Compare rebalance schedules without changing the investment question

Freeze the intended transition

Start with holdings before the decision, target holdings, decision timestamp and required completion date. These define the investment transition. Daily, weekly or monthly labels alone do not specify the dollars to trade or the exposure remaining between trades.

A schedule experiment should first hold the transition fixed. Otherwise, a lower-cost schedule may simply execute fewer of the intended trades. The original Almgren–Chriss research frames execution as moving from initial holdings to a specified final position over a defined horizon. That framing is useful here, although the workbench does not solve its optimal-control problem.

A fixed-order scheduling example

Suppose a hypothetical portfolio must buy $3 million of one security. Eligible daily dollar volume is assumed to be $15 million. Completing the order in one session gives 20% participation; spreading it evenly across three identical sessions gives 6.667% participation in each session and over the full three-session window.

With 3 bps combined fee and half-spread and a 15 bp impact coefficient, the workbench estimates 9.708 bps for the one-session case and 6.873 bps for the three-session case. Those rates imply approximately $2,912.46 versus $2,061.90. The $850.56 difference is a calculation under invented inputs, not proof that three days is a better live schedule.

Account for target deviation

If the three-day plan buys $1 million daily, $2 million remains unbought after day one and $1 million after day two. That path changes exposure. For a buy, an adverse upward price movement makes completion more expensive relative to the original decision; a downward move has the opposite effect. The heuristic does not predict either outcome.

Record target deviation in dollars and, where appropriate, in portfolio weight. On a $30 million portfolio, $2 million of uncompleted buying represents 6.667 percentage points of missing intended exposure. A committee can then assess whether the modeled saving is material relative to the permitted deviation and the reason for the trade.

Rebalancing rules change order generation

A calendar rule trades at predetermined dates. A threshold rule trades when weights leave a declared band. These rules can produce different trades, not merely different execution schedules. To compare them, preserve each rule’s generated order history and assess its own target adherence, turnover and cost assumptions.

An illustrative 5% target with a 1-percentage-point band does not trade at 5.6%, while a strict calendar reset might. If an analyst credits the band rule with lower cost, the report must also show its accepted weight drift. It would be misleading to label the reduction a pure execution improvement when it comes from changing the portfolio policy.

Evidence and boundaries

For a real study, retain all eligible decision dates, including cancelled and unfilled instructions. Specify how new signals interact with an order already in progress: replace, combine, finish or escalate. Without that rule, a multi-day backtest can execute contradictory intentions on the same security.

The example assumes constant volume, unchanged price and linear allocation of order size through time. It omits taxes, cash constraints and cross-security correlations. Use it to expose the cost-versus-target-deviation tradeoff. Selecting a live rebalance policy requires evidence about the investment objective, timing and constraints in addition to modeled execution expense.

Keep in the decision record

• Freeze the target transition before comparing execution schedules.
• Show the residual exposure path alongside estimated savings.
• Treat fewer generated trades as a portfolio-policy change, not solely an execution improvement.

Source notes

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

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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