Chapter 14 Exercises

Market Risk and the Basel Framework in Practice

Exercise 14.1: Risk Classification

Difficulty: Introductory

Classify each of the following market risk exposures by risk type (interest rate risk, equity risk, FX risk, commodity risk, credit spread risk, or volatility risk). Some exposures may involve multiple risk types.

a) A UK bank holds £50 million of fixed-rate 10-year UK government bonds b) A UK bank has made a USD-denominated loan of $30 million to a US subsidiary c) A trading desk holds 100,000 shares of a FTSE 250 technology company d) A trading desk has sold (written) options on the FTSE 100 index e) A bank holds €20 million of Italian government bonds (rated BBB) f) A commodity trading desk holds long positions in Brent crude oil futures g) A bank's funding desk has £500 million of fixed-rate 5-year deposits from retail customers h) A derivatives desk has entered an interest rate swap (receiving fixed, paying floating) on £100 million notional

For each, identify: (1) the risk type(s), (2) whether it is likely in the trading book or banking book, and (3) the directional effect if rates rise by 200 basis points.

Exercise 14.2: VaR Calculation

Difficulty: Intermediate

A simplified trading portfolio has two positions:

The correlation between daily returns of Equity A and Bond B is −0.30 (bonds tend to rise when equities fall).

a) Calculate the portfolio standard deviation σ_portfolio using the formula: σ_portfolio = √(w_A²σ_A² + w_B²σ_B² + 2×w_A×w_B×ρ×σ_A×σ_B) where weights are market values.

b) Calculate the 1-day parametric VaR at 99% confidence (z = 2.326).

c) Calculate the 10-day parametric VaR (using √10 scaling).

d) Now assume the correlation between assets rises to +0.80 (stress scenario — diversification benefit disappears). Recalculate the 1-day 99% VaR. What is the percentage increase in VaR due to correlation stress?

e) Expected Shortfall at 97.5% for a normal distribution equals σ × φ(Φ⁻¹(0.025)) / 0.025, where φ is the standard normal PDF and Φ⁻¹(0.025) ≈ −1.96. This simplifies to approximately σ × 2.338. Calculate the 1-day 97.5% ES for the portfolio (using the original correlation of −0.30).

Exercise 14.3: FRTB Desk Classification

Difficulty: Intermediate

A bank has six trading desks. For each desk, evaluate whether it would qualify for the FRTB Internal Models Approach (IMA) or must use the Standardized Approach (SA). Identify the key reason.

a) For each desk, state IMA or SA and the primary reason. b) For any desk you classify as SA: estimate whether SA capital would likely be higher or lower than IMA capital, and why. c) The bank wants to maximize the proportion of its book under IMA (lower capital). For the desk(s) that fail, what remediation steps could enable them to qualify for IMA?

Coding Exercise 14.4: Historical VaR and Backtesting

Difficulty: Coding — Intermediate

Using the HistoricalVaREngine class framework from the chapter:

1. Generate synthetic market data for 5 instruments using generate_synthetic_market_data().

2. Create a portfolio of 5 positions with diverse asset classes (equity, FX, rates, credit, commodity).

3. Run the historical VaR engine and produce: - 1-day 99% VaR - 10-day 99% VaR (√10 scaled) - 1-day 97.5% ES - 10-day 97.5% ES - Component VaR by instrument

4. Implement a rolling VaR backtest: for each day from day 251 to the last day of data: - Estimate VaR using the prior 250 days of returns - Record whether the next day's actual P&L exceeded the VaR estimate - Report total breaches and classify as Green/Yellow/Red

5. Add a stress scenario test: shock all risk factor correlations to 0.85 (correlated stress) and recalculate VaR. Report the ratio of stressed VaR to base VaR.

Exercise 14.5: IRRBB Impact Analysis

Difficulty: Intermediate

Verdant Bank's simplified banking book cash flow profile:

Assets (cash inflows): | Instrument | Notional (£M) | Maturity | Rate Type | |-----------|--------------|----------|-----------| | Fixed-rate mortgages | 450 | 15 years (avg) | Fixed 3.5% | | Variable-rate mortgages | 280 | 1 year reprice | Variable: SONIA + 2% | | Fixed-rate SME loans | 120 | 5 years (avg) | Fixed 5.0% | | Government bond | 80 | 10 years | Fixed 4.0% |

Liabilities (cash outflows): | Instrument | Notional (£M) | Maturity | Rate Type | |-----------|--------------|----------|-----------| | Retail savings (instant access) | 600 | Assumed 1 year | Variable: 2.5% | | Fixed-rate bonds (issued) | 200 | 5 years | Fixed 3.0% | | Wholesale funding | 130 | 90 days | Variable: SONIA |

a) Identify the interest rate risk characteristics of this balance sheet. Is Verdant "asset-sensitive" (benefits from rate rises) or "liability-sensitive" (benefits from rate falls)?

b) Under a +200bp parallel rate shock (rates rise 200bp), describe qualitatively the impact on: - Net Interest Income (NII) over the next 12 months - Economic Value of Equity (EVE)

c) Under a -200bp shock (rates fall sharply), describe the impact on NII and EVE.

d) The Basel IRRBB standard requires banks to hold Pillar 2 capital if the EVE shock under the standardized ±200bp scenario exceeds 15% of Tier 1 capital. If Verdant's Tier 1 capital is £140M, what is the threshold EVE sensitivity that would trigger a Pillar 2 requirement?

Research Exercise 14.6: FRTB Implementation Status

Difficulty: Research-required

FRTB was finalized by the Basel Committee in January 2019 with an original implementation date of January 2022, subsequently delayed to January 2025.

a) What is the current FRTB implementation status in the EU, UK, and US? Have all three jurisdictions implemented FRTB on the January 2025 timeline? (Search for recent regulatory announcements from the EBA, PRA, and US banking regulators.)

b) What are the key differences, if any, between how the EU (via CRR3), UK (via PRA rules), and the US have implemented FRTB? Are there jurisdiction-specific divergences from the Basel standard?

c) Industry associations (ISDA, GFMA) have published analyses of FRTB's capital impact across institutions. What do these analyses show about the aggregate capital increase from FRTB implementation? Which asset classes are most affected?

d) Write a 300-word analysis of whether FRTB represents an improvement in risk capture compared to the pre-FRTB regime, or whether it simply increases capital requirements without proportionally improving risk management quality.