Relative Spurious Regression Bias in Business-Cycle Models of Stock Momentum

Abstract

We investigate whether persistent macroeconomic variables can be reliably shown to predict momentum profits. We find that when predictor variables are persistent and the predictive relationship is estimated over a period that overlaps the momentum portfolio formation period, predicted returns will be positively correlated with past returns. This occurs even when returns are constructed to be serially uncorrelated and independent of the predictors. This means there will be a positive predicted return to momentum portfolios and the macroeconomic variables will appear to explain momentum profits, even when stock returns are unrelated to the macroeconomic variables. We show that the apparent ability of the business-cycle model in Chordia and Shivakumar (2002) to explain intermediate-term momentum profits comes from this effect, which we term a relative spurious regression bias. We demonstrate that results similar to those of Chordia and Shivakumar obtain when we replace their macroeconomic variables with random variables constructed to be persistent but independent of stock returns. Once the parameter estimation period is chosen to be prior to the portfolio formation period, the predictive power of the macroeconomic variables disappears and momentum is no longer explained by the business cycle model.

Keywords: momentum, bias, spurious

JEL Classification: G11, G14