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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).

Four major financial risk types?

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

The risk-management process?

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

Four ways to handle a risk?

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

What is systematic risk?

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

What is unsystematic risk?

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

What does beta measure?

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).

What is Jensen's alpha?

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

The information ratio?

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 formula (credit)?

Expected loss = PD × LGD × EAD.

Expected vs unexpected loss?

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

What is economic capital?

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

Probability of default (PD)?

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

Loss given default (LGD)?

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

Exposure at default (EAD)?

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

The three pillars of Basel?

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

What did Basel III add?

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

What is the leverage ratio (Basel III)?

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

What is risk appetite?

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

What is enterprise risk management (ERM)?

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

Role of the chief risk officer (CRO)?

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

What is the GARP Code of Conduct?

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

Moral hazard vs adverse selection?

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

What is a key risk indicator (KRI)?

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

Principal-agent problem?

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).

What is the cost of capital as a hurdle?

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

Properties of the normal distribution?

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

Why model prices as lognormal?

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

What is the Student's t distribution used for?

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 vs standard deviation?

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

Covariance vs correlation?

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.

Why does diversification reduce risk?

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

The crisis problem with correlation?

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 vs Type II error?

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.

What is the central limit theorem?

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

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FRM Flashcards

What is VaR?: 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).
Four major financial risk types?: Market risk, credit risk, operational risk, and liquidity risk (plus business/strategic risk).
The risk-management process?: Identify → measure → monitor → manage, then report. Risk is taken deliberately, not eliminated.
Four ways to handle a risk?: Avoid, retain, mitigate, or transfer (e.g., via insurance or hedging).
What is systematic risk?: Non-diversifiable, market-wide risk measured by beta. It is the only risk the market rewards with higher expected return.
What is unsystematic risk?: Company- or industry-specific risk that diversification can largely eliminate; it is not rewarded with extra return.
What does beta measure?: An asset's sensitivity to the overall market (its systematic risk). The market portfolio has a beta of 1.0.
The CAPM formula?: Required return = Rf + β × (Rm − Rf). It prices only systematic risk.
The Sharpe ratio?: (Rp − Rf) ÷ σp — excess return per unit of TOTAL risk (standard deviation). Higher is better.
The Treynor ratio?: (Rp − Rf) ÷ βp — excess return per unit of SYSTEMATIC risk (beta).
What is Jensen's alpha?: Portfolio return minus its CAPM-required return: Rp − [Rf + βp(Rm − Rf)]. Positive alpha = outperformance vs CAPM.
The information ratio?: Active return (vs benchmark) ÷ tracking error. Measures consistency of active management skill.
What is RAROC?: Risk-adjusted return on capital = risk-adjusted return ÷ economic capital. A unit adds value when RAROC exceeds the cost of equity.
Expected loss formula (credit)?: Expected loss = PD × LGD × EAD.
Expected vs unexpected loss?: Expected loss is the average anticipated loss (priced into spreads). Unexpected loss is its volatility — covered by capital.
What is economic capital?: The capital a firm estimates it needs to absorb unexpected losses to a chosen confidence level over a horizon.
Probability of default (PD)?: The likelihood a counterparty fails to meet its obligations over a stated horizon.
Loss given default (LGD)?: The fraction of exposure lost if default occurs = 1 − recovery rate.
Exposure at default (EAD)?: The amount outstanding to a counterparty at the moment it defaults.
The three pillars of Basel?: Pillar 1: minimum capital (credit, market, operational risk). Pillar 2: supervisory review. Pillar 3: market discipline via disclosure.
What did Basel III add?: Higher-quality capital, a leverage ratio, and two liquidity ratios — the LCR and NSFR — after the 2008 crisis.
What is the leverage ratio (Basel III)?: Tier 1 capital ÷ total exposure — a non-risk-based backstop to risk-weighted capital ratios.
The three lines of defense?: 1st: business/risk owners. 2nd: risk management & compliance. 3rd: independent internal audit.
What is risk appetite?: The amount and type of risk a firm is willing to take to pursue its objectives, set by the board.
What is enterprise risk management (ERM)?: A firm-wide, integrated approach to managing all risks together rather than in silos.
Role of the chief risk officer (CRO)?: Leads the independent risk function, reports risk to the board, and ensures limits and appetite are enforced.
What is the GARP Code of Conduct?: Principles all FRM holders/candidates agree to: professional integrity, conflict-of-interest avoidance, confidentiality, and professionalism.
Moral hazard vs adverse selection?: Moral hazard: risk-taking changes after a contract (e.g., once insured). Adverse selection: the riskiest parties are most likely to transact.
What is a key risk indicator (KRI)?: A metric that gives early warning of rising risk exposure (e.g., failed-trade rate, staff turnover).
Principal-agent problem?: Conflict between owners (principals) and managers (agents); governance and aligned incentives reduce it.
What is hedging?: Taking an offsetting position to reduce exposure to a risk factor (e.g., shorting futures against a long cash position).
What is the cost of capital as a hurdle?: A project adds value only if its risk-adjusted return exceeds the firm's cost of capital.
Properties of the normal distribution?: Symmetric, fully described by mean and variance; ~68% / 95% / 99% of values fall within 1 / 2 / 3 standard deviations.
Why model prices as lognormal?: Lognormal returns keep prices non-negative; the normal can produce negative prices.
What is the Student's t distribution used for?: Small samples and fatter tails than the normal — useful when tail risk is a concern.
What is skewness?: Asymmetry of a distribution. Negative skew (a long left tail) means large losses are more likely than a normal predicts.
What is kurtosis?: The 'fatness' of the tails. Excess kurtosis > 0 (leptokurtic) means fat tails — more extreme outcomes than the normal.
Variance vs standard deviation?: Variance (σ²) is the squared dispersion; standard deviation (σ) is its square root, in the same units as returns.
Covariance vs correlation?: Covariance gives the direction two variables move together (unscaled). Correlation standardizes it to between −1 and +1.
Correlation formula?: ρ = σxy ÷ (σx × σy). It ranges from −1 to +1; 0 means no linear relationship.
Why does diversification reduce risk?: Combining assets with correlation below 1 lowers portfolio standard deviation below the weighted average of the parts.
The crisis problem with correlation?: Correlations rise toward 1 in a crisis, so diversification fails just when it is needed most.
What is a copula?: A function that joins marginal distributions into a joint distribution, modeling tail dependence that linear correlation misses.
Type I vs Type II error?: Type I: reject a true null (probability = significance level α). Type II: fail to reject a false null.
What is a p-value?: 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.
What is the central limit theorem?: The distribution of sample means approaches normal as the sample size grows, regardless of the population's shape.
What is a confidence interval?: A range that contains the true parameter with a stated probability (e.g., 95%), given the sample.
Simple linear regression model?: 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.
What does R² tell you?: The fraction of the dependent variable's variation explained by the regression model (0 to 1).
What is heteroskedasticity?: Non-constant error variance in a regression; it makes standard errors unreliable.
What is autocorrelation (serial correlation)?: Errors correlated across observations (common in time series); it biases standard errors.
What is multicollinearity?: High correlation among regressors; it inflates standard errors and makes coefficients unstable.
What is volatility clustering?: The tendency for high-volatility and low-volatility periods to bunch together over time.
What is EWMA?: Exponentially weighted moving average — a volatility estimate that weights recent returns more via a decay factor (lambda).
What is a GARCH model?: A model of time-varying volatility that adds mean reversion to a long-run variance, capturing volatility clustering.
Arithmetic vs geometric mean?: Geometric mean (compound growth) is always ≤ the arithmetic mean; the gap widens with volatility.
What is Monte Carlo simulation?: Generating many random scenarios from a model to estimate a distribution of outcomes (e.g., for VaR).
What is bootstrapping?: Resampling observed data with replacement to estimate the distribution of a statistic without assuming a form.
What is a Bayesian update?: Revising a prior probability into a posterior as new evidence arrives, using Bayes' rule.
What is the standard error of the mean?: σ ÷ √n — the standard deviation of the sample mean; it shrinks as the sample grows.
Discrete vs continuous distribution?: Discrete takes countable values (binomial); continuous takes any value in a range (normal).
What is a Poisson distribution used for?: Counting the number of events in a fixed interval (e.g., number of defaults or operational-loss events).
What is mean reversion?: The tendency of a variable (e.g., volatility or rates) to return toward its long-run average over time.
How do bond prices and yields relate?: Inversely: when market rates rise, existing fixed-rate bond prices fall, and vice versa.
What is duration?: A bond's price sensitivity to interest-rate changes, in years. A first-order (linear) estimate of the price change.
What raises a bond's duration?: Longer maturity, a lower coupon, and a lower yield all increase duration (and price volatility).
A zero-coupon bond's duration?: Equals its maturity — the maximum duration for a given term.
What is convexity?: The curvature of the price-yield relationship; it corrects duration's straight-line estimate for large rate moves.
Modified vs Macaulay duration?: Macaulay is the weighted-average time to cash flows (years); modified duration estimates the % price change per 1% yield move.
Premium, par, or discount bond?: Premium: coupon > yield. Par: coupon = yield. Discount: coupon < yield.
What is yield to maturity (YTM)?: The single discount rate that equates a bond's price to the present value of its cash flows if held to maturity.
What is the yield curve?: A plot of yield against maturity. It is usually upward-sloping; inversion often precedes recessions.
Forward vs future?: A forward is customized OTC, settled at maturity, with counterparty risk. A future is standardized, exchange-traded, and marked to market daily.
What does marking to market mean?: Revaluing a position to current market price. Futures are marked to market daily, which limits counterparty risk.
What is a margin account (futures)?: Collateral posted to cover potential losses; a margin call demands more when the balance falls below maintenance margin.
Cost-of-carry forward price (no income)?: Forward price F0 equals the spot S0 grown at the risk-free rate to delivery: F0 = S0 × eʳᵀ (continuous compounding).
What is a swap?: An agreement to exchange cash-flow streams (classically fixed for floating interest). It behaves like a series of forwards.
Plain-vanilla interest-rate swap?: One party pays a fixed rate and receives a floating rate (e.g., SOFR) on a notional, netted each period.
What is a call option?: The right, not the obligation, to BUY the underlying at the strike by expiry.
What is a put option?: The right, not the obligation, to SELL the underlying at the strike by expiry.
Long call payoff?: Profits when the underlying rises above strike + premium; loss is limited to the premium paid.
Long put payoff?: Profits when the underlying falls below strike − premium; loss is limited to the premium paid.
American vs European option?: American can be exercised any time up to expiry; European only at expiry.
What is intrinsic vs time value?: Intrinsic value is what the option is worth if exercised now; time value is the rest of the premium, reflecting remaining uncertainty.
Put-call parity (European)?: c + X·e⁻ʳᵀ = p + S0. A call plus the present value of the strike equals a put plus the underlying.
What is a straddle?: Buying a call and a put at the same strike — a bet on a large move in either direction.
What is a covered call?: Holding the underlying and writing a call on it; collects premium but caps the upside.
What is a protective put?: Holding the underlying and buying a put to cap downside losses (like insurance).
What is a central counterparty (CCP)?: A clearinghouse that becomes buyer to every seller and seller to every buyer, netting and margining to cut systemic counterparty risk.
Counterparty-risk mitigants?: Netting agreements, collateral (margin), and central clearing.
What is contango?: A futures curve where futures prices exceed the expected spot, giving a negative roll yield for a long position.
What is backwardation?: A futures curve where futures prices are below the spot, giving a positive roll yield for a long position.
What is basis risk?: The risk that the hedge instrument's price and the hedged asset's price do not move exactly together.
What is a credit default swap (CDS)?: A contract where the buyer pays a periodic premium and the seller pays out if a reference entity defaults — insurance on credit.
Money-market vs capital-market instruments?: Money-market instruments mature in ≤ 1 year (T-bills, commercial paper); capital-market instruments are longer (bonds, equities).
What is an exchange-traded fund (ETF)?: A pooled fund that trades on an exchange like a stock, usually tracking an index, with intraday liquidity.
VaR in one sentence?: The loss not expected to be exceeded over a horizon at a confidence level (e.g., 1-day 99% VaR).
Three ways to compute VaR?: Parametric (variance-covariance), historical simulation, and Monte Carlo simulation.
Parametric VaR method?: Assumes a distribution (usually normal) and computes VaR from σ and a z-score; understates fat-tail and non-linear risk.
Historical simulation VaR?: Re-prices the portfolio over actual past returns and reads VaR off the loss distribution; assumes the past repeats.
Monte Carlo VaR?: Simulates many random scenarios from a model; flexible for non-linear products but computationally heavy and model-dependent.
Square-root-of-time rule?: VaR(T) = VaR(1) × √T — scales 1-day VaR to T days, valid only for i.i.d. returns with zero mean.
z-scores for 95% and 99% VaR?: About 1.65 for 95% and 2.33 for 99% (one-tailed). Higher confidence gives a larger VaR.
Parametric VaR quick formula?: VaR ≈ z × σ × portfolio value (for a zero-mean horizon); add the mean if non-zero.
Main weakness of VaR?: It says nothing about the size of losses beyond the cutoff, and it is not always subadditive.
What is expected shortfall (ES)?: The average loss given that the loss exceeds VaR (conditional VaR). It captures tail severity.
Why is ES preferred over VaR?: ES is a coherent risk measure (subadditive), so diversification never increases it; VaR can violate subadditivity.
Four properties of a coherent risk measure?: Monotonicity, subadditivity, positive homogeneity, and translation invariance.
What confidence level did Basel adopt for ES?: The market-risk framework moved from 99% VaR toward a 97.5% expected-shortfall measure.
What is backtesting?: Comparing predicted VaR to realized losses to check a model is calibrated; too many exceptions means the model is wrong.
Black-Scholes-Merton inputs?: Underlying price, strike, time to expiry, risk-free rate, and volatility — assuming lognormal prices and no arbitrage.
Which BSM input is unobservable?: Volatility — which is why traders back out implied volatility from market option prices.
What is implied volatility?: The volatility that makes a model price equal the option's market price.
What is the volatility smile?: The pattern where implied volatility varies by strike (higher for deep in/out-of-the-money), contradicting constant-vol assumptions.
What is delta?: An option's price change for a one-dollar move in the underlying; the basis of delta-hedging.
What is gamma?: How fast delta itself changes; it is largest near the money and drives how often a delta hedge must be rebalanced.
What is vega?: An option's sensitivity to a change in volatility; long options are long vega.
What is theta?: An option's sensitivity to the passage of time (time decay); long options are short theta.
What is rho?: An option's sensitivity to a change in interest rates; usually the smallest Greek.
What is delta-hedging?: Offsetting an option's delta with the underlying to neutralize small price moves; must be rebalanced as delta changes (gamma).
What is stress testing?: Estimating losses under severe but plausible scenarios (historical or hypothetical) to probe tail events VaR can miss.
Historical vs hypothetical stress scenario?: Historical re-runs a real event (e.g., 2008); hypothetical invents a plausible shock (e.g., a sovereign default).
What is model risk?: The risk that a model is wrong or wrongly used, leading to mispriced positions or understated risk.
What is the binomial option model?: A discrete tree of up/down price moves used to value options, especially American-style; it converges to Black-Scholes.
What is risk-neutral valuation?: Pricing a derivative by discounting its expected payoff under risk-neutral probabilities at the risk-free rate.
What is a key-rate (partial) duration?: Sensitivity of a bond's price to a change in one specific point on the yield curve, holding others fixed.
What is incremental VaR?: The change in portfolio VaR from adding (or removing) a position.
What is marginal VaR?: The change in portfolio VaR for a small change in a position's size; used to allocate risk.
What is component VaR?: The part of total portfolio VaR attributable to a position; component VaRs sum to total VaR.
What is market risk?: The risk of loss from moves in market prices — interest rates, equities, FX, and commodities.
What is VaR mapping?: Decomposing positions into standard risk factors so portfolio VaR can be computed from factor volatilities and correlations.
What is non-parametric VaR?: VaR estimated from the empirical loss distribution (e.g., historical simulation) without assuming a distribution shape.
What is the worst-case scenario measure?: An expected-loss measure focused on the most adverse outcome over a horizon, beyond standard VaR.
What is the FRTB?: The Fundamental Review of the Trading Book — Basel's overhaul of market-risk capital, including the shift to expected shortfall.
Trading book vs banking book?: Trading book holds positions for short-term resale (mark-to-market, market-risk capital); banking book holds to maturity (credit-risk capital).
What is the standardized vs internal-models approach?: Standardized uses regulator-set rules; internal-models lets approved banks use their own VaR/ES models for capital.
What is a risk factor?: A market variable (a rate, index, or price) whose movements drive a portfolio's value.
What is volatility risk?: Exposure to changes in volatility itself — important for options portfolios (vega risk).
What is curve (yield-curve) risk?: Risk from non-parallel shifts in the yield curve, not just level changes — captured by key-rate durations.
What is liquidity-adjusted VaR?: VaR widened to reflect the cost or time of unwinding a position in an illiquid market.
What is a coherent vs non-coherent measure here?: ES is coherent and is now favored for trading-book capital; VaR's lack of subadditivity is a key reason for the switch.
What is credit risk?: The risk of loss from a borrower or counterparty failing to meet its obligations.
What is a credit rating?: An agency's opinion of default risk; investment grade is BBB−/Baa3 and above, high yield (junk) below it.
What is a credit spread?: The extra yield over a risk-free benchmark that compensates for credit risk; it widens as perceived default risk rises.
Structural vs reduced-form default model?: Structural (Merton) treats default as equity falling to zero; reduced-form models default as a random hazard event.
The Merton model idea?: Equity is a call option on the firm's assets; default occurs when asset value falls below debt at maturity.
What is counterparty credit risk?: The risk the other side of a derivative defaults before settling; managed with netting, collateral, and clearing.
What is a credit valuation adjustment (CVA)?: The price adjustment for the expected loss from a counterparty's possible default on a derivative.
What is wrong-way risk?: When exposure to a counterparty rises just as its default probability rises (the two are positively correlated).
What is netting?: Offsetting positive and negative exposures with the same counterparty to a single net amount, cutting credit exposure.
What is a recovery rate?: The fraction of an exposure recovered after default; LGD = 1 − recovery rate.
What is credit VaR?: A VaR-style measure of unexpected credit loss over a horizon at a confidence level.
What is securitization?: Pooling loans and issuing tranched securities (e.g., CDOs) with different seniority and risk; senior tranches absorb losses last.
What is a default correlation?: How likely counterparties are to default together; high correlation concentrates portfolio credit risk and is modeled with copulas.
Definition of operational risk?: Loss from failed internal processes, people, and systems, or external events. Includes legal risk; excludes strategic and reputational risk.
Examples of operational risk?: Fraud, cyberattacks, system outages, model error, settlement failures, and natural disasters.
What is operational resilience?: A firm's ability to keep delivering critical operations through disruption — cyber, third-party, and business-continuity risk.
Basel Standardized Approach for op risk?: Sizes operational-risk capital from a business indicator (scaled income) and a bank's internal loss history.
What is a loss-event database?: A record of internal (and external) operational-loss events used to model frequency and severity.
Frequency vs severity in op risk?: Frequency = how often losses occur (often Poisson); severity = how large each loss is (often a fat-tailed distribution).
What is scenario analysis (op risk)?: Expert-driven estimates of rare, high-impact events that historical data alone cannot capture.
What is a key risk indicator (KRI)?: A forward-looking metric that signals rising operational risk (e.g., failed-trade rate, employee turnover).
What is cyber risk?: The risk of loss from attacks on or failures of information systems; a growing focus of operational resilience.
What is third-party (vendor) risk?: Operational risk arising from reliance on outsourced providers and suppliers.
What is business continuity planning?: Pre-arranged plans and backups to maintain or quickly restore critical operations after a disruption.
What is model risk management?: Governance over model development, validation, and use to limit losses from wrong or misused models.
Funding vs market liquidity risk?: Funding: cannot meet cash needs as they fall due. Market: cannot sell a position quickly without moving its price.
What is the Liquidity Coverage Ratio (LCR)?: A Basel III ratio: enough high-quality liquid assets to survive 30 days of stressed net cash outflows (≥ 100%).
What is the Net Stable Funding Ratio (NSFR)?: A Basel III ratio: available stable funding ÷ required stable funding ≥ 100% over a one-year horizon.
What is a liquidity spiral?: Forced selling depresses prices, triggering margin calls and more selling — funding and market liquidity reinforce each other.
What is the bid-ask spread as a liquidity cost?: The gap between buy and sell prices; wider spreads mean higher market-liquidity cost to trade.
What is funds-transfer pricing (FTP)?: Internally charging business units for the cost of the liquidity and funding they consume.
What is a high-quality liquid asset (HQLA)?: An asset that can be sold quickly with little price loss in stress (e.g., cash, central-bank reserves, top sovereign bonds).
What is a deposit run-off assumption?: An estimate of how fast deposits leave in stress; a key LCR input (retail deposits run off slower than wholesale).
What is cash-flow gap analysis?: Mapping expected inflows and outflows over time buckets to spot funding shortfalls.
What is the role of a treasury function?: Manages a firm's funding, liquidity, and balance-sheet risk, including FTP and the liquidity buffer.
What is contingent funding risk?: The risk that off-balance-sheet commitments (e.g., credit lines) are drawn just when funding is scarce.
What is asset-liability management (ALM)?: Managing the mismatch between the timing/rate of assets and liabilities to control interest-rate and liquidity risk.
What is risk transfer?: Shifting a risk to another party, e.g., via insurance, derivatives, or securitization.
What is reputational risk?: The risk of loss from damage to a firm's reputation; excluded from the Basel operational-risk definition but managed separately.
What is strategic (business) risk?: Risk to earnings from poor business decisions or adverse industry shifts; excluded from operational risk.
What is concentration risk?: Loss from large exposure to a single counterparty, sector, or risk factor; limits and diversification control it.
What is the efficient frontier?: The set of portfolios giving the highest expected return for each level of risk.
What is the capital market line (CML)?: The line from the risk-free asset through the market portfolio; the best risk-return tradeoff using total risk.
What is the security market line (SML)?: The CAPM graph of required return vs beta; a security above it is undervalued.
What is alpha?: Return above what CAPM (or a benchmark) requires for the risk taken; a measure of skill.
What is tracking error?: The standard deviation of a portfolio's active return versus its benchmark.
What is a risk limit?: A pre-set cap on exposure (e.g., a VaR or notional limit) used to control risk-taking.
What is enterprise economic capital?: The aggregate capital a firm holds for all risks, accounting for diversification across risk types.
What is the cost-of-equity hurdle in RAROC?: RAROC must exceed the firm's cost of equity for the activity to create shareholder value.
What is conditional probability?: The probability of A given B has occurred: P(A|B) = P(A and B) ÷ P(B).
What are independent events?: Events where one occurring does not change the probability of the other: P(A and B) = P(A)·P(B).
Expected value of a random variable?: The probability-weighted average of its possible outcomes.
What is a quantile?: A cut point dividing a distribution; VaR is essentially a quantile of the loss distribution.
What is the law of large numbers?: As the sample grows, the sample mean converges to the true population mean.
What is stationarity in time series?: A series whose statistical properties (mean, variance) do not change over time.
What is an AR(1) model?: A first-order autoregressive model where today's value depends on yesterday's value plus noise.
What is the bias-variance tradeoff?: More complex models reduce bias but raise variance (overfitting); the goal is the balance that generalizes best.
What is principal component analysis (PCA)?: A technique that reduces correlated factors to a few uncorrelated components (e.g., level, slope, curvature of the yield curve).
What is a hazard rate?: The instantaneous probability of an event (e.g., default) given survival so far; central to reduced-form models.
What is open interest?: The total number of outstanding futures/options contracts not yet closed; a gauge of market activity.
What is a floating-rate note (FRN)?: A bond whose coupon resets periodically to a reference rate plus a spread; little interest-rate duration.
What is accrued interest?: Interest earned since the last coupon; the buyer pays it (dirty price = clean price + accrued interest).
What is a callable bond?: A bond the issuer can redeem early; it has negative convexity and a higher yield to compensate the holder.
What is a putable bond?: A bond the holder can sell back early; this option benefits the holder, so it carries a lower yield.
What is the swap rate?: The fixed rate that makes a new interest-rate swap's value zero at inception.
What is a currency (FX) swap?: Exchanging principal and interest in one currency for those in another; manages cross-currency funding.
What is a commodity forward?: An OTC agreement to buy/sell a commodity later at a set price; pricing includes storage and convenience yield.
What is convenience yield?: The benefit of holding the physical commodity rather than a future; it lowers the forward price.
What is a forward rate agreement (FRA)?: An OTC contract locking in an interest rate on a notional for a future period.
What is the underlying of an equity index future?: A stock index (e.g., S&P 500); cash-settled to the index level at expiry.
What is short selling?: Borrowing and selling an asset to profit from a price fall, then buying it back; risk is theoretically unlimited.
What is a repo (repurchase agreement)?: A short-term secured loan: sell a security and agree to buy it back later at a higher price (the repo rate).
What is the difference between a primary and secondary market?: Primary = new issues raise capital for the issuer; secondary = existing securities trade among investors.
What is conditional VaR (CVaR)?: Another name for expected shortfall — the average loss beyond VaR.
What is a VaR exception (breach)?: A day on which the actual loss exceeds the VaR estimate; too many in backtesting signals a bad model.
What is the delta-normal method?: A parametric VaR approach that maps positions to risk factors and assumes normal factor returns.
What is full revaluation in VaR?: Re-pricing every position under each scenario (vs a delta approximation); more accurate for non-linear products.
Why does VaR understate options risk?: A linear (delta) approach ignores gamma — the non-linear payoff curvature of options.
What is the Greeks-based hedge of a portfolio?: Neutralizing delta, then gamma and vega, to immunize an options book against small and larger moves.
What is the lognormal assumption in BSM?: Asset prices are lognormally distributed, so log-returns are normal and prices stay positive.
What is early-exercise value?: The extra value of an American option's ability to exercise before expiry (relevant for puts and dividend-paying calls).
What is a risk-factor sensitivity (DV01)?: The dollar value change in a position for a one-basis-point move in rates.
What is mapping a bond to risk factors?: Decomposing its cash flows onto standard maturity buckets to compute VaR from key-rate volatilities.
What is the coherence failure of VaR?: VaR can be larger than the sum of sub-portfolio VaRs (non-subadditive), penalizing diversification — ES fixes this.
What is extreme value theory (EVT)?: A statistical approach that models the tail of a loss distribution directly, improving extreme-quantile (VaR/ES) estimates.
What is a stressed VaR?: VaR calibrated to a historical period of significant stress, required alongside current VaR under Basel.
What is the default risk charge (FRTB)?: A separate market-risk capital charge for issuer default in the trading book.
What is a non-modellable risk factor (NMRF)?: A risk factor without enough real price data to model; FRTB applies an add-on capital charge.
What is the expected shortfall horizon in FRTB?: ES is computed at 97.5% with liquidity horizons varying by risk factor.
What is a sensitivities-based method (SBM)?: FRTB's standardized approach using delta, vega, and curvature sensitivities to set capital.
What is interest-rate risk in the banking book (IRRBB)?: Risk to a bank's earnings and value from rate moves on banking-book assets and liabilities.
What is mapping FX risk?: Decomposing positions into currency exposures to aggregate FX VaR.
What is gap risk?: The risk of a sudden price jump that a continuous hedge cannot keep up with (e.g., overnight gaps).
What is volatility (vega) risk in a book?: Loss from changes in implied volatility, not the underlying price; large in options portfolios.
What is a hypothetical P&L for backtesting?: P&L from holding the portfolio static, used to test VaR against price moves only.
What is the IRB approach (Basel)?: Internal Ratings-Based approach: approved banks estimate PD (and LGD/EAD in advanced IRB) for credit capital.
Foundation vs advanced IRB?: Foundation: bank estimates PD only; regulator sets LGD/EAD. Advanced: bank estimates PD, LGD, and EAD.
What is a transition (migration) matrix?: A table of probabilities that a rating moves to another rating over a period, including default.
What is point-in-time vs through-the-cycle PD?: Point-in-time reflects current conditions; through-the-cycle averages over the economic cycle for stability.
What is a CDS spread telling you?: The market's implied annual cost to insure against default — a real-time gauge of credit risk.
What is a collateralized debt obligation (CDO)?: A securitization that tranches a pool of credit exposures into senior, mezzanine, and equity slices.
What is the equity tranche of a CDO?: The first-loss, highest-risk, highest-yield slice; it absorbs initial defaults.
What is the senior tranche of a CDO?: The last-loss, lowest-risk, lowest-yield slice; protected by the junior tranches below it.
What is single-name vs portfolio credit risk?: Single-name is one borrower's default; portfolio adds default correlation across many borrowers.
What is netting + collateral's effect on EAD?: They reduce exposure at default, lowering counterparty capital and CVA.
What is a credit limit?: A cap on exposure to a counterparty or sector to control concentration of credit risk.
What is debt valuation adjustment (DVA)?: The mirror of CVA — the gain from a firm's own default risk on its derivative liabilities.
What is the business indicator (BI) in op-risk capital?: A financial-statement-based proxy for op-risk exposure (interest, services, financial components).
What is the internal loss multiplier (ILM)?: A scalar in the Standardized Approach that raises op-risk capital for banks with a worse loss history.
What is a risk-and-control self-assessment (RCSA)?: A structured process where business units identify their risks and rate the strength of controls.
What is the difference between a near-miss and a loss event?: A near-miss could have caused a loss but did not; both are logged to improve controls.
What is severity distribution fitting?: Choosing a (often fat-tailed) distribution for loss size, then combining with frequency to model annual loss.
What is operational VaR?: A VaR-style estimate of operational loss over a year at a high confidence level.
What is fraud risk?: Operational-risk loss from internal or external deception; a major op-risk category.
What is settlement (Herstatt) risk?: The risk that one side of a trade pays but the other fails to deliver, especially across time zones in FX.
What is a critical operation (resilience)?: A service whose disruption would harm customers or financial stability; resilience planning protects it first.
What is an impact tolerance?: The maximum acceptable level of disruption to a critical operation before serious harm occurs.
What is the liquidity buffer?: A stock of HQLA a firm holds to absorb stressed outflows without fire sales.
What is wholesale vs retail funding?: Wholesale (interbank, repo, large deposits) is cheaper but flightier; retail deposits are stickier in stress.
What is maturity transformation?: Funding long-term assets with short-term liabilities — profitable but a core source of liquidity risk.
What is a run on a bank?: A rapid withdrawal of funding (deposits/wholesale) that can make a solvent firm fail for lack of liquidity.
What is encumbrance of assets?: Pledging assets as collateral; over-encumbrance reduces the unencumbered HQLA available in stress.
What is intraday liquidity risk?: The risk of not having cash to meet payment obligations during the day, even if end-of-day liquidity is fine.
What is a haircut on collateral?: A discount to a security's market value when used as collateral, to cover price and liquidity risk.
What is the role of the central bank as lender of last resort?: Providing emergency liquidity to solvent but illiquid institutions to prevent contagion.
What is a survival horizon?: How long a firm can meet obligations under a stress scenario using its liquidity buffer alone.
What is liquidity-adjusted return?: Performance measured net of the cost of holding liquidity buffers and funding.
What is risk aggregation?: Combining risks across positions and types into a firm-wide view, accounting for diversification and correlation.
What is a stress test vs a scenario analysis?: Stress test measures impact of a defined shock; scenario analysis explores a broader narrative of joint events.
What is the cost of carry?: The net cost of holding an asset (financing + storage − income); it links spot and forward prices.
What is value of information in decisions?: The expected improvement in outcome from reducing uncertainty before acting; underlies model and data investment.
What is overfitting?: A model that fits noise in the training data and generalizes poorly out of sample.
What is a Sharpe ratio limitation?: It uses total volatility and assumes normal returns, so it understates risk for fat-tailed or skewed return series.
What is a zero-coupon (spot) rate?: The yield on a single cash flow at one maturity; the building block for discounting and the par/forward curves.
What is a forward rate?: An interest rate agreed today for borrowing/lending over a future period, implied by spot rates.
What is the underlying of a CDS?: A reference entity's credit; the protection seller pays on a defined credit event (default, restructuring).
What is roll yield?: The gain or loss from rolling an expiring futures contract into a later one; positive in backwardation, negative in contango.
What is a coherent measure's translation invariance?: Adding cash to a portfolio reduces its risk measure by that cash amount.
What is the difference between ES and worst-case loss?: ES is the average of tail losses; worst-case is the single most adverse outcome in the scenario set.
What is volatility scaling of VaR?: Updating VaR with a current (EWMA/GARCH) volatility estimate rather than a long historical average.
What is the put-call parity use in risk?: It lets you build synthetic positions and check option prices for arbitrage-free consistency.
What is a liquidity horizon (FRTB)?: The assumed time to exit or hedge a risk factor in stress; longer horizons raise the ES capital charge.
What is curvature risk (FRTB)?: The additional risk from the non-linear (gamma) response of options, captured beyond delta and vega.
What is a P&L attribution test?: An FRTB check that a desk's risk model explains its actual daily P&L well enough to use internal models.
What is expected positive exposure (EPE)?: The average of expected counterparty exposure over time; a key input to CVA and counterparty capital.
What is potential future exposure (PFE)?: A high-percentile estimate of future counterparty exposure over the life of a trade.
What is a default event in a CDS?: A trigger (failure to pay, bankruptcy, restructuring) that obliges the protection seller to pay.
What is the loss data approach (LDA)?: Modeling annual operational loss by combining fitted frequency and severity distributions, often via Monte Carlo.
What is a control vs a key risk indicator?: A control reduces a risk's likelihood/impact; a KRI is a metric that signals the risk is rising.
What is the difference between LCR and NSFR horizons?: LCR covers a 30-day acute stress; NSFR ensures stable funding over a one-year horizon.
What is a deposit beta?: How much a bank's deposit rate moves when market rates move; it drives funding cost and ALM risk.
What is collateral transformation?: Swapping lower-quality assets for HQLA (e.g., via repo) to meet liquidity or margin needs; it can add risk.

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By Career EmployerUpdated Sep 12, 2026

250+ free FRM flashcards — 4 ways to study

FRM Flashcard of the DayNew daily

The classic card. Do you know this one?

Click Study Flashcards above to open the flashcard hub — 250+ FRM cards you can flip, match, type, or quiz yourself on. Every card is drawn from the GARP topic areas, so you study exactly what the exam tests.^[1] Pair them with our free practice test and study guide.

FRM Flashcard Study Modes

Flip mode turns cards one at a time at your own pace, and Match runs a timed game pairing terms with their definitions. Type shows you the definition and asks you to key the term back in, so a card like What is convexity? has to come back cold. Quiz builds multiple-choice questions from the same 293 cards for quick review sessions.

Free FRM flashcards from Career Employer — active recall for every risk topic

Why Flashcards Work for the FRM Exam

Financial Markets & Products is the largest block at 51 cards, covering instrument mechanics and payoff language that GARP leans on throughout the exam. You get prompts like What is a swap?, What is contango?, and the card that asks Long put payoff?, so derivative structure and pricing vocabulary stay separate in your head. Valuation & Risk Models adds 50 cards on measurement machinery, including What is VaR?, What is vega?, and What is model risk?

Foundations of Risk Management runs 46 cards and drills the performance and governance vocabulary that frames everything else, with fronts such as What is RAROC?, The Sharpe ratio?, and The CAPM formula? Quantitative Analysis contributes 44 cards on statistics and estimation, where cards like What is EWMA?, What is a p-value?, and What is a copula? force you to state the definition rather than recognize it.

Credit Risk holds 28 cards on default and counterparty language, including What is credit VaR?, What is wrong-way risk?, and the card that asks The Merton model idea?, which keeps structural and portfolio views distinct. Market Risk adds 25 cards on regulatory and mapping terms, with fronts such as What is the FRTB?, What is a stressed VaR?, and What is VaR mapping?

Liquidity & Treasury Risk carries 25 cards on funding and balance-sheet vocabulary, where prompts like What is a survival horizon?, What is a liquidity spiral?, and What is a deposit beta? cover terms that are easy to blur together. Operational Risk & Resilience closes the deck with 24 cards on loss, control, and resilience language, including What is cyber risk?, What is an impact tolerance?, and What is a loss-event database?

That matters for the FRM exam, which is dense with formulas (VaR, duration, the Greeks, expected loss) and frameworks (Basel, the three lines of defense) that reward repetition. Used alongside our practice test and study guide, flashcards turn review time into measurable progress.^[3]

FRM Flashcards by Topic

The cards are organized by the GARP topic areas. Weight your study toward the heaviest Part I areas — Financial Markets & Products and Valuation & Risk Models are 60% of Part I:^[1]

FRM flashcards by topic (2026 weights)
FRM topic	Part	% of part
Financial Markets & Products	Part I	30%
Valuation & Risk Models	Part I	30%
Foundations of Risk Management	Part I	20%
Quantitative Analysis	Part I	20%
Market Risk	Part II	20%
Credit Risk	Part II	20%
Operational Risk & Resilience	Part II	20%
Liquidity & Treasury Risk	Part II	15%

How to Get the Most Out of These Flashcards

Open with the biggest block. Financial Markets & Products has 51 cards and feeds every later topic, so flip it first until swap, duration, and payoff terms come back without hesitation.
Type-drill the definitions you fake. Put cards such as The Sharpe ratio? and What is EWMA? into Type mode, because typing exposes the formulas and conditions you only half remember.
Use Match for tight families. The Greeks in Valuation & Risk Models, where What is rho? and What is theta? sit side by side, sort fastest under Match’s timer pressure.
Move to the practice test once recall holds. When Quiz scores stay steady across Credit Risk, Market Risk, and Liquidity & Treasury Risk, switch to timed questions and use the study guide for gaps.
Rotate rather than sprint. Work one large domain plus one smaller one per session, so Operational Risk & Resilience and its 24 cards never get pushed to the end of the deck.

FRM Flashcards FAQ

Hundreds of free FRM flashcards, organized across all four Part I topic areas and the major Part II risk types tested on the GARP exam. They're free to use with no account required.

References

1.Global Association of Risk Professionals (GARP). “Financial Risk Manager (FRM) Certification.” GARP. ↑
2.Bank for International Settlements. “Basel III: international regulatory framework for banks.” BIS / Basel Committee. ↑
3.Institute of Education Sciences (U.S. Dept. of Education). “Organizing Instruction and Study to Improve Student Learning (Practice Guide).” What Works Clearinghouse, IES. ↑

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