Learn about execution algorithms (TWAP, VWAP, POV)

WHY do we need them?

The three classic scheduling algorithms differ in what drives the schedule:

1. TWAP — Time-Weighted Average Price

HOW — derive the slice size from first principles. Total quantity $Q$, number of slices $N$. We want each slice equal, call it $q$.

$\sum_{i=1}^{N} q = Q \implies Nq = Q \implies q = \frac{Q}{N}$

Why this step? Equal slices means the sum of $N$ copies of $q$ must equal the whole parent order $Q$; solving gives $q=Q/N$.

The benchmark price you're measured against is the simple average of prices sampled at each slice:

$\text{TWAP} = \frac{1}{N}\sum_{i=1}^{N} P_i$

Why this step? Since we traded equal quantities at times with price $P_i$, the average price paid equals the unweighted average of prices — hence "Time-Weighted."

2. VWAP — Volume-Weighted Average Price

HOW — derive the schedule. Let $u_i = \dfrac{V_i}{\sum_j V_j}$ be the fraction of the day's expected volume in slice $i$ (the volume profile, estimated from historical data). To perfectly track VWAP, trade quantity:

$q_i = Q \cdot u_i$

Why this step? If in each slice you trade the same fraction of your order as the market trades of its total volume, then your participation is constant, and your volume-weighted average price equals the market's VWAP.

Proof that this matches VWAP. Your average price is $\bar P = \frac{\sum_i P_i q_i}{\sum_i q_i} = \frac{\sum_i P_i (Q u_i)}{\sum_i Q u_i} = \frac{\sum_i P_i u_i}{\sum_i u_i}.$ Since $u_i \propto V_i$, this equals $\dfrac{\sum P_i V_i}{\sum V_i} = \text{VWAP}$. ✔ Why this step? The constant $Q$ cancels, leaving the same volume-weighted average that defines VWAP.

3. POV — Percentage of Volume (a.k.a. Participation)

HOW — the tradeoff. Your total time to finish depends on realized market volume. If total market volume over the window is $V_{\text{mkt}}$, you complete $Q_{\text{filled}} = \rho \, V_{\text{mkt}}.$ Why this step? Summing $q_i = \rho V_i$ gives $\rho \sum V_i = \rho V_{\text{mkt}}$.

So to fully fill $Q$ you need $V_{\text{mkt}} \ge Q/\rho$ of market volume to trade. You do NOT control completion time — that's the price of adaptivity.

Common Mistakes (Steel-manned)

Flashcards

Connections

• Market Impact & Slippage — the cost these algos minimize.
• Implementation Shortfall — an alternative benchmark that penalizes both impact and delay.
• Order Book Dynamics — child orders interact with bid/ask depth.
• Volume Profile & U-Shape — the intraday volume curve VWAP relies on.
• HFT Market Making — the counterparty often filling these child orders.
• Almgren-Chriss Optimal Execution — the math framework that generalizes TWAP/VWAP.

Concept Map

Hinglish (regional understanding)