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Optimal Risk Budgeting under a Finite Investment Horizon

25 Pages Posted: 7 Dec 2013 Last revised: 5 Jul 2015

Marcos Lopez de Prado

Guggenheim Partners, LLC; Lawrence Berkeley National Laboratory; Harvard University - RCC

Ralph Vince

Vince Strategies LLC

Qiji Jim Zhu

Western Michigan University

Date Written: December 24, 2013


Growth Optimal Portfolio (GOP) theory determines the path of bet sizes that maximize long-term wealth. This multi-horizon goal makes it more appealing among practitioners than myopic approaches, like Markowitz's mean-variance or risk parity. The GOP literature typically considers risk-neutral investors with an infinite investment horizon. In this paper, we compute the optimal bet sizes in the more realistic setting of risk-averse investors with finite investment horizons. We find that, under this more realistic setting, the optimal bet sizes are considerably smaller than previously suggested by the GOP literature. We also develop quantitative methods for determining the risk-adjusted growth allocations (or risk budgeting) for a given finite investment horizon.

Keywords: Growth-optimal portfolio, risk management, Kelly Criterion, finite investment horizon, drawdown

JEL Classification: G10, G60, G70, C62, E60

Suggested Citation

Lopez de Prado, Marcos and Vince, Ralph and Zhu, Qiji Jim, Optimal Risk Budgeting under a Finite Investment Horizon (December 24, 2013). Available at SSRN: or

Marcos Lopez de Prado

Guggenheim Partners, LLC ( email )

330 Madison Avenue
New York, NY 10017
United States


Lawrence Berkeley National Laboratory ( email )

1 Cyclotron Road
Berkeley, CA 94720
United States


Harvard University - RCC ( email )

26 Trowbridge Street
Cambridge, MA 02138
United States


Ralph Vince

Vince Strategies LLC ( email )

405 Lexington Ave - 26th fl
New York, NY 10174
United States


Qiji Zhu (Contact Author)

Western Michigan University ( email )

Kalamazoo, MI 49008
United States

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