Stochastic portfolio theory optimization and the origin of rule-based investing

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Acknowledgements

We would like to thank two anonymous referees for valuable comments, which made it possible to improve the first version of the manuscript.

Notes

1 For a review of portfolio separation theorems, see Ingersoll (1987), Chapter 6.

2 A portfolio choice is said to be myopic if it depends only upon current wealth and the distribution of returns currently available.

3 see Proposition 1.3.1 in Chapter 1.

4 see Proposition 1.1.5 in Chapter 1 of Fernholz (2002), for a formal proof.

5 see Lemma 1.3.4 in Chapter 1 of Fernholz (2002), for a formal proof.

6 see Proposition 1.2.5 in Chapter 1 of Fernholz (2002), for a formal proof.

7 Karatzas et al. (1989) consider the absolute wealth maximization problem, whereas in this paper we address the relative wealth maximization problem, between portfolio and market-cap-weighted index. We believe that a thorough re-derivation of the result by Karatzas et al. (1989) for the case of relative wealth maximization should be the subject of a separate paper.