Relative Wealth Effects on Investors

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:

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