  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.
