Ensemble properties of high-frequency data and intraday trading rules

Abstract

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 conditional 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 data-set 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.

Keywords:

• Anomalous scaling
• Memory
• Intraday returns
• Intraday strategy

JEL Classification:

• C
• C1
• C16
• C53
• C51

Acknowledgments

We thank M. Zamparo for useful discussions. This work is supported by ‘Fondazione Cassa di Risparmio di Padova e Rovigo’ within the 2008–2009 ‘Progetti di Eccellenza’ program.

Notes

1 Where a statistical ensemble is a collection of elements, such as a collection of realizations of a stochastic process, with given statistical properties. In the cited contributions, each daily HF data-set constitutes a single element of the ensemble. Furthermore, each element of the ensemble is assumed to be a realization of the same underlying stochastic process. The properties of the process at a given time within the day are estimated on the basis of ensemble statistics, i.e. by averaging over all available daily realizations.

2 This paper provides an extensive survey of empirical studies dealing with technical trading rules.

3 The mean empirical linear correlation of 10-min returns is .

4 For simplifying our notations, we remove the stochastic variables subscripts to the PDF’s symbols. Explicit inclusion of the arguments thus discriminates whether for instace we are talking about a single-point marginal PDF, or about a many-point joint PDF.

5 Again, for simplicity dependence on the day is understood.

6 We do not take into account the margins generally required when creating short position. We motivate this choice by the need of evaluating the strategy abilities on both long and short trades without penalizing short positions, as would be the case when margins larger than 10% would be required. Furthermore, given that the trades will last at maximum for 5 h and 50 min (from 10:10 to 16:00 pm), we believe that an implicit margin of 10% will be sufficient.

7 The standard deviation is computed over the daily returns of the simulated portfolio and then annualized. Note that days without any trading signal provide zero returns, since we did not assume any remuneration for the bank account.