A mean quadratic variation approach to optimal portfolio selection

We propose a mean quadratic variation (MQV) framework for portfolio selection as an alternative to the classical Markowitz mean–variance (MV) paradigm. Instead of measuring risk by terminal return variance, the MQV framework employs quadratic variation, a pathwise and time-additive measure of return fluctuations. This modification addresses two longstanding limitations of the MV framework: the sensitivity of covariance-based optimization in high-dimensional settings and the time-inconsistency of multi-period portfolio choice. The proposed model is straightforward to calibrate, as quadratic variation and quadratic covariation between assets can be directly estimated from realized return paths. Moreover, the additive structure of quadratic variation yields time-consistent optimal portfolio strategies in a discrete-time multi-period setting. We derive closed-form optimal portfolio weights, characterize the corresponding efficient frontier, and develop a quadratic variation-based capital asset pricing model. Extensive empirical backtests and simulation experiments show that MQV portfolios achieve competitive or improved out-of-sample performance relative to their MV counterparts across several asset universes. Overall, the results suggest that pathwise risk measurement provides a tractable and economically meaningful alternative to variance-based portfolio optimization.