Volatility Research

Information about changes in volatility has always been heavily used by market participants. One of the main motivations for trading in volatility is to diversify equity risk through long volatility exposure (Szado (2009)): volatility movements are known to be negatively correlated with stock index returns. In addition, negative correlation and high volatility are particularly pronounced in stock market downturns, offering protection against stock market losses when it is needed most and when other forms of diversification are not very effective.

EDHEC-Risk Institute has conducted extensive research on the subject of volatility:

**Equity Volatility Indexing Products***Felix Goltz, Stoyan Stoyanov*

September 2013In contrast to the traditional approaches, pure exposure to volatility can be achieved through equity volatility indexing products. Volatility ETNs in particular provide easy access for institutional and retail investors to gain long exposure to equity market volatility. The recent crisis with the TVIX product shows that investors in volatility ETNs need to be aware that (i) the underlying that the product is tracking does not correspond to the actual volatility index but rather to a systematic strategy of investing into volatility index futures, and (ii) an ETN runs the risk of a decoupling of its returns from the underlying. Product providers, on the other hand, need to ensure that sufficient education is provided to investors on the limits of such products in order for the significant growth in these products to be sustainable.

**Analysing Statistical Robustness of Cross-Sectional Volatility***Felix Goltz, Lionel Martellini, Stoyan Stoyanov*

August 2013As demonstrated by Garcia, Mantilla-Garcia and Martellini (2013), cross-sectional volatility can be accepted as a proxy for idiosyncratic volatility which, together with systematic volatility, can be used as an indicator of economic uncertainty. From a practical perspective, an important empirical feature of cross-sections of returns is the presence of significant outliers that pollute volatility estimates. This paper considers in detail the method of simultaneous estimation of location and scale through M-estimation, which deals with the statistical issues resulting from the presence of significant outliers.

*This research has benefited from the support of Fédération Bancaire Française, the French banking federation.*

**The Local Volatility Factor for Asian Stock Markets***Lixia Loh, Lionel Martellini, Stoyan Stoyanov*

August 2013The study finds strong evidence for a very significant local volatility factor in the Asian market index returns. In particular, the analysis reveals that the relationship between the Asian equity index returns and the Asian model-free option-implied (MFOI) volatility indices is significantly stronger than the relationship between Asian equity index returns and VIX. The analysis suggests either a weaker or insignificant relationship between the Asian equity market returns and the US VIX in the presence of Asian volatilities, implying that the Asian volatility indices can absorb the information content of the VIX. This research calls into question the conclusions of previous academic studies and especially the popular idea with professionals that in a period of strong turbulence the recorrelation of the markets and their volatility would suggest the use of a very liquid contract like the VIX futures, which would thereby play a role of global protection against the strong risks of volatility, whatever the portfolios’ geographical exposure.

**Tail Risk of Asian Markets: An Extreme Value Theory Approach***Lixia Loh, Stoyan Stoyanov*

August 2013This paper aims to draw inference about the tail behaviour of different markets through the fitted parameters of a GARCH-EVT model, with an emphasis on Asian markets. The empirical results indicate that the tail thickness is time-varying but there is no regional structure in the tail risk across the different regions. The comparison of the in-sample and out-of-sample tail risk measures, however, reveals higher tail risk for Asian markets indicating that the key difference over the long run is in the levels of volatility rather than in the residual tail thickness. Our findings highlight the importance of volatility modelling for tail risk estimation in the time domain and across regions.

**The Relevance of Country- and Sector-specific Model-free Volatility Indicators***Lixia Loh, Lionel Martellini, Stoyan Stoyanov*

March 2013This paper tests for the presence of local volatility factors using model-free volatility indicators in contrast to the classical model-dependent approach through GARCH-type processes. It employs three different model-free methodologies – model-free option implied volatility (MFOI), realised volatility, and cross-sectional volatility (CSV). Although MFOI volatility relates to market expectations about future volatility levels, both MFOI and realised volatility represent systematic volatility measures. In contrast, CSV represents a measure of aggregate specific volatility which is, however, not empirically disconnected from the market index return.

The analysis is in the context of hedging through a hypothetical exposure to the corresponding volatility indicator rather than predicting market returns. Still, the focus is not so much on the construction of the hedge but whether or not an exposure to a local volatility measure is more efficient compared to an exposure to the US volatility factor

*This research has benefited from the support of Fédération Bancaire Française, the French banking federation.*

**The Risks of Volatility ETNs: A Recent Incident and Underlying Issues***Felix Goltz, Stoyan Stoyanov*

September 2012Getting volatility exposure has become easier for investors after the relatively recent introduction of volatility ETNs (exchange-traded notes) and volatility ETFs (exchange-traded funds) and some of these products have enjoyed a surge in popularity. This paper uses the recent crisis with TVIX – a volatility ETN – to underline important differences between ETNs and ETFs which appear to be at the source of the observed market distortion. It also emphasises an important feature of these products – that they track constant maturity VIX futures indices rather than the VIX index itself – which has an impact on the quality of the volatility exposure because of the roll-over costs and the lack of cash-and-carry arbitrage relationship.

*A revisited version of this paper was published in the Journal of Index Investing, Fall 2013.*

**Introducing a New Form of Volatility Index: The Cross-Sectional Volatility Index***Felix Goltz, Renata Guobuzaite, Lionel Martellini*

January 2011This paper introduces a new form of volatility index, the cross-sectional volatility index. Through formal central limit arguments, it shows that the cross-sectional dispersion of stock returns can be regarded as an efficient estimator for the average idiosyncratic volatility of stocks within the universe under consideration. Among the key advantages of the cross-sectional volatility index measure over currently available measures are its observability at any frequency, its model-free nature, and its availability for every region, sector, and style of the world equity markets, without the need to resort to any auxiliary option market.

*A revisited version of this paper was published in Bankers, Markets & Investors, March 2012.*