# The Impact of Execution Delay on Kelly-Based Stock Trading: High-Frequency Versus Buy and Hold

## TL;DR

This paper examines how execution delays affect the relative performance of high-frequency trading versus buy and hold strategies using Kelly's ELG criterion, revealing delays can make buy and hold preferable even without transaction costs.

## Contribution

It provides a theoretical proof that without delays buy and hold is never better, and through simulations shows delays can reverse this, a novel insight into trading strategy performance.

## Key findings

- Without delays, buy and hold is never better than high-frequency trading.
- Execution delays can make buy and hold strategies outperform high-frequency trading.
- Simulation results confirm delays influence strategy effectiveness regardless of self-financing constraints.

## Abstract

Stock trading based on Kelly's celebrated Expected Logarithmic Growth (ELG) criterion, a well-known prescription for optimal resource allocation, has received considerable attention in the literature. Using ELG as the performance metric, we compare the impact of trade execution delay on the relative performance of high-frequency trading versus buy and hold. While it is intuitively obvious and straightforward to prove that in the presence of sufficiently high transaction costs, buy and hold is the better strategy, is it possible that with no transaction costs, buy and hold can still be the better strategy? When there is no delay in trade execution, we prove a theorem saying that the answer is ``no.'' However, when there is delay in trade execution, we present simulation results using a binary lattice stock model to show that the answer can be ``yes.'' This is seen to be true whether self-financing is imposed or not.