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FRM Part I 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.
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 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 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.
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 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.
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.
What is alternative risk transfer and when is it used?
ART encompasses captives, finite risk, multi-trigger covers, contingent capital, and capital market ILS — non-traditional risk financing tools.
How do you calculate Credit VaR for a single obligor?
Credit VaR measures the potential credit loss at a given confidence level beyond what is already expected. For a single obligor, the loss distribution is binary — either no default or full default loss — making the calculation straightforward but the interpretation nuanced.
How does cash flow mapping work for VaR calculations on fixed income positions?
Cash flow mapping is the process of converting complex positions into exposures at standard maturity points (vertices) so that VaR can be computed using a manageable covariance matrix.
How is the OTC derivatives market structured and what's the difference between bilateral and cleared trading?
The OTC derivatives market is a decentralized network where participants trade directly rather than on a centralized exchange. Key participants include dealers, end-users, inter-dealer brokers, and CCPs, with products split between bilateral and centrally cleared execution.
How is the Lloyd's of London market structured?
Lloyd's is a marketplace where syndicates backed by Members write specialist insurance, supported by a Central Fund chain of security.
What is duration gap analysis and how do banks use it to manage interest rate risk?
Duration gap analysis measures the sensitivity of a bank's equity to interest rate changes. The gap equals asset duration minus leverage-adjusted liability duration. A positive gap means equity falls when rates rise — the classic risk of borrowing short and lending long.
How do you design and implement a single-factor stress test for a portfolio?
A single-factor stress test examines how a portfolio's value changes when ONE risk factor is shocked by a large amount while all other factors remain unchanged. It complements VaR by exploring extreme scenarios.
How does a CCP's default waterfall work and why is it important for financial stability?
A CCP's default waterfall is the predefined sequence of financial resources used to absorb losses when a clearing member defaults. It starts with the defaulter's margin and fund contribution, then the CCP's own capital, before reaching mutualized resources from surviving members.
What is retrocession and why do reinsurers buy it?
Retrocession is reinsurance purchased by reinsurers to manage peak-zone accumulations, often via ILS, sidecars, and ILWs.
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