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On asymmetric relationship of India volatility index (India VIX) with stock market return and risk management

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Abstract

This study examines the asymmetric relationship between India volatility index (India VIX) and stock market returns, and demonstrates that Nifty returns are negatively related to the changes in India VIX levels, but in case of high upward movements in the market, the returns on the two indices tend to move independently. When the market takes sharp downward turn, the relationship is not as significant for higher quantiles. This property of India VIX makes it a strong candidate for risk management tool whereby derivative products based on the volatility index can be used as a tool for portfolio insurance against worst declines. We also find that India VIX captures stock market volatility better than traditional measures of volatility including ARCH/GARCH class of models. Finally, we test whether changes in India VIX can be used as a signal for switching portfolios. Our analysis of timing strategy based on change in India VIX exhibits that switching to large-cap (mid-cap) portfolio when India VIX increases (decreases) by a certain percentage point can be useful for maintaining positive returns on a portfolio.

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Notes

  1. The list of volatility indices included in the study is as follows: CBOE volatility index (VIX), Nasdaq volatility index (VXN), DJIA volatility index (VDX), Russel 2000 volatility index (RVX), Deutsche volatility index (VDAX), AEX volatility index (VAEX), BEL 20 volatility index (VBEL), CAC 40 volatility index (VCAC), FTSE 100 volatility index (VFTSE), SWX volatility index (VSMI), Dow Jones EURO STOXX 50 volatility index (VSTOXX), and Montreal exchange volatility index (MVX).

  2. The first criterion, RMSE, measures the differences between the values estimated by a model, say volatility estimated by the GARCHVOL, and the actual values (of realized volatility). Being a scale-dependent measure of accuracy, it compares different estimation errors within a dataset, and serves to aggregate the residuals into a single measure of estimation efficiency. The second one, MAE, is also used to measure how close the implied volatility estimates are to the eventual realized volatility. It is an average of the absolute error of estimation. Finally, mean absolute percent error indicate the estimation accuracy in percentage terms. These criteria are measures of efficiency which are less likely to be affected by the presence of outliers in data set.

  3. Quantile regression is a statistical technique intended to estimate, and conduct inference about, conditional quantile functions. Just as classical linear regression methods based on minimizing sums of squared residuals enable one to estimate models for conditional mean functions, quantile regression methods offer a mechanism for estimating models for the conditional median function, and the full range of other conditional quantile functions. By supplementing the estimation of conditional mean functions with techniques for estimating an entire family of conditional quantile functions, quantile regression is capable of providing a more complete statistical analysis of the stochastic relationships among random variables.

  4. \( {\text{NiftyRet}}_{t}^{ + } \) is NiftyRett if returns on the Nifty index is positive, else 0; and \( {\text{NiftyRet}}_{t}^{ - } \) takes the value of NiftyRet t if returns on the Nifty is negative, else 0.

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Acknowledgment

The paper is based on a project initiated and sponsored by the National Stock Exchange of India Ltd. (NSE), and the full report has appeared as the NSE Working Paper WP/9/2013 under NSE Working Paper Series. The financial support from the NSE is gratefully acknowledged. We would like to thank Saumitra Bhaduri, P. Krishna Prasanna, Murugappa Murgie Krishnan, and Narend S. for their constructive comments on earlier versions of the paper. We also thank the Editor and anonymous reviewers for their helpful comments. The usual disclaimers apply.

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  1. Department of Management Studies (DoMS), Indian Institute of Technology Madras, IIT P. O, Chennai, 600 036, India

    Abhijeet Chandra & M. Thenmozhi

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  1. Abhijeet Chandra
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Correspondence to Abhijeet Chandra.

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Chandra, A., Thenmozhi, M. On asymmetric relationship of India volatility index (India VIX) with stock market return and risk management. Decision 42, 33–55 (2015). https://doi.org/10.1007/s40622-014-0070-0

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