Principles of nonstationary regression estimation: A new approach to dynamic multi-factor models in finance

A new class of signal analysis problems is considered, which appear in finance when it is required to detect the hidden dynamics of an investment instrument or a portfolio in respect to certain market or economic factors. Such problems can be naturally formulated as a complex of models concerned with estimating a nonstationary linear regression under additional constraints and requirements which have been not considered in the classical methodology of signal analysis. These models are also applicable to many other engineering and scientific problems. We review existing financial multi-factor models from the standpoint of their performance in detecting hidden investment portfolio dynamics. Using practical examples, we present and analyze the shortcomings of these models in detecting both gradual and rapid changes in investment portfolio structure. We then lay the groundwork for a new approach, which we call Dynamic Style Analysis (DSA), representing a true time-series multi-factor portfolio analysis model. At the core of the methodology, we present a new dynamic regression model, which we call Constrained Flexible Least Squares (CFLS). One of the most important features of the DSA model is that it is fully adaptive, i.e., all model parameters are determined from data. The major concepts of the new methodology are gradually introduced and applied to analyses of both model portfolios and well-known public US mutual funds. By comparing publicly available holdings data with results obtained with DSA, we demonstrate both the superiority of the new model and its remarkable accuracy in detecting portfolio dynamics. We also address issues such as the computational complexity of DSA and its practical applications in the areas of risk management, performance measurement and investment research. One of the major applications of the new methodology lies in hedge fund due diligence and risk monitoring, where the importance of uncovering and controlling hidden factor dynamics is especially valuable given the limited transparency of hedge funds.