The CBOE Volatility Index, VIX, is expressed in percentage terms as an annualized one standard deviation move of returns on the S&P 500 Index. For example, for a value 20 this would mean that a one standard deviation move is expected to be: sqrt(30/365.25) * Annualized Volatility (20%) = 5.7%. In other words, for a VIX of 20, this means that the market (implied from option prices) expects the S&P 500 Index to be within +/- 5.7% for a 30 day period 68% of the time (the amount of expected observations within + and - one standard deviation).
For a detailed explanation of how the VIX is calculated, you can see the official whitepaper here: https://cdn.cboe.com/resources/vix/vixwhite.pdf
But lets go over some of the basics.
Why do we estimate 30 day?
When the VIX was first introduced, not as many option series (months) were listed. But there was generally options 1 month and 2 months listed on the regular expiration (generally the 3rd Friday of the month) meaning that mathematically can almost always interpolate a value for 30 days. As S&P 500 became more popular and more options were listed, now VIX indexes are also calculated for 9 days (VIX9D), 3 months (VIX3M), 6 months (VIX6M) and 1 year (VIX1Y). Generally these values are pretty close to each other with further months having higher values. During times of uncertainty this relationship may not hold and monitor these data points can give insist into how stable the markets are expected to be.
With VIX values normally being close for different maturities, it is convenient and more easy to recognize if prices are behaving as expected if we look at things on a 1 day forecast:
Generally, you'll be able to see 1 day change of S&P 500 and VIX Index level easily, so if VIX is 20% you can know easily if the market is up or down more than 2.1% it is not a common occurrence happening less than 5% of the time.
Can you trade this Index?
Not easily. Most people can get exposure with listed options, or trade future expectations of this value with VIX futures or VIX futures ETN/ETF (VXX). Professionals can trade this index through variance swaps. Currently the listed market isn't active so you need to have an ISDA with a bank to trade them OTC.
Takeaways:
VIX is often referred to as a "fear gauge", but it is really just measuring future uncertainty of the S&P 500 Index. If you know the value of VIX is around 20% (and use this as an estimate for 1 day move) can you expect the market daily move to be within 1% ( 68% of the time) and 2.1% (95% of the time).
If you want to see how accurate the VIX is as a forecasting instrument, let me know; but from the way options pricing work, I can tell you that it over estimates the moves on average (uncertainty premium) but when the big moves occur it is significantly larger than expected (tail risk).
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