The fear gauge : VIX volatility index and the time-varying relationship between implied volatility and stock returns

Implied volatility is the level of dispersion of asset price changes that is embedded in the market prices of option contracts written on that asset. As such, it represents market participants’ consensus on the expected volatility, or uncertainty regarding future returns, over the remaining life of the options. A proxy for aggregate stock market implied volatility is given by Chicago Board Options Exchange’s volatility index, the VIX, which is a practical implementation of the concept of model-free implied volatility that allows for extracting implied volatility directly from observed option prices without the use of a parametric option pricing model. Two well-known features of implied volatility and the VIX in particular are its mean reversion – it tends towards its mean level over time – and a significant negative contemporaneous correlation with returns on the underlying stock index. In this thesis, the time-varying dynamics of the relationship between stock market returns and implied volatility are examined empirically. Theoretical background and the construction methodology of the VIX are thoroughly discussed in order to give the reader an understanding of model-free implied volatility and the VIX. Structural stability of the time series data of the VIX daily levels ranging from January 2004 to December 2011 is tested using the method developed by Bai and Perron (1998;2003a;b;2004) for testing for structural breaks at a priori unknown times. The results suggest that statistically significant structural breaks are present in the data sample, that is, the mean level to which the VIX reverts is found to shift over time. This allows for determining distinct volatility regimes in the sample. The relationship between daily changes in the VIX and the corresponding daily stock index returns during these distinct regimes is studied by examining their cross-correlations and testing for any Granger causality that might exist. A more elaborate study is conducted on the strongly negative contemporaneous relationship by examining the effect of return shocks on volatility as well as by looking for asymmetries in volatility using linear regression. The results strongly suggest the presence of a single statistically significant structural break that coincides approximately with the outbreak of the global financial crisis in late 2007. The sample data is therefore divided into a pre-breakpoint low volatility regime and a post-breakpoint high volatility regime. No statistically significant Granger causality is found in the data, which suggests that VIX changes have no predictive power over stock index returns or vice versa. Closer scrutiny of the contemporaneous volatility-return relationship reveals asymmetries in volatility – increases in the VIX associated with negative stock market returns are found to be higher than decreases associated with positive returns of similar size. The overall inverse relationship appears to be stronger in the high volatility regime. However, the degree of asymmetry in that relationship is in turn stronger in the low volatility regime, i.e. the difference between increases and decreases in the VIX in response to negative and positive returns, respectively, turns out to be higher than in the high volatility regime. The study of structural stability of the VIX mean level provides and update to the study of Guo and Wohar (2006), whose sample period predates that of this thesis. The findings on the asymmetry of the relationship between implied volatility and stock market returns lend further support to the notion that the VIX is rather a measure of investor fear in falling markets than of investor positive sentiment in rising markets, which has earned it the moniker 'investor fear gauge'. In a low volatility regime, investors are more sensitive to any decreases in the stock markets, whereas in a high volatility regime the effects of return shocks are more pronounced regardless of their sign. The VIX constitutes a powerful indicator of investor sentiment, i.e. the expected level of volatility perceived by market participants at any given time

Investor Sentiment in the Stock Market

Real investors and markets are too complicated to be neatly summarized by a few selected biases and trading frictions. The "top down" approach to behavioral finance focuses on the measurement of reduced form, aggregate sentiment and traces its effects to stock returns. It builds on the two broader and more irrefutable assumptions of behavioral finance -- sentiment and the limits to arbitrage -- to explain which stocks are likely to be most affected by sentiment. In particular, stocks of low capitalization, younger, unprofitable, high volatility, non-dividend paying, growth companies, or stocks of firms in financial distress, are likely to be disproportionately sensitive to broad waves of investor sentiment. We review the theoretical and empirical evidence for these predictions.

Recent Volatility in U.S. Equity Markets: A Review of Key Contributing Factors and Relationships

This paper is a review of volatility trends, factors, and relationships in U.S. equity markets, with emphasis on the period of time from 1980 to the present, when volatility has been at higher levels than what had been observed earlier. Both finance academics and investment professionals are affected by this ‘high-volatility’ environment, as it impacts the traditional relationships that connect risk and return, and can therefore alter both individual asset and portfolio allocation decisions. Based on a thorough review of the literature on a stock’s idiosyncratic volatility, we explain why it has increased in recent times, discuss factors that affect volatility level, and provide an overview of the empirical relationship between current volatility levels and future expected return. At the end of each section, we pose a related idea for future research – there are ten such ideas offered. The primary purposes of the paper are to convince the reader that volatility is an important investment consideration, to identify the major findings in recent volatility research, and to highlight some unanswered volatility questions for future academics and practitioners to explore

Investor sentiment and herding - an empirical study of UK investor sentiment and herding behaviour

The objectives of this thesis are: first, to investigate the impact of investor sentiment in UK financial markets in different investment intervals through the construction of separate sentiment measures for UK investors and UK institutional investors; second, to examine institutional herding behaviour by studying UK mutual fund data; third, to explore the causal relation between institutional herding and investor sentiment. The study uses US, German and UK financial market data and investor sentiment survey data from 1st January 1996 to 30th June 2011. The impact of investor sentiment on UK equity returns is studied both in general, and more specifically by distinguishing between tranquil and financial crisis periods. It is found that UK equity returns are significantly influenced by US individual and institutional sentiment and hardly at all by local UK investor sentiment. The sentiment contagion across borders is more pronounced in the shorter investment interval. The investigation of institutional herding behaviour is conducted by examining return dispersions and the Beta dispersions of UK mutual funds. Little evidence of herding in return is found, however strong evidence of Beta herding is presented. The study also suggests that beta herding is not caused by market fundamental and macroeconomic factors, instead, it perhaps arises from investor sentiment. This is consistent between closed-end and open-ended funds. The relation between institutional herding and investor sentiment is investigated by examining the measures of herding against the measures of investor sentiment in the UK and US. It suggests that UK institutional herding is influenced by investor sentiment, and UK institutional sentiment has a greater impact as compared to UK market sentiment. Open-end fund managers are more likely to be affected by individual investor sentiment, whereas closed-end fund managers herd on institutional sentiment