TWAP and VWAP

Before anything clever, there are two schedules so simple they're used as the industry's yardsticks.

TWAP — Time-Weighted Average Price

Split the order into equal slices and trade one per interval. That's it. If you need to sell 1,000 units over 10 steps, you sell 100 each step.

Naive as it looks, Bertsimas and Lo showed TWAP is genuinely optimal under a specific set of assumptions (linear permanent impact, arithmetic random-walk prices). It's not a strawman — it's the correct answer to a particular question, and beating it requires the real market to depart from those assumptions in a way your strategy can exploit.

VWAP — Volume-Weighted Average Price

Trade in proportion to expected market volume: heavier when the market is busy, lighter when it's quiet. The intuition is that your order is less conspicuous, and less impactful, when it's a smaller fraction of concurrent flow.

$$q_t = Q \times \frac{v_t}{\sum_i v_i}$$

VWAP works well in liquid, predictable markets. Its weakness is that it's purely passive — it reacts to a historical volume profile and ignores everything happening right now: order-flow imbalance, spread widening, momentum.

Why they matter

Any learned policy must be measured against these on Implementation Shortfall using identical market conditions. A strategy that can't beat TWAP hasn't learned anything about the market — it's learned to be complicated.

They're also useful as exploration priors. Sampling random exploratory actions from a distribution centred on the TWAP schedule keeps an RL agent from destroying itself while it learns.