Your FREE FRM Flashcards 2026 – 250+ Cards

Market risk, credit risk, operational risk, and liquidity risk (plus business/strategic risk).

Identify → measure → monitor → manage, then report. Risk is taken deliberately, not eliminated.

Avoid, retain, mitigate, or transfer (e.g., via insurance or hedging).

Non-diversifiable, market-wide risk measured by beta. It is the only risk the market rewards with higher expected return.

Company- or industry-specific risk that diversification can largely eliminate; it is not rewarded with extra return.

An asset's sensitivity to the overall market (its systematic risk). The market portfolio has a beta of 1.0.

Required return = Rf + β × (Rm − Rf). It prices only systematic risk.

(Rp − Rf) ÷ σp — excess return per unit of TOTAL risk (standard deviation). Higher is better.

(Rp − Rf) ÷ βp — excess return per unit of SYSTEMATIC risk (beta).

Portfolio return minus its CAPM-required return: Rp − [Rf + βp(Rm − Rf)]. Positive alpha = outperformance vs CAPM.

Active return (vs benchmark) ÷ tracking error. Measures consistency of active management skill.

Risk-adjusted return on capital = risk-adjusted return ÷ economic capital. A unit adds value when RAROC exceeds the cost of equity.

Expected loss = PD × LGD × EAD.

Expected loss is the average anticipated loss (priced into spreads). Unexpected loss is its volatility — covered by capital.

The capital a firm estimates it needs to absorb unexpected losses to a chosen confidence level over a horizon.

The likelihood a counterparty fails to meet its obligations over a stated horizon.

The fraction of exposure lost if default occurs = 1 − recovery rate.

The amount outstanding to a counterparty at the moment it defaults.

Pillar 1: minimum capital (credit, market, operational risk). Pillar 2: supervisory review. Pillar 3: market discipline via disclosure.

Higher-quality capital, a leverage ratio, and two liquidity ratios — the LCR and NSFR — after the 2008 crisis.

Tier 1 capital ÷ total exposure — a non-risk-based backstop to risk-weighted capital ratios.

1st: business/risk owners. 2nd: risk management & compliance. 3rd: independent internal audit.

The amount and type of risk a firm is willing to take to pursue its objectives, set by the board.

A firm-wide, integrated approach to managing all risks together rather than in silos.

Leads the independent risk function, reports risk to the board, and ensures limits and appetite are enforced.

Principles all FRM holders/candidates agree to: professional integrity, conflict-of-interest avoidance, confidentiality, and professionalism.

Moral hazard: risk-taking changes after a contract (e.g., once insured). Adverse selection: the riskiest parties are most likely to transact.

A metric that gives early warning of rising risk exposure (e.g., failed-trade rate, staff turnover).

Conflict between owners (principals) and managers (agents); governance and aligned incentives reduce it.

Taking an offsetting position to reduce exposure to a risk factor (e.g., shorting futures against a long cash position).

A project adds value only if its risk-adjusted return exceeds the firm's cost of capital.

Shifting a risk to another party, e.g., via insurance, derivatives, or securitization.

The risk of loss from damage to a firm's reputation; excluded from the Basel operational-risk definition but managed separately.

Risk to earnings from poor business decisions or adverse industry shifts; excluded from operational risk.

Loss from large exposure to a single counterparty, sector, or risk factor; limits and diversification control it.

The set of portfolios giving the highest expected return for each level of risk.

The line from the risk-free asset through the market portfolio; the best risk-return tradeoff using total risk.

The CAPM graph of required return vs beta; a security above it is undervalued.

Return above what CAPM (or a benchmark) requires for the risk taken; a measure of skill.

The standard deviation of a portfolio's active return versus its benchmark.

A pre-set cap on exposure (e.g., a VaR or notional limit) used to control risk-taking.

The aggregate capital a firm holds for all risks, accounting for diversification across risk types.

RAROC must exceed the firm's cost of equity for the activity to create shareholder value.

Combining risks across positions and types into a firm-wide view, accounting for diversification and correlation.

Stress test measures impact of a defined shock; scenario analysis explores a broader narrative of joint events.

The net cost of holding an asset (financing + storage − income); it links spot and forward prices.

Symmetric, fully described by mean and variance; ~68% / 95% / 99% of values fall within 1 / 2 / 3 standard deviations.

Lognormal returns keep prices non-negative; the normal can produce negative prices.

Small samples and fatter tails than the normal — useful when tail risk is a concern.

Asymmetry of a distribution. Negative skew (a long left tail) means large losses are more likely than a normal predicts.

The 'fatness' of the tails. Excess kurtosis > 0 (leptokurtic) means fat tails — more extreme outcomes than the normal.

Variance (σ²) is the squared dispersion; standard deviation (σ) is its square root, in the same units as returns.

Covariance gives the direction two variables move together (unscaled). Correlation standardizes it to between −1 and +1.

ρ = σxy ÷ (σx × σy). It ranges from −1 to +1; 0 means no linear relationship.

Combining assets with correlation below 1 lowers portfolio standard deviation below the weighted average of the parts.

Correlations rise toward 1 in a crisis, so diversification fails just when it is needed most.

A function that joins marginal distributions into a joint distribution, modeling tail dependence that linear correlation misses.

Type I: reject a true null (probability = significance level α). Type II: fail to reject a false null.

The probability of observing a result at least as extreme as the data, if the null hypothesis is true. Small p-value → reject the null.

The distribution of sample means approaches normal as the sample size grows, regardless of the population's shape.

A range that contains the true parameter with a stated probability (e.g., 95%), given the sample.

Y = b0 + b1·X + ε. The slope b1 is the change in Y per unit of X; b0 is the intercept; ε is the error.

The fraction of the dependent variable's variation explained by the regression model (0 to 1).

Non-constant error variance in a regression; it makes standard errors unreliable.

Errors correlated across observations (common in time series); it biases standard errors.

High correlation among regressors; it inflates standard errors and makes coefficients unstable.

The tendency for high-volatility and low-volatility periods to bunch together over time.

Exponentially weighted moving average — a volatility estimate that weights recent returns more via a decay factor (lambda).

A model of time-varying volatility that adds mean reversion to a long-run variance, capturing volatility clustering.

Geometric mean (compound growth) is always ≤ the arithmetic mean; the gap widens with volatility.

Generating many random scenarios from a model to estimate a distribution of outcomes (e.g., for VaR).

Resampling observed data with replacement to estimate the distribution of a statistic without assuming a form.

Revising a prior probability into a posterior as new evidence arrives, using Bayes' rule.

σ ÷ √n — the standard deviation of the sample mean; it shrinks as the sample grows.

Discrete takes countable values (binomial); continuous takes any value in a range (normal).

Counting the number of events in a fixed interval (e.g., number of defaults or operational-loss events).

The tendency of a variable (e.g., volatility or rates) to return toward its long-run average over time.

The probability of A given B has occurred: P(A|B) = P(A and B) ÷ P(B).

Events where one occurring does not change the probability of the other: P(A and B) = P(A)·P(B).

The probability-weighted average of its possible outcomes.

A cut point dividing a distribution; VaR is essentially a quantile of the loss distribution.

As the sample grows, the sample mean converges to the true population mean.

A series whose statistical properties (mean, variance) do not change over time.

A first-order autoregressive model where today's value depends on yesterday's value plus noise.

More complex models reduce bias but raise variance (overfitting); the goal is the balance that generalizes best.

A technique that reduces correlated factors to a few uncorrelated components (e.g., level, slope, curvature of the yield curve).

The instantaneous probability of an event (e.g., default) given survival so far; central to reduced-form models.

The expected improvement in outcome from reducing uncertainty before acting; underlies model and data investment.

A model that fits noise in the training data and generalizes poorly out of sample.

It uses total volatility and assumes normal returns, so it understates risk for fat-tailed or skewed return series.

Inversely: when market rates rise, existing fixed-rate bond prices fall, and vice versa.

A bond's price sensitivity to interest-rate changes, in years. A first-order (linear) estimate of the price change.

Longer maturity, a lower coupon, and a lower yield all increase duration (and price volatility).

Equals its maturity — the maximum duration for a given term.

The curvature of the price-yield relationship; it corrects duration's straight-line estimate for large rate moves.

Macaulay is the weighted-average time to cash flows (years); modified duration estimates the % price change per 1% yield move.

Premium: coupon > yield. Par: coupon = yield. Discount: coupon < yield.

The single discount rate that equates a bond's price to the present value of its cash flows if held to maturity.

A plot of yield against maturity. It is usually upward-sloping; inversion often precedes recessions.

A forward is customized OTC, settled at maturity, with counterparty risk. A future is standardized, exchange-traded, and marked to market daily.

Revaluing a position to current market price. Futures are marked to market daily, which limits counterparty risk.

Collateral posted to cover potential losses; a margin call demands more when the balance falls below maintenance margin.

Forward price F0 equals the spot S0 grown at the risk-free rate to delivery: F0 = S0 × eʳᵀ (continuous compounding).

An agreement to exchange cash-flow streams (classically fixed for floating interest). It behaves like a series of forwards.

One party pays a fixed rate and receives a floating rate (e.g., SOFR) on a notional, netted each period.

The right, not the obligation, to BUY the underlying at the strike by expiry.

The right, not the obligation, to SELL the underlying at the strike by expiry.

Profits when the underlying rises above strike + premium; loss is limited to the premium paid.

Profits when the underlying falls below strike − premium; loss is limited to the premium paid.

American can be exercised any time up to expiry; European only at expiry.

Intrinsic value is what the option is worth if exercised now; time value is the rest of the premium, reflecting remaining uncertainty.

c + X·e⁻ʳᵀ = p + S0. A call plus the present value of the strike equals a put plus the underlying.

Buying a call and a put at the same strike — a bet on a large move in either direction.

Holding the underlying and writing a call on it; collects premium but caps the upside.

Holding the underlying and buying a put to cap downside losses (like insurance).

A clearinghouse that becomes buyer to every seller and seller to every buyer, netting and margining to cut systemic counterparty risk.

Netting agreements, collateral (margin), and central clearing.

A futures curve where futures prices exceed the expected spot, giving a negative roll yield for a long position.

A futures curve where futures prices are below the spot, giving a positive roll yield for a long position.

The risk that the hedge instrument's price and the hedged asset's price do not move exactly together.

A contract where the buyer pays a periodic premium and the seller pays out if a reference entity defaults — insurance on credit.

Money-market instruments mature in ≤ 1 year (T-bills, commercial paper); capital-market instruments are longer (bonds, equities).

A pooled fund that trades on an exchange like a stock, usually tracking an index, with intraday liquidity.

The total number of outstanding futures/options contracts not yet closed; a gauge of market activity.

A bond whose coupon resets periodically to a reference rate plus a spread; little interest-rate duration.

Interest earned since the last coupon; the buyer pays it (dirty price = clean price + accrued interest).

A bond the issuer can redeem early; it has negative convexity and a higher yield to compensate the holder.

A bond the holder can sell back early; this option benefits the holder, so it carries a lower yield.

The fixed rate that makes a new interest-rate swap's value zero at inception.

Exchanging principal and interest in one currency for those in another; manages cross-currency funding.

An OTC agreement to buy/sell a commodity later at a set price; pricing includes storage and convenience yield.

The benefit of holding the physical commodity rather than a future; it lowers the forward price.

An OTC contract locking in an interest rate on a notional for a future period.

A stock index (e.g., S&P 500); cash-settled to the index level at expiry.

Borrowing and selling an asset to profit from a price fall, then buying it back; risk is theoretically unlimited.

A short-term secured loan: sell a security and agree to buy it back later at a higher price (the repo rate).

Primary = new issues raise capital for the issuer; secondary = existing securities trade among investors.

The yield on a single cash flow at one maturity; the building block for discounting and the par/forward curves.

An interest rate agreed today for borrowing/lending over a future period, implied by spot rates.

A reference entity's credit; the protection seller pays on a defined credit event (default, restructuring).

The gain or loss from rolling an expiring futures contract into a later one; positive in backwardation, negative in contango.

Value at Risk: the maximum loss not expected to be exceeded over a set horizon at a given confidence level (e.g., a 1-day 99% VaR).

The loss not expected to be exceeded over a horizon at a confidence level (e.g., 1-day 99% VaR).

Parametric (variance-covariance), historical simulation, and Monte Carlo simulation.

Assumes a distribution (usually normal) and computes VaR from σ and a z-score; understates fat-tail and non-linear risk.

Re-prices the portfolio over actual past returns and reads VaR off the loss distribution; assumes the past repeats.

Simulates many random scenarios from a model; flexible for non-linear products but computationally heavy and model-dependent.

VaR(T) = VaR(1) × √T — scales 1-day VaR to T days, valid only for i.i.d. returns with zero mean.

About 1.65 for 95% and 2.33 for 99% (one-tailed). Higher confidence gives a larger VaR.

VaR ≈ z × σ × portfolio value (for a zero-mean horizon); add the mean if non-zero.

It says nothing about the size of losses beyond the cutoff, and it is not always subadditive.

The average loss given that the loss exceeds VaR (conditional VaR). It captures tail severity.

ES is a coherent risk measure (subadditive), so diversification never increases it; VaR can violate subadditivity.

Monotonicity, subadditivity, positive homogeneity, and translation invariance.

The market-risk framework moved from 99% VaR toward a 97.5% expected-shortfall measure.

Comparing predicted VaR to realized losses to check a model is calibrated; too many exceptions means the model is wrong.

Underlying price, strike, time to expiry, risk-free rate, and volatility — assuming lognormal prices and no arbitrage.

Volatility — which is why traders back out implied volatility from market option prices.

The volatility that makes a model price equal the option's market price.

The pattern where implied volatility varies by strike (higher for deep in/out-of-the-money), contradicting constant-vol assumptions.

An option's price change for a one-dollar move in the underlying; the basis of delta-hedging.

How fast delta itself changes; it is largest near the money and drives how often a delta hedge must be rebalanced.

An option's sensitivity to a change in volatility; long options are long vega.

An option's sensitivity to the passage of time (time decay); long options are short theta.

An option's sensitivity to a change in interest rates; usually the smallest Greek.

Offsetting an option's delta with the underlying to neutralize small price moves; must be rebalanced as delta changes (gamma).

Estimating losses under severe but plausible scenarios (historical or hypothetical) to probe tail events VaR can miss.

Historical re-runs a real event (e.g., 2008); hypothetical invents a plausible shock (e.g., a sovereign default).

The risk that a model is wrong or wrongly used, leading to mispriced positions or understated risk.

A discrete tree of up/down price moves used to value options, especially American-style; it converges to Black-Scholes.

Pricing a derivative by discounting its expected payoff under risk-neutral probabilities at the risk-free rate.

Sensitivity of a bond's price to a change in one specific point on the yield curve, holding others fixed.

The change in portfolio VaR from adding (or removing) a position.

The change in portfolio VaR for a small change in a position's size; used to allocate risk.

The part of total portfolio VaR attributable to a position; component VaRs sum to total VaR.

Another name for expected shortfall — the average loss beyond VaR.

A day on which the actual loss exceeds the VaR estimate; too many in backtesting signals a bad model.

A parametric VaR approach that maps positions to risk factors and assumes normal factor returns.

Re-pricing every position under each scenario (vs a delta approximation); more accurate for non-linear products.

A linear (delta) approach ignores gamma — the non-linear payoff curvature of options.

Neutralizing delta, then gamma and vega, to immunize an options book against small and larger moves.

Asset prices are lognormally distributed, so log-returns are normal and prices stay positive.

The extra value of an American option's ability to exercise before expiry (relevant for puts and dividend-paying calls).

The dollar value change in a position for a one-basis-point move in rates.

Decomposing its cash flows onto standard maturity buckets to compute VaR from key-rate volatilities.

VaR can be larger than the sum of sub-portfolio VaRs (non-subadditive), penalizing diversification — ES fixes this.

A statistical approach that models the tail of a loss distribution directly, improving extreme-quantile (VaR/ES) estimates.

Adding cash to a portfolio reduces its risk measure by that cash amount.

ES is the average of tail losses; worst-case is the single most adverse outcome in the scenario set.

Updating VaR with a current (EWMA/GARCH) volatility estimate rather than a long historical average.

It lets you build synthetic positions and check option prices for arbitrage-free consistency.

The risk of loss from moves in market prices — interest rates, equities, FX, and commodities.

Decomposing positions into standard risk factors so portfolio VaR can be computed from factor volatilities and correlations.

VaR estimated from the empirical loss distribution (e.g., historical simulation) without assuming a distribution shape.

An expected-loss measure focused on the most adverse outcome over a horizon, beyond standard VaR.

The Fundamental Review of the Trading Book — Basel's overhaul of market-risk capital, including the shift to expected shortfall.

Trading book holds positions for short-term resale (mark-to-market, market-risk capital); banking book holds to maturity (credit-risk capital).

Standardized uses regulator-set rules; internal-models lets approved banks use their own VaR/ES models for capital.

A market variable (a rate, index, or price) whose movements drive a portfolio's value.

Exposure to changes in volatility itself — important for options portfolios (vega risk).

Risk from non-parallel shifts in the yield curve, not just level changes — captured by key-rate durations.

VaR widened to reflect the cost or time of unwinding a position in an illiquid market.

ES is coherent and is now favored for trading-book capital; VaR's lack of subadditivity is a key reason for the switch.

VaR calibrated to a historical period of significant stress, required alongside current VaR under Basel.

A separate market-risk capital charge for issuer default in the trading book.

A risk factor without enough real price data to model; FRTB applies an add-on capital charge.

ES is computed at 97.5% with liquidity horizons varying by risk factor.

FRTB's standardized approach using delta, vega, and curvature sensitivities to set capital.

Risk to a bank's earnings and value from rate moves on banking-book assets and liabilities.

Decomposing positions into currency exposures to aggregate FX VaR.

The risk of a sudden price jump that a continuous hedge cannot keep up with (e.g., overnight gaps).

Loss from changes in implied volatility, not the underlying price; large in options portfolios.

P&L from holding the portfolio static, used to test VaR against price moves only.

The assumed time to exit or hedge a risk factor in stress; longer horizons raise the ES capital charge.

The additional risk from the non-linear (gamma) response of options, captured beyond delta and vega.

An FRTB check that a desk's risk model explains its actual daily P&L well enough to use internal models.

The risk of loss from a borrower or counterparty failing to meet its obligations.

An agency's opinion of default risk; investment grade is BBB−/Baa3 and above, high yield (junk) below it.

The extra yield over a risk-free benchmark that compensates for credit risk; it widens as perceived default risk rises.

Structural (Merton) treats default as equity falling to zero; reduced-form models default as a random hazard event.

Equity is a call option on the firm's assets; default occurs when asset value falls below debt at maturity.

The risk the other side of a derivative defaults before settling; managed with netting, collateral, and clearing.

The price adjustment for the expected loss from a counterparty's possible default on a derivative.

When exposure to a counterparty rises just as its default probability rises (the two are positively correlated).

Offsetting positive and negative exposures with the same counterparty to a single net amount, cutting credit exposure.

The fraction of an exposure recovered after default; LGD = 1 − recovery rate.

A VaR-style measure of unexpected credit loss over a horizon at a confidence level.

Pooling loans and issuing tranched securities (e.g., CDOs) with different seniority and risk; senior tranches absorb losses last.

How likely counterparties are to default together; high correlation concentrates portfolio credit risk and is modeled with copulas.

Internal Ratings-Based approach: approved banks estimate PD (and LGD/EAD in advanced IRB) for credit capital.

Foundation: bank estimates PD only; regulator sets LGD/EAD. Advanced: bank estimates PD, LGD, and EAD.

A table of probabilities that a rating moves to another rating over a period, including default.

Point-in-time reflects current conditions; through-the-cycle averages over the economic cycle for stability.

The market's implied annual cost to insure against default — a real-time gauge of credit risk.

A securitization that tranches a pool of credit exposures into senior, mezzanine, and equity slices.

The first-loss, highest-risk, highest-yield slice; it absorbs initial defaults.

The last-loss, lowest-risk, lowest-yield slice; protected by the junior tranches below it.

Single-name is one borrower's default; portfolio adds default correlation across many borrowers.

They reduce exposure at default, lowering counterparty capital and CVA.

A cap on exposure to a counterparty or sector to control concentration of credit risk.

The mirror of CVA — the gain from a firm's own default risk on its derivative liabilities.

The average of expected counterparty exposure over time; a key input to CVA and counterparty capital.

A high-percentile estimate of future counterparty exposure over the life of a trade.

A trigger (failure to pay, bankruptcy, restructuring) that obliges the protection seller to pay.

Loss from failed internal processes, people, and systems, or external events. Includes legal risk; excludes strategic and reputational risk.

Fraud, cyberattacks, system outages, model error, settlement failures, and natural disasters.

A firm's ability to keep delivering critical operations through disruption — cyber, third-party, and business-continuity risk.

Sizes operational-risk capital from a business indicator (scaled income) and a bank's internal loss history.

A record of internal (and external) operational-loss events used to model frequency and severity.

Frequency = how often losses occur (often Poisson); severity = how large each loss is (often a fat-tailed distribution).

Expert-driven estimates of rare, high-impact events that historical data alone cannot capture.

A forward-looking metric that signals rising operational risk (e.g., failed-trade rate, employee turnover).

The risk of loss from attacks on or failures of information systems; a growing focus of operational resilience.

Operational risk arising from reliance on outsourced providers and suppliers.

Pre-arranged plans and backups to maintain or quickly restore critical operations after a disruption.

Governance over model development, validation, and use to limit losses from wrong or misused models.

A financial-statement-based proxy for op-risk exposure (interest, services, financial components).

A scalar in the Standardized Approach that raises op-risk capital for banks with a worse loss history.

A structured process where business units identify their risks and rate the strength of controls.

A near-miss could have caused a loss but did not; both are logged to improve controls.

Choosing a (often fat-tailed) distribution for loss size, then combining with frequency to model annual loss.

A VaR-style estimate of operational loss over a year at a high confidence level.

Operational-risk loss from internal or external deception; a major op-risk category.

The risk that one side of a trade pays but the other fails to deliver, especially across time zones in FX.

A service whose disruption would harm customers or financial stability; resilience planning protects it first.

The maximum acceptable level of disruption to a critical operation before serious harm occurs.

Modeling annual operational loss by combining fitted frequency and severity distributions, often via Monte Carlo.

A control reduces a risk's likelihood/impact; a KRI is a metric that signals the risk is rising.

Funding: cannot meet cash needs as they fall due. Market: cannot sell a position quickly without moving its price.

A Basel III ratio: enough high-quality liquid assets to survive 30 days of stressed net cash outflows (≥ 100%).

A Basel III ratio: available stable funding ÷ required stable funding ≥ 100% over a one-year horizon.

Forced selling depresses prices, triggering margin calls and more selling — funding and market liquidity reinforce each other.

The gap between buy and sell prices; wider spreads mean higher market-liquidity cost to trade.

Internally charging business units for the cost of the liquidity and funding they consume.

An asset that can be sold quickly with little price loss in stress (e.g., cash, central-bank reserves, top sovereign bonds).

An estimate of how fast deposits leave in stress; a key LCR input (retail deposits run off slower than wholesale).

Mapping expected inflows and outflows over time buckets to spot funding shortfalls.

Manages a firm's funding, liquidity, and balance-sheet risk, including FTP and the liquidity buffer.

The risk that off-balance-sheet commitments (e.g., credit lines) are drawn just when funding is scarce.

Managing the mismatch between the timing/rate of assets and liabilities to control interest-rate and liquidity risk.

A stock of HQLA a firm holds to absorb stressed outflows without fire sales.

Wholesale (interbank, repo, large deposits) is cheaper but flightier; retail deposits are stickier in stress.

Funding long-term assets with short-term liabilities — profitable but a core source of liquidity risk.

A rapid withdrawal of funding (deposits/wholesale) that can make a solvent firm fail for lack of liquidity.

Pledging assets as collateral; over-encumbrance reduces the unencumbered HQLA available in stress.

The risk of not having cash to meet payment obligations during the day, even if end-of-day liquidity is fine.

A discount to a security's market value when used as collateral, to cover price and liquidity risk.

Providing emergency liquidity to solvent but illiquid institutions to prevent contagion.

How long a firm can meet obligations under a stress scenario using its liquidity buffer alone.

Performance measured net of the cost of holding liquidity buffers and funding.

LCR covers a 30-day acute stress; NSFR ensures stable funding over a one-year horizon.

How much a bank's deposit rate moves when market rates move; it drives funding cost and ALM risk.

Swapping lower-quality assets for HQLA (e.g., via repo) to meet liquidity or margin needs; it can add risk.