Fractal Profit Landscape of the Stock Market

TL;DR

This paper reveals that the profit landscape of a simple stock trading strategy exhibits a fractal structure, making optimization difficult and highlighting the limitations of short-term fluctuation-based trading compared to buy-and-hold.

Contribution

It demonstrates that the profit landscape is fractal, showing the complexity and difficulty of optimizing trading strategies based on simple fluctuation parameters.

Findings

Profit landscape has a fractal structure.

Optimization is hypersensitive and unreliable.

Long-term buy-and-hold outperforms fluctuation-based strategies.

Abstract

We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q. Stocks are sold and bought if the log return is bigger than p and less than -q, respectively. Repetition of this simple strategy for a long time gives the profit defined in the underlying two-dimensional parameter space of p and q. It is revealed that the local maxima in the profit landscape are spread in the form of a fractal structure. The fractal structure implies that successful strategies are not localized to any region of the profit landscape and are neither spaced evenly throughout the profit landscape, which makes the optimization notoriously hard and hypersensitive for partial or limited information. The concrete implication of this property is demonstrated by showing that optimization of one stock for future values or other stocks renders worse profit than a strategy that ignores fluctuations, i.e., a long-term buy-and-hold strategy.