VIX, often known as “fear index”, is the standard measure of volatility risk for investors in the U.S. stock market. VIX is currently based on the S&P500 Index (SPX) and is devised to
estimate the expected volatility (i.e., standard deviation) over the next thirty calendar days by
averaging the weighted prices of SPX Index options over a wide range of strike prices (CBOE,
2009). Why their is a negative correlation between VIX and global stock market returns?
Your question refers to the so called "leverage effect", i.e., the fact that we observe a negative correlation between stock returns and changes in volatility (the VIX in your case). As mentionned in Ait-Sahalia, Y., Fan, J., & Li, Y. (JFE, 2013): " The term ‘‘leverage’’ refers to one possible economic interpretation of this phenomenon, developed in Black (1976) and Christie (1982): as asset prices decline, companies become mechanically more leveraged since the relative value of their debt rises relative to that of their equity. As a result, it is natural to expect that their stock becomes riskier, hence more volatile."
Dear sir maxime bonelli
I like your arguments i.e. based on reference i will see these papers to understand the leverage effect and vix phenomeon.
Yes, leverage explanation is intuitive, but is does not seem to be supported in the data. If leverage effect would be caused by leverage, you should:
1. the impact of positive and negative returns should be opposite in sign, but similar in magnitude.
2. We should observe this effect for individual stocks also.
However, this paper shows that it is not the case:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=256109
and therefore some behavioral explanation seem to be more likely.
I agree with the points made above; there may also be a difference between the leverage effect for a company and an index. Also the magnitude and sign of the relationship can change. I think Christie (1982), or maybe someone else, found some cases where the relationship was positive for individual stocks. Black in a 1988 NBER Macro Annual article mentions that for the market as a whole, in the months leading up to the '87 crash, the usual negative sign switched to positive, as volatility and prices both rose. In a recent Quantitative Finance article, I tried to verify Black's claim using the Old VIX & S&P 100 to see if over short horizons (like a month or a quarter) that was true in other periods, and found that before periods of market turmoil ('87 crash, Tequila Crisis, Asian Crisis, 2007 Crisis) the sign reversed from negative to positive. There were a few cases I could not explain, and the only crisis when there was no sign switch was during the "Tech Bubble"; maybe that's because there was not much IT in the S&P 100 then (not sure). The sign switch could be consistent with a change (an increase specifically) in the market's expectations of volatility, whereby for a given price level, investors now expect a higher volatility. In normal times, the inverse relationship seems quite tight, and it's when expectations of volatility change that you seem to get a breakdown in the inverse relationship. I also found that was true with the (new) VIX and S&P 500 as well as for other countries.
One more thing, with the CEV process, depending on how you specify it, if the elasticity parameter equals zero, you get GBM, if it's less than zero, then the process has a lower variance than the GBM process, and if the elasticity is positive, it's an explosive process. Since it's usually negative, that would suggest that stock prices usually have a lower variance than GBM, but on rare occasions it's positive, which means it could be occasionally explosive. Of course the CEV process may not be the best way to model stock prices.
https://www.researchgate.net/publication/303830251_Macroeconomic_Determinants_of_the_Behavior_of_Dhaka_Stock_Exchange_DSE
Article Macroeconomic Determinants of the Behavior of Dhaka Stock Ex...
Hi,
You may have a look to this recent paper:
The Role of the Conditional Skewness and Kurtosis in VIX Index Valuation
European Financial management, March 2017, (pages 325–354)Simon Lalancette and Jean-Guy Simonato
Best regards
HI,
Her are two papers that may be of interest for you:
VIX Exchange Traded Products: Price Discovery, Hedging, and Trading Strategy Journal of futures Markets , February 2017, (pages 164–183)
Christoffer Bordonado, Peter Molnár and Sven R. Samda
Trading the VIX Futures Roll and Volatility Premiums with VIX Options
Journal of Futures Marketys, February 2017 (pages 184–208)
David P. Simon
Best regards
- Badges
- Science topic
- Similar topics
- Statistics
- Survey