When a counterparty quotes you a price, the price contains two pieces of information about you. The first is your direction — whether you are about to buy or sell. The second is your half-life — how long that direction is worth knowing about before it stops predicting the next tick.
Half-lives differ by orders of magnitude. A latency-arbitrage take on a stale quote contains direction that is worth knowing for milliseconds. A discretionary macro buy on a freshly-released CPI print contains direction that may be worth knowing for hours. A regulated retail broker's residual hedge from yesterday's close contains direction that is worth roughly nothing — by the time the hedge arrives, the underlying retail flow has already moved the market, if it was going to move it at all.
Why this matters for the spread you pay
A liquidity provider's optimal quote is wider for flow with a long half-life and tighter for flow with a short half-life. The reason is mechanical: if your trade predicts the next tick well, the LP needs to hedge it quickly and pays the spread on the hedge; if your trade does not predict the next tick, the LP can warehouse it and pays nothing.
The institutional desks reading this know that this is the central insight behind every serious pricing engine, and that the architecture of a fair spread is largely the architecture of measuring half-lives accurately. The retail-broker version, with a per-customer toxicity score on the wholesale hedge, is the same idea served on the other side of the lens.
Measuring your own half-life
The half-life of a trade is the time it takes for the autocorrelation between its direction and the subsequent mid move to fall below a threshold (we use 1/e, so it is a literal half-life in the radioactive-decay sense). It is straightforward to compute on your own historical fills:
- Tag each parent fill with its direction (+1 buy, -1 sell) and the mid at the moment of the last child fill.
- For each post-fill horizon t from 1ms to 1h on a log scale, compute the mean signed mid-move over your dataset: mean_t = mean over fills of direction_i × (mid_{i,t} − mid_i).
- Plot mean_t against t. The shape is your decay curve. The horizon at which mean_t crosses 1/e of its peak value is your half-life.
- Compute it per strategy, per pair, per time of day. The number is rarely a single constant; usually it is a surface.
What different half-lives look like
Sub-second: latency arb and stale-quote take
If your half-life is under one second, the predictive content of your trade is in the price itself — you are taking quotes that other LPs have not yet refreshed. Every LP pricing you knows this and quotes accordingly. There is no honest way to negotiate this down; the best you can do is route to LPs whose pricing latency is genuinely the source of the alpha you are extracting and accept the wider spread elsewhere.
Seconds to minutes: short-horizon stat-arb
If your half-life is in the seconds-to-minutes range, you are running short-horizon statistical strategies. The LP can hedge during your half-life, so the spread is wider than warehouseable flow but tighter than information-driven flow. Quality of routing matters more here than any other regime, because the children of your parent order need to land before the half-life expires.
Minutes to an hour: discretionary directional
Most macro and event-driven flow lives here. The half-life is long enough that the LP cannot warehouse but short enough that the LP can hedge mechanically. The spread is the cleanest reflection of the LP's actual cost; this is the regime in which a tighter LP genuinely matters.
Hours to days: passive hedging and end-of-day rebalancing
A regulated retail broker hedging its residual book at the end of the European session has, in pricing terms, half-life of approximately zero. The flow does not predict the next tick — it is a clearing exercise. An LP that prices this at the same level as macro discretionary flow is overcharging; an LP that prices it correctly is competing on a basis the broker can actually pay.
That is the entire premise of the B-Book to Wholesale hedging pathway — pricing the residual at its true half-life, not at the worst-case retail aggregate.
The asymmetry trap
The trap that catches sophisticated desks is assuming their half-life is constant. It usually is not. The half-life of the same strategy is shorter on Monday mornings (macro inflection points are more predictive when the market is just-opened) and longer on Friday afternoons (the residual is mostly position closing). A pricing engine that uses a single average will systematically misprice you against the time of day; a counterparty that knows this and exploits it gets the spread asymmetrically.
Drovix's pricing model is conditional on a feature set that includes time-of-week and time-relative-to-known-releases, precisely because the alternative is leaking spread to anyone whose half-life is conditional on those features. The trade-off is that the model is harder to explain in a sales pitch and is worth more in real basis points than the simpler version it replaces.
What to ask of your counterparty
- Will you price me as a single class, or do you build a per-counterparty toxicity profile? If the answer is single-class, you are subsidising the toxic side of the book.
- How quickly does my profile update after a regime change? An LP that recalibrates monthly will misprice you for the first three weeks after your strategy genuinely shifts.
- Do you publish, on request, the rough half-life bucket I am priced in? It is reasonable to refuse the precise number; it is not reasonable to refuse the bucket.
Where to go next
→ Decomposing Execution Cost — the five components your TCA should be reporting, of which adverse selection is the half-life-driven one.
→ Capacity Planning for Execution Strategies — how much you can put through the same strategy before your half-life starts changing on you.
Methodology and data
Toxicity is operationalised as the magnitude of the LP's expected loss conditional on filling a given client cohort, computed as the time-integrated mark-out from fill time out to 5 minutes, divided by the notional traded. Half-life is the exponential-decay parameter on the same path. The framework is fitted across 41 client cohorts on Drovix's aggregated panel over the trailing 12 months, using EUR/USD and USD/JPY fills only.
Limitations and scope
The 5-minute integration window is a compromise: shorter windows over-attribute toxicity to noise, longer windows pick up regime drift unrelated to the original fill. Cohort definitions are imperfect — a single account can span multiple effective cohorts depending on the strategy active that hour. The framework is most useful for steady-state segmentation, not for trading-day-by-trading-day decisions.
Further reading
→ Half-Life of Information in FX Orders — The shorter, sharper companion focused on the half-life parameter. See /blog/half-life-of-information-in-fx-orders.
→ Adverse Selection Premium — How It's Priced — How LPs convert measured toxicity into a quoted-spread premium. See /blog/adverse-selection-premium-how-priced.
Drovix Research is the in-house institutional desk of Drovix MU Ltd, regulated by the Financial Services Commission of Mauritius. All notes are informational only and do not constitute investment advice, a solicitation, or a recommendation to transact in any financial instrument.
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