How does investor competitiveness (a goal of relative rather than absolute wealth) affect optimal allocations? In their February 2019 paper entitled “The Growth of Relative Wealth and the Kelly Criterion”, Andrew Lo, Allen Orr and Ruixun Zhang compare optimal portfolios for maximizing relative wealth versus absolute wealth at both short and long investment horizons. They define an individual’s relative wealth as fraction held of total wealth of all investors. Their model assumes that investors allocate to two assets, one risky and one riskless. They identify when an investor should allocate according to the Kelly criterion (series of allocations that maximize terminal wealth over the long run) and when the investor should deviate from it. Based on derivations and modeling, they conclude that:
- The Kelly criterion generates optimal allocations for an investor seeking to maximize absolute wealth at an infinite horizon.
- However, optimal allocations of a relative wealth-motivated investor depend on behaviors of a competing investor and may deviate far from the Kelly criterion.
- Initial relative wealth (an investor’s market power) is a critical determinant of optimal behavior. In other words, optimal allocations are different for “rich” and “poor” investors.
- A “rich” investor should roughly mimic allocations of a “poor” investor whether more or less aggressive than the Kelly criterion.
- A “poor” should act about oppositely from a “rich” investor.
- Optimal allocations do not vary much with investment horizon.
- Initial relative wealth (an investor’s market power) is a critical determinant of optimal behavior. In other words, optimal allocations are different for “rich” and “poor” investors.
In summary, optimal portfolio allocations for relative wealth-motivated investors vary with current wealth. The rich should go with the flow (preserving advantage), and the poor should be contrarian (potentially escaping disadvantage).
Cautions regarding conclusions include:
- The study is hypothetical, not empirical. It does not include an investigation of the actual importance of relative wealth versus absolute wealth as motivators.
- Models only approximate actual investing.
See also “The Adaptive Markets Hypothesis” and “Adaptive Asset Allocation Policy”.
