Capacity & Liquidity: ADV-Based Ceiling

A strategy that backtests beautifully on $100k of capital may be undeployable at $10M. The constraint is liquidity — the average daily volume (ADV) of the holdings limits how much capital can enter and exit a position without moving the market. The Capacity sub-pill estimates an AUM ceiling above which the strategy becomes impractical, using participation-rate and days-to-liquidate assumptions.

The two questions capacity answers

1. How much capital can this strategy deploy? Above this AUM, position sizes exceed sensible ADV participation.
2. How many days to fully liquidate? If forced to exit on a single day, what fraction of each position's ADV would the exit consume?

The participation-rate model

Standard practice (Kissell & Glantz 2003) caps a single-day trade at p% of the security's 20-day average daily volume. Typical p:

• p = 5%: conservative; minimal market impact
• p = 10%: default in FM103; moderate impact, common for institutional execution
• p = 25%: aggressive; meaningful impact, used in liquid large-caps under time pressure

For a position of size $S in a stock with ADV value $V (dollar volume per day), days-to-trade is:

If the strategy permits a max of N days to liquidate (e.g., 5 days), the max position size is:

Aggregating to portfolio capacity

The strategy's capacity ceiling is determined by the smallest-volume holding it requires. For a top-30 portfolio in the S&P 500, capacity is set by the smallest of the 30 names. For a small-cap top-30, capacity drops by an order of magnitude.

FM103 computes per-holding S_max, then takes the weighted aggregate to produce an AUM ceiling: the maximum capital at which every position can be entered and exited within the N-day window at the p% participation rate.

Default thresholds

• Participation: 10% of 20-day ADV
• Max days to liquidate: 5 trading days

These defaults map to "intelligently executed institutional trade" — not aggressive, not glacial.

Interpretation guide

The hidden cost of operating near capacity

Backtests do not model price impact endogenously — they assume execution at the mid-price. In reality, deploying at the capacity ceiling means the strategy is consistently consuming 10% of ADV on entry and exit, and price impact is real. Cost increases approximately with the square root of (participation rate / baseline rate) per Almgren (2003). At p = 10% vs. p = 1%, impact bps is roughly sqrt(10) = 3.2× higher. Capacity ceiling deployment incurs 2–5× the transaction cost of small-scale deployment.

Liquidity premium and Amihud illiquidity

Holdings that trade thinly bear an illiquidity premium — lower prices to compensate holders for the difficulty of exiting (Amihud 2002, Acharya & Pedersen 2005, Pástor & Stambaugh 2003). A factor strategy whose alpha comes from small-cap or low-volume names is implicitly capturing this premium. Backtests that show "strong alpha in small-caps" are often capturing the illiquidity premium, not a generic anomaly. Capacity ceiling and liquidity premium go hand-in-hand: high alpha plus low capacity ceiling usually indicates premium capture.

Caveats

• ADV varies enormously over the backtest period. A stock that traded $5M/day on average may have had $500k/day periods. The 20-day average smooths but doesn't eliminate this. Capacity may be much lower in some periods.
• The participation cap is a model. Some markets (futures, ETFs) handle higher participation; some (illiquid micro-cap) require lower. Set the parameter to match the universe.
• Capacity ignores correlation. Two stocks at full capacity that move together effectively trade as one larger position. The cap assumes independent execution.