about graphic

Gradient Maximization

At Columbine, our principal tool for designing multifactor models is an optimization methodology that we call gradient maximization (grad max). This is a model construction process combining steepest ascents and multi-period portfolio simulation. Steepest ascents (or descents; the terms are used interchangeably) is a technique from the world of operations research developed to solve complex problems of multivariate optimization while satisfying constraints that are intractable using traditional calculus. Steepest ascents has been used in manufacturing and process control applications ever since computers became available, but, except for neural networks, is little used in finance.

Columbine's gradient maximization approach is a sophisticated simulation technique that relies on computer power to actively search for the optimal model among all possible combinations. No off-the-shelf software exists for grad max optimization; we have written our own. Columbine's innovative application of this process to financial model building is unique and proprietary.

Despite its resource and computational difficulties, gradient maximization offers several advantages:

  • It can exploit non-linear factors that offer most of their return at the extremes.
  • Grad max can utilize characteristics that are specific to just the desired stocks - the portfolio - unlike regression, which must fit every issue into a general rule.
  • The simulation process can be constrained to produce models that stand up to real world considerations (reasonable holding periods, transactions costs, etc.).

Starting with the same historical data as everyone else, Columbine's grad max process produces unique models with superior predictive power.

For more detailed information on the gradient maximization methodology, we recommend:

Brush, J.S., and V.K. Schock. 1995. "Gradient Maximization: An Integrated Return/Risk Portfolio Construction Procedure." Journal of Portfolio Management, vol. 21, no. 4 (Summer):89-98.