Dimension Reduction Signature Genetic Algorithm 

Abstract

Given a large set of explanatory variables, we apply a signature-genetic algorithm ('SigGA') approach to reduce the dimension of the supervised learning algorithm to a handful of variables. Then, we rank stocks and construct investment portfolios using polymodels [1], a collection of nonlinear equations on selected risk factors that have persistently driven much of stock returns' dependencies. From a practical standpoint, the SigGA helps capture volatility clustering in stocks, and polymodels are well-suited for constructing tail-concentrated hedged portfolios, especially when markets are under stress. Irrespective of the underlying models used for dimension reduction and variables mapping and their subsequent ranking, our portfolio construction methodology consists of five building blocks drawn from personal observations and years of investment management experience (fundamental and quantitative). We think qualitative or quantitative portfolio construction and stock investing will eventually necessitate portfolio managers to order, segregate, integrate, condition, exclude, and concentrate (position sizing) their investment ideas, stock selection, and stock dependencies i.e.: factors. Additionally, we use polymodels to calibrate portfolio exposures to different frequencies taking into account nonlinearity. We propose a dimension reduction technique that combines signatures with a genetic algorithm to find the optimal set of factors' relationship with a stock.