A cointegration approach to the lead-lag effect among size-sorted equity portfolios

We develop a framework which illustrates that lagged information transmission may entail cointegration between the current price of small-firm portfolios and the lagged price of large-firm portfolios. We test for cointegration using data which comprises three sets of monthly prices of equity portfolios for the period 1955-2000. The first two sets contain monthly prices of size-sorted portfolios of different capitalisation size, and the third contains portfolios of the same size. We find evidence of cointegration for both sets of different capitalisation size portfolios and no evidence of cointegration for equal-size portfolios. Large-firm portfolio prices are long-run forcing variables for small-firm portfolio prices, suggesting that capitalisation size is a driving force of the lead-lag effect in the long run. For the two sets of different-size portfolios, we estimate error correction models (ECMs) using the auroregressive distributed lag (ARDL) approach, and obtained out-of-sample forecasts of small-firm portfolios returns. These ECMs are found to have superior forecasting performance relative to models without the error correction term, further highlighting the relevance of cointegration between the lagged price of large-firm portfolios and the current price small-firm portfolios.