Seasonal Return Volatility and Firm Size: Implications for Conditional Heteroskedasticity

Abstract

This paper reports evidence that the standard deviation of stock returns exhibits seasonal patterns. The seasonal patterns are considerably different between portfolios of different market value of equity stocks. January and August are the two most volatile months for the small decile portfolio while April and November are most volatile for the largest decile portfolio. Return variance anomalies have been modeled using different variations of the general autoregressive conditional heteroskedasticity (GARCH) model. We compare two methods to account for the seasonal differences in volatility between size portfolios in conditional heteroskedastic models. The first alternative specifies one month, one quarter and one year variance lags. The second alternative uses selected monthly dummy variables in the variance structure. Of the models tested, our results suggest that the best overall model is the EGARCH(1,1)-m with seasonal dummies. The GARCH-m model with seasonal lags performs well for portfolios of large market capitalization stocks. However, none of the models were able to account for the seasonality in volatility for large stocks and the models with variance lags failed to account for the seasonality for small stocks.

JEL Classification: G12, G14