Real-Time Trading Models and the Statistical Properties of Foreign Exchange Rates

Abstract

Real-time trading models use high frequency live data feeds and their recommendations are transmitted to the traders through data feed lines instantaneously. In this paper, a widely used real-time trading model is considered as a tool to evaluate the statistical properties of foreign exchange rates. This is done by comparing the out-of-sample results of the trading model to those obtained by feeding the algorithm with data simulated from theoretical processes fitted to the real data. The out-of-sample test period is seven years of five-minute series on three major foreign exchange rates against the US Dollar and one cross-rate. Performance of the real-time trading models is measured by the annualized return, two measures of risk corrected annualized return, deal frequency and maximum drawdown. The simulated probability distributions of these performance measures are calculated with three popular processes, the random walk, GARCH and AR-GARCH. The null hypothesis that the real-time performances of the foreign exchange series are generated from these traditional processes is tested under the probability distributions of the performance measures. In other words, we compute the probability of the real performance if the distribution was originated by these processes. All four currencies yield positive annualized returns in the studied sampling period. These annualized returns are net of transaction costs. The results indicate that the excess returns of the real-time trading models, after taking the transaction costs and correcting for market risk, are not spurious. The random walk, GARCH(1,1) and AR-GARCH(1,1) processes are rejected as the data generating mechanisms for the high frequency foreign exchange rates. One important reason for this rejection is the aggregation properties of the GARCH processes. The GARCH process behaves more like a homoskedastic process at lower frequencies. Since the trading frequency is less than two deals per week, the trading model does not pick up the five minute level heteroskedastic structure at the weekly frequency. The results indicate that the foreign exchange series may possess a multi-frequency conditional mean and conditional heteroskedastic dynamics. The traditional heteroskedastic models fail to capture the entire dynamics by only capturing a slice of this dynamics at a given frequency. Therefore, a more realistic processes for foreign exchange returns should give consideration to the scaling behavior of returns at different frequencies and this scaling behavior should be taken into account in the construction of a representative process.