Optimal Portfolio Construction Using Qualitative and Quantitative Signals

Background

The literature on portfolio optimization goes back to Markowitz (1952), and there have been many variations of the model since then. However, a vexing problem that has plagued the Markowitz method (the so-called mean variance approach) for optimally constructing a portfolio of stocks has been the computational complexity involving large variance-covariance matrices. This problem becomes particularly acute when one tries to incorporate firm-specific characteristics that have been shown in recent years to be associated with the expected returns, variance, and covariance of the firm’s stock returns. A complete implementation of the Markowitz approach for portfolio optimization would demand that the moments of every individual stock and its covariance with other stocks be modeled as a function of all these firm-specific characteristics. Given that the dimensionality of the variance-covariance matrix increases nonlinearly in the number of stocks being considered, solving the Markowitz model would be a daunting task theoretically, and its implementation would prove to be impractical for most portfolio managers. In fact, if the Markowitz model has to be implemented with anything other than for investors with quadratic preferences, then an unmanageable number of higher moments have to be considered in optimizing the portfolio. While some simplifications and approximations have been proposed in the literature, most have proven to be less than satisfactory.

Recently, a promising and practical approach to portfolio optimization called the Parametric Portfolio Policy (PPP) has been proposed by Brandt, Santa-Clara, & Valkanov (2009). In their model, irrespective of investor preferences and the joint distribution of stock returns, the dimensionality of the portfolio optimization problem for a group of N characteristics is only of the order N. This sidesteps the curse of dimensionality that plagues the Markowitz approach. In addition, the optimal portfolio weights for each stock can be estimated by using well known statistical techniques.