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FRM Part I Updated
What is the quality option in Treasury bond futures, and how does the deliverable basket create optionality for the short?
The quality option is the short's right to choose among all deliverable bonds. The diverse basket of coupons and maturities creates value because the conversion factor system misprices bonds when yields deviate from 6%, allowing the short to exploit systematic biases.
How does the Nelson-Siegel-Svensson model parameterize the entire yield curve with just six parameters, and why do central banks prefer it?
The Nelson-Siegel-Svensson model captures the entire yield curve using six parameters: a level (beta_0), slope (beta_1), two curvature terms (beta_2, beta_3), and two decay rates (tau_1, tau_2). Central banks prefer it for its parsimony, smooth forwards, and economically interpretable parameters.
How does a lookback option guarantee the best possible payoff over the option's life, and why is it so expensive?
Lookback options use the most favorable price observed during the option's life to determine the payoff. Floating strike lookbacks always finish in the money (given any price movement), which is why they cost 1.5x to 3x more than vanilla options.
How do storage costs and convenience yield interact to determine whether a commodity futures curve is in contango or backwardation?
The commodity futures curve shape depends on whether storage costs plus financing exceed the convenience yield. When carrying costs dominate, the curve is in contango; when the convenience yield from holding physical inventory is high, the curve flips to backwardation.
How do swaptions work, and what determines whether you should buy a payer vs. receiver swaption?
A swaption grants the right to enter a swap at a preset fixed rate. Payer swaptions profit when rates rise (hedge future borrowing), while receiver swaptions profit when rates fall (hedge future investment). Valuation typically uses the Black model with the forward swap rate and an annuity factor.
What is the Three Lines of Defense model and how does it structure risk governance at a bank?
The Three Lines of Defense model is the foundational risk governance framework tested on FRM Part I. It establishes clear accountability for risk-taking, risk oversight, and independent assurance across business units, risk management, and internal audit.
What is a Risk Appetite Framework (RAF) and how does a bank's risk appetite statement work?
A Risk Appetite Framework (RAF) is the organizational structure through which a bank defines, communicates, and monitors the amount and types of risk it is willing to accept. It translates qualitative board statements into quantitative limits that cascade down to individual business lines.
How do you use marginal VaR to evaluate the risk impact of adding a new position to an existing portfolio?
Marginal VaR measures the partial derivative of portfolio VaR with respect to a position's weight. By comparing a new asset's MVaR per dollar to the portfolio average, risk managers determine whether the addition improves or worsens risk efficiency.
How does the duration-based hedge ratio differ from the DV01 approach, and when should each be used?
Duration-based and DV01-based hedge ratios are mathematically equivalent since DV01 equals duration times value divided by 10,000. The DV01 approach is preferred for complex instruments and cross-market hedges because it directly captures dollar sensitivity without requiring separate duration and value inputs.
How do you immunize a bond portfolio using Treasury futures to match a liability duration target?
Portfolio immunization with futures adjusts the portfolio's duration to match liability duration by going long or short the appropriate number of contracts. The formula divides the duration gap times portfolio value by the futures contract's dollar duration.
Why is the overnight index swap rate considered a better risk-free proxy than LIBOR, and how is an OIS structured?
An overnight index swap exchanges a fixed rate for the compounded overnight reference rate over a term. Because overnight lending carries minimal credit risk, the OIS rate closely approximates the risk-free rate, unlike LIBOR which embeds substantial bank credit risk.
How does a chooser option work, and when is the optimal time to decide between a call and a put?
A chooser option lets the holder decide whether it becomes a call or a put at a specified future choice date. It can be decomposed into a longer-dated call plus a shorter-dated put with an adjusted strike, making it cheaper than a straddle.
How are long-term power purchase agreements (PPAs) valued, and what are the key risk factors in pricing them?
PPA valuation requires modeling expected market prices, renewable generation volumes, and discount rates over 10-25 year horizons. Key risks include price cannibalization from growing renewables, intermittent generation volumes, locational basis, and long-dated counterparty credit exposure.
What causes natural gas basis risk, and how do producers hedge geographic price differentials?
Natural gas basis risk stems from geographic price differentials caused by pipeline constraints and local supply-demand imbalances. A producer hedging at Henry Hub remains exposed to the spread between their local delivery point and the benchmark, requiring basis swaps or locational futures to manage.
What is the difference between discount yield and money market yield on T-bill futures, and how do you convert between them?
T-bill futures are quoted using a discount yield convention, but for comparing returns across instruments you often need the money market yield. The discount yield uses face value as the denominator while the money market yield uses the purchase price.
How do Eurodollar futures work mechanically, and how does a corporate treasurer use them to lock in a borrowing rate?
Eurodollar futures were among the most liquid interest rate derivatives ever created. The futures price is quoted as 100 minus the annualized rate, with each basis point worth $25 per contract. Here is a step-by-step hedging example for a corporate borrower.
How do you value an interest rate swap that is already partway through its life?
Valuing an interest rate swap mid-life is one of the most testable skills in FRM Part I. The key insight is that a swap can be decomposed into two legs, and you value each leg separately using current market discount factors.
How is logistic regression used for predicting loan defaults, and how do you interpret the coefficients?
Logistic regression is the workhorse model for binary credit outcomes because it maps any combination of inputs to a probability bounded between 0 and 1. Instead of modeling default probability directly, it models the log-odds as a linear function.
How does the cheapest-to-deliver (CTD) bond work in Treasury futures, and why does it matter for hedging?
Treasury futures allow the short side to deliver any bond from a basket of eligible maturities, but naturally they will choose the one that minimizes their cost. This is the cheapest-to-deliver (CTD) bond. The exchange assigns each deliverable bond a conversion factor that adjusts its price as though it yielded exactly 6%.
What is kernel density estimation and when is it preferred over histograms?
Kernel density estimation (KDE) creates a smooth probability density estimate by placing a kernel (usually Gaussian) on each data point and summing them. Unlike histograms, KDE is not dependent on arbitrary bin choices. The bandwidth parameter controls the smoothness.
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