Day-of-the-week and month-of-the-year effects on French Small-Cap Volatility: the role of asymmetry and long memory

Abstract

Small-cap stocks are characterized by high volatility and offer investors the opportunity to earn higher returns. This paper empirically investigates the impact of the day-of-the-week and the month-of-the year effects on the volatility of daily and monthly CAC SMALL returns in Paris stock market during the period from 1999 to 2015. We propose the SEMIFARMA-SD-GJR-GARCH model, which incorporates stochastic trend, deterministic nonparametric trend, short-range, long-range dependence and seasonal dummy asymmetric GARCH errors. The main findings of this study are that the coefficients of the SEMIFARMA-SD-GJR-GARCH model including the long memory coefficient in the mean equation and the seasonal asymmetry in the variance equation are highly significant and the GJR-GARCH model without seasonal dummies is dominated by the GJR-GARCH model with seasonal dummies (SD-GJR-GARCH). The results indicate that the day-of-the-week and the month-of-the-year effects detected on volatility seem to improve the volatility forecasts. These results support the arbitrage opportunity hypothesis for realizing abnormal returns, and support the inefficiency of CAC small capital market.

Keywords

• semifarma model
• sd-gjr-garch model
• seasonal anomalies
• asymmetric volatility
• small capitalization