Stress Testing and Scenario Analysis

Stress Testing and Scenario Analysis

After the 2008 crisis, regulatory stress tests became a mandatory tool of bank risk management. They supplement statistical models (VaR, CVaR) by analyzing specific crisis scenarios, answering the question “What will happen if X occurs?”. Stress tests allow identifying vulnerabilities not visible under normal conditions: concentrations of risks, correlation risks in stress, liquidity holes. DFAST/CCAR (USA), EBA ST (Europe), ICAAP (internal) are the main types. Regular passage of these tests is critical for large banks and insurance companies.

Types of Stress Tests

1. Historical Scenarios. Recreation of real crises:

• The Great Depression 1929–1933.
• Black Monday October 19, 1987 (S&P −20.5% in one day).
• Asian Crisis 1997–1998 (currency devaluation, LTCM default).
• 9/11 2001 (market closure, drop in aviation, insurance).
• Lehman Brothers September 15, 2008 (paralysis of the interbank market).
• COVID 2020 (S&P −34% in a month, zero rates, Fed asset purchases).
• Banking crisis 2023 (SVB, Signature, Credit Suisse, First Republic).

Advantages: realistic, capture real correlations. Drawback: “backwards-looking”, the next crisis may be different.

2. Hypothetical Scenarios. Modeling unrealized but plausible events:

• “What if rates rise by 400 bps in a quarter?”
• “What if the dollar falls by 30%?”
• “What if China devalues the yuan by 20%?”
• “What if the largest corporate counterparty defaults?”

IMF, BIS publish recommendations on scenarios.

3. Factor Stress Tests. Shocks to individual risk factors:

• Parallel shift of the yield curve (+100, +200 bps).
• Twist (short end up, long end down).
• Volatility shock (+50%).
• Spread widening (+200 bps for investment grade, +500 bps for high yield).

Full portfolio revaluation. Correlations in stress are often higher than normal—“everything falls together” (correlation breakdown).

4. Risk scenarios for specific businesses:

• Insurers: 1-in-200-year natural catastrophes (Solvency II).
• Banks: default of the real estate sector.
• Pension funds: longevity shock + declining rate.

Regulatory Stress Tests

DFAST (Dodd-Frank Act Stress Test). For US banks > $100 billion in assets. The Fed sets three scenarios:

• Baseline: basic economic forecast.
• Adverse: moderate recession.
• Severely Adverse: deep crisis.

Banks project P&L, RWA, capital over 9 quarters. Result publication impacts approval for dividends and buybacks.

Severely Adverse Scenario 2024 (Fed):

• Real US GDP −7.6% (over 6 quarters).
• Unemployment 10% (from current 3.7%).
• S&P 500 −55%, real estate prices −36%.
• Curve inversion, spreads +500 bps.
• Eurozone GDP −5.5%, Japan −5.0%.

CCAR (Comprehensive Capital Analysis and Review). DFAST + analysis of capital plans (dividends, buybacks).

EBA ST (Europe). Once every 2 years, 70 largest EU banks. 2023: average CET1 dropped from 15.0% to 10.4% in severely adverse. No bank failed (vs. 2014, when 24 banks did not pass).

ECB SSM (Single Supervisory Mechanism). Additional supervisory stress tests for EU G-SIBs.

Bank of England ACS (Annual Cyclical Scenario). For UK banks.

Reverse Stress Tests

Idea. Instead of “what happens under scenario X?”, the question is “what scenario would cause collapse?”. Seeking a combination of factors where capital ≤ 0 (or minimum liquidity exhausted).

Application.

• Bank A: reverse stress test shows capital is wiped out if: rates +5% AND real estate falls 40% AND NPL 15%. If these events are not independent (which is likely), correlations need to be examined.
• Insurer B: “disappearance” of pandemic + stock prices −60% + rates 0%—combined scenario, loss of 80% of capital.

Reverse stress tests are mandatory under Pillar 2 (Basel) and Solvency II.

Numerical Example: Equities+Bonds Portfolio

Portfolio €100 million: 60% S&P 500 ($60 million), 40% US Treasury 10Y ($40 million).

Scenarios:

Stagflation — the worst: simultaneous drop in stocks and bonds (as in 2022, a rare crisis type with inflation).

Hedge: add VIX call options. Notional $5 million, payoff in Lehman ≈ +200% = +$10 million. Reduces Lehman losses from 23 to 13. Hedge cost ≈ $0.5 million/year—acceptable insurance.

Alternative: put options on S&P. Strike 90% (cost ~3%/year), payoff in Lehman = −max(90%·100 − 63, 0)·notional. On $60 million notional, payoff $16 million. Cost $1.8 million/year.

Liquidity Stress Tests

A separate class: modeling deposit outflows and funding loss in stress.

LCR-stress: 30 days outflow:

• Retail deposits: 5–10%.
• Corporate: 25–40%.
• Wholesale unsecured: 100%.
• Drawdowns on credit lines: 5–10% retail, 30% wholesale.

The bank must have HQLA (cash, level 1 securities) ≥ total outflow.

SVB 2023. $42 billion left out of $173 billion deposits in 2 days (24%). LCR did not help (it only covers 30 days). Lesson: social media accelerates bank runs to hours.

Real Applications

• Crisis 2008. Citigroup TARP $45 billion after failing initial stress test. AIG $182 billion bail-out—the test did not account for CDS concentration.
• EBA 2023. All 70 banks passed (minimum CET1 8.5%), but Bank of Cyprus and Banca Monte dei Paschi barely made it. Systemically important (BNP, Santander)—comfortable buffer.
• Solvency II ORSA (Own Risk and Solvency Assessment). Every insurance company must annually conduct internal stress tests with its own scenarios.
• Cyber stress tests. Growing practice: modeling simultaneous cyber-attack on the bank and its counterparties. NIST 2.0, ENISA guidelines.

Exercise. Portfolio €100 million: 60% S&P 500 stocks, 40% UST 10Y bonds (modified duration 8). (a) For historical scenarios (Lehman 2008: S&P −37%, UST yield +50bp; COVID 2020: S&P −34%, UST yield −80bp) calculate portfolio losses. (b) For hypothetical stagflation scenario (S&P −40%, UST yield +200bp): what is the loss? (c) What hedge (e.g., VIX calls or S&P puts) would reduce maximum losses to €20 million? Estimate hedge cost. (d) Reverse stress test: for which combination (ΔS&P, Δyield) does the portfolio lose 50%?