A THRESHOLD MODEL APPROACH TO ESTIMATING THE ABNORMAL STOCK RETURNS

The classical capital asset pricing model postulates a linear relationship between stockreturns and stock risks. However, a number of subsequent empirical studies have revealedsome anomalies in this relationship, especially for firms with small size and high book-tomarketvalues. A possible explanation for the anomalies is the existence of threshold effectsin the proxies of stock risks. However, conventional threshold models only allow for onethreshold variable, which limits their applicability in this context. In this paper, we addressthis issue by applying the econometric technique developed by Bai et al. (2012). We estimatethe joint threshold effects of firm size and book-to-market equity ratio on the stockreturns using a sample of 5,271 US firms. The test results yield clear evidence for theexistence of threshold effects in both firm features.We find that abnormal returns exist whenthe firm size falls below 52.04 million USD and the book-to-market ratio exceeds 0.4085.