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


formula for standard deviation in excelhow to calculate root in excelmsft stock split historyrealized volatility formulatvix optionsspx settlementhow to calculate no of days in excel 2007sp futures bloombergskewness and kurtosis interpretationvix option strategiesoptions pricing black scholesexcel option calculator13f sec filinglong short etfmacd formulacalculating implied interest ratecall option payoff graphsec filings 13fmacd divergence strategyweighted average market capblack scholes model excelrsi indicator settingsannualized formula in excelamerican option calculatorstd deviation and variancetheme notepad excel var formulacoefficient of skewtrading option greekswhat is meant by weighted average cost of capital waccadvantages and disadvantages of weighted average methodlifo fifo and weighted averagedividend formula financecurrency options calculatoraverage true range explainedoption straddle strategiesexcel formulas statisticsblack scholes xlspercent variation calculatoryahoo finance currency historical datavalue of a call option formuladefine std deviationoptions straddle calculatorblack scholes dividendstandard deviation computational formulaeasy calculation mean median modejpmorganstockvix call optionscomputation formula for standard deviationwhat is the wacc formulablack sholes modelhow to read macd indicatorkurtosis definedeviation score formulaindicative price meaningstandard deviation computational formulablack scholes calculator putnormdist excel 2010how to calculate skewness and kurtosisnorm s dist excels&p 500 correlationstatistics calculator standard deviationvar value at risk formulachart of vixpayoff diagram for optionslist of section 13f securitiesmaximum profit equationema buutgamma function excelwhat does rsi stand forblack scholes delta calculatoretf etnmean variance and standard deviation formulahow to calculate implied volatilitykurtosis and skewness formulahow to buy vix optionsberkshire hathaway hedge fund