Archimedean Lever and Center-of-Mass Portfolios From Mechanical Equilibria to Portfolio Allocations

Abstract

This paper reinterprets portfolio selection through two Archimedean mechanical principles— the lever law and center-of-mass computation—formalized as explicit constraints within classical mean-variance and factor-model frameworks. The Archimedean Lever Portfolio (ALP) requires asset-specific torques to be proportional to risk contributions; under standard mean-variance assumptions this yields a closed-form solution structurally identical to the tangency portfolio, but using the volatility-scaled signal σiμi in place of raw expected returns μi—an implicit Bayes-Stein shrinkage that lowers turnover and drawdowns. The Archimedean Center-of-Mass (ACM) portfolio is a minimum-variance allocation whose factor center of mass is aligned with the factor risk premium, yielding a second closedform solution from a low-dimensional linear system. Empirical tests on U.S. ETF equity portfolios show that Archimedean portfolios deliver competitive risk-adjusted returns across multiple estimation windows and data frequencies, with lower turnover and smaller drawdowns than the classical tangency portfolio, though results are subject to the usual caveats of a small-universe backtest.