# 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?

-

## 1 Answer

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)

-

4
nice answer @Ryogi – Quant Guy Jul 23 '12 at 13:18
Thanks, @QuantGuy. – Ryogi Jul 23 '12 at 23:59
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9204788208007812, "perplexity_flag": "middle"}