Multiscale Markowitz
Revant Nayar, Raphael Douady

TL;DR
This paper proposes a multiscale Markowitz portfolio optimization framework that incorporates the relationship between variance at different time scales, enabling more flexible and robust risk management aligned with investor preferences across multiple frequencies.
Contribution
It introduces a novel multifrequency optimization method that considers the scaling behavior of variance, extending traditional Markowitz models to better handle market complexities like crashes and regime changes.
Findings
Enables specifying target variance across multiple frequencies
Addresses limitations of traditional Markowitz in volatile markets
Provides a practical implementation framework
Abstract
Traditional Markowitz portfolio optimization constrains daily portfolio variance to a target value, optimising returns, Sharpe or variance within this constraint. However, this approach overlooks the relationship between variance at different time scales, typically described by where is the Hurst exponent, most of the time assumed to be \(\frac{1}{2}\). This paper introduces a multifrequency optimization framework that allows investors to specify target portfolio variance across a range of frequencies, characterized by a target Hurst exponent , or optimize the portfolio at multiple time scales. By incorporating this scaling behavior, we enable a more nuanced and comprehensive risk management strategy that aligns with investor preferences at various time scales. This approach effectively manages portfolio risk across multiple…
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering
