Analysis of Kelly-optimal portfolios

Details Analysis of Kelly-optimal portfolios Analysis of Kelly-optimal portfolios

2007-12-17

arxiv.org/abs/0712.2771v3

Quantitative Finance 10, 689-697 (2010)

Economy

Quantitative Finance

Portfolio Management

15 pages, 7 figures; extended list of references and some minor modifications

Scientific paper

10.1080/14697680902991619

We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. For lognormally distributed asset returns, we derive approximate analytical results for the optimal investment fractions in various settings. We show that when mean returns and volatilities of the assets are small and there is no risk-free asset, the Kelly-optimal portfolio lies on Markowitz Efficient Frontier. Since in the investigated case the Kelly approach forbids short positions and borrowing, often only a small fraction of the available assets is included in the Kelly-optimal portfolio. This phenomenon, that we call condensation, is studied analytically in various model scenarios.

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