Authors: Athanasios Fassas, Stephanos Papadamou

Title: Implied Volatility style analysis: Risk aversion vs. Uncertainty

Abstract

This paper analyses the two oldest and most followed implied volatility indices, VIX and VDAX, using returns-based style analysis, a widely used and accepted in the investment community portfolio-analysis tool.

Implied volatility is driven not only by the expected stock market uncertainty, but also by market participants’ risk aversion. Therefore, implied volatility can be decomposed into the variance risk premium, a residual measure that is more closely related to risk aversion and expected future variance of the underlying asset. In this paper we decompose VIX and VDAX, the US and German implied volatility index respectively, into two components (risk aversion and uncertainty) and examine which is the main driver of their evolution over the last thirty years.

An implied volatility index, such as VIX and VDAX, is market participants’ best collective estimate of the annualized realized volatility of the underlying equity index over the next thirty calendar days. The level of the volatility index depends directly on option prices and thus reflects any event (positive or negative) that could potentially influence the stock market. Thus, VIX and VDAX reflect both the stock market future uncertainty about S&P500 and DAX indices respectively and investors’ risk aversion in these two markets.

Our empirical analysis takes a rather unconventional view by employing the returns-based style analysis introduced by Sharpe (1988, 1992) on VIX and VDAX returns. Returns-based style analysis uses only returns data and employs a nonlinear optimization to construct a portfolio of indices to minimize the tracking error with the portfolio being analyzed.

Our data start in January 1992 and covers the period until summer 2023, resulting in more than 7.000 daily, overlapping observations. The period under review includes several crises and stock market crashes, but also prolonged periods of unprecedented calmness in stock markets and thus represents an informative period during which uncertainty and risk aversion have varied significantly. Our empirical results show that both volatility indices are driven largely on average by risk aversion (around 70%), but this is the result of the crisis observations which dominate despite representing a relatively small part of the sample. In normal times, volatility indices are again more influenced by risk aversion, but in a more balanced way (approximately 60% risk aversion, 40% uncertainty).

Our empirical findings could carry significant implications, given that shifts in risk appetite are widely recognized as pivotal determinants of asset prices and returns and gaining a clearer understanding of the factors driving the VIX contributes to achieving this objective.