Addition by Subtraction: A Better Way to Forecast Factor Returns (and Everything Else)

Abstract

Financial analysts assume that the reliability of predictions derived from regression analysis improves with sample size. This is thought to be true because larger samples tend to produce less noisy results than smaller samples. But this is not always the case. Some observations are more relevant than others, and often one can obtain more reliable predictions by censoring observations that are not sufficiently relevant. The authors introduce a methodology for identifying relevant observations by recasting the prediction of a regression equation as a weighted average of the historical values of the dependent variable, in which the weights are the relevance of the independent variables. This equivalence allows them to use a subset of more relevant observations to forecast the dependent variable. The authors apply their methodology to forecast factor returns from economic variables.

TOPICS: Portfolio management/multi-asset allocation, risk management, quantitative methods

Key Findings

• • The prediction from a linear regression equation is mathematically equivalent to a weighted average of the past values of the dependent variable, in which the weights are the relevance of the independent observations.

• • Relevance within this context is defined as the sum of statistical similarity and informativeness, both of which are defined as Mahalanobis distances.

• • Together, these features allow researchers to censor less relevant observations and derive more reliable predictions of the dependent variable.