Case Study 1: Building a Diversified Prediction Market Portfolio

Overview

This case study walks through the complete process of constructing, optimizing, and stress-testing a portfolio of 50 prediction market positions. We begin with a universe of opportunities across six event categories on three platforms, estimate correlations using structural analysis, apply portfolio Kelly optimization, enforce practical risk limits, run Monte Carlo simulations to estimate the return distribution, and perform stress tests. The goal is to demonstrate how the chapter's theoretical tools work together in practice and to illustrate the critical decisions a real portfolio manager faces.

Starting Conditions

Trader profile: - Total available capital: $50,000 - Trading capital (60%): $30,000 - Reserve capital (25%): $12,500 - Emergency fund (15%): $7,500 - Risk tolerance: Moderate (half-Kelly, 4% individual cap, 70% max deployment) - Time horizon: 3 months (one "season" of active trading)

Platforms used: - Platform A (Polymarket-style, crypto-settled): Up to 40% of trading capital - Platform B (Kalshi-style, USD-settled): Up to 40% of trading capital - Platform C (smaller exchange): Up to 25% of trading capital

The Opportunity Universe

The trader has identified 50 opportunities across six categories. Here is a representative sample showing the full diversity of the portfolio:

Political Markets (12 positions)

Economic Markets (10 positions)

Sports Markets (10 positions)

Entertainment Markets (8 positions)

Science & Technology Markets (6 positions)

Weather & Climate Markets (4 positions)

Step 1: Correlation Structure Estimation

Approach

Since historical data for these one-time events is unavailable, we estimate correlations using structural analysis. We assign correlation values based on category relationships and shared causal drivers.

Intra-Category Correlations

Inter-Category Correlations

Building the 50x50 Correlation Matrix

Using these structural estimates, we construct the full correlation matrix. The matrix is block-diagonal with intra-category blocks having elevated correlations and inter-category blocks having near-zero correlations. We ensure the matrix is positive semi-definite by computing the nearest valid correlation matrix using the alternating projections method when needed.

The resulting matrix has: - Average pairwise correlation: 0.06 - Maximum off-diagonal correlation: 0.50 (between Senate races P1-P4) - Minimum off-diagonal correlation: 0.00 (between unrelated categories) - Effective rank: 38 (indicating substantial independent variation)

Step 2: Portfolio Kelly Optimization

Configuration

• Fractional Kelly: 50% (half-Kelly)
• Individual position cap: 4% of trading capital
• Samples for optimization: 50,000

Optimization Results

Running the portfolio Kelly optimizer with the 50 opportunities, correlation matrix, and half-Kelly setting produces the following allocation (top 15 positions shown, sorted by allocation):

Key observations from optimization: - The four correlated Senate races (P1-P4) received significantly reduced allocations compared to their individual Kelly sizes. P1 alone would justify a 5% half-Kelly allocation, but with the three correlated races, it received only 2.5%. - Economic positions E2 and E4 rank highest despite similar edge to political markets because they are less correlated with other positions in the portfolio. - Entertainment and weather positions receive disproportionately high allocations relative to their edge because they provide diversification with near-zero correlation to the rest of the portfolio. - Technology position T1 (SpaceX launch at 92% probability) has a relatively small allocation despite high edge because the payout per unit risked is low (buying at $0.85 for a $0.15 potential profit).

Step 3: Applying Position Sizing Constraints

Constraint Application Pipeline

Step 3a: Individual Position Caps (4%)

No positions exceeded the 4% cap after half-Kelly sizing, so no adjustments needed at this step.

Step 3b: Correlated Group Caps (12% per group)

The Economics group slightly exceeded the 20% combined category cap, so all economic positions were scaled down by a factor of 0.934.

Step 3c: Platform Caps (40% for A and B, 25% for C)

All platforms are within limits.

Step 3d: Aggregate Deployment Cap (70%)

Total allocation after all constraints: 72.1%

This exceeds the 70% cap by 2.1 percentage points. All positions are scaled proportionally by $0.70 / 0.721 = 0.971$.

Final Portfolio Allocation

Category Allocation Breakdown

Step 4: Monte Carlo Simulation

Single-Round Simulation (All 50 bets resolve once)

We run 100,000 Monte Carlo simulations of all 50 positions resolving simultaneously, using the correlated binary outcome model.

Return Distribution:

Probability Analysis:

Risk Metrics:

Sequential Simulation (12 weekly rounds)

To model the three-month trading horizon, we simulate 12 rounds of the portfolio resolving and being re-entered. Each round, resolved positions are replaced with new opportunities of similar quality, maintaining the same portfolio structure.

Running 20,000 path simulations over 12 rounds:

Bankroll Path Statistics:

Drawdown Statistics (across all paths):

Interpretation

The Monte Carlo results are encouraging. The portfolio has a 73% chance of profit on any single round and an 89% chance of being profitable after the full 12-round season. The 95% VaR of 8.7% means that in the vast majority of rounds, the worst-case loss is under 9% of deployed capital.

The sequential simulation shows that the median drawdown over the season is only 7.6%, well within the "Normal" threshold of 10% that would not trigger any position scaling. Only about 5% of paths experience drawdowns exceeding 18%, which would trigger the "Serious" response of halving position sizes.

The risk of ruin (bankroll below 50% of starting value) is negligible at less than 0.01% over the 12-round horizon. This confirms that the half-Kelly sizing with 70% deployment creates a robust portfolio.

Step 5: Stress Testing

Scenario 1: Correlation Spike to 0.50

We re-run the simulation with all pairwise correlations set to 0.50, simulating a crisis where "everything is correlated."

Interpretation: The expected return stays the same (correlation does not affect expected return), but risk nearly doubles. The probability of a loss exceeding 20% jumps from negligible to nearly 5%. This stress test reveals the portfolio's dependence on correlation assumptions.

Scenario 2: Edge Halved (50% of estimated edge)

We re-run assuming true probabilities are midway between our estimates and market prices.

Interpretation: With halved edge, the portfolio remains profitable in expectation but the probability of profit drops to 60%. If the trader's edges are genuinely half of what they believe, the strategy still works but is marginal. This underscores the importance of accurate probability estimation.

Scenario 3: Political Category Wipeout

All 12 political positions lose simultaneously (a scenario resembling a major political surprise).

Interpretation: A complete political wipeout is painful but survivable. The 12.7% loss triggers the "Serious" drawdown level, halving position sizes going forward. Combined with reserve capital, the trader can continue operating.

Scenario 4: Platform A Failure

Platform A, holding 31.2% of deployed capital, becomes insolvent.

Interpretation: Losing the largest platform is a significant blow but does not threaten survival. The trader can redeploy reserve capital and continue trading on Platforms B and C while the Platform A situation resolves.

Scenario 5: Combined Adverse (Correlation Spike + Edge Halved)

The worst realistic scenario: correlations spike AND the trader's edge is overstated.

Interpretation: Even in this severe combined stress scenario, the expected return remains positive and the probability of catastrophic loss (>25%) is under 10%. The portfolio survives, though it would trigger significant position reductions.

Step 6: Diversification Analysis

Diversification Ratio

$$\text{DR} = \frac{\sum w_i \sigma_i}{\sigma_p} = \frac{0.1084}{0.0558} = 1.94$$

A diversification ratio of 1.94 means the portfolio's volatility is approximately half of what it would be if all positions were perfectly correlated. This represents strong diversification benefit.

Marginal Contribution to Risk (Top 5)

The top risk contributors are concentrated in political and economic markets, which have the highest intra-category correlations. No single position contributes more than 6% of total risk, indicating good risk balance.

Effective Number of Bets

$$\text{ENB} = \frac{1}{\sum w_i^2} = \frac{1}{0.0242} = 41.3$$

Out of 50 positions, the effective number of independent bets is 41.3. This is excellent. It means the portfolio is well-balanced and not dominated by a few large positions.

Conclusions and Lessons Learned

Lesson 1: The Correlation Tax on Concentrated Categories

The four Senate races each had strong individual edges (5-7 cents), but after accounting for their 0.50 intra-group correlation, the portfolio Kelly optimizer allocated less to each than their standalone Kelly fractions would suggest. The combined allocation to all four Senate races (8.2%) was less than what two uncorrelated bets of similar edge would receive. This is the "correlation tax": correlated positions dilute each other's portfolio value.

Lesson 2: Low-Correlation Mediocre Bets Can Beat High-Edge Correlated Bets

Entertainment positions N5 (Celebrity couple split, edge +0.06) and N7 (Book on NYT list, edge +0.07) received similar portfolio allocations to Senate Race P2 (edge +0.06) despite lower individual edges. The reason: zero correlation with everything else makes them more valuable to the portfolio as a whole.

Lesson 3: Stress Tests Reveal Hidden Fragility

The base-case simulation painted a rosy picture: 73% probability of profit, negligible ruin risk. But the combined stress scenario (correlation spike + edge halved) revealed that a 20%+ loss has a 9.3% probability. This is within the realm of plausible experience over a multi-season career. Knowing this in advance allows the trader to prepare psychologically and financially.

Lesson 4: Reserve Capital Is Not Wasted Capital

The trader deployed only $21,000 of their $50,000 total capital. The remaining $29,000 might seem unproductive, but it serves three critical functions: (1) it reduces effective risk to sustainable levels, (2) it provides deployment capacity for new opportunities, and (3) it ensures survival through any single-round adverse outcome.

Lesson 5: Diversification Is the Only Free Lunch

The diversification ratio of 1.94 means the portfolio achieved nearly twice the risk reduction of its individual positions through the simple act of combining uncorrelated bets. No amount of analytical sophistication can substitute for this structural benefit. A trader with 50 uncorrelated 5-cent-edge bets is in a far better position than a trader with 5 uncorrelated 10-cent-edge bets, even though the total expected return may be similar.

The complete Python code for this case study, including portfolio construction, Monte Carlo simulation, and stress testing, is available in code/case-study-code.py.