Halving assumed volume: a liquidity sensitivity, not a forecast

Change one assumption and retain the original

Start with $100 million of hypothetical capital, weights of 60% A, 30% B and 10% cash, and a 20% traded fraction in both invested sleeves. Per-session dollar ADV assumptions remain $50 million and $5 million. Preserve the two-session window, 10% participation cap, 1-basis-point fee, 2-basis-point half spread, impact coefficient 20 and 12-basis-point cost budget. Change only the common volume multiplier to 0.5.

This deliberately narrow stress is dated 16 October 2026 and uses invented inputs. It is not an assertion that actual liquidity will fall by half or that spread and impact would remain unchanged during a disruption. Holding those other parameters fixed isolates the mechanical volume channel. A richer stress should retain this version and add separately identified changes to costs, timing and access.

Read participation before interpreting costs

The orders remain $12 million and $6 million. A's window volume falls from $100 million to $50 million, and B's from $10 million to $5 million. Participation therefore rises from 12% to 24% for A and from 60% to 120% for B. B's required order is larger than all the volume assumed for the window, even before applying the much tighter 10% cap.

The equation still returns costs of 12.79795897 and 24.90890230 basis points per traded dollar, totaling $30,302.892145 or 3.03028921 basis points of capital. Treat these as extrapolated arithmetic from the illustrative curve. The 120% participation input invalidates any suggestion that the whole order can be completed within the assumed volume. A finite cost output does not repair an infeasible trading instruction.

Scale the boundary and verify the result

Because the window-volume term enters the capital boundary linearly, halving it halves each boundary while all other inputs stay fixed. B now permits 0.10 × $5 million ÷ 0.06 = $8,333,333.33. A permits $41,666,666.67. The cost-only participation allowance remains 20.25%, so the 10% participation cap remains binding. The common capital boundary is again determined by B.

At exactly $25 million divided by three of capital, orders become $1 million and $500,000. Participation is restored to 2% and 10%. Modeled costs total $1,049.070478, exactly half the dollar cost at the original boundary. Portfolio drag stays at 1.25888457 basis points because both modeled costs and capital halved. That unchanged ratio should not be mistaken for unchanged economic scale.

Define what the stress leaves unresolved

A four-session window would mechanically offset the 0.5 volume multiplier in this equation. That observation does not establish that waiting is acceptable: the signal can expire, prices can move, and access to liquidity can vary within the window. BIS research distinguishes transaction tightness, depth and resilience; a reduction in average volume alone cannot describe all three dimensions.

For a decision record, retain the base scenario, the isolated volume shock and any combined stress as separate exports. Specify whose volume is measured, the eligible sessions and whether auctions or inaccessible venues are excluded. Then state the operational response to a breached limit. This worksheet cannot automatically halt orders or monitor future market conditions; it helps expose which assumptions require evidence before a real implementation decision.

Keep in the decision record

• Volume and capital scale linearly only when other assumptions stay fixed.
• Participation above 100% is a warning against treating the result as executable.
• Liquidity stress can change spreads, access and timing as well as average volume.

Source notes

1. BIS Quarterly Review: Towards liquid and resilient government debt markets in EMEs, March 2024

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.