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VIX, a ticker symbol for Volatility Index, measures the implied annual volatility of at-the-money SP500 Index Options. Conventional wisdom presumes VIX to measure the magnitude (positive or negative) of possible movements in future equity prices, with movements being a positive function of VIX. This research investigates the nature of the relationship between VIX and SP500 volatility, and answers the question as to whether that relationship is linear or nonlinear. Based on this research paper, the authors conclude that the realized SP500 volatility is nonlinear, and grows with the level of VIX at an increasing rate. The nonlinearity relationship between VIX and SP500 has enormous implications for investment management and hedging in the financial markets. Manuel G. Russon (USA), Ahmad F. Vakil (USA) BUSINESS PERSPECTIVES LLC “СPС “Business Perspectives” Hryhorii Skovoroda lane, 10, Sumy, 40022, Ukraine www.businessperspectives.org ON THE NON-LINEAR RELATIONSHIP BETWEEN VIX AND REALIZED SP500 VOLATILITY Received on: 17th of March, 2017 Accepted on: 1 of June, 2017 INTRODUCTION VIX, a ticker symbol for Chicago Board Options Exchange Volatility Index, measures the implied 30-day volatility of at-the-money SP500 Index Options. Since its first publication on Jan. 2, 1990, VIX is regularly quoted in the broadcast and print financial media. Technically, it measures the magnitude, positive or negative, of possible movements in SP500, but it is largely viewed as measuring the magnitude and probability of a possible downward movement in the SP500. As such, the VIX is quoted as an indicator of “fear” in the equity markets. Since the VIX is a quantitative, scalable metric, futures and options contracts on VIX futures have been developed for hedging of equity portfolios. This research investigates the functional relationship of realized SP500 return volatility (SPR) to levels of VIX. We conclude that a) the level of the VIX does, in fact, act as a proxy for future actual volatility; b) the proxy for future actual volatility is without upor down-bias; c) the functional relationship between VIX and realized volatility is nonlinear with realized volatility growing with VIX at an increasing rate. The results of this research should be of interest to the entire investment community in general, but to the portfolio management and hedging community, in particular. © Manuel G. Russon, Ahmad F. Vakil, 2017 Manuel G. Russon, Ph.D., University of Mississippi; Professor, the Tobin College of Business, St. John’s University in Queens, USA. Ahmad F. Vakil, Ph.D., Temple University; Professor, the Tobin College of Business, St. John’s University in Queens, USA. This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International license, which permits re-use, distribution, and reproduction, provided the materials aren’t used for commercial purposes and the original work is properly cited. VIX, SP500 volatility, SP500 options, implied volatility

On the non-linear relationship between VIX and realized SP500 volatility