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

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 a delay is present, our simulation results using a binary lattice stock model indicate that the answer can be yes. This is seen to be true whether cash financing is imposed or not.