Day of the Week Effect on VIX: A Parsimonious Representation

Abstract

The study of significant deterministic seasonal patterns in financial asset returns is of high importance to academia and investors. This paper analyzes the presence of seasonal daily patterns in the VIX and S&P 500 returns series using a trigonometric specification. First, we show that, given the isomorphism between the trigonometrical and alternative seasonality representations (i.e. daily dummies) it is possible to test daily seasonal patterns employing a trigonometrical representation based on a finite sum of weighted sines and cosines. We find a potential evolutive seasonal pattern in the daily VIX that is not in the daily S&P 500 log-returns series. In particular, we find an inverted Monday effect in VIX level and changes, and a U-shaped seasonal pattern in VIX changes when we control for outliers. The trigonometrical representation is more robust to outliers than the one commonly used by the literature, but it is not immune to them. Finally, we do not find a day-of-the-week effect in S&P 500 returns series, what suggests the presence of a deterministic seasonal pattern in the relation between VIX and S&P 500 returns.

Keywords: volatility index, returns, Box-Cox transformation, seasonality, leverage effect

JEL Classification: C32, G13, G15