Approximating the Trading Cost of Latency in Order Execution
Summary
The document considers how to estimate the effect of trading latency on a market-making strategy. The questioner proposes treating the maximum spread observed within a time interval as a return proxy and spread variance as a risk proxy. The accepted response instead points to a model by Moallemi and Saglam, built around an execution problem in which a trader must choose between a market order and a limit order while completing execution within a fixed horizon.
That model derives an optimal strategy and an approximation for latency costs when latency is small. The stated approximation depends on price volatility, the bid-ask spread, and the latency interval, and the source says the original study also examines historical latency costs and implied latency for a basket of NYSE stocks. These references provide a theoretical framework and empirical application, but the document does not reproduce the figures or explain the model’s assumptions in depth. Its formula should therefore be understood within that specific execution setup, not as a universal measure for every market-making system.
Key ideas
- Latency cost can be studied through a constrained order execution problem involving market and limit orders.
- The cited model derives an optimal execution strategy and an approximation for small latency.
- The approximation depends on volatility, bid-ask spread, and the latency interval.
- The source reports historical cost analysis and implied latency estimates for NYSE stocks.
- The model’s conclusions depend on its execution setup and may not generalize to every market-making strategy.
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Full text
# How does one measure the effect of latency on potential returns?
# How does one measure the effect of latency on potential returns?
I am looking to evaluate the hypothetical advantage one trading system has over another in terms of the possible returns given their latency.
Irene Aldridge wrote a piece (How Profitable Are High-Frequency Trading Strategies?) which describes how to relate holding time to Sharpe ratio, although her approach seems somewhat arbitrary.
As I am investigating the effect of latency on market making strategies, I have modified this approach to use the maximal spread in a time frame to be the return and the spread's variance as risk (as the spread proxies for the risk of the market maker).
Are there any other metrics I can make use of? Does my approach thus far seem reasonable?
## Answer by Ryogi (score 15, accepted)
https://quant.stackexchange.com/a/3847
An interesting starting point is The Cost of Latency by Moallemi and Saglam. After setting up a simple order execution problem --- in which a trader must chose between a market order and a limit order and guarantee execution over a fixed interval $[0,T]$, they proceed to derive a (complex) close form solution for the optimal strategy and evaluate the impact of latency on trading costs. In particular, they derive a simple expression to approximate the cost of latency when the latency is small (i.e. in the limit $\Delta t \to 0$, where $\Delta t$ denotes some measure of the latency of the trading system). In terms of price volatility $\sigma$, the bid-ask spread $\delta$, the cost of latency is
$$\frac{\sigma\sqrt{\Delta t}}{\delta}\sqrt{\log \frac{\delta^2}{2 \pi \sigma^2 \Delta t}}$$
The profile of the latency cost according to their model is (Fig 7, The Cost of Latency by Moallemi and Saglam)
The proceed to evaluate the historical cost of latency and the implied latency for a basket of NYSE stocks (Figs 8 and 9, The Cost of Latency by Moallemi and Saglam)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.