Assessing the Risk and Return of Financial Trading Systems - a Large Deviation Approach
Automated Trader Magazine
We apply large deviation theory to assess the probability that a trading system performs below or above a certain threshold. Our technique does not require that the distribution of the performance criterion obeys a closed-form equation, and can accept as input empirical distributions given under the form of frequency histograms obtained by backtesting or from prior use of the trading system. A nice property of the technique is that it can be easily automated and integrated into a trading platform. Furthermore, the approach is not limited to a single trading system but can be applied on portfolio of trading systems. By Nicolas NAVET and René SCHOTT
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1 Introduction
Large deviation (LD) is a theory of rare events that is focused on the analysis of tails of probability distributions. Large deviation is classically used to study how random processes deviate from their expected value. If upper bounds on this quantity can be obtained through Chernov, Markov and Tchebychev inequalities, LD provides the exact rate of convergence, instead of an upper bound that is often not tight enough for real-world applications. LD has been a very active field of investigation over the last 10 years with numerous practical applications, for instance for evaluating performance of algorithms or telecommunication infrastructures. Another body of literature applies large deviation to risk analysis (see Ref. [7] for a recent and comprehensive survey), and this is actually the field of applications from which originates LD theory.
This paper belongs to this latter line of research and focuses on assessing the risk of financial trading rules. This work is aimed at giving answers to the practitioners, and thus the techniques provided can be applied with as few technical assumptions as possible. In particular, the approach developed here does not require closed-form distributions, and is able to deal with empirical distributions obtained from the backtesting step, or from experience gained using the trading rules. The interest of this approach with regard to Monte-Carlo simulations is three-fold. First, simulation is not well suited to estimate rare events because of the size of the sample that is needed to achieve reasonable error bounds. Second an analytical approach does not suffer the uncertainties of simulation (e.g., quality of the random number generators). Finally, this analysis can be integrated into a broader Value-at-Risk analysis.
2 Characterizing the Performance of a Trading System
A trading system is comprised of one or several trading rules that define entry and exit conditions, and decide the size of each position taken. A trading system can be seen as an algorithm that is implemented either as a computerized Automated Trading System (ATS) or executed, in a consistent manner, by a trader. The typical way to select trading systems is to evaluate a set of candidate systems on historical data and keep the best system or several top-scoring ones. This is the “backtesting” procedure, which is a feature nowadays available on almost any technical analysis software package. ...