Measure implementation shortfall without hiding unfilled orders

Define the paper alternative before trading

Choose a benchmark price and timestamp consistent with the decision being evaluated. A decision-time midpoint, an arrival price and a closing price represent different reference points. The original Almgren–Chriss paper relates trading cost to the difference between initial portfolio value and liquidation proceeds, illustrating why the benchmark belongs in the definition.

For this guide’s buy example, the paper alternative buys the full intended quantity at the declared decision price. The comparison values any unfilled quantity at a later, explicitly chosen evaluation price. This is an educational accounting convention, not a prediction that the full paper order could actually have executed at the benchmark.

A partially filled buy

Suppose a hypothetical instruction seeks 10,000 shares at a decision reference of $100. It fills 6,000 shares at $100.10, incurs $60 of explicit fees, and leaves 4,000 unfilled. At the chosen evaluation time the price is $100.30.

Executed-price shortfall is 6,000 × ($100.10 − $100) = $600. The missed-exposure amount is 4,000 × ($100.30 − $100) = $1,200. Adding $60 fees gives $1,860. Relative to the original $1 million intended notional, this is 18.6 bps. A fill-only report would omit the larger missed-exposure component.

Direction and horizon change the interpretation

For a sell, the adverse direction reverses: selling below the benchmark contributes positive cost. The evaluation horizon also matters. A different end price can change the measured opportunity component without changing any fill. That is why the horizon must be set consistently rather than selected after observing a favorable result.

If the unfilled buy’s evaluation price were $99.70 instead, its opportunity component would be −$1,200 under this convention. That negative number means not buying helped relative to the paper benchmark over that horizon. It does not prove that non-completion was an intentional or repeatable execution skill. Preserve the reason the order remained unfilled.

Avoid an attribution claim the data cannot support

The observed price difference can contain broad market movement, security-specific information, the order’s own influence and other participants’ activity. An accounting measure alone does not identify how much was caused by market impact. Do not label every unfavorable difference as impact or every favorable difference as price improvement skill.

Likewise, an order that beats the close may lag the decision price. Retain both comparisons if they serve declared purposes, but do not replace the decision benchmark with the better-looking one. Record delayed releases, cancelled instructions and revised quantities so analysts can distinguish implementation changes from the original investment intent.

Connect measurement to the scenario tool

The workbench predicts a simple cost rate using participation, fee and half-spread assumptions. It does not calculate full implementation shortfall or estimate unfilled-order opportunity cost. To compare its output with executions, choose an observed metric whose components and denominator match, then separately assess omitted components.

The SEC’s order-type guidance notes that a limit order may not execute. Therefore a low fill-price cost must be read alongside completion. A robust evidence table includes intended notional, executed notional, fill rate, benchmark-relative cost, explicit fees and the declared evaluation price. These columns make the example reproducible without pretending its paper alternative was executable.

Keep in the decision record

• Freeze benchmark and evaluation horizon before judging an order.
• Include unfilled quantity when evaluating the whole investment decision.
• Do not confuse measured shortfall with causal market impact.

Source notes

1. Almgren and Chriss — Optimal Execution of Portfolio Transactions, December 2000 (paper mirror)
2. SEC Investor.gov — Types of Orders

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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