When market volatility spikes or stalls, newspapers, websites, bloggers and television commentators all refer to the VIX^{®}.^{}Formally known as the CBOE Volatility Index, the VIX is a benchmark index designed specifically to track S&P 500 volatility. Most investors familiar with the VIX commonly refer to it as the “fear gauge”, because it has become a proxy for market volatility.
The VIX was created by the Chicago Board Options Exchange (CBOE), which bills itself as “the largest U.S. options exchange and creator of listed options”. The CBOE runs a forprofit business selling (among other things) investments to sophisticated investors. These include hedge funds, professional money managers and individuals that make investments seeking to profit from market volatility. To facilitate and encourage these investments, the CBOE developed the VIX, which tracks market volatility on a realtime basis.
While the math behind the calculation and the accompanying explanation takes up most of a 15page white paper published by the CBOE, we’ll provide the highlights in a lite overview. As my statistics professor once said, “It’s not so important that you are able to complete the calculation. Rather, I want you to be familiar with the concept.” Keeping in mind that he was teaching statistics to a room full of people who were not math majors, let’s take a layman’s look at the calculations behind the VIX, courtesy of examples and information provided by the CBOE.
A Lite Look for the Mildly Curious
The CBOE provides the following formula as a general example of how the VIX is calculated:
The calculations behind each part of the equation are rather complex for most people who don’t do math for a living. They are also far too complex to fully explain in a short article, so let’s put some numbers into the formula to make the math easier to follow:
Delving into the Details
The VIX is calculated using a "formula to derive expected volatility by averaging the weighted prices of outofthemoney puts and calls”. Using options that expire in 16 and 44 days, respectively, in the example below, and starting on the far left of the formula, the symbol on the left of “=” represents the number that results from the calculation of the square root of the sum of all the numbers that sit to the right multiplied by 100. To get to that number:
 The first set of numbers to the right of “=” represents time. This figure is determined by using the time to expiration in minutes of the nearest term option divided by 525,600, which represents the number of minutes in a 365day year. Assuming the VIX calculation time is 8:30am, the time to expiration in minutes for the 16day option will be the number of minutes within 8:30am today and 8:30am on the settlement day. In other words, the time to expiration excludes midnight to 8:30am today and excludes 8:30 am to midnight on the settlement day (full 24 hours excluded). The number of days we’ll be working with will technically be 15 (16 days minus 24 hours), so it's 15 days x 24 hours x 60 minutes = 21,600. Use the same method to get the time to expiration in minutes for the 44day option to get 43 days x 24 hours x 60 minutes = 61,920 (Step 4).
 The result is multiplied by the volatility of the option, represented in the example by 0.066472.
 The result is then multiplied by the result of the difference between the number of minutes to expiration of the next term option (61,920) minus the number of minutes in 30 days (43,200). This result is divided by the difference of the number of minutes to expiration of the next term option (61,920) minus the number of minutes to expiration of the near term option (21,600). Just in case you’re wondering where 30 days came from, the VIX uses a weighted average of options with a constant maturity of 30 days to expiration.
 The result is added to the sum of the time calculation for the second option, which is 61,920 divided by the number of minutes in a 365day year (526,600). Just as in the first calculation, the result is multiplied by the volatility of the option, represented in the example by 0.063667.
 Next we repeat the process covered in step 3, multiplying the result of step 4 by the difference of the number of minutes in 30 days (43,200), minus the number of minutes to expiration of the nearterm options (21,600). We divide this result by the difference of the number of minutes to expiration of the nextterm option (61,920) minus the number of minutes to expiration of the nearterm options (21,600).
 The sum of all previous calculations is then multiplied by the result of the number of minutes in a 365day year (526,600) divided by the number of minutes in 30 days (43,200).
 The square root of that number multiplied by 100 equals the VIX.
Heavy on the Math
Clearly, order of operations is critical in the calculation and, for most of us, calculating the VIX isn’t the way we would choose to spend a Saturday afternoon. And if we did, the exercise would certainly take up most of the day. Fortunately, you will never have to calculate the VIX because the CBOE does it for you. Thanks to the magic of computers, you can go online, type in the ticker VIX and get the number delivered to your screen in an instant.
Investing in Volatility
Volatility is useful to investors, as it gives them a way to gauge the market environment. It also provides investment opportunities. Since volatility is often associated with negative stock market performance, volatility investments can be used to hedge risk. Of course, volatility can also mark rapidly rising markets. Whether the direction is up or down, volatility investments can also be used to speculate.
As one might expect, investment vehicles used for this purpose can be rather complex. VIX options and futures provide popular vehicles through which sophisticated traders can place their hedges or implement their hunches. Professional investors use these on a routine basis.
Exchangetraded notes  a type of unsecured, unsubordinated debt security  can also be used. ETNs that track volatility include the iPath S&P 500 VIX ShortTerm Futures (NYSE:VXX) and the Velocityshares Daily Inverse VIX ShortTerm (NYSE:XIV).
Exchangetraded funds offer a somewhat more familiar vehicle for many investors. Volatility ETF options include the ProShares Ultra VIX ShortTerm Futures (NYSE:UVXY) and ProShares VIX MidTerm Futures (NYSE:VIXM).
There are pros and cons to each of these investment vehicles that should be thoroughly evaluated before making investment decisions.
The Bottom Line
Regardless of purpose (hedging or speculation) or the specific investment vehicles chosen, investing in volatility is not something to jump into without taking some time to understand the market, the investment vehicles and the range of possible outcomes. Failing to do the proper preparation and take a prudent approach to investing can have a more detrimental result to your personal bottom line than making a mathematical error in your VIX calculation.

Markets
Using Historical Volatility To Gauge Future Risk
Use these calculations to uncover the risk involved in your investments. 
Markets
The Uses And Limits Of Volatility
Check out how the assumptions of theoretical risk models compare to actual market performance. 
Options & Futures
Implied Volatility: Buy Low And Sell High
This value is an essential ingredient in the option pricing recipe. 
Options & Futures
Volatility  The Birth Of A New Asset Class
Learn more about the trading possibilities with the VIX. 
Mutual Funds & ETFs
Understanding Volatility Measurements
How do you choose a fund with an optimal riskreward combination? We teach you about standard deviation, beta and more! 
Options & Futures
Ratio Writing: A HighVolatility Options Strategy
Selling a greater number of options than you buy profits from a decline back to average levels of implied volatility. 
Options & Futures
The Volatility Index: Reading Market Sentiment
Using the Volatility Index can be essential for investing success. 
Options & Futures
Measure Volatility With Average True Range
Find more profitable entry and exit locations with this standard indicator. 
Economics
The Problem With Today’s Headline Economic Data
Headwinds have kept the U.S. growth more moderate than in the past–including leverage levels and an aging population—and the latest GDP revisions prove it. 
Economics
Explaining the Participation Rate
The participation rate is the percentage of civilians who are either employed or unemployed and looking for a job.

PrincipalAgent Problem
The principalagent problem develops when a principal creates ... 
ExchangeTraded Fund (ETF)
A security that tracks an index, a commodity or a basket of assets ... 
Discount Bond
A bond that is issued for less than its par (or face) value, ... 
Compound Annual Growth Rate  CAGR
The Compound Annual Growth Rate (CAGR) is the mean annual growth ... 
Internal Rate Of Return  IRR
A metric used in capital budgeting measuring the profitability ... 
Net Line
The amount of risk that an insurance company retains after subtracting ...

Do penny stocks pay dividends?
Because of the small market capitalization and revenues typical of most penny stocks, there are very few that offer dividends. ... Read Full Answer >> 
Can you buy penny stocks in an IRA?
It is possible to trade penny stocks through an individual retirement accounts, or IRA. However, penny stocks are generally ... Read Full Answer >> 
Where do penny stocks trade?
Generally, penny stocks are traded through the use of the Over the Counter Bulletin Board (OTCBB) and through pink sheets. ... Read Full Answer >> 
Where can I buy penny stocks?
Some penny stocks, those using the definition of trading for less than $5 per share, are traded on regular exchanges such ... Read Full Answer >> 
Is my IRA/Roth IRA FDICInsured?
The Federal Deposit Insurance Corporation, or FDIC, is a governmentrun agency that provides protection against losses if ... Read Full Answer >> 
Can my child have an IRA/Roth IRA?
One of the best assets a person can have is an individual retirement account (IRA), and children can have one as long as ... Read Full Answer >>