Quiz -- Chapter 16: Arbitrage in Prediction Markets
Test your understanding of the core concepts from Chapter 16. Try to answer each question before revealing the answer.
Scoring Guide
| Section | Points per Question | Total Points |
|---|---|---|
| Section 1: Multiple Choice (12) | 2 | 24 |
| Section 2: True/False (6) | 2 | 12 |
| Section 3: Calculation (4) | 5 | 20 |
| Section 4: Short Answer (3) | 6 | 18 |
| Total | 74 |
| Score | Rating | Recommendation |
|---|---|---|
| 66--74 | Excellent | You are ready for Chapter 17 |
| 52--65 | Good | Review sections you missed, then proceed |
| 37--51 | Fair | Re-read the chapter with focus on weak areas |
| Below 37 | Needs work | Re-read the chapter carefully and redo exercises |
Section 1: Multiple Choice
Choose the single best answer for each question.
Q1. A binary prediction market has YES at \$0.46 and NO at \$0.51. What is the gross arbitrage profit per pair?
(a) \$0.03 (b) \$0.05 (c) \$0.46 (d) There is no arbitrage
Answer
**(a) \$0.03** Total cost = \$0.46 + \$0.51 = \$0.97. Guaranteed payout = \$1.00. Gross profit = \$1.00 - \$0.97 = \$0.03.Q2. Which of the following is the defining characteristic that distinguishes true arbitrage from quasi-arbitrage?
(a) True arbitrage yields higher returns (b) True arbitrage guarantees profit in every possible outcome (c) True arbitrage only works on a single platform (d) True arbitrage requires less capital
Answer
**(b) True arbitrage guarantees profit in every possible outcome** True arbitrage has zero risk of loss -- every possible outcome results in a profit. Quasi-arbitrage is statistically likely to profit but has some scenarios where a loss is possible.Q3. In a 5-outcome market, the ask prices are [0.30, 0.22, 0.18, 0.14, 0.08]. The sum is 0.92. What does this indicate?
(a) The market has an 8% overround (b) The market has an 8% underround, and a buyer's arbitrage exists (c) The market is perfectly efficient (d) No conclusion can be drawn without bid prices
Answer
**(b) The market has an 8% underround, and a buyer's arbitrage exists** When the sum of ask prices for mutually exclusive and exhaustive outcomes is less than 1.00, buying all outcomes costs less than the guaranteed \$1.00 payout. The 8-cent gap is a gross arbitrage profit.Q4. You execute a cross-platform arbitrage: buy YES on Platform A at \$0.55, buy NO on Platform B at \$0.40. Platform A has no fees, Platform B charges a 10% settlement fee on profits. If YES wins, what is your net profit?
(a) \$0.05 (b) \$0.45 (c) \$0.05 minus any settlement fee (d) \$0.05 (fees only apply to the losing side)
Answer
**(a) \$0.05** If YES wins: You receive \$1.00 from Platform A (no fees). You lose your \$0.40 on Platform B (no settlement fee because you lost -- the 10% fee applies only to profits, and you made no profit on B). Net = \$1.00 - \$0.55 - \$0.40 = \$0.05. The settlement fee on Platform B only matters if NO wins (when you would profit on B).Q5. For the same trade as Q4, what is the net profit if NO wins?
(a) \$0.05 (b) \$0.05 - 10% of \$0.60 = -\$0.01 (c) \$1.00 - 10% of \$0.60 - \$0.55 - \$0.40 = -\$0.01 (d) \$1.00 - \$0.40 - 10% \times (1.00 - 0.40) - \$0.55 = -\$0.01
Answer
**(d) \$1.00 - \$0.40 - 10% \times (1.00 - 0.40) - \$0.55 = -\$0.01** If NO wins: You receive \$1.00 from Platform B, but pay a 10% settlement fee on the profit (\$0.60). Fee = \$0.06. You lose your \$0.55 on Platform A. Net = \$1.00 - \$0.06 - \$0.55 - \$0.40 = -\$0.01. This is a loss! The arbitrage does not survive Platform B's settlement fee in this direction. The guaranteed profit is min(\$0.05, -\$0.01) = -\$0.01, meaning there is actually no arbitrage after fees.Q6. What is the primary reason cross-platform arbitrage opportunities persist in prediction markets?
(a) Market makers intentionally create them to attract liquidity (b) Platforms are fragmented with no cross-platform order routing (c) Arbitrage is illegal in most jurisdictions (d) All platforms use the same pricing algorithm
Answer
**(b) Platforms are fragmented with no cross-platform order routing** Prediction markets operate on isolated platforms with different user bases, different fee structures, and no mechanism for prices to equilibrate across platforms. This fragmentation, combined with barriers to capital flow (different currencies, KYC requirements, withdrawal delays), allows price discrepancies to persist.Q7. The annualized return formula $R_{annual} = (1 + ROI)^{365/T} - 1$ is used because:
(a) It accounts for inflation (b) It converts a holding-period return into a comparable annual figure (c) It adjusts for taxes (d) It is required by regulators
Answer
**(b) It converts a holding-period return into a comparable annual figure** A 3% return over 7 days and a 5% return over 180 days are not directly comparable. Annualization converts both to what they would yield over a full year if the opportunity could be repeated, making them comparable. The 3% over 7 days annualizes to roughly 332%, while 5% over 180 days annualizes to only about 10.3%.Q8. Which of the following is an example of a related-market arbitrage (not cross-platform)?
(a) Buying YES on Polymarket and NO on Kalshi for the same event (b) Selling "X wins the general election" and buying "X wins the primary" when the general election price is higher (c) Buying YES and NO on the same market when they sum to less than \$1.00 (d) Buying a contract today and selling it tomorrow at a higher price
Answer
**(b) Selling "X wins the general election" and buying "X wins the primary" when the general election price is higher** This exploits a sequential constraint: winning the general election requires first winning the primary, so P(general) must be <= P(primary). When the general election is priced higher, the relationship is violated, creating an arbitrage opportunity. This involves two different but logically related markets.Q9. In the context of arbitrage execution, what is "leg risk"?
(a) The risk that your internet connection fails (b) The risk that one leg of a multi-leg trade fails to execute, leaving you with an unhedged directional position (c) The risk that the event resolution is ambiguous (d) The risk that fees change between order placement and execution
Answer
**(b) The risk that one leg of a multi-leg trade fails to execute, leaving you with an unhedged directional position** Leg risk is the fundamental execution challenge in arbitrage. If you successfully buy YES on Platform A but fail to buy NO on Platform B (due to price movement, insufficient liquidity, or platform issues), you are left with a naked directional position -- the opposite of a risk-free trade.Q10. You are considering an arbitrage that yields \$500 profit but locks up \$10,000 for 6 months. Your opportunity cost of capital is 8% per year. What is the lock-up cost?
(a) \$200 (b) \$400 (c) \$800 (d) \$40
Answer
**(b) \$400** Lock-up cost = Capital x Rate x (Days / 365) = \$10,000 x 0.08 x (182/365) = \$398.90, approximately \$400. Since the profit (\$500) exceeds the lock-up cost (\$400), the arbitrage is still worthwhile on an opportunity-cost basis, but the true economic profit is only about \$100.Q11. Statistical arbitrage in prediction markets differs from true arbitrage because:
(a) It requires more capital (b) Individual trades can result in losses; profitability relies on statistical edge over many trades (c) It can only be done within a single platform (d) It is illegal in most jurisdictions
Answer
**(b) Individual trades can result in losses; profitability relies on statistical edge over many trades** Statistical arbitrage exploits statistical relationships (such as mean-reverting spreads between correlated markets) to generate expected profits. Unlike true arbitrage, there is no guarantee on any individual trade. The edge materializes over many trades, making it a portfolio strategy rather than a single-trade guarantee.Q12. When executing a cross-platform arbitrage, which leg should you execute first?
(a) Always the YES leg (b) Always the cheaper leg (c) The less liquid leg (harder to fill) (d) It does not matter; both should be simultaneous
Answer
**(c) The less liquid leg (harder to fill)** Best practice is to execute the less liquid leg first. If the less liquid leg fails to fill, you have not committed any capital. If you execute the more liquid leg first and the less liquid leg fails, you are stuck with an unhedged directional position. Executing the hard leg first reduces the risk of partial execution.Section 2: True/False
Q13. True or False: If the sum of YES and NO prices on a single binary market is exactly \$1.00, no arbitrage opportunity exists on that market.
Answer
**True.** When YES + NO = \$1.00, buying both costs exactly \$1.00 and pays out exactly \$1.00, yielding zero profit. There is no within-platform arbitrage. However, the individual YES or NO price might still differ from another platform, creating a cross-platform opportunity.Q14. True or False: Cross-platform arbitrage is truly risk-free as long as the math shows a positive profit.
Answer
**False.** Cross-platform arbitrage carries multiple risks even when the mathematics indicate a profit: resolution risk (platforms may resolve the "same" event differently), execution risk (legs may not fill simultaneously), settlement risk (platform insolvency), capital lock-up risk, and regulatory risk. The phrase "risk-free" applies only to the mathematical outcome, not to real-world execution.Q15. True or False: An arbitrage opportunity with a 2% return settling in 10 days has a higher annualized return than a 6% return settling in 200 days.
Answer
**True.** 2% in 10 days: $(1.02)^{365/10} - 1 \approx 106\%$ annualized. 6% in 200 days: $(1.06)^{365/200} - 1 \approx 11.1\%$ annualized. The short-duration trade is dramatically better when annualized, assuming it can be repeated.Q16. True or False: In an AMM-based prediction market, you can always buy at the displayed price regardless of your order size.
Answer
**False.** AMMs adjust prices dynamically based on order flow. The displayed price is for an infinitesimally small trade. As you buy larger quantities, the price moves against you (slippage). Your average fill price will be worse than the displayed price, potentially eliminating an apparent arbitrage opportunity.Q17. True or False: The capital lock-up cost of an arbitrage trade is always less important than the gross profit.
Answer
**False.** The capital lock-up cost can exceed the gross profit, especially for long-dated markets with small profit margins. For example, a \$300 profit on a \$10,000 position locked for 6 months has a lock-up cost of \$400 at an 8% opportunity cost of capital, making the trade a net negative on an economic basis.Q18. True or False: If one platform resolves a market as YES and another platform voids the same market (returning all capital), a cross-platform arbitrageur always at least breaks even.
Answer
**False.** If the arbitrageur bought YES on Platform A (the one that resolves YES) at \$0.55 and bought NO on Platform B (the one that voids) at \$0.40, then: Platform A pays \$1.00 (profit of \$0.45), Platform B refunds \$0.40 (zero profit, zero loss). Net = \$1.00 + \$0.40 - \$0.55 - \$0.40 = \$0.45 -- a profit here. But if the arbitrageur bought YES on the voiding platform and NO on the resolving platform, they would receive a refund on YES and lose their NO bet: Net = \$0.55 (refund) + \$0.00 - \$0.55 - \$0.40 = -\$0.40 -- a loss. The outcome depends on which platform voids and which side you are on.Section 3: Calculation
Show your work for full credit.
Q19. A cross-platform arbitrage opportunity has these parameters:
- Platform A: Buy YES at \$0.52, trading fee 1% of price, settlement fee 0%
- Platform B: Buy NO at \$0.43, trading fee \$0.03/contract, settlement fee 0%
Calculate: (a) Total cost per pair. (b) Net profit if YES wins. (c) Net profit if NO wins. (d) Guaranteed profit per pair.
Answer
**(a)** Cost for YES on A = \$0.52 x 1.01 + \$0.00 = \$0.5252. Cost for NO on B = \$0.43 + \$0.03 = \$0.46. Total cost per pair = \$0.5252 + \$0.46 = **\$0.9852**. **(b)** If YES wins: Payout from A = \$1.00 (no settlement fee). Net = \$1.00 - \$0.9852 = **\$0.0148**. **(c)** If NO wins: Payout from B = \$1.00 (no settlement fee). Net = \$1.00 - \$0.9852 = **\$0.0148**. **(d)** Guaranteed profit = min(\$0.0148, \$0.0148) = **\$0.0148 per pair** (about 1.50% return). Note: Because neither platform charges a settlement fee, the net profit is the same regardless of which side wins.Q20. You identify an arbitrage: buy YES on Platform A at \$0.60, buy NO on Platform B at \$0.35. Platform A: no fees. Platform B: 10% settlement fee on profits, 5% withdrawal fee.
(a) Net profit if YES wins. (b) Net profit if NO wins (before withdrawal fees). (c) Account for the 5% withdrawal fee on the profit you withdraw from Platform B (assume you only withdraw profit, not principal, from B when B wins). What is the final net profit if NO wins? (d) Is this a valid arbitrage?
Answer
**(a)** If YES wins: Payout from A = \$1.00. Loss on B = \$0.35. Net = \$1.00 - \$0.60 - \$0.35 = **\$0.05**. **(b)** If NO wins: Payout from B = \$1.00. Settlement fee on B = 10% x (\$1.00 - \$0.35) = 10% x \$0.65 = \$0.065. Net before withdrawal = \$1.00 - \$0.065 - \$0.60 - \$0.35 = **-\$0.015** (a loss!). **(c)** Since the pre-withdrawal result is already negative, the withdrawal fee makes it worse. But even if it were positive, the withdrawal fee would apply: the withdrawal fee would be 5% of the profit being withdrawn. With a -\$0.015 net, there is no profit to withdraw. **(d)** **No, this is not a valid arbitrage.** The guaranteed profit is min(\$0.05, -\$0.015) = -\$0.015. The settlement and withdrawal fees on Platform B destroy the arbitrage when NO wins.Q21. An arbitrage yields \$0.04 per pair on a \$0.96 cost per pair. The market settles in 21 days.
(a) What is the simple ROI? (b) What is the annualized return? (c) If you can repeat this trade every 21 days for a full year (approximately 17.4 times), what is your total return on the capital?
Answer
**(a)** ROI = \$0.04 / \$0.96 = **4.17%**. **(b)** $R_{annual} = (1 + 0.0417)^{365/21} - 1 = (1.0417)^{17.38} - 1 \approx 1.040 - 1 = **104.0%**$ (approximately; the exact value is $(1.0417)^{17.38} - 1 \approx 1.04$, meaning a 104% annualized return). More precisely: $\ln(1.0417) \times 17.38 = 0.04082 \times 17.38 = 0.7095$. $e^{0.7095} - 1 = 1.033$, so approximately **103%** annualized. **(c)** If repeated 17.4 times: $(1.0417)^{17.4} - 1 \approx 103\%$. You would approximately double your capital in a year by reinvesting, or earn about 17.4 x 4.17% = 72.5% without compounding.Q22. A 6-outcome market has these ask prices: [0.32, 0.24, 0.16, 0.11, 0.07, 0.04]. The platform charges a 3% settlement fee on profits.
(a) What is the sum of all ask prices? (b) What is the gross arbitrage profit? (c) What is the worst-case net profit? (Identify which outcome winning creates the worst case.) (d) What is the return percentage?
Answer
**(a)** Sum = 0.32 + 0.24 + 0.16 + 0.11 + 0.07 + 0.04 = **0.94**. **(b)** Gross profit = 1.00 - 0.94 = **\$0.06**. **(c)** The worst case is when the **cheapest** outcome (0.04) wins, because the winning profit is largest (1.00 - 0.04 = 0.96), and the settlement fee is 3% of 0.96 = 0.0288. Net = 0.06 - 0.0288 = **\$0.0312**. Wait -- actually, we need to reconsider. The fee is on the profit of the winning contract only. When the cheapest outcome wins: profit = 1.00 - 0.04 = 0.96, fee = 0.03 x 0.96 = 0.0288. Total paid out = 1.00 - 0.0288 = 0.9712. Net = 0.9712 - 0.94 = 0.0312. When the most expensive outcome wins: profit = 1.00 - 0.32 = 0.68, fee = 0.03 x 0.68 = 0.0204. Payout = 0.9796. Net = 0.9796 - 0.94 = 0.0396. The worst case is indeed when the cheapest outcome wins: **\$0.0312**. **(d)** Return = 0.0312 / 0.94 = **3.32%**.Section 3: Short Answer
Q23. Explain why starting with the less liquid leg is recommended when executing a cross-platform arbitrage. What happens if you start with the more liquid leg and the less liquid leg fails?
Answer
When executing a two-leg arbitrage, there is always a risk that the second leg fails to fill at the expected price (or at all). If you start with the more liquid leg, it fills easily, committing your capital. Then if the less liquid leg fails -- because of insufficient depth, price movement, or platform issues -- you are left with an unhedged directional bet. By starting with the less liquid leg first, if it fails to fill, you have not committed any capital on the first leg, and you can simply walk away with no loss. If the less liquid leg does fill, you then execute the more liquid leg, which has a higher probability of filling quickly and at the expected price. The worst-case outcome of starting with the liquid leg is an unwanted directional position. The worst-case outcome of starting with the illiquid leg is a missed opportunity (no trade). The latter is strictly preferable.Q24. A fellow trader claims they found a "risk-free" cross-platform arbitrage yielding 8% between Polymarket and a new, unregulated offshore prediction market. List at least four specific risks they may be underestimating, and explain each in one sentence.
Answer
1. **Platform insolvency/fraud risk**: An unregulated offshore platform may not have the financial reserves to pay out winning contracts, or it may disappear entirely with user funds. 2. **Resolution risk**: The offshore platform may have vaguely defined or unilaterally changeable resolution criteria, meaning they could resolve the market differently than Polymarket or simply void it. 3. **Withdrawal risk**: Even if the market resolves in your favor, the platform may delay or deny withdrawals, impose unexpected fees, or have insufficient liquidity to process withdrawals. 4. **Regulatory/legal risk**: Trading on an unregulated offshore platform may violate local gambling or securities laws, exposing the trader to legal liability regardless of the trade's profitability. 5. **Counterparty risk**: Without regulation, there is no deposit insurance, no segregated accounts, and no recourse if the platform acts in bad faith. 6. **KYC/AML risk**: The trader may face complications if they need to explain the source of funds from an unregulated platform to their bank or tax authority.Q25. Describe the difference between temporal arbitrage and cross-platform arbitrage. Why is temporal arbitrage generally considered quasi-arbitrage rather than true arbitrage? Under what conditions could temporal arbitrage approach true arbitrage?