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FRM Part I Updated
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 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.
How do you calculate expected shortfall from a loss distribution, and why is it preferred over VaR?
Expected shortfall calculates the average loss in the tail beyond VaR. For continuous normal distributions, ES = mu + sigma x phi(z)/(1-alpha). For discrete distributions, ES is simply the average of all losses exceeding the VaR threshold.
What were the major milestones and challenges in the global transition from LIBOR to alternative reference rates like SOFR?
The LIBOR transition spanned from 2012 to 2023, affecting $400 trillion in notional exposure. Key challenges included tough legacy contracts without fallback language, structural differences between term and overnight rates, and multi-currency complexity across five jurisdictions.
How do Bermuda option exercise windows work, and where do they fall in the American-European pricing spectrum?
Bermuda options allow exercise only on specific predetermined dates, pricing them between European and American options. They are priced using backward induction with early exercise evaluation only at permitted nodes, and are especially common in fixed income markets.
What constitutes a 'credit event' under ISDA definitions, and how does the determination process work for CDS contracts?
Under ISDA definitions, a credit event is a predefined occurrence that triggers CDS settlement. The six categories include bankruptcy, failure to pay, restructuring, obligation acceleration, obligation default, and repudiation/moratorium. The ISDA Credit Determinations Committee decides whether an event qualifies.
What are insurance-linked securities (ILS), and how do catastrophe bonds transfer risk from insurers to capital markets?
Insurance-linked securities are financial instruments whose value is tied to insurance loss events. Catastrophe bonds allow insurers to transfer peak risk to capital markets via a special purpose vehicle, with different trigger types balancing basis risk and moral hazard.
What is a credit-linked note and what risks does the investor face?
A credit-linked note (CLN) is a funded credit derivative that packages a credit default swap inside a bond structure. The investor buys the note, puts up cash, and receives coupon payments that include a spread for bearing the credit risk of a reference entity.
How does the convenience yield affect commodity forward pricing, and what is the full formula?
The convenience yield is one of the trickiest concepts in commodity forwards because it represents a benefit that is invisible in the cash flows but very real in pricing. The full formula is F_0 = S_0 x e^{(r + u - y) x T}.
What are structural breaks in time series data and how do they affect risk models?
A structural break occurs when the underlying data-generating process changes permanently, causing model parameters like volatility and correlations to shift. The Chow test is the standard detection method, comparing model fit across sub-periods split at the suspected break point.
What is a total return swap and why do institutions use them instead of buying the reference asset directly?
A total return swap (TRS) is an OTC derivative where one party transfers the full economic performance of a reference asset — coupons, price appreciation, and depreciation — to the counterparty in exchange for a funding rate, typically SOFR plus a spread.
How do AIC and BIC work for model selection, and when would they disagree?
AIC and BIC both penalize model complexity to prevent overfitting, but BIC applies a heavier penalty that grows with sample size. They disagree when a complex model offers modest fit improvement — AIC accepts extra parameters more readily than BIC.
Why do Eurodollar futures (and now SOFR futures) need a convexity adjustment when used for swap pricing?
The convexity adjustment is one of the trickiest concepts in fixed-income derivatives. Futures contracts are marked to market daily, creating a systematic bias that makes futures rates higher than equivalent forward rates.
What are AR and MA models and when do you use each for financial time series?
AR models relate the current value to its own past values (persistent patterns), while MA models relate it to past error terms (shock effects). AR is identified by PACF cutoff, MA by ACF cutoff. ARMA combines both for more complex patterns.
What are longevity swaps and how do pension funds use them?
Longevity swaps allow pension funds to exchange fixed payments (based on expected mortality) for floating payments (based on actual mortality), transferring the risk that beneficiaries live longer than projected to reinsurers or capital market investors.
How is PCA used to decompose yield curve risk into principal components?
PCA decomposes yield curve movements into three main factors: level (parallel shift, ~88% of variance), slope (steepening/flattening, ~8%), and curvature (butterfly, ~3%). This reduces a high-dimensional risk problem to three independent, interpretable factors.
What's the intuition behind barrier option pricing and when are knock-ins cheaper than vanillas?
Barrier options activate (knock-in) or deactivate (knock-out) when the underlying hits a specified level. The key pricing relationship is in-out parity: knock-in plus knock-out equals the vanilla option price. Knock-ins are cheaper because they only have value along specific price paths.
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