Your FREE CFA Level 2 Flashcards 2026 – 200+ Cards

CFA Level 2 Flashcards

Code & Standards at Level II — what changes?

The Code and seven Standards are identical to Level I, but tested inside richer vignettes. You must identify the exact sub-standard violated and the recommended action from competing facts.

Law vs. Code — which governs?

Follow the stricter of applicable law or the Code and Standards. If a law is less strict or silent, you still meet the Code; if a law requires violating the Code, comply with the law.

The seven Standards of Professional Conduct?

I Professionalism, II Integrity of Capital Markets, III Duties to Clients, IV Duties to Employers, V Investment Analysis, VI Conflicts of Interest, VII Responsibilities as a Member/Candidate.

Standard II(A) — Material Nonpublic Information?

Members must not act, or cause others to act, on material nonpublic information. Information is material if a reasonable investor would want it or it would affect price.

What is the mosaic theory?

Combining public information with non-material non-public information to reach a conclusion is permitted — even if the conclusion is material. It is a defense against an MNPI allegation under II(A).

Recommended control for MNPI?

An information barrier (firewall) restricting the flow of information between departments, plus restricted and watch lists.

Standard III(B) — Fair Dealing?

Treat all clients fairly when disseminating recommendations and taking action — fair, not necessarily identical, treatment. Don't favor some clients in a hot issue.

Standard III(C) — Suitability?

Recommendations must fit the client's written objectives and constraints (the IPS). Judge a single security in the context of the total portfolio.

Standard VI — Conflicts of Interest?

Disclose conflicts (VI-A), give clients and employers priority over personal transactions (VI-B), and disclose referral fees (VI-C).

Standard V(A) — Diligence & Reasonable Basis?

Have a reasonable and adequate basis, supported by research and investigation, for any analysis, recommendation, or action.

What is GIPS?

Global Investment Performance Standards — voluntary, ethical standards for calculating and presenting investment performance so results are fair and comparable across firms.

Who can claim GIPS compliance?

Only an entire firm (a distinct business entity), not a single composite, product, or individual. Compliance is firm-wide and all-or-nothing.

What is a GIPS composite?

An aggregation of all discretionary portfolios managed to a similar strategy or objective. Performance is presented at the composite level.

Time-weighted vs money-weighted return for presentation?

GIPS and Standard III(D) favor time-weighted returns for performance presentation because they remove the effect of client cash-flow timing the manager doesn't control.

Standard IV(A) — Loyalty to employer?

Act for the employer's benefit; don't deprive it of your skills or take confidential information or client lists when leaving.

Standard VII — Reference to the CFA designation?

Use the marks correctly; don't overstate the meaning of the designation or misrepresent candidacy. 'CFA' is an adjective, never a noun.

Standard I(B) — Independence & Objectivity?

Maintain independence and objectivity; pay your own travel, refuse lavish gifts from issuers you cover, and don't let relationships compromise analysis.

Standard III(E) — Confidentiality?

Keep current, former, and prospective client information confidential unless it concerns illegal activity, disclosure is required by law, or the client permits it.

Multiple regression equation?

Y = b0 + b1·X1 + b2·X2 + … + ε. Each slope b_j is the effect of that variable holding the others constant.

t-test vs F-test in regression?

The t-test checks whether one coefficient is individually significant; the F-test checks whether the regression is jointly significant (at least one slope ≠ 0).

R² vs adjusted R²?

R² is the fraction of the dependent variable's variation explained. Adjusted R² penalizes adding variables, so it can fall when a useless variable is added.

What is heteroskedasticity?

Non-constant variance of the regression error term. Conditional heteroskedasticity (variance related to the X's) biases standard errors, making t- and F-tests unreliable.

Detect & fix heteroskedasticity?

Detect with the Breusch-Pagan test; fix with robust (White) standard errors or generalized least squares. Coefficients stay unbiased; only standard errors are wrong.

What is serial correlation?

Correlation between regression errors across observations. It biases the standard errors (often understating them), inflating t-statistics. Detect with Durbin-Watson.

What is multicollinearity?

High correlation among independent variables. It inflates coefficient standard errors, so individual t-tests are insignificant even with a high R² and a significant F-test.

The classic multicollinearity symptom?

A high R² and a significant F-test but insignificant individual t-statistics — the model explains the data, yet no single variable looks important.

Fix for multicollinearity?

Drop one of the correlated variables, or collect more or different data. Do not simply add more correlated predictors.

What is a dummy variable?

A 0/1 variable representing a qualitative condition. Use n − 1 dummies for n categories to avoid the dummy-variable trap (perfect multicollinearity).

Assumptions of the classical linear model?

Linearity, independent variables uncorrelated with the error, homoskedasticity (constant error variance), no serial correlation, and normally distributed errors.

What is a unit root / random walk?

A time series with a unit root is non-stationary (a random walk: x_t = x_t-1 + ε). Test with Dickey-Fuller; difference the series to make it stationary.

What is covariance stationarity?

A time series has a constant mean, constant variance, and constant covariance with lagged values over time — required before fitting an autoregressive model.

What is an autoregressive (AR) model?

A model where the variable is regressed on its own past values: x_t = b0 + b1·x_t-1 + ε. Check for serial correlation in residuals and seasonality.

Supervised vs unsupervised learning?

Supervised learning trains on labeled data to predict an output (regression, classification); unsupervised learning finds structure in unlabeled data (clustering, dimension reduction).

What is overfitting?

A model that fits the training data's noise rather than its signal, so it performs poorly out of sample. Combat it with cross-validation and regularization.

Covered interest rate parity?

A no-arbitrage condition: the forward premium or discount on a currency equals the interest-rate differential between the two currencies. It holds exactly because the position is hedged with a forward.

Uncovered interest rate parity?

The unhedged version: the expected change in the spot exchange rate equals the interest-rate differential. It relies on expectations and holds only on average over time.

Purchasing power parity (PPP)?

The expected change in the exchange rate equals the inflation differential between the two countries. Relative PPP links currency moves to relative inflation.

International Fisher relation?

The nominal interest-rate differential between two countries equals their expected inflation differential, assuming equal real rates.

Higher-yielding currency under covered parity?

It trades at a forward discount. The interest advantage is exactly offset by an expected depreciation embedded in the forward rate — so no arbitrage.

Direct vs indirect exchange-rate quote?

A direct quote is domestic currency per one unit of foreign currency; an indirect quote is the reverse (foreign per one unit of domestic).

Sources of long-run economic growth?

Growth in labor, growth in capital, and total factor productivity (technology/efficiency), combined in a production-function (growth-accounting) framework.

Why does regulation exist (economic rationale)?

To address market failures: externalities, public goods, information asymmetry, and the need to protect consumers and ensure market integrity.

What is a forward premium?

When a currency's forward rate is higher than its spot rate. Under covered parity, the lower-interest-rate currency trades at a forward premium.

Bid-ask spread in FX — what drives it?

Dealer spreads widen with lower liquidity, higher volatility, and larger transaction size, and differ across currency pairs and times of day.

Mundell-Fleming model — what does it analyze?

How monetary and fiscal policy affect output and exchange rates under different capital mobility and exchange-rate regimes.

Carry trade — what is it?

Borrowing in a low-interest-rate currency to invest in a high-interest-rate currency, profiting if uncovered parity fails. It earns the differential but bears crash risk.

Intercorporate investments — what drives the method?

The degree of influence: under ~20% a financial asset (fair value/amortized cost); 20–50% significant influence (equity method); over 50% control (consolidation).

What is the equity method?

For significant influence (20–50%): the investment is one balance-sheet line, increased by the investor's share of the associate's profit and reduced by dividends received.

What is consolidation?

For control (over 50%): the parent combines all of the subsidiary's assets, liabilities, revenues, and expenses, reporting any non-controlling interest in equity and income.

Equity method vs consolidation — net income?

Net income is the SAME under both. Consolidation grosses up revenue, assets, and liabilities, so margins fall and leverage rises versus the equity method.

What is goodwill?

The excess of a business combination's purchase price over the fair value of identifiable net assets acquired. It is tested for impairment, not amortized.

Funded status of a defined-benefit plan?

Fair value of plan assets minus the benefit obligation (PV of promised benefits). Positive = overfunded (net asset); negative = underfunded (net liability).

Effect of a lower pension discount rate?

A lower discount rate raises the present value of the benefit obligation, worsening the funded status and increasing the reported pension liability.

Key DB pension actuarial assumptions?

The discount rate, the expected rate of compensation growth, and (where used) the expected return on plan assets. Optimistic assumptions can flatter results.

Current-rate translation method?

Used when the local currency is functional: assets and liabilities at the current rate, income at the average rate, with the translation gain/loss reported in equity (CTA).

Temporal translation method?

Used when the parent's currency is functional: monetary items at the current rate, non-monetary items at historical rates, with the gain/loss in net income.

Which translation method makes earnings more volatile?

The temporal method, because it runs the translation gain or loss through net income rather than equity.

Signs of low financial reporting quality?

Aggressive revenue recognition, capitalizing costs that should be expensed, classifying operating cash outflows as investing, and frequent 'one-time' charges.

What is the Beneish M-score?

A statistical model combining eight ratios to estimate the likelihood that earnings have been manipulated. A higher score flags higher manipulation risk.

Clean-surplus relation — why it matters?

Ending book value = beginning book value + net income − dividends. It underlies the residual income model; items bypassing income (dirty surplus) require adjustment.

Equity method impairment trigger?

Objective evidence that the recoverable amount of the investment is below its carrying value; the loss is recognized in profit or loss.

Proportionate consolidation vs equity method (JV)?

IFRS requires the equity method for joint ventures; proportionate consolidation (combining your share line-by-line) is generally not permitted under current standards.

Modigliani-Miller Proposition I (no taxes)?

In perfect markets with no taxes, a firm's value and its WACC are independent of its capital structure — leverage doesn't change firm value.

Modigliani-Miller Proposition II (no taxes)?

The cost of equity rises linearly with the debt-to-equity ratio, exactly offsetting the cheaper debt, so the WACC stays constant.

MM with corporate taxes?

Interest is tax-deductible, so debt creates a tax shield that raises firm value as leverage increases — favoring more debt, absent other costs.

Trade-off theory of capital structure?

The optimal capital structure balances the tax shield benefit of debt against the rising expected costs of financial distress and agency costs.

Pecking-order theory?

Firms prefer internal funds first, then debt, and issue equity last, because financing choices signal information to the market.

Dividends vs share repurchases — equivalence?

Absent taxes, a cash dividend and an equal-size buyback are economically equivalent; they differ in signaling, flexibility, and tax treatment.

When does a buyback raise EPS?

Only when the after-tax cost of funds used for the repurchase is less than the earnings yield (E/P) of the stock.

Residual dividend policy?

Pay out as dividends whatever earnings remain after funding all positive-NPV projects at the target capital structure — so dividends are volatile.

Agency costs of equity vs debt?

Equity agency costs arise from manager-shareholder conflicts (perks, empire building); debt agency costs arise from shareholder-creditor conflicts (asset substitution).

Role of ESG in issuer analysis?

Environmental, social, and governance factors are integrated into credit and equity analysis as material risks affecting cash flows and the cost of capital.

Static trade-off — optimal debt level?

The point where the marginal tax-shield benefit of additional debt equals the marginal expected cost of financial distress.

Choosing an equity valuation model?

Match the model to the firm: DDM for stable dividend payers, FCFF/FCFE for non-payers, residual income for negative early cash flow, multiples for quick relative checks.

Gordon constant-growth model?

V0 = D1 ÷ (r − g), valid only when g < r. It values a stock as the present value of dividends growing at a constant rate forever.

Two-stage DDM?

Model an explicit high-growth period of dividends, then capitalize a terminal value with the Gordon model at a stable long-run growth rate, and discount both to today.

What is the H-model?

A two-stage DDM where the growth rate declines linearly from a high initial rate to a stable long-run rate over 2H years, approximating a gradually maturing firm.

Free cash flow to the firm (FCFF)?

Cash available to all capital providers after operating costs, taxes, and investment: FCFF = NI + NCC + Int(1 − tax) − FCInv − WCInv. Discount at the WACC.

Free cash flow to equity (FCFE)?

Cash for shareholders after debt flows: FCFE = FCFF − Int(1 − tax) + net borrowing. Discount at the cost of equity to value equity directly.

FCFF vs FCFE — when to use which?

Use FCFE when leverage is stable; use FCFF when leverage is changing or FCFE is negative, because the WACC is more stable than the cost of equity then.

Residual income model?

Value = current book value + present value of future residual income, where residual income = net income − (equity × cost of equity). It recognizes value early.

When is the residual income model preferred?

When a firm pays no dividends, has negative early free cash flow, or has an uncertain terminal value — book value anchors much of the value upfront.

Justified P/E from fundamentals?

Leading justified P/E = (D1/E1) ÷ (r − g) — the payout ratio divided by (required return minus growth). Compare it to the market multiple.

Enterprise value (EV)?

Market value of equity + debt − cash. It is the cost to acquire the whole firm; EV/EBITDA is capital-structure-neutral.

Why is EV/EBITDA useful?

It is independent of capital structure and ignores non-cash depreciation, so it compares firms with different leverage and depreciation policies.

Private company valuation approaches?

The income approach (DCF/capitalized cash flow), the market approach (guideline public companies/transactions), and the asset-based approach.

DLOM and DLOC discounts?

A discount for lack of marketability (private shares are illiquid) and a discount for lack of control (minority stakes can't direct the firm) reduce private-company value.

Sustainable growth rate?

g = retention ratio × return on equity (b × ROE). It is the growth a firm can fund without changing leverage or issuing equity.

Blume vs fundamental beta adjustment?

Beta is adjusted toward 1.0 (e.g., 0.67·raw + 0.33·1.0) because estimated betas tend to revert to the market beta over time.

Spot rate vs forward rate?

A spot rate is today's yield on a single payment received at one future date (zero-coupon). A forward rate is an interest rate set today for a loan starting in the future.

What is bootstrapping (spot rates)?

Deriving spot (zero-coupon) rates from the prices of coupon bonds one maturity at a time, so each cash flow can be discounted at its own spot rate.

Spot curve slopes up — implied forwards?

When the spot curve slopes upward, implied forward rates lie above the spot rates.

Pure (unbiased) expectations theory?

Forward rates equal expected future spot rates; the yield curve's shape reflects only rate expectations, with no term premium.

Liquidity preference theory?

Investors demand a term premium for holding longer maturities, so forward rates are upward-biased estimates of expected future spot rates.

Segmented markets theory?

Supply and demand within each maturity sector set its rate independently; investors don't move across maturities.

Preferred habitat theory?

Investors have a preferred maturity but will move for a sufficient premium, allowing premiums to be positive or negative across the curve.

Arbitrage-free valuation of a bond?

Discount each individual cash flow at its own spot rate. If the bond's price differs from this value, a risk-free arbitrage exists between it and a portfolio of strips.

Binomial interest-rate tree — use?

To value bonds with embedded options. Calibrate the tree to the benchmark curve and roll values back, applying the call/put rule at each node.

Callable bond node value rule?

At each node the value is the lower of the call price and the computed value — the issuer calls when it benefits the issuer.

Putable bond node value rule?

At each node the value is the higher of the put price and the computed value — the holder puts when it benefits the holder.

Option-adjusted spread (OAS)?

The constant spread added to the rate tree that makes the model price equal the market price after removing the embedded option, allowing comparison across bonds.

Z-spread vs OAS?

The Z-spread is the constant spread over the spot curve ignoring options. OAS = Z-spread minus the option cost, so OAS reflects only credit and liquidity risk.

Effective duration vs modified duration?

Effective duration is used for bonds with embedded options because their cash flows change with rates; modified duration assumes fixed cash flows.

Structural credit model?

Models default as the equity holders' option to default when firm asset value falls below debt — based on option-pricing theory (Merton model).

Reduced-form credit model?

Models default as a statistical hazard driven by observable variables, without modeling the firm's asset value directly.

Credit spread components?

The spread compensates for expected loss (probability of default × loss given default) plus a risk premium for liquidity and uncertainty.

No-arbitrage forward price?

F0 = S0 × (1 + r)ᵀ, adjusted for carry: add storage costs and subtract any income or convenience yield on the underlying.

Value of a forward after initiation?

The present value of the difference between the current forward price and the original contract price — zero at inception, then moving with the underlying.

How is a swap priced?

As a series of forwards (or off-market forwards) so its value at initiation is zero; that condition determines the fixed swap rate.

One-period binomial — up/down?

The underlying moves to S0·u (up) or S0·d (down) over one period. u > 1 and d < 1 define the size of the moves.

Risk-neutral probability formula?

π = (1 + r − d) ÷ (u − d), where r is the per-period risk-free rate. It is a pricing device, not a real-world probability.

Why are real-world probabilities irrelevant?

Because the option can be replicated with the stock and risk-free borrowing, no-arbitrage pricing depends only on the risk-neutral probability.

Binomial option value?

Discount the risk-neutral expected payoff: value = [π·c⁺ + (1 − π)·c⁻] ÷ (1 + r), rolling back through the tree.

American option in a binomial tree?

At each node compare the value of holding versus exercising, and take the higher — capturing the early-exercise premium.

Black-Scholes-Merton inputs?

Five: the underlying price, strike, time to expiration, risk-free rate, and volatility. Volatility is the only input not directly observable.

BSM assumptions / limits?

Lognormal prices, constant volatility and rates, no early exercise (European), frictionless markets. It does not directly value American options.

What is implied volatility?

The volatility that makes the BSM model price equal the option's market price — the market's expectation of future movement, backed out of prices.

Option delta?

The change in option price for a small change in the underlying. Calls have delta 0 to 1; puts 0 to −1. It is the hedge ratio.

Option gamma?

The rate of change of delta as the underlying moves. It is largest for at-the-money, near-expiry options, requiring more frequent re-hedging.

Option vega?

The change in option price for a 1-point change in volatility. Long options have positive vega; it is largest for at-the-money options.

Option theta?

The change in option price as time passes (time decay). It is generally negative for long options — value erodes as expiration approaches.

Delta hedging — what it achieves?

Holding the underlying in the opposite direction of the option's delta to neutralize small price moves; it must be rebalanced as delta changes (gamma).

Put-call parity (deeper)?

c + PV(X) = p + S0 for European options. Rearranging builds synthetic positions; a violation is an arbitrage.

Three approaches to value real estate?

The income approach (capitalize NOI or discount cash flows), the cost approach (replacement cost less depreciation plus land), and the sales-comparison approach.

Direct capitalization method?

Value = NOI ÷ cap rate. A lower cap rate implies a higher value and typically a lower-risk, prime property.

What is net operating income (NOI)?

Potential rental income minus vacancy and collection losses and operating expenses, before financing and taxes — the numerator in direct capitalization.

Cost approach — when used?

For special-purpose properties (e.g., a school or hospital) with few comparable sales; value = land + replacement cost − depreciation.

REIT valuation multiples?

Net asset value (NAV), price-to-FFO (funds from operations), and price-to-AFFO (adjusted FFO) — FFO adds back real-estate depreciation to net income.

Private equity — buyout vs venture?

Buyout funds acquire mature companies using leverage; venture capital funds back early-stage, high-growth startups. Both target high IRRs over a multi-year horizon.

The 2-and-20 fee structure?

A typical private fund charges a 2% annual management fee on assets plus 20% carried interest on profits, often above a hurdle rate.

What is carried interest?

The share of fund profits (often 20%) paid to the general partner as a performance incentive, usually after limited partners earn a hurdle return.

Hedge fund strategy categories?

Equity long/short, event-driven (e.g., merger arbitrage), relative value (arbitrage), and global macro / managed futures.

Commodities — sources of return?

Spot price changes, collateral yield (on cash margin), and roll yield (positive in backwardation, negative in contango).

Contango vs backwardation?

Contango: the futures price exceeds the expected spot (upward curve) → negative roll yield. Backwardation: futures below spot (downward curve) → positive roll yield.

Why do alternatives appeal — and their drawbacks?

They add diversification and potentially higher returns, but bring illiquidity, high fees, leverage, and valuation difficulty (often appraisal-based, smoothed returns).

Smoothed (appraisal) returns — effect?

Appraisal-based real-estate returns are smoothed, understating true volatility and overstating diversification benefits; analysts unsmooth them.

Survivorship bias in hedge-fund indexes?

Failed funds drop out of indexes, so reported index returns overstate the average fund's performance and understate risk.

What is a multifactor model?

Expected return = risk-free rate + Σ (factor sensitivity × factor risk premium). It generalizes the single-factor CAPM to several systematic factors.

Arbitrage pricing theory (APT)?

A multifactor model in which expected return is a linear function of several systematic factor betas and their risk premiums, derived from a no-arbitrage condition.

Carhart four-factor model?

Extends Fama-French with market, size (SMB), value (HML), and momentum (WML) factors to explain equity returns and judge active managers.

Macroeconomic vs fundamental factor models?

Macroeconomic models use surprises in variables like inflation and growth as factors; fundamental models use attributes like size, value, and momentum.

What is the information ratio?

Active return (portfolio − benchmark) divided by tracking error. It measures consistent value added by active management per unit of active risk.

What is tracking error?

The standard deviation of a portfolio's active return (its return minus the benchmark's). It quantifies how closely the portfolio follows the benchmark.

Fundamental law of active management?

The information ratio ≈ information coefficient × √breadth — skill times the number of independent active decisions, scaled by the transfer coefficient.

What is value at risk (VaR)?

An estimate of the minimum loss over a period at a given confidence level — e.g., a 5% one-day VaR of $1M means a 5% chance of losing at least $1M in a day.

Three ways to compute VaR?

Parametric (variance-covariance, assumes normality), historical simulation (uses past returns), and Monte Carlo simulation (generates random scenarios).

Main limitation of VaR?

It says nothing about the magnitude of losses beyond the cutoff. Use conditional VaR (expected shortfall) to capture the tail, plus stress tests.

What is conditional VaR (CVaR)?

The expected loss given that the loss exceeds the VaR threshold — the average of the tail beyond VaR. It captures tail severity that VaR ignores.

Active return vs active risk?

Active return is portfolio return minus benchmark return; active risk (tracking error) is its standard deviation. The information ratio relates the two.

Stress testing vs scenario analysis?

Stress testing pushes risk factors to extreme values; scenario analysis evaluates the portfolio under specific hypothetical or historical event sets.

Sharpe vs information ratio?

The Sharpe ratio uses total risk relative to the risk-free rate; the information ratio uses active risk relative to a benchmark — isolating manager skill.

Treynor ratio?

Excess return per unit of systematic risk: (Rp − Rf) ÷ beta. It rewards return earned for market exposure, suitable for diversified portfolios.

Backtesting — purpose and pitfalls?

Testing a strategy on historical data to gauge performance; pitfalls include look-ahead bias, survivorship bias, and overfitting to the sample.

Standard III(A) — Loyalty, Prudence, and Care?

Act for the benefit of clients, place their interests before the firm's and your own, and exercise reasonable care and prudent judgment.

Standard I(C) — Misrepresentation?

Do not knowingly make false or misleading statements about investments, your qualifications, or performance, including plagiarism and guaranteeing returns.

Standard I(D) — Misconduct?

Do not engage in conduct involving dishonesty, fraud, or deceit, or any act that reflects adversely on professional reputation or integrity.

Standard II(B) — Market Manipulation?

Do not engage in practices that distort prices or artificially inflate trading volume to mislead market participants — transaction- or information-based.

Standard V(B) — Communication with clients?

Disclose the basic format and general principles of the investment process, identify limitations and risks, and distinguish fact from opinion.

Standard V(C) — Record Retention?

Develop and maintain records supporting analyses, recommendations, and actions. Records are the firm's property; keep them per regulation (often 7 years).

Standard IV(B) — Additional Compensation?

Do not accept gifts or compensation that compete with or create a conflict with your employer's interest without written consent from all parties.

Standard IV(C) — Responsibilities of Supervisors?

Make reasonable efforts to prevent and detect violations by those under your supervision, with adequate compliance procedures in place.

Standard VI(B) — Priority of Transactions?

Client and employer transactions take priority over a member's personal transactions; personal interests must not disadvantage clients.

GIPS — minimum performance history?

A firm claiming compliance must present a minimum of five years of compliant history (or since inception if shorter), then build to ten years.

GIPS verification — required?

Independent third-party verification is recommended but not required; it applies firm-wide, not to a single composite.

Standard error of estimate (SEE)?

The standard deviation of the regression residuals; a smaller SEE means the model's predictions fit the data more tightly.

Confidence interval for a slope coefficient?

Estimated coefficient ± (critical t) × (coefficient standard error). If the interval excludes zero, the coefficient is significant at that level.

Type I vs Type II error?

A Type I error rejects a true null (probability equals the significance level α); a Type II error fails to reject a false null.

What is a p-value?

The smallest significance level at which the null can be rejected. Reject the null when the p-value is below the chosen α.

Log-linear time-series model — when to use?

When a series grows at a roughly constant rate (exponential growth); modeling the natural log linearizes it for an AR or trend model.

Mean reversion in an AR(1) model?

A series reverts to b0 ÷ (1 − b1); if the current value is above this level it tends to fall, and below it tends to rise, when |b1| < 1.

Root mean squared error (RMSE)?

A measure of out-of-sample forecast accuracy; the model with the lower RMSE is preferred for forecasting.

Cointegration?

Two non-stationary series share a long-run equilibrium relationship, so a regression between them can be valid despite each having a unit root.

Real vs nominal exchange rate?

The nominal rate is the quoted price of one currency in another; the real rate adjusts for relative price levels and measures purchasing-power competitiveness.

Marshall-Lerner condition?

A currency depreciation improves the trade balance only if the sum of the export and import demand elasticities exceeds one.

J-curve effect?

After a depreciation, the trade balance worsens before it improves, because volumes adjust more slowly than prices.

Cross rate?

An exchange rate between two currencies derived from each one's rate against a third currency (often the U.S. dollar).

Triangular arbitrage?

Exploiting inconsistent cross rates among three currencies to lock in a riskless profit; it forces quoted cross rates into alignment.

Capital mobility and policy effectiveness?

Under high capital mobility and a floating rate, monetary policy is potent and fiscal policy is weaker (the Mundell-Fleming result).

Acquisition method for business combinations?

Identifiable assets and liabilities are recorded at fair value at acquisition; the excess of price over fair value of net assets is goodwill.

Bargain purchase gain?

When the fair value of net assets exceeds the purchase price, the difference is recognized as a gain in profit or loss.

Held-to-maturity vs available-for-sale (debt)?

Held-to-maturity (amortized cost) for fixed-maturity debt the firm intends to hold; fair value (with changes in OCI or P&L) otherwise.

Service cost in pension expense?

The present value of benefits earned by employees during the current period; it is recognized in profit or loss.

Past service cost?

The change in the obligation from a plan amendment affecting prior service; recognized in P&L under IFRS, in OCI then amortized under U.S. GAAP.

Remeasurements / actuarial gains and losses?

Changes in the obligation or asset return from assumption changes; reported in OCI under IFRS (not recycled) and OCI under U.S. GAAP (amortized).

FIFO vs LIFO under rising prices (recap)?

FIFO gives higher ending inventory and net income; LIFO gives higher COGS, lower income and taxes. IFRS prohibits LIFO.

Why analysts adjust for off-balance-sheet items?

Operating leases, special-purpose entities, and the like can hide debt; analysts capitalize them to compare leverage fairly across firms.

Cost of equity via CAPM?

Required return = risk-free rate + beta × (market return − risk-free rate). It prices only systematic risk.

WACC formula?

WACC = wd·rd·(1 − tax) + we·re, weighting the after-tax cost of debt and the cost of equity by their market-value proportions.

Why use the after-tax cost of debt?

Interest is tax-deductible, so the firm's true cost of debt is rd × (1 − tax rate). Omitting (1 − tax) overstates the WACC.

Operating vs financial leverage?

Operating leverage comes from fixed operating costs (magnifies sales → operating income); financial leverage comes from debt (magnifies operating income → net income).

Degree of total leverage?

The product of the degree of operating leverage and the degree of financial leverage — the combined sensitivity of net income to a change in sales.

Capital budgeting decision rule?

Accept positive-NPV projects; for mutually exclusive projects in conflict, follow NPV over IRR. Use incremental after-tax cash flows and ignore sunk costs.

Yield to maturity (YTM)?

The single discount rate that makes a bond's price equal the present value of its cash flows, assuming it is held to maturity and coupons reinvest at the YTM.

Par, premium, and discount bonds?

Coupon = market yield → priced at par; coupon > yield → premium; coupon < yield → discount. Prices pull to par as maturity nears.

Money duration vs duration?

Duration is a percentage price sensitivity; money (dollar) duration is the price change in currency units for a given yield move.

Key rate (partial) duration?

The sensitivity of a bond's price to a change in the yield at one specific maturity, holding others constant — captures non-parallel curve shifts.

Convexity — what it adds?

Convexity corrects duration's straight-line estimate for large yield changes; positive convexity helps the holder, gaining more when yields fall than it loses when they rise.

Z-spread definition?

The constant spread added to each spot rate that makes the present value of a bond's cash flows equal its market price.

Forward rate from spot rates?

(1 + z2)² = (1 + z1) × (1 + 1y1y forward), so the implied one-year forward one year out is solved from the two- and one-year spot rates.

Expected loss on a bond?

Probability of default × loss given default × exposure. Loss given default = 1 − recovery rate.

Forward rate agreement (FRA)?

An OTC forward on an interest rate: one party locks a rate on a notional deposit for a future period, settling on the difference from the reference rate.

Notional principal in a swap?

The amount used to compute swap payments; it is generally not exchanged in an interest-rate swap, only the net interest difference is.

Plain-vanilla interest-rate swap?

One party pays a fixed rate and receives floating; the fixed rate is set so the swap's value is zero at initiation.

Replicating portfolio for an option?

A position of n shares of the underlying plus risk-free borrowing/lending that reproduces the option's payoff — the basis of no-arbitrage pricing.

Why convenience yield lowers the forward price?

Holding the physical asset provides a benefit (availability), reducing the net cost of carry and thus the no-arbitrage forward price.

Cost of carry — full expression?

Forward = spot compounded at the risk-free rate, plus storage costs, minus income and any convenience yield over the contract life.

Lower bound on a European call?

A European call is worth at least the underlying minus the present value of the strike (and never less than zero).

Direct vs sequential real-estate cash flows?

Direct capitalization uses a single stabilized NOI and cap rate; discounted cash flow models each year's NOI plus a terminal value, useful for changing cash flows.

Going-in vs terminal cap rate?

The going-in cap rate values the property today; the terminal (exit) cap rate values the expected sale at the end of the holding period.

REIT — funds from operations (FFO)?

Net income plus real-estate depreciation and amortization, minus gains on property sales — a better cash-earnings measure than net income for REITs.

Committed vs invested capital (PE)?

Limited partners commit capital that the GP draws down (calls) over time to make investments; uncalled commitments are 'dry powder'.

J-curve in private equity?

Returns are negative early (fees and write-downs) before investments mature and are exited, producing the J-shaped cumulative return path.

Vintage year?

The year a private fund makes its first investment; comparing funds within a vintage controls for the market environment.

Hurdle rate and clawback?

The hurdle is the LP return earned before the GP takes carried interest; a clawback returns excess carry to LPs if later losses occur.

Strategic vs tactical asset allocation?

Strategic allocation sets long-run target weights from the IPS; tactical allocation makes short-term deviations to exploit perceived mispricing.

Rebalancing — why and how?

Returning a portfolio to target weights controls risk drift; calendar rebalancing uses fixed dates, percentage-of-portfolio uses tolerance bands.

Liability-driven investing (LDI)?

Structuring assets to match the characteristics of liabilities (e.g., a pension's), focusing on funding the obligations rather than a market benchmark.

Risk budgeting?

Allocating a portfolio's total risk among positions or factors deliberately, so active risk is spent where the manager has the most skill.

Behavioral biases in markets?

Cognitive errors (anchoring, availability) and emotional biases (loss aversion, overconfidence) can move prices and challenge market efficiency.

Capital allocation line (CAL)?

The line of risk-return combinations from mixing the risk-free asset with a risky portfolio; its slope is the Sharpe ratio.

Capital market line (CML)?

The CAL using the market portfolio; only total risk (standard deviation) is priced for efficient portfolios on the line.

Security market line (SML)?

The graph of CAPM: required return versus beta. A security above the SML is undervalued; below it is overvalued.

M-squared (M²) measure?

Risk-adjusted performance stated as the return a portfolio would earn if levered to the market's risk — comparable directly to the market return.

Active vs passive management trade-off?

Active management seeks alpha but adds fees and tracking error; passive management minimizes cost and tracking error but forgoes outperformance.

Factor investing — smart beta?

Rules-based strategies that tilt toward rewarded factors (value, size, momentum, quality, low volatility) between pure active and pure passive.