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> investments that maximize growth don't maximize your utility unless your utility is log(wealth) This needs a slight adjustment to be exactly true: > investm
by 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...