2025 FRM Exam Part II: Market Risk Measurement and Management Flashcards

Comprehensive practice flashcards for the FRM Part II Market Risk exam, covering definitions and concepts from the core curriculum modules.

Value-at-Risk (VaR)

A mathematical concept that measures the loss that a given portfolio is expected not to exceed over a specific time interval and at a predetermined confidence level.

Expected Shortfall (ES)

The probability-weighted average of tail losses, often calculated as an average of 'tail VaRs' associated with probability slices in the tail region.

Arithmetic Return

Defined as the profit/loss over a period $t$ divided by the value of the asset at the end of period $t - 1$, implicitly assuming interim payments do not earn a return.

Geometric Return

The natural logarithm of the ratio of the asset value at time $t$ (plus interim payments) to the value at time $t - 1$, ensuring asset prices never become negative.

Historical Simulation (HS)

A non-parametric method that estimates VaR by ordering past loss observations and identifying the quantile that demarcates the tail region.

Quantile-Quantile (QQ) Plot

A diagnostic tool for identifying a distribution by plotting empirical quantiles against their theoretical equivalents; linearity indicates a good fit.

Bootstrap Procedure

A method of assessing the accuracy of parameter estimators by simulation-based resampling from a given data set with replacement.

Age-weighted Historical Simulation

Adjusts the probability weights of observations based on their age using a decay factor $\lambda$, making the model more responsive to recent market events.

Volatility-weighted Historical Simulation

Rescales historical returns to reflect current market conditions by adjusting them by the ratio of current volatility to the volatility estimated at the time of the historical observation.

Filtered Historical Simulation (FHS)

A semi-parametric bootstrap that combines the non-parametric nature of HS with conditional volatility models like GARCH to scale standardized returns by current volatility forecasts.

Extreme-Value Theory (EVT)

A branch of applied statistics focusing on low-probability, high-impact events governed by extreme-value theorems rather than central limit theorems.

Fisher-Tippett Theorem (1928)

States that as sample size $n$ gets large, the distribution of extremes converges to a Generalized Extreme-Value (GEV) distribution.

Frechet Distribution

A special case of the GEV distribution where the tail index $\xi > 0$, applicable to heavy-tailed parent distributions like the Student-t distribution.

Gumbel Distribution

A special case of the GEV distribution where the tail index $\xi = 0$, corresponding to parent distributions with exponential tails like the Normal distribution.

Peaks-Over-Threshold (POT) Approach

A method in EVT that models the distribution of excess losses over a high threshold, which converges to a Generalized Pareto (GP) distribution.

Backtesting

A formal statistical framework that consists of verifying whether actual losses are in line with projected losses by comparing VaR forecasts with associated portfolio returns.

Type I Error (Backtesting)

The probability of committing a false rejection, such as rejecting a correct VaR model simply because of a rare cluster of high losses.

Type II Error (Backtesting)

The probability of not rejecting a model that is actually incorrect or understates risk.

Basel 'Yellow' Zone

A penalty zone defined by the Basel Committee for 5 to 9 exceptions in a 250-day period, where the supervisor has discretion to increase the capital multiplier $k$.

VaR Mapping

The process by which the current values of portfolio positions are replaced by exposures on selected elementary or primitive risk factors.

Specific Risk

Risk that is due to issuer-specific price movements after accounting for general market factors.

Principal Component Analysis (PCA)

A method to construct uncorrelated interest rate factors (Principal Components) that explain the maximum possible variance of rate changes across the term structure.

Probability Integral Transform (PIT)

The cumulative probability of observing a loss below the actual profit and loss realization, used to backtest the entire forecasting distribution.

Financial Correlation Risk

The risk of financial loss due to adverse movements in correlation between two or more variables.

Wrong-Way Risk (WWR)

A specific type of correlation risk where the present value of a protection (like a CDS) decreases as the default correlation between the reference asset and counterparty increases.

Mean Reversion

The tendency of a variable, such as an interest rate or correlation, to be pulled back toward its long-term equilibrium value or mean.

Autocorrelation

The degree to which a variable's current value is correlated to its past values, often referred to as 'persistence' in finance.

Copula Function

A statistical joiner that allows the joining of multiple univariate marginal distributions into a single multivariate distribution.

Option-Adjusted Spread (OAS)

The spread added to the model's discount rates such that the calculated fair value matches the current market price of the security.

Vasicek Model

A term structure model assuming a mean-reverting risk-neutral process for the short-term rate, expressed as $dr = k(\theta - r)dt + \text{σ}dw$.

Ho-Lee Model

An arbitrage-free term structure model characterized by a time-dependent drift, allowing it to fit the initial term structure of rates exactly.

Cox-Ingersoll-Ross (CIR) Model

A term structure model where the basis-point volatility of the short rate is proportional to the square root of the rate, preventing rates from becoming negative.

Gauss+ Model

A multi-factor model with a cascade structure where the short rate reverts to a medium-term factor, which in turn reverts to a long-term factor, capable of matching a hump-shaped volatility structure.

Volatility Smile

The empirical relationship where implied volatility varies by strike price, typically appearing U-shaped for currency options and downward sloping (skewed) for equity options.

Volatility Surface

A three-dimensional plot or table that combines the volatility smile (variation by strike) with the volatility term structure (variation by maturity).

Fundamental Review of the Trading Book (FRTB)

A set of Basel Committee revisions that transition market risk capital requirements from 99% VaR to 97.5% stressed Expected Shortfall using liquidity horizons.

Liquidity Horizon

The period of time required to exit or hedge a risk factor in stressed market conditions without significantly affecting market prices, ranging from 10 to 120 days in FRTB.

Non-Modelable Risk Factors (NMRC)

Risk factors under FRTB with insufficient historical observations (less than 24 per year), which must be handled by special rules involving stress tests.