Abstract
The 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.
Highlights
The Growth-Optimal Portfolio (GOP) theory is influential in portfolio management Kelly
In Vince and Zhu (2015), Vince and Zhu observed that the GOP neglected two important practical considerations
Risk is a critical factor for any investment decision. Incorporating these two practical considerations in analyzing the bet size of the game of blackjack, Vince and Zhu showed in Vince and Zhu (2015) analytically and experimentally that the optimal bet size suggested by Kelly’s formula Kelly (1956), a predecessor of the GOP theory, needs to be adjusted downward considerably
Summary
The Growth-Optimal Portfolio (GOP) theory is influential in portfolio management Kelly (1956); Latane (1959); Markowitz (1959); Thorp and Kassouf (1967) along with modern portfolio theory Markowitz (1952). As demonstrated in Vince and Zhu (2015), we scale the Kelly criterion answer using the worst case, so as to comport to being an actual fraction to risk so that multiple, simultaneous propositions can be considered properly (relative to each other), short sales considered, etc., such that we are always using a fraction and bounding the axes of the leverage space manifold at zero and one for all possible simultaneous propositions This is discussed further at the beginning of Section 3. We show that the inflection points on different return/risk paths are all on one manifold determined by Sylvester’s criterion of negative definiteness of a matrix involving the derivatives of the return functions and provides a reasonable approximation.
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