Financial Risk Manager (FRM) Market Risk Measurement and Management Flashcards

24 sample cards from the Market Risk Measurement and Management deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. What is a Collateralized Mortgage Obligation (CMO) and what is tranching meant to accomplish?

   A CMO redirects the cash flows of mortgage pass-throughs into multiple bond classes (tranches) with different priorities and risk profiles. Tranching redistributes prepayment (extension/contraction) risk across tranches to meet different investor maturity/risk preferences, even though total prepayment risk is unchanged.

2. Describe a sequential-pay CMO structure.

   In a sequential-pay CMO, all principal (scheduled + prepayments) is paid first to Tranche A until fully retired, then to B, then C, etc., while every outstanding tranche receives interest. Earlier tranches (A) have short, more certain lives (low extension risk); later tranches absorb more extension risk and have longer average lives.

3. Explain PAC and Support (companion) tranches in a CMO.

   A Planned Amortization Class (PAC) receives principal on a fixed schedule as long as prepayment speeds stay within a PAC collar (e.g. 100-300% PSA), giving stable, predictable cash flows and low prepayment risk. The Support/companion tranche absorbs prepayment variability — getting excess principal in fast-pay periods and being deferred in slow periods — so it bears amplified extension and contraction risk.

4. Describe an Interest-Only (IO) and Principal-Only (PO) strip and how each reacts to falling rates.

   A PO receives only principal payments; its value RISES when rates fall (faster prepayments return principal sooner) — positive duration-like behavior. An IO receives only interest on the outstanding balance; its value FALLS when rates drop because faster prepayments shrink the balance generating interest. IOs often have negative effective duration.

5. How is the effective (option-adjusted) duration of an MBS computed?

   $$D_{\text{eff}} = \frac{P_{-} - P_{+}}{2 \times P_0 \times \Delta y}$$ where $P_{-}$ and $P_{+}$ are prices from re-running the prepayment/OAS model after shifting rates down and up by $\Delta y$, holding OAS constant. Because prepayments are re-estimated at each shift, it captures the option's effect, unlike modified duration.

6. What is negative convexity in MBS, and write effective convexity.

   Negative convexity means price appreciation when rates fall is LESS than price depreciation when rates rise — caused by the homeowner's prepayment option capping upside. $$C_{\text{eff}} = \frac{P_{+} + P_{-} - 2P_0}{P_0 (\Delta y)^{2}}$$ For MBS this is often negative over the refinancing region; the price/yield curve bends the 'wrong' way.

7. Define implied volatility and how it is obtained.

   Implied volatility is the volatility input that, when plugged into an option pricing model (e.g. Black-Scholes), makes the model price equal the observed market price. It is the market's forward-looking expectation of volatility, backed out by numerical inversion since the model is not analytically invertible for $\sigma$.

8. Define the implied volatility term structure and what an upward- vs downward-sloping structure implies.

   It is the plot of implied volatility against option maturity (for a fixed moneyness). An upward slope implies the market expects volatility to RISE over time (often when current vol is low/mean-reverting up); a downward slope implies expected falling volatility (often after a vol spike). It reflects mean reversion of volatility.

9. Define the volatility skew/smile and the typical equity-index pattern.

   The volatility skew/smile is implied volatility plotted against strike (or moneyness) for fixed maturity. For equity indices, there is a pronounced skew: low-strike (OTM puts) have HIGHER implied vol than high-strike calls, reflecting crash fear and the leverage effect — fat left tail. This contradicts Black-Scholes' constant-vol assumption.

10. How does the volatility smile reveal the market's implied return distribution versus lognormal?

    A symmetric smile implies fatter tails than lognormal (excess kurtosis) — both deep OTM puts and calls priced richer. An equity skew (higher left-side vol) implies a left-skewed distribution: a heavier left tail and thinner right tail than Black-Scholes lognormal assumes. Currency options typically show a more symmetric smile.

11. What is correlation trading and which products provide direct exposure to correlation?

    Correlation trading takes positions on the realized vs implied correlation among assets. Key vehicles: dispersion trades (sell index volatility, buy single-name volatility — long correlation if index is rich), correlation swaps, and basket options. Index implied volatility embeds an implied correlation linking constituent vols to the index vol.

12. Give the relationship linking index variance to constituent variances and average correlation in a basket.

    For weights $w_i$, single-name vols $\sigma_i$, and average correlation $\bar{\rho}$: $$\sigma_{\text{index}}^{2} = \sum_i w_i^{2}\sigma_i^{2} + \sum_{i\neq j} w_i w_j \rho_{ij}\sigma_i\sigma_j$$ Higher correlation raises index variance toward the weighted-average of single-name vols; lower correlation creates a larger diversification gap (the basis dispersion traders exploit).

13. Define a variance swap payoff and explain why variance (not volatility) swaps are commonly traded.

    $$\text{Payoff} = N_{\text{var}} \times \left(\sigma_{\text{realized}}^{2} - K_{\text{var}}^{2}\right)$$ where $N_{\text{var}}$ is the variance notional and $K_{\text{var}}$ the strike (variance). Variance swaps are favored because their payoff in variance is exactly replicable with a static portfolio of options across all strikes plus dynamic delta-hedging, whereas volatility (the square root) is not.

14. Relate variance notional to vega notional and explain the convexity of a variance swap.

    $$N_{\text{vega}} = 2 K_{\text{var}} \times N_{\text{var}}$$ A variance swap is long convexity in volatility: because payoff is in $\sigma^{2}$, gains from rising vol exceed losses from equal falling vol, so realized variance swaps tend to price above (at a premium to) at-the-money implied volatility (the variance risk premium).

15. Define vega, gamma, and vanna as higher-order option risks in an options book.

    Vega: sensitivity of value to implied volatility, $\frac{\partial V}{\partial \sigma}$. Gamma: $\frac{\partial^{2} V}{\partial S^{2}}$, the rate of change of delta. Vanna: $\frac{\partial^{2} V}{\partial S \partial \sigma}$, cross-sensitivity of delta to vol (or vega to spot). Volga (vomma): $\frac{\partial^{2} V}{\partial \sigma^{2}}$, vega's sensitivity to vol — drives skew/smile hedging.

16. Why can't a single vanilla option hedge all higher-order risks, and how are skew/smile risks hedged?

    Delta-hedging neutralizes only first-order spot risk; gamma, vega, vanna, and volga remain. Because implied vol varies by strike (skew), hedging vega at one strike leaves exposure at others. Risk managers hedge with a portfolio of options across multiple strikes/maturities (e.g. risk reversals to hedge vanna/skew, butterflies/strangles to hedge volga/smile curvature).

17. Outline the evolution of the Basel market risk framework from 1996 to Basel 2.5.

    1996 Market Risk Amendment introduced capital for trading-book market risk via Standardized and Internal Models (10-day, 99% VaR) approaches. After the 2007-09 crisis, Basel 2.5 (2009) added Stressed VaR, the Incremental Risk Charge (IRC) for default/migration, and a Comprehensive Risk Measure (CRM) for correlation trading — roughly tripling trading-book capital.

18. What were the key deficiencies of the pre-FRTB (VaR-based) regime that motivated reform?

    (1) VaR is not coherent (not sub-additive) and ignores tail severity; (2) a fuzzy, arbitrageable boundary between banking and trading books allowing regulatory capital arbitrage; (3) VaR uses a single liquidity horizon, ignoring varying market liquidity; (4) procyclicality and inadequate capture of tail/credit-spread risk during stress.

19. What is the Fundamental Review of the Trading Book (FRTB) and its two capital approaches?

    FRTB (Basel III final market-risk standard) overhauls trading-book capital. Two approaches: the Standardized Approach (SA) — sensitivities-based method plus default risk charge and residual risk add-on; and the Internal Models Approach (IMA) — requires regulatory approval. FRTB makes the SA mandatory to compute (as a floor/fallback) for all banks.

20. Which two major risk-measurement changes did FRTB introduce in the Internal Models Approach?

    (1) It replaces 99% VaR with 97.5% Expected Shortfall (a coherent, tail-sensitive measure) calibrated to a stress period. (2) It replaces a single 10-day horizon with five liquidity horizons (10, 20, 40, 60, 120 days) assigned by risk-factor liquidity, scaling ES for varying market liquidity.

21. How does FRTB redefine the boundary between the banking book and trading book?

    FRTB sets a stricter, more objective boundary based on intent and instrument type to curb arbitrage. Instruments are presumptively assigned (e.g. trading intent, market-making, equities go to trading book); reclassification between books is heavily restricted and any capital benefit from switching is disallowed, reducing regulatory capital arbitrage.

22. Under the FRTB Internal Models Approach, what tests must each trading desk pass to retain model approval?

    Each desk must pass: (1) Backtesting of 1-day VaR against actual and hypothetical P&L (limits on exceptions), and (2) P&L Attribution (PLA) test comparing the risk model's P&L (RTPL) to the front-office hypothetical P&L (HPL) using Spearman correlation and Kolmogorov-Smirnov metrics. Failing desks fall back to the Standardized Approach. Non-modellable risk factors (NMRFs) get a separate stressed capital add-on.

23. In FRTB's sensitivities-based Standardized Approach, what three risk components are aggregated?

    (1) Delta (linear sensitivity to risk factors), (2) Vega (sensitivity to implied volatility), and (3) Curvature (capturing non-linear/gamma risk from large up/down shocks). These are computed per risk class with regulatory risk weights and prescribed correlations, then added to a Default Risk Charge (DRC) and a Residual Risk Add-On (RRAO).

24. Why is Expected Shortfall considered superior to VaR as a risk measure, referencing coherence?

    ES is the expected loss conditional on exceeding VaR: $$\mathrm{ES}_{\alpha} = E[L \mid L \geq \mathrm{VaR}_{\alpha}] = \frac{1}{1-\alpha}\int_{\alpha}^{1}\mathrm{VaR}_u\,du$$ ES is a coherent risk measure — it satisfies sub-additivity (diversification never increases risk), which VaR can violate. ES also accounts for the magnitude of tail losses beyond the VaR threshold, which VaR ignores.

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