Slippage Decomposition

Specification

An order's execution slippage is defined as:

$$slippage_{bps} = sideSign \times \frac{MarketAvgPrice-OrderAvgPrice}{MarketAvgPrice} \times 10000$$

where

$$sideSign = \begin{cases} 1, & \text{for buy order}, \\ -1, & \text{otherwise} \end{cases}$$

Let's split the whole order duration into $N$ equal time periods and introduce the following notations:

• $P_{m,i}$: the market average price in period $i$
• $V_{m,i}$: the market volume traded in period $i$
• $P_{o,i}$: the order average execution price in period $i$
• $V_{o,i}$: the order quantity executed in period $i$

With above notation, we have

$$MarketAvgPrice = \frac{\sum_{i=1}^{N} P_{m,i} \cdot V_{m,i}}{\sum_{i=1}^{N} V_{m,i}} = \sum_{i=1}^{N} P_{m,i} \cdot \frac{V_{m,i}}{\sum_{i=1}^{N} V_{m,i}} = \sum_{i=1}^{N} P_{m,i} \cdot \rho_{m,i}$$

where $\rho_{m,i} = \frac{V_{m,i}}{\sum_{i=1}^{N} V_{m,i}}$, i.e. the proportion of market volume traded in period $i$. By the same token, we have

$$OrderAvgPrice = \frac{\sum_{i=1}^{N} P_{o,i} \cdot V_{o,i}}{\sum_{i=1}^{N} V_{o,i}} = \sum_{i=1}^{N} P_{o,i} \cdot \frac{V_{o,i}}{\sum_{i=1}^{N} V_{o,i}} = \sum_{i=1}^{N} P_{o,i} \cdot \rho_{o,i}$$

where $\rho_{o,i} = \frac{V_{o,i}}{\sum_{i=1}^{N} V_{o,i}}$, i.e. the proportion of order quantity traded in period $i$.

Let's introduce one more notation for the predicted volume profile $\hat{\rho}_{o,i}$. So we can rewrite the numerator of the slippage definition as:

$$\sum_{i=1}^{N} P_{m,i} \cdot \rho_{m,i} - \sum_{i=1}^{N} P_{o,i} \cdot \rho_{o,i} = \sum_{i=1}^{N} (P_{m,i} - P_{o,i}) \cdot \rho_{m,i} + \sum_{i=1}^{N} P_{o,i} \cdot (\rho_{m,i} - \hat{\rho}_{o,i}) + \sum_{i=1}^{N} P_{o,i} \cdot (\hat{\rho}_{o,i} - \rho_{o,i})$$

In this way, the performance slippage is decomposed into three components:

• $\sum_{i=1}^{N} (P_{m,i} - P_{o,i}) \cdot \rho_{m,i}$ is the price component, which indicates how much an order's execution price deviates from market price, i.e. how much spread is captured by the order.
• $\sum_{i=1}^{N} P_{o,i} \cdot (\rho_{m,i} - \hat{\rho}_{o,i})$ is the tolerance component, which indicates the cost paid due to how closely the order follows the target volume profile.
• $\sum_{i=1}^{N} P_{o,i} \cdot (\hat{\rho}_{o,i} - \rho_{o,i})$ is the profile component, which indicates the slippage due to difference between the estimated volume profile and realized volume profile from the market.

Implementation

API

decomposeSlippage[executions;trades;profile;params]

• executions: a table of order executions with the following columns:

  • time: the time when each execution is transacted
  • quantity: the executed shares of each execution
  • price: the price of each execution
  • flag: a symbol with value `open, `continuous or `close

• trades: a table of market trades with the following columns:

  • time: the time when each market print is transacted
  • volume: the executed shares of each market print
  • price: the price of each market print
  • flag: a symbol with value `open, `continuous or `close

• profile: a table of minute bar volume profile with the following columns:

  • time: the start time of minute bar
  • percent: the volume percent for a given minute
  • flag: a symbol with value `open, `continuous or `close

  The volume profile must be a full-day volume profile with volume percent for both open and close auction. The time for open auction is the start time of continuous trading session and the time for close auction is the end time of continuous trading session.

• params: a dictionary of parameters with the following keys:

  • startTime: the order start time
  • endTime: the order end time
  • includeOpen: a boolean indicating whether participation in open is enabled
  • includeClose: a boolean indicating whether participation in close is enabled

Details