Capacity Estimation for a Trading Strategy

Capacity is the size at which a strategy's own trading erases its edge, and the square root impact law explains why capacity is often far smaller than expected.

Capacity is the maximum amount of capital a strategy can trade before its own market impact erodes the edge that made it profitable in the first place. A strategy can show an excellent Sharpe ratio in a backtest run at a small notional size and still be worthless to a fund that needs to deploy hundreds of millions of dollars, because the backtest never modelled what the strategy's own orders would do to the price at that larger size.

The standard working model for market impact is the square root law, which states that the cost of executing an order scales with the square root of the ratio between order size and average daily volume, not linearly with size. Doubling a position's size does not double the cost of getting into it, it multiplies the cost by roughly 1.4, the square root of 2. Trading four times the original size multiplies impact cost by 2, the square root of 4, rather than by 4.

This relationship means impact cost grows more slowly than size at first, which is exactly why a strategy can look deceptively scalable when tested only at small sizes near the flat, early part of the curve, before the cost curve steepens relative to what a linear extrapolation from a small test would have suggested.

Applying the relationship concretely: if trading a size equal to 1 percent of a stock's average daily volume costs approximately 5 basis points in impact, trading a size equal to 4 percent of average daily volume, four times as large, costs approximately 10 basis points, since the square root of 4 is 2 and 5 basis points times 2 equals 10 basis points. A strategy with a gross edge of 4 basis points per trade, the figure used as a reference case in Transaction Cost Modelling Inside a Backtest, is already unprofitable at that 4 percent size before any commission or spread is even added, which sets the strategy's practical capacity somewhere below that size, not near it.

A signal that predicts price moves well but requires trading a large fraction of a name's average daily volume to express meaningfully is not a strong signal from a capacity standpoint, it is a strong signal with a low ceiling. Signals built from data with limited breadth, such as a relationship that only applies to a handful of large capitalization names, hit their capacity limit faster than signals built from data with wide breadth across thousands of instruments, because breadth is what allows a fund to spread the same total capital across many small, individually low impact trades rather than concentrating it into a few trades that each move the price significantly.