Chapter 10 Quiz
Test your understanding of bid-ask spreads, transaction costs, and fee structures in prediction markets. Try to answer each question before revealing the answer.
Question 1
A prediction market shows Bid = $0.60, Ask = $0.64. What is the quoted spread, the midpoint, and the relative spread?
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**Quoted spread** = $0.64 - $0.60 = $0.04 **Midpoint** = ($0.64 + $0.60) / 2 = $0.62 **Relative spread** = $0.04 / $0.62 = 6.45%Question 2
Name the three fundamental reasons why bid-ask spreads exist.
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1. **Adverse selection cost** — the risk of trading against better-informed counterparties 2. **Inventory risk** — the risk of accumulating a directional position that moves against you 3. **Order processing costs** — the operational costs of providing liquidity (technology, capital, time)Question 3
A trader buys 100 contracts at $0.57 when the midpoint is $0.54. What is the effective spread?
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$S_{\text{effective}} = 2 \times |P_{\text{trade}} - M| = 2 \times |0.57 - 0.54| = 2 \times 0.03 = 0.06$ The effective spread is $0.06 (6 cents). This is wider than the quoted spread would suggest because the trade executed above the ask (likely due to walking through the order book).Question 4
What is the difference between the effective spread and the realized spread? What does the gap between them measure?
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The **effective spread** measures the cost to the trader at the time of the trade: $S_{\text{eff}} = 2|P_{\text{trade}} - M_t|$. The **realized spread** measures the market maker's actual profit after some time interval: $S_{\text{real}} = 2 \times D \times (P_{\text{trade}} - M_{t+\tau})$, where $D$ indicates direction. The gap between them measures the **adverse selection component**: $\text{AS} = S_{\text{eff}} - S_{\text{real}}$. This represents the portion of the spread that compensates for trading against informed counterparties, which the market maker ultimately loses as the price adjusts.Question 5
On Kalshi, the taker fee is min($0.01, price/15) per contract. For a contract priced at $0.12, what is the taker fee?
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$\text{Fee} = \min(0.01, 0.12/15) = \min(0.01, 0.008) = 0.008$ The taker fee is $0.008 per contract. The 1/15th rule kicks in for cheap contracts (below $0.15), reducing the fee proportionally.Question 6
Why is PredictIt's fee structure (10% profit fee + 5% withdrawal fee) particularly punishing for trades on high-probability events?
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For a high-probability event (say, priced at $0.90): - If you buy at $0.90 and win, your profit is only $0.10 per contract - The 10% profit fee takes $0.01 from that $0.10 profit - The 5% withdrawal fee takes another chunk from your total withdrawal - But if you lose, you lose the entire $0.90 The fee as a percentage of potential profit is very high (10% + withdrawal fee), while the downside is large ($0.90). Your maximum upside after fees is roughly $0.10 × 0.90 × 0.95 ≈ $0.085, but your downside is $0.90. This extreme asymmetry means you need the true probability to be very close to 1.0 to justify the trade.Question 7
What is the breakeven probability for buying a "Yes" contract at $0.55 with total costs of $0.03 per contract?
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$p_{\text{breakeven}} = P_{\text{ask}} + C = 0.55 + 0.03 = 0.58$ You need the true probability to be at least 58% for this trade to have positive expected value. Since the ask is $0.55, you need at least 3 cents of edge above the ask price (or equivalently, more than 3 cents above the midpoint if the midpoint is close to the ask).Question 8
In a three-outcome market, the ask prices are $0.45, $0.35, and $0.25. What is the overround? What does it represent?
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$\text{Overround} = 0.45 + 0.35 + 0.25 - 1.00 = 0.05 = 5\%$ The overround represents the guaranteed loss to a trader who buys all outcomes at ask prices. They would pay $1.05 for a basket that will pay exactly $1.00 — a 4.76% loss ($0.05/$1.05). It is the aggregate "tax" extracted by the market from participants through the bid-ask spread.Question 9
Using proportional normalization, convert the ask prices from Question 8 ($0.45, $0.35, $0.25) to implied true probabilities.
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Sum of prices = $1.05 - $\hat{p}_1 = 0.45 / 1.05 = 0.4286$ (42.86%) - $\hat{p}_2 = 0.35 / 1.05 = 0.3333$ (33.33%) - $\hat{p}_3 = 0.25 / 1.05 = 0.2381$ (23.81%) Sum = $1.0000$ Proportional normalization assumes the overround is distributed evenly across outcomes relative to their prices.Question 10
For a binary Yes/No market, prove that the overround equals the bid-ask spread.
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In a binary market: - Yes Ask = $P_{\text{ask}}$ - No Ask = $1 - P_{\text{bid}}$ (the ask for "No" is 1 minus the bid for "Yes") $\text{Overround} = P_{\text{ask}} + (1 - P_{\text{bid}}) - 1 = P_{\text{ask}} - P_{\text{bid}} = S$ The overround equals exactly the bid-ask spread on the "Yes" contract. This is a clean result unique to binary markets.Question 11
The square-root impact model states $\Delta P = \alpha \sigma \sqrt{Q/V}$. If you double your order size, by what factor does the price impact increase? By what factor does the total impact cost ($\Delta P \times Q$) increase?
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If $Q \to 2Q$: **Price impact**: $\Delta P' = \alpha \sigma \sqrt{2Q/V} = \sqrt{2} \cdot \alpha \sigma \sqrt{Q/V} = \sqrt{2} \cdot \Delta P$ The price impact increases by a factor of $\sqrt{2} \approx 1.414$. **Total impact cost**: $\text{Cost}' = \Delta P' \times 2Q = \sqrt{2} \cdot \Delta P \times 2Q = 2\sqrt{2} \cdot (\Delta P \times Q)$ The total impact cost increases by a factor of $2\sqrt{2} \approx 2.83$. This sub-linear scaling of impact (but super-linear scaling of total cost) is why splitting large orders reduces overall cost.Question 12
What is a TWAP execution strategy? When is it appropriate for prediction markets?
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**TWAP** (Time-Weighted Average Price) divides a large order into $N$ equal slices executed at equal time intervals. For example, a 1,000-contract order split into 10 pieces of 100 contracts each, executed every hour. It is appropriate when: - Your order is large relative to daily volume (>10% participation rate) - Your edge is persistent (will not decay quickly) - You want to minimize market impact - You do not need the full position immediately It is **not** appropriate when: - You are trading on time-sensitive information (edge decays quickly) - The market is trending against you (you accumulate at worse prices each slice) - Your trading pattern is predictable and could be front-runQuestion 13
Why do prediction market spreads differ from equity market spreads? Name at least three structural differences.
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1. **Bounded payoffs**: Prediction market contracts pay $0 or $1, limiting the range of possible prices and affecting how market makers manage risk near the boundaries. 2. **Terminal date**: All prediction market contracts have a resolution date, unlike stocks. This affects how spreads evolve over time and eliminates perpetual inventory risk. 3. **Width**: Prediction market spreads (1-10%) are typically much wider than liquid equity spreads (<0.01%), reflecting higher adverse selection and lower competition among market makers. 4. **No regulation against informed trading**: Anyone can trade on private information in prediction markets, increasing adverse selection costs for market makers. 5. **Fewer professional market makers**: Equity markets have dozens of competing market makers; prediction markets may have only a handful, reducing competitive pressure to narrow spreads. 6. **Tick size relative to price**: A $0.01 tick on a $0.50 prediction contract is 2% of the price, much larger in relative terms than a $0.01 tick on a $100 stock (0.01%).Question 14
You place a limit order to buy at $0.52 in a market with midpoint $0.53 and ask $0.55. What are the advantages and disadvantages compared to a market order at $0.55?
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**Advantages of the limit order:** - Save 3 cents per contract ($0.55 - $0.52) - Earn the spread instead of paying it - May qualify for maker rebates (zero or negative fees) - Avoid slippage — you get exactly your price **Disadvantages of the limit order:** - **Execution risk**: The order may never fill (price may move up without coming back to $0.52) - **Adverse selection**: If the order fills, it may be because the price is falling through $0.52, meaning you are catching a falling knife - **Opportunity cost**: While waiting for the fill, the price may move to $0.60 and you miss the entire opportunity - **Partial fills**: You may get only some contracts filled - **Information leakage**: Your resting order is visible and could attract front-runningQuestion 15
In the Glosten-Milgrom model, what happens to the spread as the fraction of informed traders ($\pi$) approaches 1?
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As $\pi \to 1$, the spread approaches the maximum possible range: - The ask approaches $V_H$ (the high value, which is 1 for a prediction market) - The bid approaches $V_L$ (the low value, which is 0 for a prediction market) - The spread approaches $V_H - V_L = 1$ In the limit where all traders are informed, the market maker faces guaranteed adverse selection on every trade and would need to set the ask at 1 and bid at 0 — effectively shutting down the market. No trade can occur because the market maker will always lose. In practice, markets with very high informed trading fractions have extremely wide spreads and very low liquidity, approaching this theoretical limit.Question 16
What is the difference between slippage and market impact?
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**Slippage** is the difference between the expected execution price and the actual execution price. It includes all sources of price deterioration: - Walking through the order book (consuming multiple price levels) - Price movement between decision time and execution time - Other orders arriving ahead of yours **Market impact** is specifically the price change *caused by your order*. It has two parts: - **Temporary impact**: The short-term price displacement from consuming order book liquidity (partially reverses) - **Permanent impact**: The lasting price change from the information signal your trade sends Market impact is a *subset* of slippage. Slippage can also include price changes from other traders' activity or news, which are not caused by your order. All market impact creates slippage, but not all slippage is market impact.Question 17
A market maker posts Bid $0.47, Ask $0.53 in a market where 30% of order flow is from informed traders and the true probability is 0.55. Is the market maker profitable? Explain.
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The market maker's spread is 6 cents. The midpoint ($0.50) is 5 cents below the true probability ($0.55). **Revenue per round trip**: $0.06 (spread) on uninformed flow. **Adverse selection loss**: When an informed buyer trades at $0.53, the true value is $0.55, so the market maker loses $0.02 on each informed buy. When an informed seller trades at $0.47, the true value is $0.55, so the market maker gains $0.08 on each informed sell. But informed traders will mostly buy (since price < true value), so informed sells are rare. More precisely: Informed traders buy at $0.53 when the event will happen (prob 0.55) and sell at $0.47 when it will not (prob 0.45). The market maker's expected loss on informed flow: - Informed buys: 0.55 × (1.00 - 0.53) = 0.55 × 0.47 = $0.2585 expected payout vs $0.53 expected value → actually, the loss per informed buy is $(0.55 - 0.53) = 0.02$ in expectation (the true value is 0.55 but they paid 0.53, so the market maker sold something worth 0.55 for 0.53). Wait — the correct analysis: the market maker sells at 0.53 and the contract is worth 0.55, so they lose $0.02 per informed buy. Informed traders sell at 0.47 and the contract is worth 0.55, so the market maker buys at 0.47 something worth 0.55 — gaining $0.08 per informed sell. But informed traders buy more than sell when the true probability exceeds 0.50. The profitability depends on the exact proportions and is not straightforward to determine without knowing the full distribution of informed vs uninformed flow. However, with a 6-cent spread and the midpoint only 5 cents away from the true value, the market maker has a reasonable chance of profitability, especially with 70% uninformed flow earning the full 6-cent spread.Question 18
You have identified a trade with 4 cents of edge (true probability is 4 cents above the ask price). The half-spread is 1.5 cents, taker fee is 1 cent, and gas fee is 0.5 cents. Should you take the trade?
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Total cost = half-spread + taker fee + gas fee = 1.5 + 1.0 + 0.5 = **3.0 cents** Edge = 4.0 cents Net edge after costs = 4.0 - 3.0 = **1.0 cents** The trade has positive expected value after costs, so **yes, you should take it**. However, with only 1 cent of net edge, you should: - Size the position conservatively (1 cent of net edge has a low Sharpe ratio) - Try to use a limit order to save the 1.5 cents of spread cost - Consider whether your edge estimate has enough precision to be confident in a 4-cent advantage A good rule of thumb is to require net edge to be at least 1.5x the cost, which here would need 4.5 cents of edge. The trade is marginal.Question 19
On a platform with 0% maker fees and 1% taker fees, you plan to provide liquidity by posting limit orders. Your fill rate is 40% per day. What is the expected daily cost savings compared to using market orders, if you would otherwise make 10 trades per day at $0.50 per contract (100 contracts each)?
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**Market order cost (taker)**: 10 trades × 100 contracts × $0.50 × 1% = $5.00 per day **Limit order cost (maker)**: 0% fee, but only 40% fill rate. - Expected fills: 10 × 40% = 4 fills per day (400 contracts) - Fee on fills: $0.00 - But you still need the other 600 contracts. If you eventually use market orders for unfilled quantities: - Additional taker cost: 6 trades × 100 contracts × $0.50 × 1% = $3.00 **Total cost with limit-first strategy**: $0.00 + $3.00 = $3.00 **Daily savings**: $5.00 - $3.00 = **$2.00 per day** This represents a 40% cost reduction. The savings increase as the fill rate improves.Question 20
A prediction market has an AMM (Automated Market Maker) with a constant-product formula ($x \cdot y = k$). The pool has 5,000 "Yes" tokens and 5,000 "No" tokens ($k = 25,000,000$). What is the price impact of buying 500 "Yes" tokens?
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Initial state: $x = 5000$ (Yes), $y = 5000$ (No), $k = 25{,}000{,}000$ Initial price of "Yes" = $\frac{y}{x+y} = \frac{5000}{10000} = 0.50$ After buying 500 "Yes" tokens, the buyer adds "No" tokens to the pool. Using the constant-product formula: - New Yes reserves: $x' = 5000 - 500 = 4500$ (tokens leave the pool) - New No reserves: $y' = k / x' = 25{,}000{,}000 / 4500 = 5555.56$ - Cost: $y' - y = 5555.56 - 5000 = 555.56$ "No" tokens New price of "Yes" = $\frac{5555.56}{4500 + 5555.56} = \frac{5555.56}{10055.56} = 0.5526$ **Price impact**: $0.5526 - 0.5000 = 0.0526$ (5.26 cents) **Average execution price**: $555.56 / 500 = 1.111$ "No" per "Yes", which corresponds to a probability of about $\frac{1.111}{2.111} \approx 0.526$ **Effective spread cost**: $2 \times (0.526 - 0.50) = 0.052$Question 21
Why might a prediction market have wider spreads on election day compared to a week before, even though volume is much higher on election day?
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Several factors contribute to wider spreads on election day despite higher volume: 1. **Higher adverse selection risk**: On election day, some traders may have early information (exit polls, precinct results, leaked data) that has not been publicly released. Market makers face a higher probability of trading against someone with superior information. 2. **Increased volatility**: Prices can move rapidly as results come in. Market makers must widen spreads to compensate for the risk that their quotes become stale before they can update them. 3. **Binary resolution risk**: The event is about to resolve, meaning any position the market maker holds will go to 0 or 1 with no time to unwind. This inventory risk is maximal. 4. **Stale quote risk**: In fast-moving markets, limit orders may be executed against at prices that are already obsolete, causing losses for liquidity providers. 5. **Market maker withdrawal**: Some market makers reduce their activity during high-volatility periods, reducing competition and allowing remaining makers to charge wider spreads. The key insight is that volume and liquidity are not the same thing. High volume can coexist with poor liquidity if the volume is driven by informed traders rather than uninformed flow.Question 22
Calculate the total transaction cost drag on a strategy that makes 200 round-trip trades per year, with an average spread of 3 cents, platform fee of $0.01 per contract per side, and average position size of 50 contracts. Express the result as a total dollar amount and as a percentage of a $50,000 bankroll.
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**Per round-trip trade:** - Spread cost: 3 cents × 50 contracts = $1.50 - Entry fee: $0.01 × 50 = $0.50 - Exit fee: $0.01 × 50 = $0.50 - Total per trade: $1.50 + $0.50 + $0.50 = **$2.50** **Annual cost:** - 200 trades × $2.50 = **$500 per year** **As percentage of bankroll:** - $500 / $50,000 = **1.0%** This 1% annual drag from transaction costs means the strategy needs to generate at least 1% return just to break even. For a strategy with, say, 10% expected annual return, costs consume 10% of the profits. For a strategy with 3% expected return, costs consume 33% of profits.Question 23
Explain the "maker rebate strategy" and under what conditions it is profitable.
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The **maker rebate strategy** involves deliberately placing limit orders (maker orders) rather than market orders, specifically to earn the maker rebate (or avoid the taker fee) offered by some platforms. **How it works:** 1. Identify a market where you want to trade 2. Instead of crossing the spread with a market order, place a limit order at or near the bid (for buys) or ask (for sells) 3. Wait for natural order flow to fill your order 4. Earn the maker rebate (e.g., $0.002 per contract on some platforms) while paying zero taker fee **Conditions for profitability:** 1. **Sufficient fill rate**: Your limit orders must fill often enough to actually execute your strategy. A 0% fill rate means zero maker rebates. 2. **Low adverse selection**: If your limit orders consistently fill only when the price is moving against you (informed traders picking you off), the rebate will not cover your losses. 3. **Patient capital**: You must not be in a rush to trade; urgency means switching to taker orders and losing the rebate. 4. **Two-way flow**: The market needs organic order flow on both sides; in a one-directional market, your limit orders on the opposite side will rarely fill. 5. **Edge is persistent**: If your informational edge decays quickly, the time spent waiting for fills may cost more than the rebate saves. The strategy is essentially a mild form of market making, except you only post orders on one side based on your directional view.Question 24
In the context of prediction markets, what is a "liquidity cliff" and why is it dangerous for large traders?
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A **liquidity cliff** is a point in the order book where available liquidity drops sharply, causing the marginal cost of additional contracts to spike dramatically. For example: - 200 contracts available at $0.55 (good liquidity) - 50 contracts available at $0.56 - 10 contracts available at $0.60 (liquidity cliff) - 5 contracts available at $0.70 A trader buying 260 contracts would get the first 250 at reasonable prices ($0.55 - $0.56) but the last 10 at $0.60 — a 4-cent jump. **Why it is dangerous:** 1. **Surprise costs**: The average execution price degrades non-linearly, and the last contracts can be extremely expensive. 2. **Information leakage**: After consuming the cheap levels, the price jumps to the cliff level, signaling to the market that a large buyer is active. 3. **Partial fill dilemma**: You may decide to stop at the cliff, leaving you with an incomplete position. 4. **Market impact magnification**: The cliff means your order creates a disproportionately large price impact per contract at the margin. Large traders should always examine the full depth of the order book before trading, not just the best bid/ask. They should set maximum execution prices ("limit" on their "market" orders) and plan to split orders to avoid cliffs.Question 25
True or False (with explanation): "On a platform with zero trading fees (like Polymarket), transaction costs are zero."