# 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