Is Volatility Mean Reverting?

Is Volatility Mean Reverting?

The answer is yes, volatility does revert to its mean. This is true for both realized and implied volatility, which are of course closely related.

Nevertheless, volatility is not necessarily mean reverting on all time horizons. I will illustrate it on the VIX index, which is the best known volatility index. Its official name is CBOE Volatility Index and it measures 30-day implied volatility of S&P500 options. The behaviour of volatility of other assets on particular time horizons can be slightly different, although the differences are not that big for most risk assets (especially stocks and most commodities).

Volatility Trending / Mean Reverting Over Various Time Horizons

In general, volatility (in this case the VIX index) is:

Below I will demonstrate typical behaviour of volatility over different time horizons on charts of the VIX.

Intraday: Trending

VIX (CBOE Volatility Index) - 5 minute bars

Volatility is usually trending quite well intraday. Above you can see a chart of the VIX (CBOE Volatility Index) over 4 days (7-10 January 2013). Each bar represents 5 minutes.

Medium Term: Mean Reverting

VIX (CBOE Volatility Index) - daily bars

In the medium term volatility is usually mean reverting. Sometimes the mean reversion happens from day to day, with one day up move in volatility being offset by a down move the next day. Sometimes the waves take much longer, with the VIX trending in one direction for a week or two and then back. The chart above is the VIX in the second half of 2012 (daily bars).

Long Term: Mean Reverting, But Quite Specific

VIX (CBOE Volatility Index) - weekly bars

In the very long term (5 and more years), the VIX stays in the same area, with long-term minimum just below 10 and most of the time spent between 10 and 30. A characteristic feature of volatility in the long term is that it sometimes spikes up very fast (when the stock market crashes) and then returns back down gradually. On the VIX chart above (2008-2012, weekly bars) you can see such spikes in September-October 2008 (after Lehman), May 2010 (Flash Crash), and August 2011 (European sovereign debt crisis).

Related pages

double vix etfcboe vix historical dataoption trading booksblack scholes model derivationmacd histogramdays calculator exceloptions profit loss calculatorquantitative hedge fund strategiesoption payoff graphsvix futures marginmoving average graph exceldelta hedging put optionoption straddle strategyhow to calculate cumulative in excelcboe vixhighest sharpe ratioinverse sp500 etfexcel formula variancesp futures bloombergsharpe ratio analysisblack scholes in excelweighted average unit cost formulaquote cboeput payoff diagramdow jones price weighteddow jones weightingunbiased standard deviation calculatorsample covariance in excelcomputational formula for the sample variancebloomberg vixstdev pvariance covariance varmedian advantages and disadvantagesjohn c hull solutionslogarithm in excelvxx ipathmacd histogram divergenceimplied volatility explainedexcel formulas symbolsstraddle options examplebull put spreadkurtosis normal distributionshort strangle strategyproshare ultraintraday volatilitycboe vix volatility indexaverage equation for excelexcel calculate rate of returnexcel variance functionput payoff diagrametf short s&phow is dow jones industrial average calculatedsell put option graphcontinuous compounding excelformula to calculate dividend yieldcfe vixmean and sd calculatorlong straddle option strategyarithmetic in excelblack scholes simplifiedvelocitysharesrelative strength index calculatorubs e-tracsblack scholes formula put optionhow to average percentages in excelformula kurtosis13f sec filingderiving square rootshow to download stock prices from yahoo financestandard deviation of returns calculatorexcel square root formulasample kurtosiswhat is a straddle positionstraddle example