Portfolio turnpikes

Profolio turnpike theorems show that if preferences at largewealth levels are similar to power utility, then the investmentstrategy converges to the power utility strategy as the horizonincreases. We state and prove two simple and general portfolioturnpike theorems. Unlike existing literature, our main resultdoes not assume independence of returns and depends only ondiscounting of future cash flows. We also provide a critiqueof portfolio turnpike results, based on the observations that(1) the time required for convergence is often too large tobe relevant, and (2) there is no convergence for consumptionwithdrawal problems.