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Dequantification: Optimal Balance Pairs

Published in Automated Trader Magazine Issue 27 Q4 2012

A common problem encountered by Automated Trader readers who use strategies such as pairs trading is determining the optimal ratio of securities to buy/sell when executing a trade. Automated Trader talks to Agnes Tourin of the Department of Finance and Risk Engineering at the Polytechnic Institute of NYU about how the stochastic control approach proposed in a recent paper1 she co-authored may offer a possible solution.

Agnes Tourin

Automated Trader: Why did you decide to explore this approach to modelling the relative dollar amounts to apply in pairs trading?

Agnes Tourin: I've been working in the area of stochastic control for some 15 years. Originally the applications I worked on were fairly academic, so not necessarily particularly relevant for the trading industry. The idea in the paper originally came from my co-author Raphael Yan, who is in charge of risk management in an internal hedge fund at Blackrock, although this question was not directly linked to his work there. I helped him formulate the model, compute the solution and illustrate with the example. Raphael was previously a PhD student of mine at McMaster University in Canada and he had been thinking for a while about using stochastic control for computing optimal trading strategies.

Automated Trader: Stochastic control techniques don't seem to have seen much use in the finance industry. Why is that?

Agnes Tourin: It is probably not regarded as a 'new' field, as the techniques have been developed progressively over many years. The concepts are demanding to grasp and require an extensive training at the PhD level for several years, plus years of experience gained from doing research.

Finally, stochastic control techniques have obvious limitations in the sense that the problems are still very hard to solve in most cases.

Automated Trader: In which case, why choose to use them for the problem of determining the optimal dollar ratio of securities in a pairs trade?

Agnes Tourin: Stochastic control techniques are good for computing optimal decisions under uncertainty, a situation that clearly applies to the problem of determining the relative quantities of the two instruments to buy/sell.

Another advantage to stochastic control is that it is dynamic in time, so you can adapt your strategies as you receive more information on the asset price, volume, volatility etc. The time series to which you are applying the technique needs to exhibit the Markov property ('memorylessness') for this approach to work, but fortunately this is true at least some of the time in the case of many financial time series.

Finally - as was the case in the example we developed for the paper - the problem may have a closed form solution, which massively reduces the computation and complexity involved.

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