  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.
