medium · Market Microstructure market-impact

If a trader halves the execution horizon from T to T/2 while keeping the total order size fixed, and temporary impact dominates permanent impact, how does total expected cost change?

1. Total expected cost approximately doubles, because temporary impact cost is proportional to (trading rate squared) times horizon, and halving the horizon while keeping total shares fixed doubles the trading rate, which quadruples the rate-squared term but only for half as long — netting to double the cost.
2. Total expected cost quadruples, because the trading rate doubles once the execution horizon is halved, and temporary impact cost scales with the square of that rate, so cost rises fourfold, regardless of the shorter session, which contradicts the correct linear-scaling relationship implied by this reasoning.
3. Total expected cost is roughly halved, because completing the order in half the original time sharply cuts the trader's total exposure to permanent price impact and to adverse price drift risk across the whole execution horizon window, under this flawed piece of reasoning about speed and impact.
4. Total expected cost is essentially unchanged, because permanent impact is entirely speed-independent by construction, and this fixed component is mistakenly assumed here to precisely and fully offset any rise in temporary impact cost that results from trading at the considerably faster execution rate that is involved.

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