Volatility. Love it or hate it; it gives traders jobs, can make the market fun to watch, and helps portfolio managers hedge exposure. One of the ways that we can measure this volatility is the VIX. The VIX, which is the ticker symbol for the CBOE’s (Chicago Board of Option) Volatility Index, is a mathematical index of volatility in the market. To understand how it’s calculated, you’ll have to have a little background in finance to get the full picture.
The VIX came about in 1993. It technically measures the implied volatility of the S&P 500 over the next 30 days. The CBOE uses call and put options to determine the variance, therefore the VIX is a derivative index. It is important to note that the VIX is forward looking, so it isn’t perfect at predicting the volatility of the S&P.
The actual calculation of it is my favorite part because I’m a masochist.
This equation is how everything starts. They take the forward price of the S&P 500 and find the two closest strike prices for puts and calls above and below their “moneyness” to create two out of the money option portfolios or “strips”. This formula creates the average price of each of those out of the money strips to give you a variance to work with.
Essentially, they are creating an “at-the-money” option with a forward price for the S&P 500 and calculating the premium on what that “at-the-money” option would be. That works because option premium on an “at-the-money” contract is just time value, which can loosely be considered the “risk/volatility” of the S&P 500.
Then
the CBOE then annualizes the variance, multiplies it by 100, and that’s the VIX. That was the speed run. If 30 day options aren't available, they'll just weight two of the closest contracts on either side of 30 days to make a 30 day expiration.
You might have been thinking that this is pretty redundant since Black Scholes tells us a lot about volatility and risk already. Well Black Scholes kind of does, and it kind of doesn’t. The Black Scholes formula is one method of pricing options that investors consider, but option premium is also priced by the supply and demand of contracts in the open market. In 1987, there was a market crash, and after that crash the Black Scholes developed a skew 
pattern to it. This is because Black Scholes used a standard distribution in its calculation of risk, and if you know anything about the market, you know it’s anything but a standard distribution. The VIX may be a better measure of volatility because it is backed out of option prices, meaning that the VIX considers investor sentiment through the supply and demand forces present in the exchange.
The VIX has many practical uses.
It is often said to “buy when the VIX is high, and go when the VIX is low”. When the VIX is above 30, that’s usually a sign that the market is a little panicky. Asset prices can be either low or falling. When the VIX is below 20, that means that the market is calm and asset prices are relatively stable. The VIX is a mean reverting index, meaning that if it swings to an extreme, it will return to the range that it’s used to. This can sometimes create a self-fulfilling prophecy among investors because if an investor sees that the VIX is high, they may sell out of their asset because they believe the market ahead is rocky, and selling can exacerbate the issue. The VIX is valuable for banks and large portfolios because it helps them hedge the massive exposures that they have.
You can even trade the VIX! But it isn’t recommended. You can buy and sell options on the VIX, but the underlying value of those options is just the index. There are also 24 Exchange Traded Products that allow you trade the VIX, but these ETPs are just collections of VIX options, some with leverage and some inverted. This means that when you are trading a VIX ETP, you are trading a derivative of a VIX option, which is a derivative of the VIX Index, which is created using a formula of S&P 500 derivatives. Your correlations are loose at best. When you are using these ETPs, it’s important to note that you’re subject to contango because you lose portfolio value to the option contract renewals.
There are other measures of volatility for the market which may be helpful for you to know about. The VXN tracks the NASDAQ 100 and the VXD tracks the Dow Jones. There is also something called the VIX of VIX, which is a measure of volatility of the VIX, ticker VVIX. If you are looking for a more accurate fear gauge, CNN’s Fear and Greed indicator takes seven indicators into account to judge market sentiment. Created by the CBOE, there are many other measures for the volatility of other things.
The VIX is a great tool to have in the toolbelt when trading, but it’s not to be used alone. It’s tough for typical traders to trade the VIX or trade equities by watching the VIX because technical analysis often exposes supply and demand opportunities, but since the VIX is entirely a mathematical formula, there are no supply and demand forces present. Trading the VIX itself is not for the faint of heart, but understanding what it is and how it works is a pretty useful thing to know and to watch. The VIX is low right now, so the markets seem pretty calm, but watch the VIX along with some future pullbacks to see how the whole system works. Maybe think about getting into some VIX ETP contracts for those capital gains while you're at it? How brave do you feel?
Sources:
CBOE Futures Exchange. (2017). All About VIX. Retrieved from CBOE.com: http://cfe.cboe.com/education/vixprimer/about.aspx
Chenard, M. (2017). What you need to know about the Volatility Index, otherwise referred to as the VIX. Retrieved from StockTiming.com: https://www.stocktiming.com/Stock_Investing_Course/vix-volatility-chart-explainedPart1.htm
Elmerraji, J. (2011, October 6). How to Trade the VIX. Retrieved from TheStreet: https://www.thestreet.com/story/11271042/3/how-to-trade-the-vix.html
Investopedia. (2017). VIX - CBOE Volatility Index. Retrieved from http://www.investopedia.com/terms/v/vix.asp
Williams, M. (2013, February 28). VIX: What Is It, What Does It Mean, And How To Use It. Retrieved from SeekingAlpha: http://seekingalpha.com/article/1233251-vix-what-is-it-what-does-it-mean-and-how-to-use-it?page=2