Capacity & alpha decay

Every edge has a capital ceiling: trade more and impact eats the alpha; stay public and crowding erodes it. Capacity is why a small book can hold an edge a large one cannot.

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What is strategy capacity?

Capacity is the amount of capital a strategy can run before its own market impact eats its edge. As you trade larger, gross edge per unit stays roughly constant but impact cost per unit rises (the square-root law), so net edge per unit falls and eventually goes negative. Capacity is the size at which deploying more capital stops adding net profit.

A small order glides into the book unnoticed and captures the full edge. Double the size and the cost is more than double-noticeable: you consume depth, move the price against yourself, and signal your intent. The edge per unit shrinks with size. Capacity is simply the point where shrinking edge meets rising impact and the next pound you deploy earns nothing net. The mechanism is market impact, priced by the square-root law: impact per trade scales as $Y\,\sigma\,\sqrt{Q/V}$, where $Q$ is order size, $V$ daily volume, $\sigma$ volatility and $Y$ a calibrated constant from estimating impact.

Use the curve above: gross edge per unit is flat, impact cost per unit rises with $\sqrt{Q}$, and the resulting net edge starts positive, peaks and crosses zero at the ceiling. But the size you should actually run is below the break-even ceiling, because total net P&L is $gQ - cQ^{3/2}$, which is maximised at a smaller size than where the per-unit edge hits zero. Slide the capital control past the ceiling and the region beyond turns negative: every extra pound there destroys money.

Why won't a profitable backtest scale?

Because a backtest runs at infinitesimal size against historical prices it cannot move. It assumes you get filled at the recorded price for any size, but at real scale your orders consume depth and move the market, a cost the backtest never charged. The edge is real at the backtest's size and gone at deployable size.

Most backtests fill at the historical mid or touch as if your order had no effect. That is true for one lot and false for a meaningful book. The backtest's P&L is the capacity-zero edge (the edge in the limit of infinitely small size), which is the best the strategy will ever look and not the size you would run. There are two scaling failures, in order of how often they kill a strategy. First, impact (the capacity ceiling): as size rises, the square-root-law cost eats the edge, and a signal worth +3 bps per trade at one lot can be worth −1 bps at the size you need to make it a business. Second, liquidity availability: beyond impact on price, there may simply not be enough volume to trade your target size. You cannot deploy £200m into a market that trades £50m a day at any price you would accept.

The honest reframing of this whole guide: a backtest measures the capacity-zero, pre-crowding, in-sample edge, three optimistic conditions at once. Capacity corrects the first, decay corrects the second, and honest backtesting and simulation corrects the third. The headline number is the strategy at its most flattering. Drag the capital slider above from backtest size up toward and past the ceiling, and watch net edge per unit fall through zero: this is what the backtest never showed you.

What is alpha decay and what sets a signal's half-life?

Alpha decay is the erosion of an edge over time as the market adapts, the inefficiency is arbitraged away and competitors crowd in. Every edge has a half-life, the time for its magnitude to fall by half. Decay is driven by crowding (more capital chasing the same trade) and by structural change (the inefficiency being designed out).

An edge exists because of an inefficiency: a predictable pattern, a slow participant, a structural quirk. The moment it pays, it attracts capital, and that capital trades the inefficiency away. An edge is a depleting resource; the only question is how fast it depletes.

What sets the rate? Crowding is the dominant driver: each new participant trading the same signal both competes for the same fills (cutting the per-unit edge) and adds impact that moves the price toward fair value faster (killing the inefficiency). Crowding couples decay to capacity: the more capital in a trade, the lower the edge and the lower the remaining capacity. Structural change (tick-size regimes, fee changes, new order types, regulation, a venue redesign) can extinguish an edge overnight, independent of crowding. And adaptation: counterparties learn, so a signal that exploits a predictable participant fades as that participant randomises or upgrades, increasingly to adaptive/ML execution in 2026. The crowding-decay panel above raises $\lambda$ as competitors enter and visibly shortens the half-life, making "crowding is what kills your edge" tactile.

Why do published alphas die fastest?

Because publication is maximal crowding. The instant a profitable signal is written down (in a paper, a blog, a course) everyone can run it, capital floods the same trade, and the inefficiency is arbitraged away. This is why live alpha is rarely published, and why a strategy you read about is, by construction, already decaying or dead.

A signal's edge is a function of how few people exploit it. Publishing it sets that number to "everyone", the fastest possible crowding event. Several studies of published equity anomalies find their returns roughly halve after publication. The canonical reference is McLean & Pontiff, "Does Academic Research Destroy Stock Return Predictability?" (Journal of Finance, 2016), direct empirical evidence of decay-by-publication.

The corollary every reader needs: the existence of a freely available description of an edge is evidence the edge is weak or gone. The strongest live alphas are precisely the ones not written down. This is not cynicism; it is the logic of a depleting resource. Anyone with a genuine, high-capacity, slow-decaying edge has every incentive to keep it private. What this means for a self-taught quant in 2026, in the honest, non-despairing version: the published canon teaches you the machinery (the models, the microstructure, the cost laws) which does not decay, even as the specific signals in the papers do. Your edge comes from applying that machinery faster, in a less-crowded venue, or with a better cost model than the crowd, not from running a textbook signal verbatim. That is the thesis of going independent in 2026 and the honest answer on is HFT still profitable in 2026.

How do capacity and decay together decide what an edge is worth?

An edge is worth capacity × net-edge × remaining lifetime, not its backtest height. A high edge with tiny capacity is a hobby; a modest edge with large capacity and a long half-life is a business. Capacity caps how much capital it can earn on; decay caps how long; multiply, and most flashy backtests are worth far less than they look.

A backtest reports a high net edge per unit at zero size and is silent on both capital and lifetime. This is the allocation logic of a trading firm and the bridge to the business topic: capital flows to edges with the best product of size and durability, not the highest backtest Sharpe. A 6-Sharpe edge with £200m capacity and a two-year half-life beats a 12-Sharpe edge with £3m capacity and a three-month half-life, every time, which is also why a high Sharpe ratio is fragile to both capacity and decay.

And why a firm is a pipeline, not a strategy: because every edge decays, a firm that stops researching is a firm whose P&L is decaying to zero on a clock. Continuous research to replace decaying alphas is not optional growth; it is survival. This is the engine behind the research-to-production pipeline. Relocate your intuition from the curve's peak to its area: what an edge is worth is the capacity × durability rectangle, not the backtest height.

Worked example

A synthetic short-horizon equity signal, as of 2026; all figures illustrative and reproducible with the curve above. Gross edge is $g = 4$ bps per unit of notional traded, roughly constant with size. Impact cost per unit scales as $c\sqrt{Q}$ with $c$ calibrated so that at £10m deployed the impact cost is 1 bp per unit: that is $c\sqrt{10} = 1 \Rightarrow c = 0.316$ bps per $\sqrt{\pounds\text{m}}$.

The profit-maximising size, from the derivation $Q_{\max} = \tfrac{4}{9}Q^\star$, is about $0.44 \times 160 \approx \pounds 71\text{m}$. Run the book around £70m, not £160m: past £71m each extra pound earns shrinking marginal net edge, and at £160m the marginal pound earns nothing. Total net P&L is $Q(4 - 0.316\sqrt{Q})$ in bps·£m: about 30 at £10m, about 142 (the maximum) at £71m, and 0 at £160m. The backtest at £1m reported +3.94 bps per unit, gorgeous, and a near-total misrepresentation of the £200m book the author imagined deploying into.

Now add decay. Suppose the signal's half-life is 9 months, so $\lambda = \ln 2 / 9 \approx 0.077$ per month, and crowding is accelerating it. After 9 months the 4 bps gross is about 2 bps, which collapses break-even capacity to $Q^\star = (2/0.316)^2 \approx \pounds 40\text{m}$ and profit-maximising size to about £18m. The edge has not just shrunk; its capacity has shrunk with it, because a weaker gross edge is overwhelmed by impact at much smaller size. Capacity and decay compound against you. The honest read: a backtest screaming "+3.94 bps per unit" describes a strategy whose sensible deployable size is about £70m today, about £18m in nine months, and whose lifetime value is a fraction of what the equity-curve height implied. Nothing in the backtest showed the £160m ceiling or the nine-month clock, which is the entire reason this page exists. All figures synthetic.