Liquidity Adjusted Position Sizing

When to Use

Invoke this skill when sizing positions across a universe with mixed liquidity profiles (large-caps, micro-caps, thinly traded options/futures). A fixed-fractional rule ($5%$ of NAV) sizes on the portfolio and ignores the instrument: the same $$500{,}000$ is trivial in a mega-cap and a multi-week exit in a micro-cap. This skill caps the position at the size the instrument can actually absorb, measured as Days-to-Liquidate (DTL) at a bounded participation rate and, optionally, as a multiple of displayed book depth.

The output is a size, and it belongs on the pre-trade path, downstream of the strategy's target and upstream of the order router.

When NOT to Use

As a market-impact or cost model. It returns shares, never a predicted cost. Impact estimation belongs in transaction-cost-analysis-tca-integration.
As portfolio construction. It sizes one instrument at a time. Ten independently liquidity-capped positions in the same crowded factor still exit through one door — see correlation-aware-exposure-limits and concentration-risk-single-name-limits.
When the binding constraint is volatility rather than liquidity — see dynamic-position-sizing-based-on-realized-volatility. The two caps compose (take the tighter); neither substitutes for the other.
As the execution schedule. A DTL of 3 days is a statement about capacity, not an instruction to work the order over 3 days. Scheduling is execution-algo-twap-vwap-slicing and participation-of-volume-pov-execution.
On an ADV you have not sanity-checked. ADV is an input, not a forecast; see the first pitfall below.

Prerequisites

Target capital allocation $V_{\text{target}}$, in the currency of $S$. May be negative for a short — the magnitude is capped and the sign preserved.
Price $S$ per unit of the ADV series. For futures and options that is the price per contract (quote $\times$ multiplier), with ADV in contracts; a raw quote paired with contract volume oversizes the position by the multiplier.
20-day Average Daily Volume $\text{ADV}_{20d}$ in shares/contracts, strictly positive and finite.
Max participation rate $\alpha$ (policy default $10%$) and max DTL $DTL_{\text{max}}$ (policy default $1.0$ day). These are internal policy, not regulatory limits — see references/standards.md for what is actually regulator-set.
Optional: a snapshot of reachable book depth in shares, if the depth cap is to be applied.

Workflow

Compute the daily liquidity capacity and the size cap: $$\text{DailyCapacity} = \frac{\alpha}{100} \times \text{ADV}{20d}, \qquad \text{MaxShares}{\text{adv}} = \text{DailyCapacity} \times DTL_{\text{max}}$$
- Decision point — the real control is $\alpha \times DTL_{\text{max}}$, a cap on size relative to ADV. Metaorder impact follows a square-root law in total size over daily volume and is, to a first approximation, insensitive to the participation rate and to how long the order is worked (Tóth et al. 2011). Raising $DTL_{\text{max}}$ to fit a bigger position does not make that position cheaper to trade — it only lengthens the exit. Widen it because you accept a longer liquidation horizon, never because you want less impact.
Apply the optional book-depth cap: $$\text{MaxShares}{\text{depth}} = m \times \text{BookDepth}{\text{shares}}$$
- Decision point — use it when ADV and depth disagree. ADV inflated by a handful of block prints or one index rebalance describes volume that will not be there on the day you exit. Depth is the cross-check. It is a snapshot that can be pulled, so it tightens the ADV cap, never replaces it. There is no standard value for $m$; calibrate it from your own execution data.
Cap the magnitude, preserve the side, floor to whole units: $$\text{FinalShares} = \operatorname{sign}(V_{\text{target}}) \times \left\lfloor \min\left(\left|\frac{V_{\text{target}}}{S}\right|,\ \text{MaxShares}{\text{adv}},\ \text{MaxShares}{\text{depth}}\right) \right\rfloor$$
- Decision point — a short is capped exactly like the mirror long. Covering a short in a name that cannot absorb the flow is at least as hard as selling the long, and worse in the tail. Never let a negative target take an unbounded path.
- Share counts are floored, never rounded. A limit may only be approached from below; rounding a cap of $9{,}999.999$ up to $10{,}000$ breaches the limit it exists to enforce.
Handle the degenerate outcomes explicitly:
- Decision point — a cap that floors to zero is an answer, not an error. If $\text{MaxShares} < 1$, the instrument admits no position under this policy. Drop it or widen the policy deliberately; do not round up to one lot.
- Non-finite or non-positive inputs must raise, never size. MiFID II RTS 6 Art. 15 requires pre-trade volume limits to act as hard blocks, and a limit that cannot evaluate its inputs has not blocked anything.
Emit the liquidity scaling audit: record target and final shares, both DTL figures, the scaling factor, and binding_constraint — which of the two ceilings actually bound. A capped result whose audit line does not say why cannot be reviewed later.

Full procedure: see references/workflows.md. Standards reference: see references/standards.md. Printable pre-flight checklist: see assets/checklist.md.

Common Pitfalls

Treating ADV as a forecast. A 20-day mean spanning a holiday stretch, an expiry, or one index-rebalance print overstates the volume that will be available on the day you need to exit — and the exit that matters is the stressed one, when volume is lowest and everyone in the crowded trade is leaving at once. Feed a stressed or haircut ADV; the sizer cannot detect an optimistic one.
Reading a NaN as a pass. Every comparison against NaN is False, so a NaN price or ADV slips through both price <= 0 and target > cap and takes the uncapped branch. The pre-2.0.0 engine returned a NaN share count labelled "Liquidity Sizing OK" with a scaling factor of $1.0$. Reject non-finite inputs at the boundary — a sizer that emits NaN on corrupt reference data is worse than none, because the caller has been told the position passed.
Letting shorts bypass the cap. -50,000 > 10,000 is False, so a signed target compared directly against a positive cap is never constrained. Cap the magnitude.
A misconfigured limit inverting the trade. An unvalidated negative $\alpha$ produces a negative cap and returns a short where a long was requested. Validate the policy at construction, not at first use.
Rounding a risk cap to two decimals. round(9_999.999, 2) is 10_000.0 — one share past the limit. Floor.
Reporting only the pre-cap DTL. The requested position's DTL and the returned position's DTL are different numbers; showing the first next to a message asserting the limit was met makes the audit trail contradict itself. Report both.
Sizing derivatives on the raw quote. ADV in contracts with price per share oversizes by the contract multiplier — precisely on the thinly traded instruments this skill exists to protect.
Confusing the participation cap with the execution schedule. The cap says the position is exitable in $DTL_{\text{max}}$ sessions at $\alpha$; it does not commit the router to trading at $\alpha$, and the router trading faster silently invalidates the assumption behind the cap.

Verification

Run python -m unittest discover -s skills/liquidity-adjusted-position-sizing/scripts and confirm a 100% pass rate. The suite pins the behaviour below.

Cap binds. LiquidityPositionSizer(max_participation_pct=10.0, max_dtl_days=1.0) with calculate_size("ILLIQ", 500_000.0, price=10.0, adv_shares_20d=100_000.0): capacity is $0.10 \times 100{,}000 = 10{,}000$ shares/day, so the cap is $10{,}000$ shares. Verify liquidity_capped_shares == 10_000.0, liquidity_capped_capital_usd == 100_000.0, scaling_factor == 0.2, dtl_days_target == 5.0, dtl_days_final == 1.0, binding_constraint == "adv_dtl".
Short is symmetric. The same call with -500_000.0 returns -10_000.0 shares and is_liquidity_constrained true.
Depth binds. With adv_shares_20d=10_000_000.0 (ADV cap $1{,}000{,}000$ shares) and book_depth_shares=5_000.0 at max_book_depth_multiple=1.0, verify the result is $5{,}000$ shares with binding_constraint == "book_depth".
Floor, not round. With adv_shares_20d=99_999.99 the cap is $9{,}999.999$ shares; verify the result is $9{,}999$, not $10{,}000$.
At the limit is allowed. A request of exactly $10{,}000$ shares against a $10{,}000$-share cap is not constrained; $10{,}001$ is.
Negative checks. NaN or $\pm\infty$ in any of target/price/ADV/depth, a non-positive price/ADV/depth, a numeric string, a blank symbol, $\alpha \le 0$ or $\alpha > 100$, and a non-positive max_dtl_days or max_book_depth_multiple must each raise ValueError.

When to Use

When NOT to Use

Prerequisites

Workflow

Common Pitfalls

Verification

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Handed off from 12

When to Use

When NOT to Use

Prerequisites

Workflow

Common Pitfalls

Verification

Related Skills

Hands off to 8

Handed off from 12