Calculating Implied Range Based On VIX

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We have a quick question from both Akib asking how we go about calculating the implied range of something like the S&P based on the VIX, and another question from Ayman who says he heard us mention the rule of 16 and asked for some clarity on that.

So, both these two questions really touch on the same thing guys, so I’ll answer both the questions in this video.

So, let’s start with a few quick points about the VIX, what it is and what we use it for. The VIX is a real-time measure of volatility which was developed by Cboe. The index has a very complicated mathematical equation which we luckily don’t need to know, but what is important to know is what it measures, and what it measures is the 30-day implied volatility for the S&P’s returns based on S&P options.

Now the one thing that is slightly confusing to some traders is the value, what does it mean when we see a VIX trading at 30. This is where things get slightly more complicated, but it makes a lot of sense when you understand what it means. The index is expressed as an annualized number, which means the number you see as the VIX value is the implied percentage move in the S&P over the next 12 months.

For example, right now we are trading at a VIX of close to 30, so that means the market is basically pricing in a 30% move in the S&P from here, whether up or down. So, obviously, the higher this number goes the more uncertain the markets are about the expected moves in the S&P.

So, now that we know this is actually an annualized number, we can look at how we can turn that number in a daily or even weekly implied range. Keep in mind that volatility is proportional to the square root of time, so if we want to convert the annualized number to a daily value, we can simply divide the VIX value by the square root of the number of trading days in a year.

So, let’s get our calculator up, by the way you won’t have to do these calculations every time I’m just showing you how we get to the numbers we use. Right, so we need to divide the VIX number by the square root of the total trading days in a year. We know that there are approximately 252 trading days in a year due to weekends etc. Thus, we just need to find the square root of 252, which is 15.87.

So, to find the daily implied volatility from the VIX, we simply take the VIX number we see and divide that by 15.87. That is where we get to the rule of 16 Ayman, the rule of 16 is simply rounding the 15.87 to the nearest round number which is 16. The difference between dividing VIX by 15.87 and by 16 is so small it’s negligible.

Right, so let’s see how we go about calculating this to get a daily range. Let’s take VIX at 32, so on our calculator we take 32 and divide that by 16, which of course gives us 2, so, at a VIX of 32 there is a 2% implied range for the S&P. So, if we want to calculate that we can take the price of the S&P, let’s take the current price of 3770 to round it off.

That means at a price of 3770 and a daily range of 2%, gives us a range of 75 points. The one thing to keep in mind is that this range isn’t set in stone, as implied volatility rises and falls that range will narrow or widen in real time, so it’s a moving target if that makes sense.

Also keep in mind the confidence level that the market will stay within one standard deviation of that range is about 68%. So, guys, I hope that helps, any other questions just let me know.

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