Ensemble properties of high frequency data and intraday trading rules

Regarding the intraday sequence of high frequency returns of the S&P index as daily realizations of a given stochastic process, we first demonstrate that the scaling properties of the aggregated return distribution can be employed to define a martingale stochastic model which consistently replicates conditioned expectations of the S&P 500 high frequency data in the morning of each trading day. Then, a more general formulation of the above scaling properties allows to extend the model to the afternoon trading session. We finally outline an application in which conditioned forecasting is used to implement a trend-following trading strategy capable of exploiting linear correlations present in the S&P dataset and absent in the model. Trading signals are model-based and not derived from chartist criteria. In-sample and out-of-sample tests indicate that the model-based trading strategy performs better than a benchmark one established on an asymmetric GARCH process, and show the existence of small arbitrage opportunities. We remark that in the absence of linear correlations the trading profit would vanish and discuss why the trading strategy is potentially interesting to hedge volatility risk for S&P index-based products.