Research Pricing
What a two-cent spread pays for
The gap between our bid and our offer on a binary contract pays for specific risks and costs. This note explains each one, shows why the same width carries different risk at different prices, and works through a simple example.
A binary event contract pays $1 if the event happens and nothing if it does not, so its price in cents reads as a probability. Suppose our estimate of fair value for a contract is 62¢,1 and we quote 61¢ bid and 63¢ offered. The two cents between those prices pays for the risks and costs of standing ready to trade in both directions. This note explains how we think about each of them. It describes our own approach to pricing and is not a description of any specific market.
What the spread compensates
The first thing is immediacy. A trader who wants a position now, without waiting for someone with the opposite view to show up, is using a service. We provide it by keeping a price on both sides. The half-spread, one cent in this example, is what that trader pays for not having to wait.
The second is adverse selection. Many people who trade with us have no particular edge over our estimate. Some do. Someone who has read a release a few seconds before we have, or who simply has a better model of the event, will trade with us mainly when our price is wrong in their favor. We cannot tell those traders apart from everyone else in advance, so the spread has to be wide enough that what we earn from ordinary flow covers what we lose to informed flow. This risk is uneven over time. It peaks right after news, when fair value has moved and our quote may not have caught up.
The third is inventory risk. Every trade leaves us holding something until we can offset it. If we sell YES at 63¢, we are short a contract that will settle at 0 or 100. Fair value can drift while we hold it, and at resolution it jumps all the way to one edge. Sometimes we can lay the position off cheaply. Sometimes we cannot, and we carry it to the end.
The fourth is cost: trading fees, market data, the systems that run the quotes, and capital held as collateral against open positions. Per contract these are small. A spread that fails to cover them still loses money on a day when nothing else goes wrong.
Same width, different risk
Write the price as a fraction, p. The contract pays 1 with probability p and 0 otherwise. Its expected payoff is p, and the variance of that payoff is p(1 − p).2 That quantity is largest at 50¢ and falls toward the edges.
| Price | p(1 − p) | Standard deviation of payoff |
|---|---|---|
| 50¢ | 0.250 | 50.0¢ |
| 62¢ | 0.236 | 48.5¢ |
| 80¢ | 0.160 | 40.0¢ |
| 90¢ | 0.090 | 30.0¢ |
| 97¢ | 0.029 | 17.1¢ |
A two-cent spread at 50¢ is two cents set against the most uncertain payoff a binary contract can have. At 90¢ the same two cents is set against a payoff whose standard deviation is three-fifths as large. Measured against the risk, a fixed width is generous near the edges and thin in the middle, which is why we do not use one width at every price.
Variance is not the whole picture near the edges, because the outcomes there are lopsided. Someone who buys YES at 95¢ gains 5¢ most of the time and loses 95¢ when the unlikely outcome arrives. A market maker who ends up long at that price holds a small, likely gain and a large, unlikely loss. The informed trader we worry about at those prices is the one who knows the unlikely outcome has already happened. So near the edges we look at the size of the loss in the bad outcome as well as the variance when we set width and size.
A worked example
The numbers here are hypothetical and chosen to be easy to follow. Fair value is 62¢. We quote 61¢ bid and 63¢ offered, 100 contracts on each side.
On an ordinary stretch, one trader buys 100 contracts from us at 63¢ and another, later, sells us 100 at 61¢. We end flat, having sold at 63¢ and bought at 61¢, and keep 2¢ × 100 = $2.00. That is the spread doing its job.
Now change one thing. Just before a release, a buyer lifts our offer for 100 contracts at 63¢.3 A few seconds later the news moves fair value to 70¢. We are short 100 contracts at 63¢ that are now worth 70¢, a marked loss of 7¢ × 100 = $7.00. Nothing is locked in until resolution, but the expected result is the same. At resolution this short ends at +63¢ per contract if the event does not happen and −37¢ if it does. At a 70% probability, that averages 0.30 × 63¢ − 0.70 × 37¢ = −7¢ per contract, the same loss the mark shows.
Earning back $7.00 at one cent per contract takes 700 contracts traded with counterparties who know no more than we do. One informed trade of 100 contracts erased the edge on seven ordinary trades of the same size. That ratio is what the width has to account for.
Suppose instead the release was on the calendar and we had widened ahead of it to 59¢ bid, 67¢ offered, with 50 contracts a side. The same buyer could have bought at most 50 contracts at 67¢. The marked loss would have been 3¢ × 50 = $1.50.
Scheduled news, and staying in the market
Some information arrives on a timetable: a monthly inflation release, a temperature reading at a fixed hour, the first results in an election count. Ahead of these, we know fair value is about to move a long way in a short time, and that the traders most eager to deal in the minutes around the release are the ones most likely to know something. So we widen and cut size, and for a short window around the release itself we sometimes step back completely. That is pricing a known risk honestly.
What we try to avoid is the opposite habit: a very tight quote in quiet periods that disappears at the first sign of movement. From a venue’s point of view, that quote looks good in a report of average spreads and offers nothing at the moment traders most need a price. A slightly wider quote that stays up through the news, at reduced size if necessary, gives people something they can actually trade against when it matters. When we do step back for a release, we want the gap to be brief and predictable, and we want the quote back as soon as our estimate has absorbed the new information.
Given the choice, we would rather quote three cents wide and be there than one cent wide and gone.
Footnotes
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Fair value here means our own estimate of the probability that the event happens, written in cents. ↩
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For a payoff X that equals 1 with probability p and 0 otherwise, E[X²] = p, so the variance is E[X²] − (E[X])² = p − p² = p(1 − p). The standard deviation is the square root of that, shown in cents in the table. ↩
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“Lifting the offer” means buying at our asking price. A marked loss is measured at current fair value, before the contract resolves. ↩