Spectral Analysis of High-Frequency Finance

Popular across a wide range of fields, spectral analysis is a powerful technique for studying the behavior of complex systems. It decomposes a signal into many different periodic components, each associated with a specific cycle length. We argue that the application of spectral analysis to finance leads to natural interpretations in terms of horizon-specific behaviors. A spectral framework provides a few main advantages over conventional time domain approaches to financial analysis: (1) improved computational efficiency for the evaluation of behaviors across a spectrum of time horizons, (2) reduced vulnerability to aliasing effects, and (3) more convenient representations of inherently cyclic dynamics, e.g. business cycles, credit cycles, liquidity cycles, etc. In this paper we first present a set of spectral techniques, including a frequencyspecific correlation and a frequency decomposition of trading strategy profits. Then, we demonstrate the application of these techniques in an empirical analysis of highfrequency dynamics over the years 1995-2014. Our results consist of three parts: (1) an analysis of individual stock returns and various portfolio returns, (2) an analysis of contrarian trading strategies and the introduction of a novel technique for managing frequency exposures of general strategies, and (3) a case analysis of recent market shocks. The great extent to which our empirical results align with financial intuition attests to the practicality of spectral approaches to financial analysis. It demonstrates that many real phenomena can be captured through a spectral lens. Thesis Supervisor: Andrew W. Lo Title: Charles E. and Susan T. Harris Professor