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Samuelson's argument basically comes down to the fact that the investments that maximize growth don't maximize your utility unless your utility is log(wealth),
by joker3 8y ago
Samuelson's argument basically comes down to the fact that the investments that maximize growth don't maximize your utility unless your utility is log(wealth), and to him it was completely obvious that people should act to maximize their own utilities.
However, there have been a couple recent developments that somewhat undercut his line of thinking. First of all, to the extent that people's behavior can be described by utility theory, we all roughly have isoelastic utilities (https://en.wikipedia.org/wiki/Isoelastic_utility https://en.wikipedia.org/wiki/Isoelastic_utility) with a parameter not too much greater than one. As a result, the ideal investments for most of us are near Kelly.
Second, there's a body of theory that asks what the optimal strategy for investment is given a certain number of years, and it turns out that the ideal strategy is to follow the Kelly approach until near the deadline and then to switch to the investments that maximize your own utility as the time to act grows short. This work is known as turnpike theory for reasons that never really made sense to me.
There are still concerns about Kelly investments, but Samuelson's argument isn't really one of them.
- sarosh 8y agoThank you for this insight! Would you be so kind as to provide some pointers to the concerns you’ve mentioned? Any pointers on turnpike theory would also be appreciated!
- evrydayhustling 8y ago> investments that maximize growth don't maximize your utility unless your utility is log(wealth) This needs a slight adjustment to be exactly true: > investments that maximize growth don't maximize your utility at a specific time horizon unless your utility is log(wealth) The reason is that in situations of repeated investment, Kelly's policy actually does maximize many time-indefinite notions consistent with linear utility -- for example, if you have a fixed wealth goal (retirement) that is enough successful wagers away, Kelly will minimize the expected time to get there [1]. For me, the important limitation for Kelly is that it is designed around timescales that involve many many repeated bets. Like most asymptotic results, Kelly can win marathons and lose sprints -- so it's important to consider which situation you're in. [1] https://www.stat.berkeley.edu/~aldous/157/Papers/Good_Bad_Kelly.pdf https://www.stat.berkeley.edu/~aldous/157/Papers/Good_Bad_Ke...
- OscarCunningham 8y ago> Second, there's a body of theory that asks what the optimal strategy for investment is given a certain number of years, and it turns out that the ideal strategy is to follow the Kelly approach until near the deadline and then to switch to the investments that maximize your own utility as the time to act grows short. This work is known as turnpike theory for reasons that never really made sense to me. Could you give some examples? I searched for "turnpike" and "kelly criterion" together and I couldn't find any examples of situations for which people had proven that the Kelly criterion was optimal even for nonlogarithmic utility functions.