LZLZL/Prediction markets/Market making
FREEDO IT B · RebatesReal cost

Pair rate and naked legs
tenor decides everything

2026-08-21 · including a self-falsification: my own estimate was 2.1× too high

A maker quotes both sides and accumulates inventory. What pairs into sets is safe — merge it and the spread is locked. What does not pair carries all the risk. So the metric that matters is not spread, it is pair rate — and pair rate is set almost entirely by tenor.

1Two kinds of inventory, two fates

Paired into a setNaked leg
Worthexactly $1, regardless of outcomeeither $1 or $0
Realising itmerge at any timewait for settlement, or sell at market
Risknone — price movement is irrelevantall of the directional risk
You earnthe two legs' prices summed, minus $1

Which explains something counter-intuitive: the higher your pair rate, the less your fill prices matter. A completed set is $1 whatever the market does. Conversely, at a low pair rate you are not really market making — you are taking directional positions.

2Tenor sets pair rate

Simple reason: the longer you hold, the more chances the other leg has to arrive. Truncating one real market-making wallet's flow to different holding windows:

Holding windowPair rateNaked exposure
5 minutes47.0%53.0%
15 minutes70.9%29.1%
30 minutes87.4%12.6%
60 minutes95.4%4.6%

From five minutes to an hour, naked exposure falls from over half to under 5%. That is what "tenor decides everything" means — same approach, same person, different business.

3What a naked share costs

−$111.51 ÷ 825 shares = −13.5¢ per share against a maker rebate of about +0.25¢/share

Fifty-four times. One unpaired share in every 54 fills wipes out the rebate entirely — and on five-minute boards more than half go unpaired.

4★ But that pair-rate table is itself overstated

This is the part of the entry worth keeping, because it overturns the part above.

Those numbers came from truncated replay: take an hourly wallet's real flow, pretend it were a five- or fifteen-minute holding window, recompute. That is an approximation — and it assumes short-tenor flow looks like long-tenor flow, which it does not.

Later I ran a full replay against recorded real books plus complete tape:

TenorTruncated replay saidFull simulationOverstated by
5 minutes47.0%36.3%1.3×
15 minutes70.9%33.6%2.1×
1 hour95.4%54.9%1.7×
⚠ The lesson: state the direction of an approximation's bias, in advance

Fifteen minutes had been "undecided" — 70.9% looked high enough to be worth trying. The full simulation returned 33.6%, worse than five minutes. Killed outright.

The problem is not that the approximation was inaccurate — approximations are. It is that I had not decided in advance which way it would err. Thinking through "does simulating short tenors from long-tenor flow overstate or understate pairing" would have marked 70.9% as an optimistic upper bound, unusable for a decision.

This is now a house rule: every replay and approximation states its bias direction. Method in replays must state their bias.

5And the "positive" hour is fake too

In the full simulation the hourly row looks positive (+4.31¢/share of trading return). Broken out: one board out of six contributed +$667; the other five had a median of −$19.

the P&L is driven by settlement luck, not spread capture static laddering lost money on the typical board at every tenor tested

A common trap: small sample plus fat tail means the mean is meaningless. When you see a set of backtest results, ask for the median first, then ask what is left after removing the single best case.

6Practical conclusions

ConclusionNote
Pair rate is the first metricit tells you whether you are making markets or taking direction
Tenor is its main drivernot quoting technique — tenor
Static laddering loses on short tenors5m and 15m both ruled out
Discount any modelled pair ratemeasured overstatement of 1.3× to 2.1×
Read medians, not meansone lucky board can carry an entire set of results

7One line to keep

Paired inventory does not care what the price does; the unpaired part carries everything. So what a maker is really betting on is not the spread — it is whether the other leg shows up. And that is decided mostly by tenor, not by how well you quote.

EvidenceCheck it yourself

Truncated replay real flow re-cut to holding windows: 5m 47.0% / 15m 70.9% / 30m 87.4% / 60m 95.4%. An approximation, biased optimistic.
Full simulation recorded real books plus complete tape, conservative queue assumptions: 5m 36.3% (60 boards) / 15m 33.6% (24) / 1h 54.9% (6).
Naked-leg cost −$111.51 ÷ 825 shares = −13.5¢/share against a +0.25¢/share rebate; ratio 54.
The hour is a lottery one of six boards contributed +$667; the remaining five had a median of −$19.
Bias direction every replay figure here is labelled conservative or optimistic. House rule.
Checked 2026-07 to 2026-08.
Not included my own wallet addresses, hosts, or any strategy parameters.

NextWhere to go

B · REBATES
Where naked legs come from
A · MECHANICS
Merge: realising matched inventory early
B · REBATES
Queue position and conservative assumptions
F · METHOD
Replays must state their bias
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