Optimal Buy-and-Hold Strategies for Financial Markets with Bounded Daily Returns

TL;DR

This paper develops an optimal static online algorithm for buy-and-hold investment strategies with bounded daily returns, providing theoretical guarantees and practical comparisons with dollar averaging using real market data.

Contribution

It introduces a novel online planning game framework and derives the first optimal static algorithm with exact competitive ratio for long-term stock investment.

Findings

Optimal static online algorithm with proven competitive ratio

Comparison showing the algorithm's performance against dollar averaging

Application of the framework to real market data

Abstract

In the context of investment analysis, we formulate an abstract online computing problem called a planning game and develop general tools for solving such a game. We then use the tools to investigate a practical buy-and-hold trading problem faced by long-term investors in stocks. We obtain the unique optimal static online algorithm for the problem and determine its exact competitive ratio. We also compare this algorithm with the popular dollar averaging strategy using actual market data.