Portfolio turnpike theorems show that if preferences at large wealth levels
are similar to power utility, then the investment strategy converges to th
e power utility strategy as the horizon increases. We state and prove two s
imple 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 converge
nce for consumption withdrawal problems.