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FRM Updated
How does exponential smoothing work for forecasting and how is it different from a moving average?
Exponential smoothing assigns exponentially declining weights to past observations, giving the most importance to recent data. Unlike a simple moving average which weights all observations equally, the smoothing parameter alpha controls how quickly old data fades out.
What is the output floor under Basel III finalization, and how does the phase-in schedule work?
The output floor ensures that banks using internal models cannot produce capital requirements less than 72.5% of what the standardized approach would require. It phases in gradually from 50% to 72.5% over several years.
How do you calculate the duration of a portfolio containing multiple bonds?
Portfolio duration is a weighted average of individual bond durations, where the weights must be based on market values, not face values or par amounts. This is a common exam trap.
What is correlation risk, and how does wrong-way risk amplify losses during market stress?
Correlation risk arises when dependency structures change unexpectedly, often spiking during crises. Wrong-way risk amplifies this by increasing exposure precisely when counterparty credit deteriorates, creating maximum loss at maximum default probability.
How do you assess sovereign credit risk, and what makes it different from corporate credit risk?
Sovereign credit risk assessment combines quantitative fiscal/economic metrics with qualitative political and governance factors. Unlike corporates, sovereign default involves willingness-to-pay considerations and lacks a bankruptcy framework for enforcement.
What is stationarity, why does it matter for risk models, and how do you test for it?
Stationarity requires constant mean, variance, and autocovariance structure over time. Non-stationary data produces spurious regressions and invalid test statistics. The ADF test checks for unit roots using special critical values.
How does the repo market work, and why are haircuts so important for managing counterparty risk?
A repurchase agreement (repo) is economically a short-term collateralized loan structured as a sale-and-repurchase. Haircuts protect the cash lender by requiring the borrower to post collateral worth more than the loan amount.
How does the clearing and settlement process work for exchange-traded vs OTC derivatives?
Clearing and settlement are the post-trade processes ensuring both counterparties fulfill their obligations. Exchange-traded derivatives use central counterparties with novation and daily margining, while OTC derivatives have transitioned from bilateral to central clearing for standardized contracts post-2008.
How do banks classify operational loss events for reporting?
Basel II/III defines seven operational risk event type categories, each with a precise scope and a set of Level-2 sub-categories...
How do catastrophe bonds work as insurance-linked securities?
Cat bonds transfer catastrophe risk via SPVs where investor principal collateralizes payouts on indemnity, industry loss, or parametric triggers.
What is the ASRF model and why is it the backbone of Basel IRB capital?
ASRF model assumes infinite granularity and single systematic factor. Conditional PD = Φ((Φ⁻¹(PD) + √R·Φ⁻¹(0.999))/√(1-R)). Portfolio invariance lets banks add capital per loan...
What is operational resilience and how does it differ from traditional operational risk management?
Operational resilience assumes failures will happen and focuses on the organization's ability to continue delivering critical services through disruption. Unlike operational risk management (which prevents failures), resilience sets impact tolerances and tests scenarios against them.
How does bootstrapping work for constructing confidence intervals in risk analysis?
Bootstrapping is a resampling technique that estimates the sampling distribution of a statistic by repeatedly drawing samples with replacement from the observed data. It doesn't require assumptions about the underlying distribution, making it ideal for complex risk metrics.
What is the ICAAP under Pillar 2, and how does it differ from Pillar 1 minimum capital?
The ICAAP is a bank's own comprehensive assessment of whether its capital is adequate for ALL material risks — not just the risks captured by Pillar 1 formulas. It covers IRRBB, concentration risk, business risk, and more.
What is key rate duration and when should I use it instead of regular modified duration?
Key rate duration (KRD) solves one of the biggest limitations of traditional duration: the assumption that the entire yield curve shifts in parallel. It measures sensitivity to yield changes at specific maturity points.
What are the main strategies for hedging tail risk, and what are their costs and tradeoffs?
Tail risk hedging strategies range from protective puts (expensive but direct) to variance swaps (convex payoff), put spreads (cost-reduced), trend following, and dynamic hedging. Each involves a fundamental cost-protection tradeoff.
What is country risk beyond sovereign default, and how do banks measure transfer and convertibility risk?
Country risk goes beyond sovereign default to include transfer and convertibility risk, political risk, and economic risk. Banks use proprietary scorecards, set country exposure limits, and employ mitigation techniques like political risk insurance and offshore escrow accounts.
How do ARCH and GARCH models capture volatility clustering, and how do you estimate them?
GARCH(1,1) models time-varying volatility with three parameters: omega (baseline), alpha (shock reaction), and beta (persistence). Estimated via MLE, it captures volatility clustering and provides multi-step forecasts that revert to long-run levels.
How do storage costs and convenience yield affect commodity futures pricing?
Commodity futures pricing extends the cost-of-carry model by adding storage costs and convenience yield. Storage costs raise futures prices, while convenience yield — the benefit of physical possession — reduces them.
Can someone explain initial margin vs variation margin for futures with a numerical example?
Margin for futures contracts is a system of collateral deposits designed to ensure both parties can honor their obligations. Initial margin is the upfront deposit, maintenance margin is the minimum balance, and variation margin reflects daily mark-to-market gains or losses.
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