Estimating VWAP Implementation Shortfall from Spread, Volatility, and Volume
Summary
The document explains that the signed difference between an order’s average execution price and its arrival mid-price is usually treated as implementation shortfall. It presents an approximate model with a spread-related term and a market-impact term that scales with volatility and the square root of order size relative to average daily volume. The coefficients must be calibrated on the trader’s own data.
The response points to research on market impact and crowded orders as background, and interprets one coefficient as reflecting execution skill while describing the other as more broadly applicable. It offers a practical functional form rather than a full estimation procedure or empirical validation. Results will depend on the instrument, data, order type, and execution conditions; the source gives no sample, calibration diagnostics, or evidence that the relationship holds universally.
Key ideas
- Implementation shortfall compares an order’s average execution price with its arrival price, adjusted for trade direction.
- The proposed model combines a spread component with an impact component based on volatility and order size relative to average daily volume.
- The impact term grows with the square root of normalized order size.
- Both model coefficients require calibration, and execution quality may affect the spread-related coefficient.
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# Modelling VWAP Slippage with HFT data
# Modelling VWAP Slippage with HFT data
I heard that VWAP slippage (relative difference between the VWAP and the initial mid-price, $\varepsilon \ . \ \frac{P_{VWAP}-P_{arrival}}{P_{arrival}}$ with $\varepsilon = +1 \ or \ -1 $ the trade sign) could be modelled as a function of volume, spread and volatility. Have you ever had experience for that?
Thank you for your guidance.
## Answer by lehalle (score 2)
https://quant.stackexchange.com/a/57591
Usually the the difference between your average price between $t_0$ and $T$ and the price at $t_0$ is called the Implementation Shortfall (IS).
They are a lot of references to do this, just cite these two ones:
- Market Impacts and the Life Cycle of Investors Orders, by Bacry, Iuga, Lasnier and L
- Modelling Transaction Costs When Trades May Be Crowded: A Bayesian Network Using Partially Observable Orders Imbalance, by Brière, L, Nefedova and Raboun (it is one of the chapter of the book Machine Learning for Asset Management)
This Figure comes from the second paper (you see how it is square-rooted):
The formula is, for a traded quantity $Q$ $$IS(Q)\simeq a \cdot \phi + b \cdot\sigma\sqrt{\frac{Q}{\rm ADV}},$$ where
- $\phi$ is the bid-ask spread
- $\sigma$ is the volatility
- $\rm ADV$ is the Average Daily Volume on the instrument.
$a$ and $b$ are two constants to be calibrated on your data. Typically: $a$ corresponds to your trading skills (if you are very smart in good liquidity chasing and if you have good execution predictors, $a$ can be close to 20%), and $b$ is somehow universal.
[EDIT] last paragraph removed (following @mbz0 remark).Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.