Improving Quantitative Models Through Optimization

Abstract

Q uantitative active management and Markowitz-type optimization techniques have both become quite popular over the past twenty years. Bernstein and PradhumTn [1993] demonstrate that institutional equity managers appear to have increased their use of more quantitatively derived methods of stock selection such as earnings estimate revision or equity duration over the past five years. The increased popularity of index hnds and, in particular, tilted index funds, combined with the availability of computer optimization packages and data bases, has led to the widespread use of optimization techniques. With the exception of a relatively small group of managers that offer tilted index funds, however, few active equity managers regularly use optimization techniques in conjunction with quantitative stock selection models. Although most quantitative equity managers have been schooled on portfoliobased concepts developed by Markowitz [1959] and Sharpe [1970], such managers seem to focus on stock selection, and forget their quantitative portfolio-oriented “roots.” Many of today’s quantitative models attempt to forecast expected returns on an individual stock basis, and ignore the ramifications of combining those individual stocks into a portfolio. Most models have an implicit assumption that if one buys the model’s most attractive stocks, then one will be investing in the best possible portfolio. Active quantitative managers will often equal-weight the component stocks, market-weight the stocks, or pick individual stocks off the “best buy” list accord-. ing to their feelings regarding their own skill at stock selection. We demonstrate that optimizing a quantitative model’s “best buy” portfolio can provide superior performance when compared to more traditional weighting or stock selection schemes. In addition, the value-added that a mediocre manager can expect to achieve that is attributable to stock selection pales in comparison to that achievable through optimization techniques. In general, ignoring the correlation and covariant risk and weighting of a quantitative model’s “best” stocks can result in hundreds of basis points per year in lost performance. To support these contentions, we studied the results of a traditional quantitative equity technique, the dividend discount model (DDM), and found that returns could be enhanced significantly by simply