Shared Liquidity and Cross-Impact Across Different Instruments

1. Can two separate instruments share a capacity constraint?

Yes. Different instruments may draw on common portfolio counterparties, hedging channels or risk-bearing capacity. That possibility does not mean their displayed volume can simply be pooled. It means separate per-instrument cost estimates may omit interactions. Cross-impact describes a model of how trading demand across instruments relates to price response or execution cost. Return correlation alone is not such a model and does not determine the sign or size of those interactions. Start by identifying the mechanism and execution window being proposed, then ask what data could distinguish shared demand effects from common news, coincident orders and ordinary market movement.

2. Keep three aggregation problems separate

Same-security overlapping orders should first be reconciled by identity, account ownership and time window. Different-security cross-impact is another question because no share quantities can be netted across names merely because their returns correlate. Portfolio liquidity can also vary through the session, changing how common counterparties respond at different times. Min, Maglaras and Moallemi develop a stylized model linking single-name and portfolio liquidity with coupled execution. That supports considering an interaction mechanism; it does not supply coefficients for this publication. Preserve the distinction between aggregating identical demand, modeling related demand and falsely treating distinct traded instruments as one fungible pool of volume.

3. Inspect an invented signed-demand cost contract

Let q-A and q-B denote signed orders measured in units of one million dollars. Define a purely synthetic total-cost function in dollars as one hundred times the sum of two q-A squared, two q-B squared and two q-A times q-B. The last term is the interaction. With one-million-dollar buys in both instruments, total cost is six hundred dollars, versus four hundred if the interaction is omitted. With a one-million buy and a one-million sell, the toy cost is two hundred dollars. Gross external notional is two million in both cases. This static illustration is not a calibrated impact equation or a proposed trading strategy.

4. A lower interaction term is not permission to change the portfolio

The opposite-signed toy basket has a smaller modeled cost because that particular function rewards its signed combination. Reversing a legitimate investment instruction to obtain that result changes the exposure and is not an execution improvement for the same task. The total function remains nonnegative: its inner expression can be written as q-A squared plus q-B squared plus the square of (q-A + q-B). This is a useful algebraic check on the example, not a complete test of dynamic no-manipulation conditions. Real models need time structure, permissible trading paths and empirical evidence that are absent from this static contract.

5. Correlation does not identify the interaction coefficient

Common price moves can reflect public information or broader factor exposure rather than the basket's own activity. An empirical cross-impact study needs signed orders, timestamps, execution outcomes and compatible market observations, together with a design that addresses those confounding channels. Reading a correlation matrix cannot supply that evidence. Mastromatteo and coauthors' author abstract describes a multivariate execution framework and the consequences of omitting cross-impact within its setting. Only the public abstract was reviewed for that citation; this guide does not attribute its invented coefficients or dollar savings to the paper. A source's model result should not become a universal empirical law.

6. Use interaction sensitivity without pretending to calibrate it

Where lawful representative execution evidence is unavailable, retain the independent-row scenario and add clearly labeled interaction sensitivities rather than claiming a fitted portfolio capacity. State which assumptions are changed, whether timing remains fixed and which orders share potential counterparties. Do not add a cross-impact allowance to an all-in observed cost metric without checking for double counting. The workbench's row-level square-root heuristic has no interaction matrix or joint scheduling optimizer. This guide does not extend its implementation. A useful memo identifies the omitted dependence explicitly and explains which conclusion would need reconsideration if shared liquidity proved material at the proposed scale.

7. Questions before adding up individual capacity results

Do the orders overlap in time and compete for related portfolio flow? Are the supposed independent pools genuinely independent, or merely different ticker labels? What evidence supports the interaction mechanism and its units? Does an alternative schedule preserve the original investment instructions? Common failures include using return correlation as an impact coefficient, netting different instruments into a smaller external order and presenting one assumed interaction sign as established fact. Keep per-name constraints, gross traded notional and any portfolio interaction scenario visible together. The toy arithmetic demonstrates why additivity is an assumption; it does not certify executable scale or forecast the cost of a real basket.

Keep in the decision record

• Different instruments need not draw on independent liquidity.
• Return correlation is not an impact coefficient.
• Preserve intended exposures when comparing execution alternatives.

Source notes

1. Min, Maglaras and Moallemi: Cross-Sectional Variation of Intraday Liquidity and Portfolio Execution, author paper
2. Mastromatteo et al.: Trading Lightly, Cross-Impact and Optimal Portfolio Execution, public author abstract reviewed

Sources inform the definitions and limitations. Scenario inputs and arithmetic are publication illustrations, not extracted market observations. Access checks are dated in the source inventory.

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