The Capacity-Sharpe Frontier

Two strategies can have the same backtested Sharpe ratio and be completely different businesses, because Sharpe alone says nothing about how much money can chase it before the edge disappears. The capacity-Sharpe frontier is the curve that plots achievable Sharpe against assets under management, and it's the honest way to compare ideas of very different sizes.

Why Sharpe alone misleads

A small-cap reversal signal might backtest at a Sharpe of 2.5 on $50 million of capital, trading names where the researcher's own orders barely move the price. Push the same strategy to $2 billion and participation limits force it into larger, more liquid, less mispriced names, or force each trade to be spread over more days, both of which erode the edge. The Sharpe at $2 billion might be 0.6 — a completely different, and much less attractive, strategy. Reporting only the small-book Sharpe overstates what the idea is worth to a fund that actually needs to deploy capital at scale.

The frontier is built by re-running the backtest (or a market-impact model) at a series of AUM levels and recording the resulting Sharpe at each. Every real strategy's frontier slopes downward eventually; what differs is how steep the slope is and where the knee — the point past which Sharpe falls off a cliff — sits.

A worked example

Strategy A backtests at a Sharpe of 2.2 on $100 million, but a market-impact model shows Sharpe dropping to 1.0 by $400 million and 0.4 by $800 million — a steep knee. Strategy B backtests at a Sharpe of 1.3 on $100 million but only drops to 1.1 at $800 million — a gradual, nearly flat frontier. A fund with $150 million to allocate should prefer A; a fund needing to deploy $700 million should prefer B even though its small-book Sharpe looked worse on the first slide.