Stick it out or even it out?

Towards a robust multi-period efficient frontier

History of portfolio selection

  • 1952, Markowitz: Efficient frontier for one-off investments
  • 1956, Kelly: Optimize expected terminal wealth for repeated games
  • 1991, Cover: Kelly without statistical assumptions

Modern portfolio theory

Portfolio should be risk/return Pareto efficient

Does not use intermediate info

Online portfolio selection

Investing is a repeated game

Kelly: if distribution known, calculate terminal wealth optimizer

Cover: no assumptions, compare with a good benchmark

The main idea

No statistical assumptions

Define a 'best strategy in hindsight' a la Markowitz

Minimize maximum distance to best strategy

Repeat for different risk preferences to build efficient frontier

Why no statistical assumptions?

Assets get (de)listed

Trump starts a tariff war

Why that arbitrary benchmark?

Next steps

Find efficient frontier

Include transaction costs

Optimal rebalancing frequency

Theorems, proofs

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