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FRM Part I Updated
What are distortion risk measures, and how do they transform probability to capture risk aversion?
Distortion risk measures transform the survival function of losses using a concave distortion function, systematically overweighting extreme loss probabilities. Common distortions include the proportional hazard, dual power, and Wang transform, each producing coherent risk measures used in insurance and risk management.
What is Stressed VaR, how is the stress period selected, and how does it enter the market risk capital calculation?
Stressed VaR is calibrated to a 12-month historical stress period that would produce the largest VaR for the bank's current portfolio. It was introduced by Basel 2.5 because regular VaR, calibrated to recent benign data, severely underestimated tail risk during the 2008 crisis.
What is Conditional VaR (CVaR / Expected Shortfall), and why did Basel III replace VaR with ES for market risk capital?
Conditional VaR (CVaR) or Expected Shortfall measures the average loss in the worst alpha-percent of scenarios, capturing tail severity that VaR ignores. Basel III replaced VaR with ES for market risk capital because ES is subadditive, rewards diversification, and penalizes all tail scenarios.
Why is the Poisson distribution used for operational loss frequency and how do you apply it?
The Poisson distribution is the standard choice for modeling how many loss events occur in a fixed time period. It's ideal for operational risk because it models the count of rare, independent events with a single parameter lambda.
What drives the shape of the volatility term structure, and how does mean reversion flatten it?
The volatility term structure describes how implied or expected volatility changes across different option maturities. Mean reversion is the key force that shapes the long end — when current vol is high, it creates a downward-sloping term structure.
What are the main pitfalls of correlation estimation in risk management, and how can you address them?
Correlation estimation has major pitfalls: correlations spike during crises, Pearson correlation assumes normality, short samples produce noisy estimates, and non-stationarity creates spurious relationships. Solutions include EWMA, copulas, and shrinkage estimators.
What's the difference between a credit-linked note (CLN) and a total return swap (TRS), and when would a bank use each?
Both CLNs and TRS transfer credit exposure, but they differ fundamentally. A CLN is funded — the investor puts up cash and receives higher yield with principal at risk. A TRS is unfunded — transferring full economic exposure including price changes.
How do historical and hypothetical scenario analyses differ, and how should a risk manager design effective stress tests?
Scenario analysis evaluates portfolio performance under specific adverse conditions, either drawn from historical events or constructed from hypothetical narratives. A structured five-step framework helps risk managers design internally consistent and actionable stress tests.
How do risk factor sensitivities like DV01, delta, and vega help a risk manager understand portfolio exposures?
Risk factor sensitivities like DV01, delta, and vega measure how portfolio value changes for small moves in individual risk factors. They are actionable, decomposable, and transparent building blocks that complement VaR for day-to-day risk management.
Why do we model operational loss severity with a lognormal distribution?
The lognormal distribution is preferred for loss severity modeling because it's always positive, right-skewed, and captures the multiplicative nature of operational losses. Most losses are small, but the long right tail accommodates the occasional massive outlier.
How do you forecast volatility multiple steps ahead using a GARCH(1,1) model?
Multi-step forecasting with GARCH(1,1) is a critical skill for FRM because risk managers need volatility estimates over holding periods longer than one day. The key formula shows the forecast converging to the long-run variance.
How does Cholesky decomposition generate correlated random variables for Monte Carlo simulation?
Cholesky decomposition converts independent random variables into correlated ones by factoring the correlation matrix into C = L x L-transpose. Multiplying independent normals by L produces correlated variables with the exact desired correlation structure.
Can someone walk through securitization from start to finish — origination, SPV, tranching, and waterfall?
Securitization transforms illiquid assets into tradable securities through a chain of origination, SPV creation for bankruptcy remoteness, tranching into different risk layers, and a strict cash flow waterfall that determines payment priority.
What are the Basel Accords, and how do Basel I, II, and III differ in their approach to bank capital requirements?
The Basel Accords evolved from simple risk-weight categories (Basel I) to a three-pillar framework with internal models (Basel II) to post-crisis reforms with higher capital quality, liquidity requirements, and countercyclical buffers (Basel III). Each iteration addressed shortcomings revealed by financial crises.
What is a risk parity portfolio, how does it differ from traditional 60/40 allocation, and what role does leverage play?
Risk parity equalizes risk contributions across asset classes rather than capital weights. A traditional 60/40 portfolio has ~90% of its risk from equities. Risk parity overweights bonds and underweights equities, often adding leverage to achieve competitive returns.
What are the practical limitations of mean-variance optimization, and how do risk managers address them?
Mean-variance optimization is extremely sensitive to input estimates, often producing concentrated and unstable portfolios. Practical remedies include adding allocation constraints, using Black-Litterman to blend equilibrium returns with views, and resampling the efficient frontier.
How does the ARIMA model work for time series forecasting in risk management?
ARIMA stands for AutoRegressive Integrated Moving Average and combines three components: AR(p) for autoregressive terms, I(d) for differencing to achieve stationarity, and MA(q) for moving average error terms. Choosing the right parameters requires stationarity tests and ACF/PACF analysis.
How do you detect heteroskedasticity in a linear regression, and why does it matter for FRM?
Heteroskedasticity is the condition where the variance of regression residuals is not constant across observations. In risk management, this is extremely common due to volatility clustering.
What are the key simulation techniques and variance reduction methods used in risk management?
Monte Carlo estimates are noisy, especially for tail risk metrics. Variance reduction techniques — antithetic variates (using Z and -Z), control variates (benchmarking), and importance sampling (shifting the distribution) — improve precision without extra simulations.
How do CDOs work, and what's the difference between cash CDOs and synthetic CDOs?
A CDO is a securitization where the collateral pool consists of debt instruments. Cash CDOs physically purchase bonds, while synthetic CDOs use CDS contracts to gain credit exposure without buying the underlying assets.
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