Case Study 1: Anatomy of a Multi-Outcome Election Market

Overview

This case study dissects a realistic multi-outcome prediction market for a U.S. presidential election. We will examine how contracts are structured, calculate the overround, trace several trades through the full lifecycle, and analyze the P&L outcomes for different traders with different strategies. All data is based on plausible market dynamics, though the candidates and exact figures are illustrative.

The Market

Contract: "Who will win the 2028 U.S. Presidential Election?"

Resolution criteria: The contract resolves to the candidate who wins a majority of Electoral College votes as certified by Congress. If no candidate wins a majority and the election is decided by the House of Representatives, the contract resolves to the person the House selects as President.

Resolution date: January 6, 2029 (date of Congressional certification), or earlier if all major news organizations (AP, Reuters, CNN, Fox News, NBC) have called the race for the same candidate.

Outcomes:

Initial Market State (18 months before election)

The market opens with the following prices, reflecting early polling and political analysis:

Overround Calculation

Using ask prices (the cost to buy):

$$\text{Sum of asks} = 0.31 + 0.24 + 0.16 + 0.13 + 0.09 + 0.12 = 1.05$$

$$\text{Overround} = 1.05 - 1.00 = 0.05 = 5\%$$

Using midpoints:

$$\text{Sum of mids} = 0.300 + 0.230 + 0.145 + 0.115 + 0.075 + 0.105 = 0.970$$

The midpoint sum is below 1.00, which is normal — the spread accounts for the difference. A buyer pays the ask (sum > 1) and a seller receives the bid (sum < 1).

Normalized Implied Probabilities

Using ask prices (the buyer's perspective):

The Traders

We follow four traders, each with a different strategy and level of sophistication.

Trader 1: Alice — The Conviction Buyer

Background: Alice is a political analyst who believes DeSantis will win the Republican primary and then the general election. She estimates his true probability at 35%, well above the market's 23%.

Strategy: Buy DeSantis and hold through settlement.

Trade: Buys 500 contracts of DeSantis at the ask price of $0.24.

• Total cost: 500 x $0.24 = **$120.00**
• Maximum profit (DeSantis wins): 500 x ($1.00 - $0.24) = $380.00
• Maximum loss (DeSantis loses): 500 x $0.24 = **-$120.00**
• Break-even: DeSantis must win (binary outcome).

Trader 2: Bob — The Portfolio Builder

Background: Bob believes the next president will be a Democrat but is unsure whether it will be Harris or Newsom. He wants exposure to a "Democrat wins" portfolio.

Strategy: Buy both Harris and Newsom to create a combined position.

Trades: - Buys 300 contracts of Harris at $0.31. Cost: 300 x $0.31 = $93.00 - Buys 300 contracts of Newsom at $0.16. Cost: 300 x $0.16 = $48.00 - Total cost: $141.00

P&L by outcome:

Bob profits $159 if either Democrat wins, loses $141 otherwise. His combined implied probability of a Democrat winning is (0.31 + 0.16) / 1.05 = 44.8%.

For this trade to have positive expected value, Bob needs to believe the probability of a Democrat winning exceeds $141 / ($141 + $159) = 47.0%.

Trader 3: Carol — The Arbitrageur

Background: Carol notices that the same election market on another platform (Platform B) has different prices. She spots an arbitrage opportunity.

Platform A ask prices (from above): Harris $0.31, DeSantis $0.24, Newsom $0.16, Haley $0.13, Ramaswamy $0.09, Other $0.12. Total: $1.05.

Platform B ask prices: Harris $0.28, DeSantis $0.26, Newsom $0.18, Haley $0.11, Ramaswamy $0.07, Other $0.10. Total: $1.00.

Strategy: Buy each outcome at the cheaper platform:

Carol buys 1,000 contracts of each at the best available price.

• Total cost: 1,000 x $0.96 = **$960.00**
• Guaranteed payout: 1,000 x $1.00 = **$1,000.00** (one outcome always wins)
• Guaranteed profit: $40.00 (4.2% return, risk-free)

Practical complications: Carol needs accounts funded on both platforms. She faces withdrawal fees, timing risk (prices may change while she executes), and the fact that Platform B might have limited liquidity at those ask prices.

Trader 4: Dave — The Active Trader

Background: Dave trades actively, adjusting his positions as news develops.

Phase 1 — Initial position (18 months before): - Buys 400 Harris at $0.31 = $124.00

Phase 2 — Haley surges in polls (12 months before): Market prices shift. Haley rises from $0.13 to $0.22. Harris falls from $0.31 to $0.28. DeSantis drops from $0.24 to $0.18.

Dave decides to: - Sell 200 Harris at $0.28, Realized P&L: 200 x ($0.28 - $0.31) = -$6.00 - Buy 200 Haley at $0.22 = $44.00

Phase 3 — DeSantis drops out (8 months before): DeSantis suspends his campaign. Market adjusts: DeSantis crashes to $0.02. Harris rises to $0.38. Haley rises to $0.30.

Dave's current positions: - 200 Harris (avg cost $0.31, current $0.38): Unrealized P&L = 200 x ($0.38 - $0.31) = +$14.00 - 200 Haley (avg cost $0.22, current $0.30): Unrealized P&L = 200 x ($0.30 - $0.22) = +$16.00

Dave decides to take profits on Haley: - Sell 200 Haley at $0.30. Realized P&L: 200 x ($0.30 - $0.22) = +$16.00

Phase 4 — Final state (holds 200 Harris at avg cost $0.31)

Resolution

The election takes place and Harris wins. Let us calculate each trader's final P&L.

Alice (Held DeSantis)

Alice loses her entire investment. Her conviction was wrong.

Bob (Held Harris + Newsom)

Bob's Democrat portfolio pays off handsomely. His return on investment is $159 / $141 = 112.8%.

Carol (Arbitrageur — all outcomes)

Carol's guaranteed profit materialized regardless of who won. Return: 4.2%.

Dave (Active trader)

Dave's total investment at peak was $124.00 (Harris) + $44.00 (Haley) - $56.00 (Harris sale proceeds) = $112.00 net capital at risk. His total P&L of +$148.00 represents an excellent return, but he also left money on the table — if he had not sold 200 Harris, he would have earned an additional 200 x ($1.00 - $0.31) = $138, minus the $16 Haley profit. The lesson: active trading involves trade-offs.

Comparative Analysis

*Dave's total cost is the sum of all purchases ($124 + $44), gross of sale proceeds.

Key Takeaways from the Comparison

1. Conviction bets are high risk: Alice had an informed view but was wrong, losing everything. The all-or-nothing nature of prediction markets means a single wrong bet results in a 100% loss.

2. Diversification within a thesis works: Bob's "any Democrat" portfolio outperformed Alice's single-candidate bet even though he paid more overall. By covering two candidates, he increased his probability of winning while keeping his payoff structure favorable.

3. Arbitrage offers guaranteed but small returns: Carol's profit was certain but small (4.2%). Arbitrage opportunities are rare, short-lived, and require capital on multiple platforms.

4. Active trading can be profitable but is not easy: Dave made good decisions (cutting losses on Harris, buying Haley at a good price, taking profits) but also made a mistake (selling Harris before the final rally). Active trading requires constant attention and good judgment.

Overround Evolution

The overround changed throughout the lifecycle of this market:

This pattern is typical: overround shrinks as the event approaches because more traders enter the market, competition between market makers increases, and more information is available. The market becomes most efficient right before resolution.

Multi-Outcome Market Dynamics

Price Conservation

When DeSantis dropped out (Phase 3), his contract value collapsed from $0.18 to $0.02. That probability had to go somewhere. The redistribution was approximately:

Notice that the total probability approximately conserves: the sum still hovers around 1.03. DeSantis's lost probability was absorbed primarily by Harris and Haley (the other frontrunners), reflecting the market's belief that DeSantis voters would largely shift to the remaining major candidates.

Correlation Between Outcomes

In multi-outcome markets, prices are inherently correlated. If one candidate's price rises, others must fall (to keep the sum near 1). This creates natural hedging opportunities and also means that a single piece of news (like a dropout) ripples through all contracts simultaneously.

Code

Full Python code for this case study is available in code/case-study-code.py, including: - Market state simulation across four time periods - P&L calculations for all four traders - Overround tracking - Probability redistribution analysis

Discussion Questions

1. If you were Alice and believed DeSantis had a 35% chance, how much of a $1,000 bankroll should you have allocated to this bet? (Hint: think about the Kelly Criterion, which we will cover in a later chapter.)

2. Carol's arbitrage required capital on two different platforms. If she earns 4.2% on a trade that takes 18 months to resolve, what is the annualized return? Is this competitive with a savings account?

3. Dave sold Harris too early. In hindsight, should he have held? How would you distinguish between "taking profits wisely" and "selling too early"?

4. The overround shrank from 5% to 0.5% as the election approached. Who benefits more from the low overround — retail traders or professional market makers?

5. If you had an informational edge (say, access to an internal campaign poll), which trader's strategy would you adopt, and how would you modify it?