A longer execution window buys volume and introduces delay

Distinguish calendar time from trading opportunity

The workbench multiplies ADV by window days and the volume multiplier. Window days represent equivalent eligible trading sessions, not elapsed calendar days. A weekend does not create two sessions of liquidity. A half-day, restricted venue or narrow intraday interval should use a documented volume adjustment, not an unexplained fraction chosen to achieve a desired result.

The model assumes the same adjusted volume per equivalent day. It does not know the intraday volume curve, an upcoming announcement or whether the signal expires before the window ends. Record these constraints outside the arithmetic before comparing durations. Otherwise, the tool may reward a schedule that the investment process cannot use.

Reconcile the time-and-cost tradeoff

For a hypothetical $2 million order and $10 million daily volume, one day implies 20% participation; four days imply 5%. With an illustrative cost rule of 1 bp fees, 2 bps half-spread and a 20 bp impact coefficient, the modeled rates are 11.944 bps and 7.472 bps. Dollar costs are approximately $2,388.85 and $1,494.43.

The difference is about $894.42. It is a saving within the chosen heuristic, not an expected saving calibrated from executions. If a buy is delayed and the unfilled exposure rises in price, that movement can dominate the modeled saving. A 1% price rise on $1 million still unbought corresponds to $10,000 of missed exposure relative to the earlier price.

Why execution research includes risk

Almgren and Chriss’s original execution paper studies the tradeoff between transaction costs and uncertainty while a portfolio is being liquidated. Its analytical framework is a useful conceptual reference for why slowing down is not a free improvement. The simple participation workbench does not implement that optimization or estimate its parameters.

For an internal scenario memo, show a completion schedule alongside the cost row. A four-day plan that trades evenly leaves approximately 75%, 50% and 25% of the initial order unfinished after the first three sessions, ignoring price changes. That residual path matters to market exposure, cash availability and the strategy’s intended timing.

Use deadlines as inputs, not post-processing

A cash need, benchmark transition, investment restriction or signal horizon can impose a latest completion time. Enter a feasible window first, then evaluate its participation. If no feasible schedule meets the selected limits, record the conflict. Quietly extending the window changes the task rather than solving it.

Partial completion also needs a decision rule. The remaining quantity might be cancelled, deferred for review or assigned a revised instruction. Those choices have different portfolio consequences. A calculator that assumes full completion should never describe a partially executed instruction as successfully implemented just because its observed spread was low.

Limits of the comparison

The SEC’s after-hours materials describe different liquidity and execution conditions outside regular sessions. Adding overnight hours is not equivalent to multiplying regular-session ADV by elapsed hours. Venue access, order types and available counterparties must be investigated for the specific route.

The workbench omits price paths, alpha decay, overnight gaps and opportunity cost. Report its output as a duration sensitivity under fixed assumptions. A useful conclusion identifies what additional evidence would decide between feasible schedules, such as realized volume profiles and timestamped completion records, rather than selecting the smallest modeled cost by default.

Keep in the decision record

• Use equivalent eligible sessions, not calendar days.
• Compare modeled cost savings with the uncompleted exposure path.
• Respect a predeclared deadline even when a longer window looks cheaper.

Source notes

1. Almgren and Chriss — Optimal Execution of Portfolio Transactions, December 2000 (paper mirror)
2. SEC — After-Hours Trading: Understanding the Risks

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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