Spectral Portfolio Theory

Abstract

Economic shocks can have diverse effects on financial market dynamics at different time horizons, yet traditional portfolio management tools do not distinguish between short- and long-term components in alpha, beta, and covariance estimators. In this paper, we apply spectral analysis techniques to quantify stock-return dynamics across multiple time horizons. Using the Fourier transform, we decompose asset-return variances, correlations, alphas, and betas into distinct frequency components. These decompositions allow us to identify the relative importance of specific time horizons in determining each of these quantities, as well as to construct mean-variance-frequency optimal portfolios. Our approach can be applied to any portfolio, and is particularly useful for comparing the forecast power of multiple investment strategies. We provide several numerical and empirical examples to illustrate the practical relevance of these techniques.