Case Study 2: Stress Testing Through a Black Swan Event

Overview

This case study models the impact of an unexpected "black swan" event on a prediction market portfolio. We start with a well-diversified portfolio similar to the one constructed in Case Study 1, then simulate a major geopolitical shock that sends correlations spiking, probability estimates shifting, and markets into turmoil. We track the portfolio through the initial shock, the drawdown period, and the recovery, demonstrating how pre-committed risk management rules determine whether the trader survives.

The event is modeled on the pattern of real historical shocks: the 2016 U.S. election surprise, the onset of COVID-19, and the Brexit referendum --- events that prediction markets priced as highly unlikely until they happened.

Initial Portfolio State

Portfolio Before the Shock

The trader has been operating for 8 weeks with the following portfolio and bankroll history:

Bankroll trajectory (weeks 1-8):

The trader has achieved a 9.0% cumulative return over 8 weeks, with a smooth equity curve and no drawdown exceeding 1.2%. The drawdown monitor shows all-clear status with full position sizing.

Active Portfolio Composition (Week 8)

The portfolio holds 42 active positions (8 from the original 50 have resolved profitably and been replaced). Deployed capital: $22,890 (70% of $32,700).

Category breakdown:

The Black Swan Event

Week 9: The Shock

On a Tuesday morning of Week 9, an unexpected geopolitical crisis erupts. A major international incident creates immediate and widespread uncertainty:

• A military confrontation between two major powers escalates rapidly
• Global financial markets drop 4% within hours
• Emergency government sessions are convened
• Oil prices spike 15% in a single day
• Consumer and business confidence metrics are expected to collapse

This event was not on anyone's radar. No prediction market had priced it in. The market-implied probability of such an event within this quarter was effectively zero.

Immediate Market Impact

The geopolitical shock propagates through the portfolio in three distinct waves:

Wave 1 (Hours 1-4): Direct impact on political and economic markets

The crisis directly affects government decision-making, economic expectations, and policy paths:

Wave 2 (Hours 4-12): Correlation contagion

Markets that have no direct connection to the geopolitical event begin moving as fear spreads and liquidity dries up:

Wave 3 (Days 2-5): Second-order effects and reassessment

Some markets partially recover as initial panic subsides, but others worsen as the full implications become clear:

Correlation Structure During the Crisis

Before the shock, the average pairwise correlation across the portfolio was 0.06. During the crisis:

The "correlation spike to 0.38" confirms a key lesson from Section 17.11: during crises, the average correlation can jump by 5-6x, dramatically reducing diversification benefits.

Portfolio Impact Assessment

Mark-to-Market Loss (End of Day 1)

To calculate the mark-to-market impact, we compute the unrealized P&L for each position based on the price change and position weight:

Loss decomposition by category:

Bankroll After Day 1

Bankroll After Week 9 (Day 5)

After the full week plays out, including second-order effects and partial recoveries:

The portfolio is teetering at the edge of the "Normal" zone. One more bad day could push it into the "Warning" territory (10-15%), triggering a reduction to 75% position sizing.

Decision Point: Stay the Course or Reduce?

The Trader's Dilemma

At the end of Week 9, the trader faces a critical decision. The drawdown monitor shows "Normal" status, meaning the rules say to continue trading at full size. But the trader feels nervous --- this is the worst drawdown they have experienced, and the geopolitical situation is still unresolved.

Option A: Follow the Rules (Stay at Full Size)

The pre-committed rules say to maintain full position sizing since the drawdown is still under 10%. The argument for this:

1. The rules were set when thinking rationally, not in the heat of a crisis.
2. Many positions moved against the trader on market sentiment, not on changed fundamentals for those specific events (sports, entertainment).
3. If the crisis resolves, the positions that moved on sentiment may snap back, creating recovery profits.
4. Reducing size at the bottom locks in losses and misses recovery.

Option B: Override the Rules (Reduce Proactively)

The argument for proactive reduction:

1. The geopolitical situation is unprecedented and still evolving. True probabilities may have shifted more than the trader recognizes.
2. The correlation spike means the portfolio is less diversified than it was, creating hidden concentration risk.
3. Several probability estimates need revision, and the trader has not yet had time to re-analyze all 42 positions.
4. Preserving capital to trade another day is paramount.

The Chosen Path

The trader chooses a hybrid approach, demonstrating the practical wisdom that rules need judgment:

1. Follow the drawdown rules by not reducing overall sizing (the 10% threshold has not been breached).
2. Re-evaluate every position and update probability estimates in light of the new information.
3. Close positions where the edge has disappeared or reversed due to the crisis.
4. Reduce correlated political and economic positions where the uncertainty is genuinely higher.
5. Hold uncorrelated positions (sports, entertainment) where the price moved on sentiment rather than fundamentals.

Portfolio Adjustments (Week 9, Weekend)

Revised portfolio: - Positions: 39 (down from 42) - Deployed capital: $21,210 (down from $22,890) - Deployment ratio: 65% (down from 70%)

The Recovery Phase

Weeks 10-12: Gradual Stabilization

The geopolitical crisis stabilizes (but does not fully resolve) over the next three weeks:

What Drove the Recovery

Snap-back profits (positions that moved on sentiment, not fundamentals):

These positions moved against the trader on contagion fear, not because their fundamentals changed. By holding through the panic, the trader captured the mean reversion.

New opportunity profits (positions opened during the crisis):

The increased position in E4 (Fed rate cut, bought more at $0.65) and E6 (Oil > $90, increased at $0.55) both gained further as the crisis strengthened the case for these outcomes.

Permanent losses (positions closed at a loss):

P7 (Bill X), P11 (UN Resolution), and P12 (Treaty) were closed at losses totaling approximately $680 because the crisis genuinely changed the probability of these political outcomes. These losses are real and permanent --- they represent the irreducible cost of a truly unexpected event.

Week 12 Bankroll Assessment

Weeks 13-16: Full Recovery and New Peak

The trader continues with the adjusted portfolio, now operating in the "new normal" of slightly elevated correlations and revised probability estimates:

The portfolio achieves a new all-time high in Week 15, just 6 weeks after the black swan event. Total recovery time from trough to new peak: 6 weeks.

Counterfactual Analysis

What If the Trader Had Panicked?

Scenario: Close all positions on Day 1 and wait 4 weeks to re-enter

Panicking and closing all positions would have locked in the Day 1 losses plus forfeited the recovery profits on sentiment-driven positions. The total cost of panic: approximately $1,456 in foregone recovery.

What If Drawdowns Had Continued?

Scenario: The crisis escalates for 4 more weeks instead of stabilizing

If the crisis had deepened, with continued correlation elevation and further probability shifts:

In this counterfactual, the drawdown rules would have kicked in automatically: - Week 10: 75% sizing limits further damage - Week 11: 50% sizing significantly slows the bleeding - Even after 4 weeks of continued crisis, the bankroll remains above $25,000 (83% of peak)

The graduated position reduction acts as a natural shock absorber, slowing losses during adverse periods while maintaining some exposure for recovery.

What If the Trader Had No Position Limits?

Scenario: Full Kelly with no caps, 100% deployment

If the trader had used full Kelly sizing with no position caps and deployed 100% of capital:

The aggressive approach would have produced higher returns before the shock (+27% vs +9%) but suffered a devastating 26% drawdown that triggered "Critical" status and would have required 18 weeks to recover. The risk of ruin --- the probability of the bankroll dropping below 10% of its starting value during the trading career --- jumps from negligible to 3.2%.

Lessons from the Black Swan

Lesson 1: Correlations Are Not Constants

The portfolio's base-case average correlation of 0.06 jumped to 0.38 during the shock --- a 6x increase. The diversification ratio that was 1.94 under normal conditions dropped to approximately 1.25 during the crisis. Any risk model that treats correlations as fixed will dramatically underestimate tail risk.

Practical takeaway: Always run stress tests with correlation levels 3-5x higher than your base assumptions. If the portfolio cannot survive the stressed scenario, reduce exposure.

Lesson 2: Not All Price Moves Are Informational

During the crisis, sports and entertainment positions moved down 4-8% despite having no fundamental connection to the geopolitical event. This is "contagion" --- fear-driven selling across all markets regardless of relevance. Traders who can distinguish between informational price moves (genuinely changed probabilities) and contagion moves (sentiment-driven, temporary) can profit from the recovery.

Practical takeaway: Before closing positions during a crisis, ask: "Has the true probability of this specific event actually changed?" If not, the price move is likely temporary and represents an opportunity, not a risk.

Lesson 3: Pre-Committed Rules Save You from Your Worst Instincts

The trader's pre-committed drawdown rules prevented both panic (closing everything) and denial (ignoring the crisis). The hybrid approach --- follow the rules, re-evaluate fundamentals, adjust selectively --- produced a better outcome than either extreme.

Practical takeaway: Write down your crisis response plan before a crisis occurs. Include specific triggers, specific actions, and specific criteria for determining whether a price move is informational or contagion.

Lesson 4: Recovery Time Is Asymmetric

The portfolio experienced a 9.1% drawdown in one week but required 6 weeks to recover to a new peak. This 1:6 ratio between shock duration and recovery duration is typical and has important implications for bankroll management: the longer you spend in drawdown, the more rounds of potential returns you forgo.

Practical takeaway: Recovery time is inversely proportional to your expected return per round. If you reduce sizing during the drawdown (as the rules prescribe), recovery takes even longer. Budget for recovery periods when planning your trading career.

Lesson 5: Reserves Are Insurance, Not Idle Capital

The trader's $12,500 in reserve capital was never deployed during this episode, but its existence was crucial for psychological stability. Knowing that even a worst-case scenario would not threaten survival allowed the trader to think clearly and make rational decisions.

Practical takeaway: Maintain at least 30% of total capital in reserves. View this as insurance premium --- it costs you some expected return but protects against catastrophic loss.

Lesson 6: Black Swans Are Not Black When You Prepare for Them

The trader's stress test in Case Study 1 included a "correlation spike to 0.50" scenario and a "combined adverse" scenario. The actual black swan produced a correlation spike to 0.38 --- less severe than the stress test. Because the trader had already seen (in simulation) what a correlation spike would do, the real event was shocking but not bewildering.

Practical takeaway: Run extreme stress tests regularly. Even if you never experience the exact scenario, the exercise of thinking through extreme outcomes prepares you mentally and financially for whatever does happen.

Summary Timeline

Bottom line: A well-constructed portfolio with disciplined risk management turned a black swan event into a 6-week detour, not a career-ending disaster. The total cost of the episode was approximately 4 weeks of foregone growth relative to the pre-shock trajectory.

The complete Python code for this case study, including the shock simulation, drawdown tracking, and counterfactual analysis, is available in code/case-study-code.py.