Portfolio turnpikes

Portfolio turnpike theorems show that if preferences at large wealth levels are similar to power utility, then the investment strategy converges to the power utility strategy as the horizon increases. We state and prove two simple and general portfolio turnpike theorems. Unlike existing literature, our main result does not assume independence of returns and depends only on discounting of future cash flows. We also provide a critique of portfolio turnpike results, based on the observations that (1) the time required for convergence is often too large to be relevant, and (2) there is no convergence for consumption withdrawal problems.