FRM Part II flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Parametric VaR formula

VaR = (z x sigma - mu) x position value. For a one-day 95% horizon z is about 1.645; the method assumes normally distributed, independent returns and constant volatility.

Expected shortfall coherence

ES is the average loss conditional on exceeding the VaR threshold. It is subadditive and coherent, whereas VaR can violate subadditivity and says nothing about loss severity beyond the quantile.

Square-root-of-time rule

Multi-day VaR is obtained as one-day VaR multiplied by the square root of the horizon only when returns are independent and identically distributed; autocorrelation and volatility clustering break the rule.

EWMA volatility update

Variance today equals lambda times yesterday's variance plus one minus lambda times yesterday's squared return. RiskMetrics uses lambda near 0.94 for daily data; higher lambda gives smoother, slower reactions.

GARCH(1,1) long-run variance

Variance depends on a constant, the last squared shock and the last variance. Persistence is alpha plus beta and long-run variance equals omega divided by one minus alpha minus beta, requiring persistence below one.

Delta-normal VaR limitation

The linear delta approximation ignores option gamma, so it understates risk for long-gamma positions. Full revaluation or delta-gamma approaches are required for portfolios containing options.

Basel backtesting traffic light

Over 250 days at 99% VaR, zero to four exceptions is green, five to nine is yellow with an increasing capital multiplier, and ten or more is red.

Merton distance to default

Distance to default equals the log of asset value over debt face value plus drift less half variance, all divided by volatility times root time; probability of default is the normal CDF of negative distance to default.

Expected loss formula

Expected loss equals probability of default times loss given default times exposure at default. Unexpected loss is the volatility of credit losses around expected loss and drives economic capital.

Vasicek worst-case default rate

The stressed default rate equals the normal CDF of the sum of the inverse normal of PD and root-rho times the inverse normal of confidence, divided by root one minus rho; it rises with asset correlation.

CDS spread approximation

For small default probabilities the annual CDS spread approximates probability of default times loss given default; equivalently the hazard rate approximates spread divided by one minus recovery.

CreditMetrics transition approach

A loan is revalued under every possible rating migration using forward zero curves, producing a full distribution of portfolio values rather than a default-only loss distribution.

Standardised measurement approach

Basel operational capital equals the business indicator component times the internal loss multiplier, where the component is 15% of average positive gross income and the multiplier depends on average historical losses.

Loss distribution approach

Frequency (often Poisson) and severity (often lognormal or extreme value) are modelled separately, then convolved or simulated to produce the aggregate loss distribution from which capital is taken.

Recovery time objective

RTO is the maximum acceptable downtime for a business process after disruption; RPO is the maximum tolerable data loss expressed as time, and both are set through business impact analysis.

Seven operational risk event types

Internal fraud, external fraud, employment practices and workplace safety, clients and business practices, damage to physical assets, business disruption and system failures, and execution and process failures.

Operational risk heavy tails

Severity distributions are fat-tailed, so aggregate operational VaR is driven by a handful of large losses and capital estimates are highly sensitive to the assumed tail model.

Liquidity coverage ratio

The ratio of high-quality liquid assets to net cash outflows over a 30-day stressed horizon; Basel requires at least 100% so the buffer covers assumed run-off.

Net stable funding ratio

Available stable funding divided by required stable funding, required to be at least 100% over a one-year horizon, penalising reliance on short-term wholesale funding of illiquid assets.

Liquidity-adjusted VaR

Liquidity-adjusted VaR adds to ordinary VaR a term of half the bid-ask spread times position size for exogenous spread cost, plus an endogenous add-on when the position is large relative to normal volume.

Roll bid-ask estimator

Roll's measure infers the effective bid-ask spread from negative serial covariance in transaction price changes, with spread equal to two times the square root of minus that covariance.

Funding versus market liquidity

Funding liquidity risk is the inability to meet obligations as they fall due; market liquidity risk is the inability to trade without moving prices, and margin calls can convert one into the other.

Information ratio

The information ratio equals active return divided by tracking error, measuring active return per unit of active risk relative to a benchmark; leverage that scales both equally leaves it unchanged.

Treynor ratio

Excess portfolio return divided by portfolio beta. Because it uses systematic risk only, it suits well-diversified portfolios and comparisons against market risk rather than total volatility.

Component VaR

Component VaR for a position equals its weight times its marginal VaR, equivalently portfolio VaR times the position beta; the components sum to total portfolio VaR.

Jensen's alpha

Realised return minus the CAPM-required return given portfolio beta: alpha equals portfolio return less risk-free rate less beta times the market excess return; positive alpha indicates risk-adjusted outperformance.

Hedge fund database biases

Survivorship bias arises because failed funds leave databases, and backfill bias because successful funds report history retroactively, both overstating average returns and Sharpe ratios.

SOFR benchmark

SOFR is a secured overnight financing rate based on US Treasury repo transactions; it replaced USD LIBOR for new contracts from mid-2023 and is nearly risk-free compared with term LIBOR.

Physical versus transition climate risk

Physical risk is loss from acute events and chronic shifts in climate; transition risk is loss from policy, technology or preference changes toward a low-carbon economy.

Automated market maker risk

AMMs price trades with a deterministic formula against pooled liquidity, creating impermanent loss for providers, exposure to smart contract exploits and acute fragility under large trades.

Machine learning model risk

ML models add overfitting, non-stationarity, data leakage and interpretability problems to conventional model risk, requiring out-of-sample and adversarial validation plus ongoing performance monitoring.

Stablecoin depeg risk

Stablecoins can lose their peg when reserves are insufficient or redemptions surge, transmitting stress through collateral haircuts and forced liquidations of leveraged crypto positions.