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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?

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1 Answer 1

up vote 11 down vote accepted

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)

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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)

enter image description here enter image description here

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4  
nice answer @Ryogi –  Quant Guy Jul 23 '12 at 13:18
    
Thanks, @QuantGuy. –  Ryogi Jul 23 '12 at 23:59
    
The thing is that when $\Delta t \rightarrow 0$ the volatility $\sigma$ is challenging to estimate... –  statquant Nov 17 '13 at 20:40

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