Ergodic Behavior of Returns in a Buy Low and Sell High Type Trading Strategy

Abstract

In algorithmic trading strategies aiming at “Buying Low and Selling High” a given asset is a recurrent topic for many practitioners and still pose challenges for researchers. We may ask, for example, what happens in the long run if we set price levels $\underline{\theta }<\overline{\theta }$ and buy the asset if its price goes below $\underline{\theta }$ and sell it if the price exceeds $\overline{\theta }$? In their recent paper, Lovas and Rásonyi proved that under suitable conditions, the distribution of the log-rate of returns realized in each cycle converges to a unique limit distribution in total variation at geometric speed. Furthermore, the law of large numbers holds for bounded and measurable functionals of the returns. We tested these findings by executing the strategy on real stock exchange data consists of in about 2.3 million records, providing empirical evidence for the law of large numbers.

The first author was supported by the EFOP-3.6.3-VEKOP-16-2017-00007 “Young researchers from talented students” project. The second author benefited from the support of the “Lendület” grant LP 2015-6 of the Hungarian Academy of Sciences.