)*Convexity*(delta YTM)^2
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.
Variables
$D_{M} o d$
Modified duration
$Conv$
Convexity— curvature measure
$ΔYTM$
Change in yield to maturity· decimal
Effective Duration
$E f f D u r = \frac{P V _{-} - P V _{+}}{2 \times Δ C u r v e \times P V _{0}}$ EffDur = (PV- - PV+)/(2*delta Curve*PV0)
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).
Variables
$P V_{-}$
Price after yield curve shifts DOWN by Δ
$P V_{+}$
Price after yield curve shifts UP by Δ
$P V_{0}$
Current price
$ΔCurve$
Magnitude of parallel curve shift
Repo Price
$Repo price = Purchase price \times (1 + Repo rate \times \frac{Days}{360})$ Repo price = Purchase price * (1 + Repo rate * Days/360)
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.
Variables
$Purchase price$
Initial sale price of bond
$Repo rate$
Annualised interest charged
$Days$
Term of repo agreement
Expected Loss (Credit)
$E [L oss] = P (Default) \times Loss severity, Loss severity = 1 - Recovery rate$ E[Loss] = P(Default)*Loss severity; Loss severity = 1 - Recovery rate
Use when. Pricing credit risk, computing credit spreads, loan-loss provisioning.
Probability of default × loss when it happens. Foundation of credit-risk modelling.
Variables
$P(Default)$
Probability of default
$Loss severity$
Loss given default (LGD)
$Recovery rate$
Fraction of face recovered after default
Debt Service Coverage (CMBS)
$D S C = \frac{N O I}{Debt service}, N O I = Rental income - Cash operating expense - Replacement reserves$ DSC = NOI / Debt service
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.
Variables
$NOI$
Net operating income
$Debt service$
Periodic interest + principal payments

Topic

Portfolio Management

Portfolio Management formulas encompass the Capital Asset Pricing Model (CAPM), Sharpe ratio, Treynor ratio, Jensen's alpha, and mean-variance optimisation.

Beta
$β_{i} = \frac{Cov ( R _{i} , R _{M} )}{σ _{M}^{2}} = ρ_{i, M} \frac{σ _{i}}{σ _{M}}$ Beta = Cov(Ri,RM)/sigma_M^2 = rho*sigma_i/sigma_M
Use when. As the systematic-risk input for CAPM, Treynor ratio, Jensen alpha, and equity risk-premium adjustments.
How much an asset's returns swing relative to the market. β = 1 moves with the market; β > 1 amplifies; β < 1 dampens; β < 0 moves opposite.
Variables
$β_{i}$
Beta of asset i
$C o v (R_{i}, R_{M})$
Covariance of asset and market returns
$σ_{M}^{2}$
Variance of market returns
$ρ_{i, M}$
Correlation between asset and market
$σ_{i}, σ_{M}$
Std dev of asset / market
Utility Function
$U = E (r) - \frac{1}{2} A σ^{2}$ U = E(r) - (1/2)*A*sigma^2; A > 0 risk averse
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.
Variables
$U$
Investor utility
$E(r)$
Expected return
$A$
Risk-aversion coefficient— 0 = neutral; higher = more averse
$σ²$
Variance of returns
Capital Allocation Line
$E (R_{p}) = R_{f} + \frac{E [ R _{i} ] - R _{f}}{σ _{i}} σ_{p}$ E(Rp) = Rf + ((E[Ri]-Rf)/sigma_i)*sigma_p
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.
Variables
$E (R_{p})$
Expected portfolio return
$R_{f}$
Risk-free rate
$E [R_{i}] - R_{f}$
Risk premium on chosen risky asset / portfolio
$σ_{i}, σ_{p}$
Std dev of risky asset and chosen portfolio
Capital Market Line
$E (R_{p}) = R_{f} + \frac{E [ R _{M} ] - R _{f}}{σ _{M}} σ_{p}$ CML: E(Rp) = Rf + ((E[RM]-Rf)/sigma_M)*sigma_p
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.
Variables
$E (R_{M}) - R_{f}$
Market risk premium
$σ_{M}$
Std dev of market
$σ_{p}$
Std dev of portfolio (on CML)
CAPM
$E (R_{i}) = R_{f} + β_{i} [E (R_{M}) - R_{f}]$ E(Ri) = Rf + beta_i*(E(RM) - Rf)
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.
Variables
$E (R_{i})$
Expected return on asset i
$R_{f}$
Risk-free rate
$β_{i}$
Asset i's beta— sensitivity to market returns
$E (R_{M}) - R_{f}$
Market risk premium
Sharpe Ratio
$\frac{R _{p} - R _{f}}{σ _{p}}$ Sharpe = (Rp - Rf) / sigma_p
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.
Variables
$R_{p}$
Portfolio return
$R_{f}$
Risk-free rate— India: 91-day T-bill ~7%
$σ_{p}$
Standard deviation of portfolio returns
Treynor Ratio
$\frac{R _{p} - R _{f}}{β _{p}}$ Treynor = (Rp - Rf) / beta_p
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.
Variables
$R_{p}$
Portfolio return
$R_{f}$
Risk-free rate
$β_{p}$
Portfolio beta— systematic risk
Jensen's Alpha
$α = R_{p} - [R_{f} + β_{p} (R_{M} - R_{f})]$ Jensen's alpha = Rp - (Rf + beta_p*(RM - Rf))
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.
Variables
$α$
Jensen's alpha — abnormal return
$R_{p}$
Realized portfolio return
$R_{f}$
Risk-free rate
$β_{p}$
Portfolio beta
$R_{M}$
Market return
M-Squared
$M^{2} = (R_{p} - R_{f}) \frac{σ _{M}}{σ _{p}} + R_{f}$ M^2 = (Rp - Rf)*(sigma_M/sigma_p) + Rf
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.
Variables
$R_{p}, R_{f}$
Portfolio and risk-free returns
$σ_{p}, σ_{M}$
Std dev of portfolio and market

Topic

Quantitative Methods

Quantitative Methods covers time value of money (TVM), descriptive statistics, probability distributions, hypothesis testing, and linear regression — foundational formulas used throughout the CFA curriculum.

Nominal Risk-free Rate
$(1 + r_{n o m}) = (1 + r_{r e a l}) (1 + π) \Rightarrow r_{n o m} \approx r_{r e a l} + π$ (1 + Nominal risk-free rate) = (1 + Real risk-free rate)(1 + Inflation premium); Nominal risk-free rate ≈ Real risk-free rate + Inflation premium
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.
Variables
$r_{n} o m$
Nominal risk-free rate
$r_{r} e a l$
Real (inflation-adjusted) risk-free rate
$π$
Expected inflation rate
Holding Period Return
$R = \frac{P _{1} - P _{0}}{P _{0}} + \frac{I}{P _{0}} or R = [(1 + R_{1}) (1 + R_{2}) \dots (1 + R_{n})] - 1$ R = (P1 - P0)/P0 + I/P0; or multi-period: R = [(1+R1)(1+R2)...(1+Rn)] - 1
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.
Variables
$P_{0}, P_{1}$
Price at beginning / end of period
$I$
Income (dividend, coupon) during the period
$R_{i}$
Single-period return
Arithmetic Mean Return
$\overset{ˉ}{R}_{A M} = \frac{\sum _{i = 1}^{n} R _{i}}{n}$ Arithmetic mean return = (Sum of returns) / n
Use when. Forecasting next-period expected return.
Simple average of period returns. Best estimate of return for a single future period (unbiased estimator).
Variables
$R_{i}$
Return in period i
$n$
Number of periods
Geometric Mean Return
$R_{GM} = n \prod_{i = 1}^{n} (1 + R_{i}) - 1$ Geometric mean return = (Product of (1+Ri))^(1/n) - 1
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.
Variables
$R_{i}$
Period return
$n$
Number of periods
Harmonic Mean Return (Cost Averaging)
$\overset{ˉ}{X}_{H} = \frac{n}{\sum _{i = 1}^{n} \frac{1}{X _{i}}}$ Harmonic mean = n / (Sum of 1/Xi); If returns volatile: Arithmetic > Geometric > Harmonic; (Arithmetic)(Harmonic) = (Geometric)^2
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.
Variables
$X_{i}$
Observed value (e.g. price paid)
$n$
Number of observations
Future Value and Present Value
$F V_{n} = P V (1 + r)^{n} \Leftrightarrow P V = \frac{F V _{n}}{( 1 + r ) ^{n}}$ FV = PV(1+r)^n; PV = FV/(1+r)^n
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.
Variables
$PV$
Present value— amount today
$FV$
Future value— amount after n periods
$r$
Periodic interest rate· decimal
$n$
Number of compounding periods
FV/PV with Periodic Compounding
$F V_{n} = P V (1 + \frac{r _{s}}{m})^{m T} \Leftrightarrow P V = \frac{F V _{n}}{( 1 + \frac{r _{s}}{m} ) ^{m T}}$ FV = PV(1 + rs/m)^(mT); PV = FV/(1 + rs/m)^(mT)
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).
Variables
$r_{s}$
Stated annual rate· decimal
$m$
Compounding periods per year
$T$
Number of years
$PV$
Present value
$FV$
Future value
Continuously Compounded Returns
$F V_{T} = P V \cdot e^{r_{cc} T}$ FV = PV * e^(r_cc * 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).
Variables
$r_{c} c$
Continuously compounded rate (force of interest)
$T$
Time in years
$e$
Euler's number ≈ 2.71828
Real Returns
$(1 + Real return) = \frac{( 1 + r _{n o m} ) ( 1 + Risk premium )}{1 + Inflation premium}$ (1 + Real return) = (1 + r_nom)(1 + Risk premium) / (1 + Inflation premium)
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.
Variables
$r_{n} o m$
Nominal real risk-free rate
$Risk premium$
Excess return over risk-free rate
$Inflation premium$
Expected inflation rate
Leveraged Return
$R_{L} = R_{i} + \frac{V _{d}}{V _{e}} (R_{i} - r_{d})$ Leveraged return = Ri + (Vd/Ve)(Ri - rd)
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.
Variables
$R_{L}$
Levered return on equity
$R_{i}$
Return on the investment (unlevered)
$r_{d}$
Cost of debt
$V_{d} / V_{e}$
Debt-to-equity ratio
Coupon Bond PV
$P V = \frac{P M T _{1}}{( 1 + r ) ^{1}} + \frac{P M T _{2}}{( 1 + r ) ^{2}} + \dots + \frac{P M T _{n} + F V _{n}}{( 1 + r ) ^{n}}$ PV = sum of PMT_t/(1+r)^t + FV_n/(1+r)^n
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.
Variables
$P M T_{t}$
Coupon payment at time t
$F V_{n}$
Face value paid at maturity
$r$
Periodic discount rate (YTM per period)
$n$
Number of periods to maturity
Perpetuity
$P V = \frac{P M T}{r}$ PV = PMT / r
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.
Variables
$PMT$
Constant payment received each period (forever)
$r$
Periodic discount rate· decimal
Annuity
$P V = A [\frac{1 - ( 1 + r ) ^{- n}}{r}]$ PV = A * (1 - (1+r)^(-n)) / r
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.
Variables
$A$
Annuity payment per period
$r$
Periodic interest rate· decimal
$n$
Number of payments
Constant Dividends
$P V = \frac{D}{r}$ PV = D / r
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.
Variables
$D$
Constant dividend per period
$r$
Required return
Constant Dividend Growth (Gordon)
$P V = \frac{D _{1}}{r - g} = \frac{D _{0} ( 1 + g )}{r - g}$ PV = D1/(r-g) = D0(1+g)/(r-g)
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.
Variables
$D_{0}$
Most recent dividend (just paid)
$D_{1}$
Next-year dividend = D_0 × (1+g)
$r$
Required rate of return on equity· decimal
$g$
Constant dividend growth rate· decimal
Discount Bond Implied Return
$r = (\frac{F V _{n}}{P V})^{1/ n} - 1$ r = (FV/PV)^(1/n) - 1
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.
Variables
$F V_{n}$
Maturity face value
$PV$
Current price (discount)
$n$
Periods to maturity
Equity Required Rate of Return
$r = \frac{D _{1}}{P V} + g$ r = D1/PV + g
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).
Variables
$D_{1}$
Next-year dividend
$PV$
Current stock price
$g$
Constant dividend growth rate
Forward P/E
$\frac{P _{0}}{E _{1}} = \frac{D _{1} / E _{1}}{r - g}$ P0/E1 = (D1/E1)/(r - g)
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.
Variables
$D_{1} / E_{1}$
Payout ratio (next year)
$r$
Required return on equity
$g$
Constant earnings growth rate
Sample Mean
$\overset{ˉ}{X} = \frac{1}{n} i = 1 \sum n X_{i}$ Sample mean = (1/n) * Sum of Xi
Use when. Central tendency of a sample; an unbiased estimator of population mean.
Best single-number summary of a sample's center.
Variables
$X_{i}$
Sample observation i
$n$
Sample size
Interquartile Range
$I QR = Q_{3} - Q_{1}$ IQR = Q3 - Q1
Use when. Describing dispersion when distribution is skewed or has outliers.
Spread of the middle 50% of data, ignoring extreme tails. Robust to outliers.
Variables
$Q_{1}$
First quartile (25th percentile)
$Q_{3}$
Third quartile (75th percentile)
Location of yth Percentile
$L_{y} = (n + 1) \frac{y}{100}$ Ly = (n+1) * y/100; use linear interpolation if not integer
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.
Variables
$y$
Percentile (1-99)
$n$
Number of observations
$L_{y}$
Index of the yth percentile in sorted data
Range
$Range = Max - Min$ Range = Maximum value - Minimum value
Use when. Quick first look at how spread out a dataset is.
Crudest measure of dispersion. Uses only two observations.
Variables
$Max$
Largest observation
$Min$
Smallest observation
Mean Absolute Deviation
$M A D = \frac{1}{n} i = 1 \sum n ∣ X_{i} - \overset{ˉ}{X} ∣$ MAD = (1/n) * Sum of |Xi - Xbar|
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.
Variables
$X_{i}$
Observation i
$X̄$
Sample mean
Required Rate of Return
$Interest rate = Real risk-free rate + Inflation premium + Default risk premium + Liquidity premium + Maturity premium$ Interest rate = Real risk-free rate + Inflation premium + Default risk premium + Liquidity premium + Maturity premium
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.
Variables
$Real risk-free rate$
Return on a risk-free asset adjusted for inflation
$Inflation premium$
Compensation for expected inflation
$Default risk premium$
Compensation for issuer default risk
$Liquidity premium$
Compensation for illiquidity
$Maturity premium$
Compensation for longer maturities (rate-risk)
Sample Variance
$s^{2} = \frac{1}{n - 1} i = 1 \sum n (X_{i} - \overset{ˉ}{X})^{2}$ Sample variance s^2 = (1/(n-1)) * Sum (Xi - Xbar)^2
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.
Variables
$s^{2}$
Sample variance
$X̄$
Sample mean
$n - 1$
Degrees of freedom (Bessel's correction)
Target Semideviation
$s_{t a r g e t} = \frac{\sum _{X_{i} < B} ( X _{i} - B ) ^{2}}{n - 1}$ Target semideviation: sqrt of sum (Xi - B)^2 for Xi < B over (n-1)
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.
Variables
$B$
Target / threshold return
$X_{i}$
Return observation
Coefficient of Variation
$C V = \frac{s}{X ˉ}$ CV = s / Xbar
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.
Variables
$s$
Sample standard deviation
$X̄$
Sample mean
Skewness
$Skewness \approx \frac{1}{n} i = 1 \sum n \frac{( X _{i} - X ˉ ) ^{3}}{s ^{3}}$ Skewness ≈ (1/n) * Sum ((Xi - Xbar)^3 / s^3)
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).
Variables
$X_{i}$
Observation
$X̄$
Sample mean
$s$
Sample standard deviation
Excess Kurtosis
$K_{e} \approx \frac{1}{n} i = 1 \sum n \frac{( X _{i} - X ˉ ) ^{4}}{s ^{4}} - 3$ Excess kurtosis = (1/n)*Sum ((Xi-Xbar)^4/s^4) - 3
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.
Variables
$X_{i}$
Observation
$X̄$
Sample mean
$s$
Sample standard deviation
Sample Covariance
$s_{X Y} = \frac{\sum _{i = 1}^{n} ( X _{i} - X ˉ ) ( Y _{i} - Y ˉ )}{n - 1}$ Covariance = Sum (Xi-Xbar)(Yi-Ybar) / (n-1)
Use when. Portfolio variance, regression slope, beta calculation.
How two variables move together. Positive = same direction; negative = opposite directions; zero = no linear relationship.
Variables
$X_{i}, Y_{i}$
Paired observations
$X̄, Ȳ$
Sample means
Sample Correlation
$r_{X Y} = \frac{s _{X Y}}{s _{X} s _{Y}}$ r = s_XY / (s_X * s_Y)
Use when. Diversification analysis; relationship strength assessment.
Standardised covariance, bounded between -1 and +1. ±1 = perfect linear relationship; 0 = no linear relationship.
Variables
$s_{X} Y$
Sample covariance
$s_{X}, s_{Y}$
Sample standard deviations
Expected Value
$E (X) = \sum_{i = 1}^{n} P (X_{i}) X_{i}$ E(X) = Sum P(Xi)*Xi
Use when. Decision-making under uncertainty; valuing probabilistic cash flows.
Probability-weighted average of all possible outcomes. The mean of a random variable.
Variables
$X_{i}$
Possible outcome
$P (X_{i})$
Probability of outcome i
Variance (Probability)
$σ^{2} (X) = \sum_{i = 1}^{n} P (X_{i}) [X_{i} - E (X)]^{2} = E (X^{2}) - [E (X)]^{2}$ Variance = Sum P(Xi)(Xi - E(X))^2 = E(X^2) - (E(X))^2
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.
Variables
$E(X)$
Expected value
$P (X_{i})$
Probability of outcome i
Total Probability Rule for Expected Value
$E (X) = E (X ∣ S_{1}) P (S_{1}) + \dots + E (X ∣ S_{n}) P (S_{n})$ E(X) = E(X|S1)P(S1) + ... + E(X|Sn)P(Sn)
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.
Variables
$E (X ∣ S_{i})$
Expected value of X given scenario i
$P (S_{i})$
Probability of scenario i
Bayes' Formula
$P (Event ∣ Info) = \frac{P ( Info ∣ Event )}{P ( Info )} \times P (Event)$ P(Event|Info) = P(Info|Event)/P(Info) * P(Event)
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.
Variables
$P(Event|Info)$
Posterior probability
$P(Info|Event)$
Likelihood
$P(Event)$
Prior probability
$P(Info)$
Marginal probability of information
Portfolio Expected Return
$E (R_{p}) = \sum_{i = 1}^{n} w_{i} E [R_{i}]$ E(Rp) = Sum wi*E[Ri]
Use when. Any portfolio expected-return calculation.
Expected return is linear in weights. Just multiply each asset's expected return by its weight, and add.
Variables
$w_{i}$
Portfolio weight of asset i— sum to 1
$E [R_{i}]$
Expected return on asset i
Portfolio Variance
$σ^{2} (R_{p}) = \sum_{i = 1}^{n} \sum_{j = 1}^{n} w_{i} w_{j} Cov (R_{i}, R_{j})$ Portfolio variance = Sum wi*wj*Cov(Ri,Rj)
Use when. Computing portfolio risk; mean-variance optimisation.
Unlike expected return, variance is NOT linear — covariances matter. Diversification benefits come from negative or low covariances across assets.
Variables
$w_{i}, w_{j}$
Portfolio weights
$C o v (R_{i}, R_{j})$
Covariance between assets
Correlation
$ρ (R_{i}, R_{j}) = \frac{Cov ( R _{i} , R _{j} )}{σ ( R _{i} ) σ ( R _{j} )}$ Correlation = Cov(Ri,Rj) / (sigma(Ri)*sigma(Rj))
Use when. Diversification analysis; pair-trading; assessing strength of co-movement.
Standardised covariance. Always between -1 and +1, independent of units.
Variables
$C o v (R_{i}, R_{j})$
Covariance between assets
$σ (R_{i}), σ (R_{j})$
Standard deviations
Two-Asset Portfolio Variance
$σ^{2} (R_{p}) = w_{1}^{2} σ^{2} (R_{1}) + w_{2}^{2} σ^{2} (R_{2}) + 2 w_{1} w_{2} Cov (R_{1}, R_{2})$ Two-asset: sigma^2(Rp) = w1^2*sigma^2(R1) + w2^2*sigma^2(R2) + 2*w1*w2*Cov(R1,R2)
Use when. Most exam portfolio-variance questions; quick portfolio risk estimates.
Two-asset case of the general formula. The cross-term shows the diversification benefit when correlation is < 1.
Variables
$w_{1}, w_{2}$
Asset weights
$σ^{2} (R_{i})$
Variances of each asset
$C o v (R_{1}, R_{2})$
Covariance between assets
Roy's Safety-First Ratio
$S F Ratio = \frac{E ( R _{p} ) - R _{L}}{σ _{p}} \Rightarrow P (R_{p} < R_{L}) = N (- S F Ratio)$ SF Ratio = (E(Rp) - RL) / sigma_p; P(Rp < RL) = N(-SF Ratio)
Use when. Pension/endowment portfolio decisions with hard minimum-return constraints.
Maximise the number of standard deviations between expected return and a downside threshold. Higher SF ratio = lower probability of failure (returns below R_L).
Variables
$E (R_{p})$
Expected portfolio return
$R_{L}$
Minimum acceptable / threshold return
$σ_{p}$
Portfolio standard deviation
$N(.)$
Standard normal CDF
Lognormal: Mean and Variance of Y
$μ_{Y} = e^{μ + σ^{2} /2}, σ_{Y}^{2} = e^{2 μ + σ^{2}} (e^{σ^{2}} - 1)$ Mean of Y = e^(mu + sigma^2/2); Variance of Y = e^(2mu+sigma^2)(e^sigma^2 - 1)
Use when. Asset-price modelling; Black-Scholes underlying assumption.
If ln(Y) is normal, then Y is lognormal — always positive, skewed right. Used to model stock prices since prices can't be negative.
Variables
$μ, σ²$
Mean and variance of ln(Y)
$μ_{Y}, σ_{Y}^{2}$
Mean and variance of Y
Continuously Compounded Return
$r_{0, T} = ln (\frac{S _{T}}{S _{0}})$ r_0,T = ln(ST/S0)
Use when. Time-series analysis, GBM models, statistical tests on returns.
Log return. Symmetric (a +10% then -10% log-return ends back at start), additive across periods.
Variables
$S_{0}, S_{T}$
Price at time 0 and time T
$r_{0, T}$
Continuously compounded return over [0,T]
Standard Error of Sample Mean
$σ_{\overset{ˉ}{X}} = \frac{σ}{n} or s_{\overset{ˉ}{X}} = \frac{s}{n}$ Standard error = sigma/sqrt(n) or s/sqrt(n)
Use when. Building confidence intervals, computing t-statistics, hypothesis testing on means.
Standard deviation of the sample mean across many possible samples. Shrinks with √n — larger samples produce more precise estimates of the mean.
Variables
$σ$
Population std dev (or s if estimated)
$n$
Sample size
t-Statistic (Single Mean)
$t = \frac{X ˉ - μ _{0}}{s / n}, df = n - 1$ t = (Xbar - mu0) / (s/sqrt(n)); df = n-1
Use when. Testing hypothesis about a single population mean when σ is unknown (usually).
"How many standard errors is the sample mean from the hypothesised mean?" Large |t| → reject null.
Variables
$X̄$
Sample mean
$μ_{0}$
Hypothesised population mean
$s$
Sample standard deviation
$n$
Sample size
t-Statistic (Difference in Means)
$t = \frac{( X ˉ _{1} - X ˉ _{2} ) - ( μ _{1} - μ _{2} )}{s _{p}^{2} / n _{1} + s _{p}^{2} / n _{2}}, s_{p}^{2} = \frac{( n _{1} - 1 ) s _{1}^{2} + ( n _{2} - 1 ) s _{2}^{2}}{n _{1} + n _{2} - 2}$ t = ((Xbar1-Xbar2)-(mu1-mu2)) / sqrt(sp^2/n1 + sp^2/n2); pooled variance sp^2
Use when. A/B test of two groups (e.g. portfolio A vs B average return).
Tests whether two population means differ. Pooled variance assumes equal population variances.
Variables
$\overset{ˉ}{X}_{1}, \overset{ˉ}{X}_{2}$
Sample means of two groups
$s_{p}^{2}$
Pooled sample variance
$n_{1}, n_{2}$
Sample sizes
Chi-Square (Single Variance)
$χ^{2} = \frac{( n - 1 ) s ^{2}}{σ _{0}^{2}}, df = n - 1$ Chi^2 = (n-1)s^2 / sigma_0^2; df = n-1
Use when. Testing if a fund's volatility matches a benchmark; risk-management variance tests.
Tests whether the population variance equals a hypothesised value. Chi-square is right-skewed and only takes non-negative values.
Variables
$s²$
Sample variance
$σ_{0}^{2}$
Hypothesised population variance
$n - 1$
Degrees of freedom
F-Test (Two Variances)
$F = \frac{s _{1}^{2}}{s _{2}^{2}}, d f_{1} = n_{1} - 1, d f_{2} = n_{2} - 1$ F = s1^2/s2^2; df1 = n1-1, df2 = n2-1
Use when. Validating equal-variance assumption before t-test; comparing volatility of two funds.
Tests whether two populations have equal variances. F is the ratio of larger to smaller variance.
Variables
$s_{1}^{2}, s_{2}^{2}$
Sample variances
$n_{1}, n_{2}$
Sample sizes
t-Statistic (Correlation)
$t = \frac{r n - 2}{1 - r ^{2}}, df = n - 2$ t = r*sqrt(n-2)/sqrt(1-r^2); df = n-2
Use when. Validating significance of pairwise correlations in factor analysis or pair trading.
Tests whether a sample correlation is statistically different from zero (i.e., whether there is a real linear relationship).
Variables
$r$
Sample correlation coefficient
$n$
Sample size
Chi-Square (Contingency Table)
$χ^{2} = \sum \frac{( O _{ij} - E _{ij} ) ^{2}}{E _{ij}}$ Chi^2 = Sum (Oij - Eij)^2 / Eij
Use when. Cross-tabs: e.g. industry × credit-rating frequencies.
Tests whether two categorical variables are independent. Large chi-square = observed counts diverge from independent expectation.
Variables
$O_{i} j$
Observed count in cell (i,j)
$E_{i} j$
Expected count under independence
Regression Slope
$\hat{b}_{1} = \frac{Cov ( Y , X )}{Var ( X )} = \frac{\sum ( Y _{i} - Y ˉ ) ( X _{i} - X ˉ )}{\sum ( X _{i} - X ˉ ) ^{2}}$ b1_hat = Cov(Y,X)/Var(X)
Use when. Linear regression, factor models, beta estimation.
OLS slope = covariance / variance. Tells you the change in Y for a 1-unit change in X. Same formula gives stock's beta when X = market return.
Variables
$\hat{b}_{1}$
Estimated regression slope
$Cov(Y,X)$
Covariance of dependent and independent variables
$Var(X)$
Variance of independent variable
Regression Intercept
$\hat{b}_{0} = \overset{ˉ}{Y} - \hat{b}_{1} \overset{ˉ}{X}$ b0_hat = Ybar - b1_hat*Xbar
Use when. Reading regression output; computing predicted Y for any X.
The regression line passes through the means (X̄, Ȳ). The intercept is just whatever's left after fitting the slope.
Variables
$\hat{b}_{0}$
Estimated intercept
$Ȳ, X̄$
Sample means of Y and X
Coefficient of Determination
$R^{2} = \frac{S S R}{S S T} = r^{2} (one regressor)$ R^2 = SSR/SST = r^2 for simple regression
Use when. Model-fit assessment.
Fraction of variation in Y explained by the regression. R² = 0.6 means 60% of variability in Y is captured by X.
Variables
$SSR$
Sum of squares regression (explained)
$SST$
Total sum of squares
$r$
Sample correlation
F-Statistic (Regression)
$F = \frac{M S R}{M S E} = \frac{S S R / k}{S S E / ( n - ( k + 1 ))}$ F = MSR/MSE
Use when. Overall model significance in multivariable regression.
Tests the joint significance of all slope coefficients (H0: all slopes = 0). Large F → at least one X explains Y.
Variables
$MSR$
Mean square regression
$MSE$
Mean square error
$k$
Number of regressors
$n$
Sample size

How to use this CFA Level 1 formula sheet

A simple 5-step approach to turn this sheet into real CFA Level 1 exam prep — not just a wallpaper for your desk.

Pick the topic you're studying
Use the side navigation to jump to the topic you're currently studying — Quantitative Methods, FSA, Fixed Income, etc.
Read the formula and the 'use when' trigger
For each formula, read the title, the equation, and especially the 'use when' line. Knowing when to use a formula is more valuable than memorising it blindly.
Study the variables and intuition
Each card lists the variables (with units) and a short plain-English intuition. Read these so you can rebuild the formula from first principles.
Practise on questions
Apply the formula on at least 5–10 practice questions. Active recall beats re-reading every time.
Run formula-only revision passes
In the final 2–3 weeks before the exam, scroll through this sheet and recite every formula from memory. Mark the ones you can't recall and drill them.

CFA Level 1 Formula Sheet — Frequently Asked Questions

Is this CFA Level 1 formula sheet updated for 2026?: Yes. This formula sheet is aligned with the 2026 CFA Level I curriculum and is updated whenever CFA Institute publishes curriculum changes.
Is the OneQuest CFA Level 1 formula sheet free?: Yes. The OneQuest CFA Level 1 formula sheet is 100% free to view online. No sign-up, no email, and no payment is required to use it.
Can I use this formula sheet during the actual CFA exam?: No. The CFA exam is closed-book. You may not bring formula sheets, notes, or printed materials into the testing centre. Use this sheet for study and revision only.
How many formulas do I need to know for CFA Level 1?: Most candidates need to memorise roughly 50–70 core formulas across all 10 topic areas. This sheet covers every key formula from the curriculum so you can review them in one place.
What topics are covered in this formula sheet?: All 10 CFA Level I topic areas: Quantitative Methods, Economics, Financial Statement Analysis, Corporate Issuers, Equity Investments, Fixed Income, Derivatives, Alternative Investments, Portfolio Management, and Ethical & Professional Standards.
How should I use this formula sheet in my study plan?: Keep the relevant topic section open while you study, use it as a quick reference during practice questions, and run fast formula-review passes in your final weeks before the exam.
Which CFA Level 1 formulas are most important to memorise?: High-yield formulas include time value of money (PV/FV/annuities), DuPont decomposition, ratio analysis, CAPM, WACC, bond duration and convexity, put-call parity, and the Sharpe ratio. They appear repeatedly across topics and exam questions.
Does the CFA Level 1 exam provide a formula sheet?: No. CFA Institute does not provide a formula sheet during the exam. Candidates are expected to memorise all formulas, though common financial calculator functions (BA II Plus or HP 12C) may be used.
How is this formula sheet different from a CFA cheat sheet?: Most cheat sheets are just LaTeX dumps. This sheet pairs every formula with its 'use when' trigger, plain-language intuition, and variable definitions — designed for actual revision, not just decoration.

Alternative Investments

Multiple of Invested Capital

Performance Fee (Hard Hurdle)

Corporate Issuers

Return on Invested Capital

Cash Conversion Cycle

Current Ratio

Quick Ratio

Net Present Value

Weighted Average Cost of Capital

Cost of Equity (Modigliani-Miller)

Firm Value with Taxes

Derivatives

Forward Price (Benefits/Income and Costs)

Currency Forward Price

Forward Valuation

Implied Forward Rate

Interest Rate Futures Price

Swap Periodic Settlement

Call Value at Expiry

Put Value at Expiry

Call Lower Bound

Put-Call Parity

Binomial Hedge Ratio

Risk-Neutral Probability

Economics

Profit Maximization

Fiscal Multiplier

Real Exchange Rate

Trade Balance

Forward Exchange Rate

Cross-Rate

Equity Investments

Dividend Discount Model

Perpetual Preferred Stock

Gordon Growth Model

Forward P/E (Gordon)

Enterprise Value

Price Return (Single Period)

Total Return (Single Period)

Leverage Ratio

Financial Statement Analysis

Basic EPS

Free Cash Flow to Firm

Free Cash Flow to Equity

Straight-Line Depreciation

Double-Declining Balance

Total Asset Turnover

Inventory Turnover

Days of Inventory on Hand

Receivables Turnover

Days of Sales Outstanding

Debt-to-Equity

Interest Coverage

ROE (DuPont)

Operating Income

Degree of Operating Leverage

Degree of Financial Leverage

Degree of Total Leverage

Fixed Income

Bond PV (Market Discount Rate)

Full Price and Accrued Interest

Current Yield

Yield to Worst

Z-Spread

Option-Adjusted Spread

Macaulay Duration

Modified Duration

Convexity Adjustment

Effective Duration

Repo Price

Expected Loss (Credit)

Debt Service Coverage (CMBS)

Portfolio Management

Beta

Utility Function

Capital Allocation Line

Capital Market Line

CAPM

Sharpe Ratio