# What is Implied Volatility Rank?

To understand what is Implied Volatility Rank we first need to understand the crucial concept of Implied Volatility (IV).

Implied Volatility (IV) is a prediction of how much a stock could move in the future.

To use a simplified example, let’s say a stock is \$100 and an Implied Volatility or IV of 30%. This means that in one year’s time the stock has a 68% chance to be between \$70 and \$130.

Often this "68% chance" is left out and people assume it is closer to 100%. I think it’s a good idea to have at least some understanding of where this 68% figure and some of these terms such as mean, standard deviation, normal distribution, probability, and Implied Volatility Percentile come from.

We will also look at some of the math and probability behind them and free resources you can use to find this important trading data.

So let’s go right back to an example of a random event. The illustrations are taken from Option Volatility and Pricing: Advanced Trading Strategies and Techniques by Sheldon Natenberg

We should be familiar with this carnival game. Imagine dropping a ball, it is random, it can go left or right when it hits a nail, and it will end up in one of the 15 troughs at the bottom.

If we take an infinite sample of balls it will look like this.

This is called normal distribution and using common sense this is what we expect to see. Drop a ball and it can finish in any of the troughs from 1-15, 1 means it goes left every time, 15 means it goes right every time., which of course is highly unlikely. In general there will usually be a mix of lefts and rights.

There is an area of statistics called the empirical formula and the key numbers are 68%, 95%, 99.7%.

These are very important numbers, though the actual calculation of them is outside my wheelhouse, you will need to consult a specialist statistics resource.

Let's look at some of these numbers and what they represent.

You can see top left that mean is 7.5, this is the average outcome

How do we calculate the mean?

Simply add up or sum the total of possible outcomes:

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15 = 120

And then divide it by the number of possible outcomes, i.e. the 15 troughs.

The mean or average outcome is 120/15 = 7.5

In reality 7.5 cannot happen, we don't have a trough 7.5, so on average a ball will end up in trough 7 or trough 8 on average.

You can see in the image that the Standard Deviation is 3, sadly the calculation of this is beyond my knowledge, according to Natenberg it is actually 3.02, but even he doesn't go into the details of how to calculate this, so again you will need to consult a specialist statistics/probability resource.

But we can use this mean and standard deviation data, and the empirical formula, to make some very useful conclusions.

## Examples of using Mean, Standard Deviation and Empirical Formula

One standard deviation

7.5(the mean) - 3(standard deviation) = 4.5 ( round it up to 5)

7.5(the mean) + 3(standard deviation) = 10.5 (round it down to 10)

This means that 68% of the time a ball (taken from our empirical formula)will end up in trough 5 to 10.

Two standard deviations

We can go one step further.  Using 2 standard deviations

7.5(the mean) - 6( 2 standard deviation) = 1.5(round up to 2)

7.5(the mean) + 6 (2 standard deviations) = 13.5 (round down to 13)

This means that 95% of the time a ball will end up in trough 2 to 13.

Three standard deviations

7.5(the mean) - 9 (3 standard deviation) = -1.5

7.5(the mean) + 9 (3 standard deviations) = 16.5

We only have 15 troughs, so trough -1 and trough 16 don't exist, so we can say that 99.7% of the time a ball will land in trough 1 to 15.

### IQ Intelligence Quotient

Another good real world example is IQ, intelligence quotient, where the mean is 100, that is to say the average person has an IQ of 100. So above 100 is above average, below 100 is below average and the standard deviation is 15.

This means from the empirical formula we can immediately know that 68% of people have an IQ of between 85 (100-15) and 115 (100 +15).

And also 95% of the population is between 70 (100 - 2 *15) and 130 (100 + 2 * 15).

And finally that 99.7% of the population has an IQ between 55 ( 100 - 3 *15) and 145 (100 + 3 * 15).

Pretty cool that from some understanding of the fundamentals of statistics that we can calculate some findings so quickly.

### So what does this mean for volatility in stocks?

According to Natenberg, volatility is standard deviation.

So a \$100 stock with 30% volatility, means a \$100 stock with standard deviation of \$30, there is a 68% chance the stock will be between \$70 and \$130 in one year.

That means we know immediately there is a 95% chance that it will be between \$40 (100- 2 * 30) and \$170 (100 + 2*30) in a years time.

So volatility is routed in statistics.

## What is Implied Volatility Rank?

The Implied Volatility Rank ranks implied volatility against the past year of Implied Volatility values for a stock or another commodity. It tells investors where the current Implied Volatility ranks compared to the past year.

This Implied Volatility changes all the time, the most well-known being before earnings as often a stock can rise or fall sharply immediately after an earnings report.

## Confusion Between Implied Volatility Rank and Implied Volatility Percentile

### How to Calculate Implied Volatility Percentile

Be very careful, that there is a lot of confusion between Implied Volatility Rank and Implied Volatility Percentile.

In fact, so much that there is evidence the brokers and broker software don't know the difference!

Let's look at IV percentile first, as this is most useful to traders. It is calculated on a daily basis.

So let’s take some example Implied Volatilities for a stock for 10 days, and let's say today’s IV is 30%.

10, 30, 25, 50, 70, 95, 80, 65, 45, 15.

We are comparing today’s implied volatility against these values, a percentile of 0% means it is trading at the lowest percentage or below the lowest percentage of our range. Its volatility is higher than 0% of the days in your sample.

In this case if you have an implied volatility of 10% or lower means the implied percentile is 0%. That is there are zero days in our sample of 10 that have an implied volatility of lower than 10, 0/10 = 0%.

That shows that 10% volatility is indeed very low for this stock.

An implied volatility of 95% or higher will give implied percentile of 100%.  95% is equal to or higher volatility than all 10 days in our sample, therefore 10/10 = 100%

As we said, we have an implied volatility of 30%, so we have the days where it is 10, 30, 25, and 15 which is 4 days.

That means the Implied Percentile is 4/10 or 40%, i.e. today's volatility is higher than 40% of days in our sample.

So you can conclude that it is a little on the low side, but not much. You can make this judgement very quickly.

However, let's say we have the same 30% volatility for today but our 10 volatilities were:

10, 30, 15, 17, 40, 12, 45, 10, 20, 15.

Now the Implied Volatility percentile is

8/10 = 80%

So 30% volatility is actually very high for this stock, 30% volatility is higher than 80% of days in our sample.  We should not take the implied volatility of a stock as high or low, it is a far better idea to compare today's volatility to the volatitlities over a period of time.

Of course 10 days is quite a small sample to take, so you can take it over a longer time, and on most broker software of financial websites it is 252 which is the number of trading days per year, the number days that the markets are open each year.

So as shown Implied Volatility Percentile is extremely useful for seeing if the volatility of a stock is actually high or low for that stock. From this data you can decide if a something like a stock option is actually cheap or expensive.

### How to Calculate Implied Volatility Rank

Now let's look at Implied Volatility Rank.

### Implied Volatility Rank

100 x (the current IV level - the 52 week IV low) / (the 52 week IV high - 52 week IV low)

Using our first sample of 10 days which are: 10, 30, 25, 50, 70, 95, 80, 65, 45, 15 and today's volatility of 30.

Implied Volatility Rank is:

100 X (30-10) / (95-10) =

100 X 20 / 85 = 23.5

And what is this figure useful for?  Beats me!

However one conclusion we can draw from these figures is this, an IV rank of 50 means that the IV is exactly midway between its lowest and highest IV this year.

Also you will notice that 95-10= 85,

85 / 2 = 42.5

This means 10 + 42.5 = 52.5% volatility.

52.5% is mid point between highest and lowest volatility for the year. It means that 52.5%  has an IV rank of 50.  However there is absolutely no guarantee that the IV actually ever was 52.5% for any day.

### Why is this distinction between Implied Volatility Rank and Implied Volatilty Precentile important?

From our calculations we can see how useful Implied Volatility Percentile is, and we can see that Implied Volatility Rank is not really that useful.

However, unfortunately there is a huge amount of confusion and mislabelling of these two terms.

When people talk about Implied Volatility Rank, what they usually mean is Implied Volatility Percentile.

And it is not just ordinary retail traders that make this mistake, articles on websites and even brokers/broker software have this mislabelling!

This means we need to be sure that we know what is being calculated. If we are adding code to our broker software or trading software, or using an indicator we should double check the math behind the code, and by using the calculations we made above we can see what is actually being calculated.

To show the confusion take a look at this article they call it IV rank but you can see they are calculating the IV percentile.

This article claims that the Thinkorswim IV Rank is actually IV percentile, which makes sense as the IV percentile is a very useful piece of information, whereas IV rank is not. In the images you can see the label is IV rank but it actually calculates IV percentile. So this confusion is also happening with brokers.

### Examples of Implied Volatility Rank and Implied Volatilty Precentile

Barchart.com carries Implied Volatility Rank and Implied Volatility Percentile and they are aware of the confusion between IV Rank and IV Percentile

They label Implied Volatility Percentile as IV%, and when you hover your cursor over IV Rank you get this helpful pop up explaining what Implied Volatility Rank is, see image below.

If you can't read it from the image it says “the ATM average implied volatility relative to the highest and lowest values over the past year. If IV rank is 100% this means the IV is at its highest level over the past year”.

Let's take a look at some of the entries, the image below was taken during premarket on February 7th 2023. The day before this on February 6th BBBY was up over 120% at one point during the session, TSLA had also gained about 90% or more in the previous 5 or 6 weeks.

What we are really interested in is IV%, the IV percentile, and a quick look at the chart tells us for TSLA that its current implied volatility of 72.51% is higher volatility than for 81% of the last 252 trading days in the last calendar year.

Or we can see that META's volatility of 41.58% is only higher than 7% of the 252 trading days in the last year. So like in our 10 day sample above 41% might "feel" like quite high volatility but it is not for META, in fact it is very low.

Since it is so low you can plan strategies for the implied volatility to rise. Using implied volatility percentile (often mislabelled IV rank) can help traders to plan out their trades in a more strategic manner.

So a quick glance at the IV percentile will tell you if that volatility is actually high or not. It is a very useful metric.

By sheer good luck we have an IV rank and an IV percentile of 100 for AMC Cinemas. So this means its IV of 255.28% is the highest IV for the last 252 trading days, which we can see from IV rank. We can also see its IV percentile of 100% tells us that this IV is higher than 100% of the last 252 trading days.

We also have more good luck that the 72.51% implied volatility for TSLA is pretty much bang on in the middle of its range of IV as its IV rank is 50.41%.

So 72.51% is half way between its lowest and highest volatility for the last year, but as we have shown IV rank isn't really terribly useful.

However this figure of 72.51% is higher than on 81% of the last 252 trading days, or the last calendar year, which is useful. It shows that this IV is relatively high for TSLA and this is a good illustration of the difference between IV rank and IV Percentile. So perhaps you might think that IV will drop in the future and plan for that.

I think it’s very important to be clear on this as these terms are very similar sounding and are very easily confused, and this confusion carries over into articles as shown above and worse, broker labelling and actual code you add to your trading software.

We will show this confusion when trying to implement Implied Volatility Rank and/or Implied volatility Percentile on Thinkorswim in a blog post coming soon.

## Why Implied Volatility is Useful

Investors commonly use implied volatility values to calculate contract prices. When the implied volatility is high, it means that a stock’s futures will be priced at a higher rate (premium pricing). The reverse will also be true, and low implied volatility means that contracts can be interpreted as being priced at a discount.

It also gives you a range of prices to expect. Investors use this range to plan their investments, trade entries, and exits.

The implied volatility rank is an add-on index that helps investors know where the stock’s potential volatility stands compared to the entire year. In addition, it adds context to the implied volatility value, making it easier for investors to decide what position to take.

To conclude, be very careful that you know the difference between Implied Volatility Rank and implied Volatility Percentile. By knowing what calculations are being used in an indicator or code you can be sure you ahve the correct information.

You might be also interested in What is a Long Volatility Strategy? and What is an Implied Earnings Move?