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FRM Updated
What is maximum likelihood estimation (MLE) and how is it used in risk modeling?
Maximum Likelihood Estimation (MLE) finds parameter values that maximize the probability of observing the actual data. Unlike OLS which minimizes squared errors, MLE works by maximizing a likelihood function under a distributional assumption.
How do conversion factors work in Treasury bond futures, and why does the cheapest-to-deliver bond matter so much?
Treasury bond futures are unique because the short side can deliver any eligible bond (maturity 15+ years) against the contract. Since bonds have different coupons and maturities, the exchange uses conversion factors (CF) to normalize them.
What is marginal VaR and how does it relate to optimal portfolio construction?
Marginal VaR is the rate of change of portfolio VaR per unit change in a position's weight: MVaRᵢ = ∂VaR/∂wᵢ. At the optimal portfolio, the ratio of excess return to marginal VaR is equal across all positions, enabling efficient risk budgeting.
How does collateral management work in OTC derivatives and what are best practices?
Collateral management under ISDA CSAs involves daily MTM-based variation margin calls (threshold, MTA, eligible collateral) plus initial margin for uncleared OTC derivatives under ISDA SIMM. Post-2008 rules mandate two-way, segregated initial margin exchange.
How does Bayesian estimation work and how is it used in risk management?
Bayesian estimation updates a prior belief about a parameter with observed data to produce a posterior distribution: Posterior ∝ Likelihood × Prior. It is especially valuable in risk management when data is limited (low-default portfolios) or expert judgment is available.
How do weather derivatives work and who uses them?
Weather derivatives have payoffs tied to measurable weather variables like temperature (HDD/CDD). Energy companies, agriculture, and retailers use them to hedge revenue sensitivity to weather. They settle based on official weather station data with no physical delivery.
Can someone walk through how the CreditMetrics model works step by step?
CreditMetrics is a mark-to-market credit portfolio model that estimates the distribution of portfolio value changes due to credit migrations and defaults. It combines transition matrices, asset correlations, and bond revaluation across scenarios.
How does risk budgeting work using marginal VaR and component VaR?
Risk budgeting uses marginal VaR (sensitivity of portfolio VaR to position changes) and component VaR (each position's additive contribution to total VaR) to decompose and allocate risk capital. Component VaRs sum to total VaR, and negative component VaR indicates a position is reducing portfolio risk.
What is wrong-way risk and can you give concrete examples of how it amplifies credit losses?
Wrong-way risk occurs when exposure to a counterparty increases exactly when that counterparty's default probability rises. Classic examples include commodity swaps with producers, sovereign CDS from local banks, and FX forwards with emerging market counterparties. It can amplify expected losses 2-5x beyond independent models.
How does Extreme Value Theory (POT method) improve VaR estimation in the tails?
Extreme Value Theory's Peaks-Over-Threshold method fits a Generalized Pareto Distribution to losses exceeding a high threshold, providing much more accurate tail risk estimates than the normal distribution. For 99% VaR, EVT typically produces estimates 20-40% higher.
How do storage costs and convenience yield affect commodity forward pricing?
Commodity forwards differ from financial forwards because physical commodities have storage costs that push the forward above spot, and convenience yield from holding inventory that can pull it below. When convenience yield exceeds carry costs, the market enters backwardation.
How do netting and collateral reduce counterparty credit risk exposure in OTC derivatives?
Netting and collateral are the two primary tools for reducing counterparty credit risk in OTC derivatives. Close-out netting consolidates all trades under an ISDA agreement to a single net amount upon default, while CSA collateral further reduces residual exposure. Together they can reduce gross exposure by 80-95%.
What is model risk, and how do banks validate their risk models to avoid catastrophic failures?
Model risk arises when risk models produce incorrect outputs due to specification errors, implementation bugs, calibration issues, or misapplication. Banks validate models through conceptual soundness reviews, backtesting, benchmarking, sensitivity analysis, and ongoing outcomes monitoring under the SR 11-7 framework.
How does VaR backtesting work under Basel, and what is the traffic light system?
VaR backtesting is where risk models meet regulatory reality. Banks compare daily VaR predictions against actual P&L over a 250-day window. The Basel traffic light system classifies results into green (0-4 exceptions), yellow (5-9, with capital penalty), and red (10+, severe penalty) zones, directly impacting the capital multiplier.
How does a sovereign wealth fund approach risk management?
SWF risk management balances long-horizon real return goals with intergenerational equity, domestic economy diversification, and governance.
How do I choose the right hypothesis test for FRM exam questions? I keep picking the wrong test statistic.
Choosing the correct hypothesis test on the FRM exam depends on three factors: what parameter you are testing, whether the population variance is known, and your sample size. Use z-tests when variance is known, t-tests when it is not (especially with small samples), chi-square for single variance, and F-test for comparing two variances.
How do GARCH models capture volatility clustering, and when are they better than historical volatility?
GARCH(1,1) models capture volatility clustering by making today's variance a weighted combination of long-run variance, yesterday's squared return, and yesterday's variance. The key parameters are alpha (shock sensitivity) and beta (persistence), with their sum determining how slowly volatility reverts to its long-run level.
When should I use Monte Carlo simulation instead of parametric VaR, and how does it actually work?
This is one of the most important conceptual questions in FRM Part I Quantitative Analysis. The parametric method assumes returns are normally distributed and portfolio value changes linearly with risk factors. This breaks down with non-linear instruments like options, fat-tailed distributions, and complex multi-factor portfolios.
What is ERM and why do so many banks struggle to implement it effectively?
Enterprise Risk Management (ERM) is a holistic approach that views all of a firm's risks as an integrated portfolio rather than managing each in isolation. While conceptually powerful, most implementations struggle with data silos, aggregation challenges, cultural resistance, and strategic disconnect.
What should a Contingency Funding Plan (CFP) include and when does it get activated?
A Contingency Funding Plan (CFP) is a bank's playbook for surviving a liquidity crisis. Essential components include a governance framework, early warning indicators, contingent funding sources, severity-based action playbooks, communication protocols, and a regular testing schedule.
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