## Volatility

This page is a summary of various resources and other pages on volatility, including topics such as historical volatility, implied volatility, volatility indices, volatility calculation, practical use, and volatility trading. Follow the links to see more details about individual topics.

## Historical Volatility

Historical volatility is the volatility that has been observed in the market. It is calculated from historical market data.

- Historical Volatility Start Page
- Historical Volatility Calculation
- Historical Volatility Excel Calculator + PDF guide

## Implied Volatility

Implied volatility is the volatility that is priced in option prices. It is derived from option prices, typically using an option pricing model.

Implied volatility is closely related to historical volatility, but the two can have hugely different values for the same security sometimes. While historical volatility is something that has already happened (and therefore it is certain and fully known), implied volatility reflects market’s expectations towards the future. Implied volatility is often different even on different options on the same underlying security.

- Implied Volatility Start Page
- Calculating Implied Volatility in Excel
- Black-Scholes Calculator & Simulator + PDF Guide

## Volatility Indices and Derivatives

There has been a growing universe of volatility indices on various assets. The best known of the is the VIX (CBOE Volatility Index), which measures 30-day implied volatility of S&P500 options. Similar volatility indices exist for other equity indices, stocks, ETFs, and other securities around the world. Futures and options are available on some of the volatility indices.

- VIX (CBOE Volatility Index) Start Page
- What Is VIX?
- VIX Calculation
- VIX Futures
- VIX Options
- Trading the VIX

## Frequently Asked Questions about Volatility

The following are commonly asked questions about the basic properties of volatility.

### Volatility Calculation and Mathematical Meaning

Although there are different methods of its calculation and interpretation, volatility is commonly understood as standard deviation of returns. It is usually expressed in percent per annum. When transforming volatility to different time units, the square root of the time unit ratio must be used.

- Is Volatility Variance or Standard Deviation?
- Is Volatility the Same as Variance?
- Is Volatility and Standard Deviation the Same?
- Is Volatility Sigma or Sigma Squared?
- Is Volatility a Percentage?
- Why Is Volatility Proportional to the Square Root of Time?

### Volatility Value Range

Volatility can theoretically reach any value from zero to positive infinite. Most securities trading in real world have volatility between 0 and 100%, although volatility above 100% is far from uncommon. Zero volatility means that a security has constant price (doesn’t move at all).

- Is Volatility Constant?
- Can Volatility Be Negative?
- Can Volatility Be Zero?
- Can Volatility Be Greater than 1?
- Can Volatility Be Over 100?

### Using Volatility

While some people (including some academics and financial professionals) consider volatility an asset class, others don’t. It is believed that adding long volatility can improve risk adjusted return of a portfolio under some circumstances. Volatility futures, options, and exchange traded products (especially those on the VIX) have become popular also for short-term trading.

### Trading Volatility

Although volatility trading can be very rewarding, it is far from easy. As a trading vehicle, volatility has many specifics, especially a return distribution that is unlike any other asset class. While it is commonly believed that volatility is mean reverting (which it generally is), it is not necessarily true on all time horizons.

- Is Volatility Mean Reverting?
- Can You Buy a Volatility Index?
- Volatility Is Your Friend. Is It?
- Is Volatility Good for Traders?

## VIX (CBOE Volatility Index)

This is the main page of Macroption coverage of the **VIX** (CBOE Volatility Index). Below you can find links to various pages providing information and resources for various things regarding the VIX, its futures, options, and ETNs.

## Basic Information about the VIX Index

What Is VIX? – this page answers this and several other frequently asked questions about the VIX. If you are totally unfamiliar with the VIX and volatility indices in general, start here.

VIX Calculation – this page is a bit more advanced – it explains the calculation of the VIX index step-by-step. It focuses on the logic of the calculation rather than the exact mathematics (for those who also want the formulas, there is a link to the original CBOE VIX White Paper).

VIX Chart – this page contains a few charts of the VIX index, in case you need a basic idea of its range and behaviour. I don’t update it very frequently, but there are also links to websites where you can see the latest chart.

## VIX Index Values and Relationship to S&P500

VIX All-Time High and VIX All-Time Low – overview of highest and lowest VIX values recorded in history – the highest/lowest close, the highest/lowest intraday value, number of days with VIX below 10 or above 80, long-term historical chart, and more statistics from VIX history

VIX-SPX Correlation – correlation of daily moves in VIX and S&P500 overall and in individual years, chart of 252-day trailing VIX-SPX correlation, relationship between average VIX value and VIX-SPX correlation

VIX and S&P500 in the Same Direction – statistics on the number of days when VIX moves in the same direction as S&P500 – up days, down days, and what happens on the next day

## Trading the VIX

You may have already heard that the VIX index is quite specific as a trading vehicle. In fact, the index itself is not directly tradable (see explanation why), but you can trade it indirectly using futures, options, and exchange traded products (see details below).

Trading the VIX – this page summarizes the reasons why you may want to trade the VIX and the many specifics of doing so.

## VIX Futures, Options, and Term Structure

VIX Futures – the main page and basic information about VIX futures, which includes contract specifications such as multiplier, tick size, contract months available, expiration and settlement, and trading hours, as well as various links to other pages and resources concerning VIX futures.

VIX Futures Curve – this page explains what the VIX futures curve is, how it looks, what contango and backwardation mean, and how they occur on the VIX.

VIX Term Structure – this page explains the VIX Term Structure, which is not the same as VIX futures curve as many people believe.

VIX Options – the main page and basic information about VIX options, which includes contract specifications, available strikes, exercising them, expiration and settlement, and other resources.

VIX Expiration Calendar (Futures & Options) – VIX expiration calendar for 2013 and 2014 and full history of VIX expiration dates since start of VIX futures trading (2004)

## VIX and VIX Derivatives Historical Data

VIX Historical Data – this page provides links to CBOE pages where you can download the VIX index and VIX futures daily historical data for free. It also includes a few notes concerning navigation on the download pages and the differences between the individual files and symbols.

VIX Options Historical Data – basic instructions and links for getting historical data for VIX options

VIX COT (Commitment of Traders) Reports – the CFTC COT reports for VIX futures: where and how to get them

## VIX Exchange Traded Products

VIX ETF & ETN List – lists of VIX exchange traded products that provide various kinds of exposures (long, 2x long, short, spreads) to various parts of the VIX futures curve; several lists arranged by exposure, by provider, list of most liquid VIX ETFs/ETNs, list of VIX ETFs/ETNs with available options, and list of all VIX ETFs/ETNs sorted by ticker symbol in alphabetical order, including discontinued products

## VIX ETF & ETN List

## VIX ETF & ETN Lists

On this page you can find an overview of VIX ETFs (exchange traded funds) and ETNs (exchange traded notes). Click on the symbol links to see more details about trading exposure and links to official website, factsheet, prospectus, quotes, and charts for individual products. For convenience, the ETFs/ETNs are arranged in several lists here:

- 8 most liquid VIX ETFs and ETNs
- VIX ETFs and ETNs with options available on them
- VIX ETFs and ETNs by exposure (long, short, leveraged)
- VIX ETFs and ETNs by provider (iPath, ProShares, VelocityShares etc.)
- All VIX ETFs and ETNs in alphabetical order (by ticker symbol, including discontinued products)

## Most Liquid VIX ETFs and ETNs

The following VIX ETFs and ETNs have average daily volume at least in hundreds of thousands of shares; some of them in millions; VXX in tens of millions; updated in March 2013):

**VXX** = iPath S&P 500 VIX Short-Term Futures ETN

**UVXY** = ProShares Ultra VIX Short-Term Futures ETF

**XIV** = VelocityShares Inverse VIX Short-Term ETN

**TVIX** = VelocityShares Daily 2x VIX Short-Term ETN

**VIXY** = ProShares VIX Short-Term Futures ETF

**SVXY** = ProShares Short VIX Short-Term Futures ETF

**VXZ** = iPath S&P 500 VIX Mid-Term Futures ETN

**VIIX** = VelocityShares VIX Short-Term ETN

## VIX ETFs and ETNs with Available Options

These VIX ETFs and ETNs have options available on them. However, except for VXX and a few others to some extent, the options are very illiquid.

**VXX** = iPath S&P 500 VIX Short-Term Futures ETN

**UVXY** = ProShares Ultra VIX Short-Term Futures ETF

**VIXY** = ProShares VIX Short-Term Futures ETF

**SVXY** = ProShares Short VIX Short-Term Futures ETF

**VXZ** = iPath S&P 500 VIX Mid-Term Futures ETN

**VIIX** = VelocityShares VIX Short-Term ETN

**VIXM** = ProShares VIX Mid-Term Futures ETF

## VIX ETFs and ETNs by Exposure

ETFs/ETNs in each group are sorted by liquidity (average trading volume) from the most liquid to less liquid.

### 2x Long (Leveraged) – Short-Term VIX Futures

**UVXY** = ProShares Ultra VIX Short-Term Futures ETF

**TVIX** = VelocityShares Daily 2x VIX Short-Term ETN

### 2x Long (Leveraged) – Medium-Term VIX Futures

**TVIZ** = VelocityShares Daily 2x VIX Medium-Term ETN

### 1x Long (Unleveraged) – Short-Term VIX Futures

**VXX** = iPath S&P 500 VIX Short-Term Futures ETN

**VIXY** = ProShares VIX Short-Term Futures ETF

**VIIX** = VelocityShares VIX Short-Term ETN

### 1x Long (Unleveraged) – Medium-Term VIX Futures

**VXZ** = iPath S&P 500 VIX Mid-Term Futures ETN

**VIXM** = ProShares VIX Mid-Term Futures ETF

**VIIZ** = VelocityShares VIX Medium-Term ETN

### 1x Short – Inverse (Unleveraged) – Short-Term VIX Futures

**XIV** = VelocityShares Inverse VIX Short-Term ETN

**SVXY** = ProShares Short VIX Short-Term Futures ETF

**XXV** = iPath Inverse S&P 500 VIX Short-Term Futures ETN

**IVOP** = iPath Inverse S&P 500 VIX Short-Term Futures ETN II

### 1x Short – Inverse (Unleveraged) – Medium-Term VIX Futures

**ZIV** = VelocityShares Inverse VIX Medium-Term ETN

### Relative Value (Spreads)

**XVIX** = ETRACS Daily Long-Short VIX ETN

## VIX ETFs and ETNs by Provider

Products by individual providers are sorted alphabetically by ticker symbol.

### iPath & Barclays

**IVOP** = iPath Inverse S&P 500 VIX Short-Term Futures ETN II

**VQT** = Barclays ETN+ ETNs Linked to the S&P 500 Dynamic VEQTORTM Total Return Index

**VXX** = iPath S&P 500 VIX Short-Term Futures ETN

**VXZ** = iPath S&P 500 VIX Mid-Term Futures ETN

**XVZ** = iPath S&P 500 Dynamic VIX ETN

**XXV** = iPath Inverse S&P 500 VIX Short-Term Futures ETN

### ProShares

**SVXY** = ProShares Short VIX Short-Term Futures ETF

**UVXY** = ProShares Ultra VIX Short-Term Futures ETF

**VIXM** = ProShares VIX Mid-Term Futures ETF

**VIXY** = ProShares VIX Short-Term Futures ETF

### VelocityShares

**TVIX** = VelocityShares Daily 2x VIX Short-Term ETN

**TVIZ** = VelocityShares Daily 2x VIX Medium-Term ETN

**VIIX** = VelocityShares VIX Short-Term ETN

**VIIZ** = VelocityShares VIX Medium-Term ETN

**XIV** = VelocityShares Inverse VIX Short-Term ETN

**ZIV** = VelocityShares Inverse VIX Medium-Term ETN

### ETRACS

**XVIX** = ETRACS Daily Long-Short VIX ETN

### Other Providers

**CVOL** = C-Tracks Citi Volatility Index TR ETN

**PHDG** = Powershares S&P 500 Downside Hedged

**VIXH** = First Trust CBOE S&P 500 VIX Tail Hedge Fund

## All VIX ETFs and ETNs in Alphabetical Order

This list is sorted by ticker symbol. It also includes discontinued products.

**AAVX** = ETRACS Daily Short 1-Month S&P 500 VIX Futures ETN (closed on 12 September 2012)

**BBVX** = ETRACS Daily Short 2-Month S&P 500 VIX Futures ETN (closed on 12 September 2012)

**CCVX** = ETRACS Daily Short 3-Month S&P 500 VIX Futures ETN (closed on 12 September 2012)

**CVOL** = C-Tracks Citi Volatility Index TR ETN

**DDVX** = ETRACS Daily Short 4-Month S&P 500 VIX Futures ETN (closed on 12 September 2012)

**EEVX** = ETRACS Daily Short 5-Month S&P 500 VIX Futures ETN (closed on 12 September 2012)

**FFVX** = ETRACS Daily Short 6-Month S&P 500 VIX Futures ETN (closed on 12 September 2012)

**IVO** = iPath Inverse January 2021 S&P 500 VIX Short-Term Futures ETN (closed on 12 September 2011)

**IVOP** = iPath Inverse S&P 500 VIX Short-Term Futures ETN II

**PHDG** = Powershares S&P 500 Downside Hedged

**SVXY** = ProShares Short VIX Short-Term Futures ETF

**TVIX** = VelocityShares Daily 2x VIX Short-Term ETN

**TVIZ** = VelocityShares Daily 2x VIX Medium-Term ETN

**UVXY** = ProShares Ultra VIX Short-Term Futures ETF

**VIIX** = VelocityShares VIX Short-Term ETN

**VIIZ** = VelocityShares VIX Medium-Term ETN

**VIXH** = First Trust CBOE S&P 500 VIX Tail Hedge Fund

**VIXM** = ProShares VIX Mid-Term Futures ETF

**VIXY** = ProShares VIX Short-Term Futures ETF

**VQT** = Barclays ETN+ ETNs Linked to the S&P 500 Dynamic VEQTORTM Total Return Index

**VXAA** = ETRACS 1-Month S&P 500 VIX Futures ETN (closed on 12 September 2012)

**VXBB** = ETRACS 2-Month S&P 500 VIX Futures ETN (closed on 12 September 2012)

**VXCC** = ETRACS 3-Month S&P 500 VIX Futures ETN (closed on 12 September 2012)

**VXDD** = ETRACS 4-Month S&P 500 VIX Futures ETN (closed on 12 September 2012)

**VXEE** = ETRACS 5-Month S&P 500 VIX Futures ETN (closed on 12 September 2012)

**VXFF** = ETRACS 6-Month S&P 500 VIX Futures ETN (closed on 12 September 2012)

**VXX** = iPath S&P 500 VIX Short-Term Futures ETN

**VXZ** = iPath S&P 500 VIX Mid-Term Futures ETN

**VZZ** = iPath Long Enhanced S&P 500 VIX Mid-Term Futures ETN (closed on 11 July 2011)

**VZZB** = iPath Long Enhanced S&P 500 VIX Mid-Term FuturesTM ETN II (closed on 15 October 2012)

**XIV** = VelocityShares Inverse VIX Short-Term ETN

**XVIX** = ETRACS Daily Long-Short VIX ETN

**XVZ** = iPath S&P 500 Dynamic VIX ETN

**XXV** = iPath Inverse S&P 500 VIX Short-Term Futures ETN

**ZIV** = VelocityShares Inverse VIX Medium-Term ETN

## Jump to:

- 8 most liquid VIX ETFs and ETNs
- VIX ETFs and ETNs with options available on them
- VIX ETFs and ETNs by exposure (long, short, leveraged)
- VIX ETFs and ETNs by provider (iPath, ProShares, VelocityShares etc.)
- All VIX ETFs and ETNs in alphabetical order (by ticker symbol, including discontinued products)

I will try to do my best to keep these lists complete and up to date, but (you know how fast the developments in this area are) if you find something inaccurate or missing, please let me know. Thanks!

## Options Basics

*This is a summary of the very basic terms and concepts of options, including calls and puts, option premium, intrinsic value, time value, implied volatility, and the Greeks. You can follow the links to get a more detailed explanation with examples.*

## Definition and Basic Logic of Options

**Option**represents a right, but not obligation, so it is generally better to own options than not own options.- Options are
**derivative securities**and every option is derived from an**underlying asset**or security. - There are options on various types of underlying assets including stocks, ETFs, indexes, currencies, bonds, interest rates, futures, swaps, and many more.
**Call options**represent the right to buy the underlying asset.**Put options**represent the right to sell the underlying asset.- Read more: What an option is, call options, and put options

## Trading and Exercising Options

- The owner of an option can
**decide to exercise it or not**. - Every option has
**limited life**and after that time period it expires. **American options**can be exercised at any time before or at expiration.**European option**s can be exercised only at expiration.- Read more: Exercising options and expiration
- Some options trade on
**option exchanges**and their contracts are standardized. Options on US stocks traded on the CBOE (Chicago Board Options Exchange) are an example. - Other options trade
**OTC**(over-the-counter), without an exchange.

## Strike Price of an Option

- Every option has a
**fixed strike price**, which is the price that applies to the buying or selling of the underlying asset when the option’s owner exercises the option.

## Market Price and Intrinsic Value of Options

**Market price of an option**(or market value or**option premium**) consists of**intrinsic value**and**time value**. Market price is something totally different from strike price.- Read more: Strike price vs. market price vs. underlying’s price
**Intrinsic value**is the difference between the strike price and current market price of the underlying.- Intrinsic value can’t be negative.
- When the underlying asset’s price grows,
**intrinsic value of a call option**goes up as well. - Read more: Strike price and intrinsic value of call options
**Intrinsic value of put options**moves inversely to the underlying’s price and to intrinsic value of call options. When the underlying asset’s price grows, intrinsic value of a put option falls.- Like with a call, intrinsic value of a put option can’t be negative.
- Read more: Strike price and intrinsic value of put options

## In the Money, At the Money, Out of the Money

- Options with
**intrinsic value**are said to be**in the money**. - Options whose strike price is equal or very close to the current market price of the underlying asset are said to be
**at the money**. - Other options, which have no intrinsic value, are said to be
**out of the money**. **Call options**are in the money when their strike price is lower than the current market price of the underlying asset.**Put options**are in the money when their strike price is higher than the current market price of the underlying asset.- Read more: In the Money, At the Money, Out of the Money Options

## Time Value of Options and Time Decay

**Time value of an option**depends on many factors, primarily on the option’s**moneyness**,**time left to expiration**, and**volatility**.- Read more: Time value of in the money call options, in the money put options, and out of the money options
- The more time is left to expiration, the higher the
**time value**(other things being equal). - The decrease in options’ time value with passing time is called
**time decay**.

## Historical and Implied Volatility

- The higher the volatility, the higher the time value (other things being equal).
- We distinguish historical and implied volatility.
- Here you can find more information and resources on volatility.
**Historical volatility**is volatility observed on the underlying asset’s price in the past. We can calculate historical volatility using historical data.**Implied volatility**is volatility of the underlying asset’s price expected by market participants and reflected in option prices. We can calculate implied volatility using an option’s market price and an**option pricing model**(we need to set the other parameters in the model).- An example of option pricing models is the Black-Scholes Option Pricing Model.
- Different options on the same underlying asset and same expiration can have different implied volatility.

## Delta, Gamma, Theta, and Vega

**Options’ exposures to external factors**can be measured by the so called**Greeks**.- The most important Greeks are delta, gamma, theta, and vega.
**Delta**measures exposure of an option’ market price to changes in market price of the underlying asset.- Read more: Measuring directional exposure with delta
**Gamma**measures exposure of an option’s delta to changes in market price of the underlying asset.**Theta**measures exposure of an option’s market price to passing time.**Vega**measures exposure of an option’s market price to volatility.

## Summary Statistics

*The following is a basic explanation of commonly used summary statistics (including mean, median, variance, standard deviation, skewness, kurtosis, and percentiles), which you can calculate in Excel using the Descriptive Statistics Calculator. Follow the links for more details concerning calculation and interpretation of individual measures.*

## Population or Sample Size (N)

The **size of the data set** (sample or population) is simply how many observations (values) you use to calculate all the summary statistics. It is usually marked as *N* (or *n*). In Excel you can easily get N using the COUNT function. In the Descriptive Statistics Calculator, N is in cell D8.

## Arithmetic Mean

**Arithmetic mean** is the most commonly known and used of all the summary statistics. It is the arithmetic average of all values in a data set. Arithmetic average is calculated as the sum of all values divided by the data set size (N). In Excel, you get arithmetic mean using the AVERAGE function. It is cell D9 in the calculator.

The simplicity of its calculation and interpretation is the main advantage of artihmetic mean. However, there are also **drawbacks**. In some cases (for example when there are extreme values in the data set), other measures tell a better story about the data (one of them is median – see below).

More about arithmetic average:

- How to Calculate Arithmetic Average: The Very Basics
- Arithmetic Average Advantages and Disadvantages
- Arithmetic Average: When to Use It and When Not

## Median

**Median** often complements arithmetic mean as a measure of central tendency (average or most “typical” value) of a data set. Median is the value which is greater than half of all the other values and smallar than the other half. If you sorted all the values in a data set from smallest to greatest, median would be ranked in the middle. In Excel, the function is MEDIAN. The cell in the Descriptive Statistics Calculatoris is D10.

You can see more detailed explanation of median and its calculation here:

## Variance & Standard Deviation

**Variance** is a **measure of dispersion** or variability in the data. It is defined as the **average squared deviation from the mean** and therefore it’s always non-negative. Low variance is interpreted as little variability in the data set (the values tend to be very similar), while high variance indicates a very diverse data set with big differences in individual values.

### Variance vs. Standard Deviation: Units and Use

**Standard deviation** is a more common measure of dispersion (or volatility). It is directly derived from variance – in fact standard deviation is just a **square root of variance**. Its advantage and the main reason why standard deviation is used more frequently than variance is that it is measured in the same units as the underlying data, while variance is measured in the units squared.

For example, standard deviation of a set of prices is measured in dollars, while variance is measured in dollars squared. Standard deviation of investment returns (historical volatility) is measured in percent, while variance would be measured in percent squared.

Variance is still very useful for various tests and analyses (e.g. Analysis of Variance – ANOVA) or as an input for calculation of other measures or indices. With variance, you don’t need to be bothered with the square root as with standard deviation.

### Variance & Standard Deviation Calculation

The exact **calculation of variance and standard deviation** is slightly different depending on the data set being a **sample** or the **entire population**. The respective Excel functions are VAR.S, VAR.P, STDEV.S, and STDEV.P. Variance is in cell D11 and standard deviation in D12 in the Descriptive Statistics Calculator. You can set whether your data set is sample or population in the combo in cell D6.

Here you can see more detailed explanation of variance and standard deviation and their calculation:

- Calculating Variance and Standard Deviation in 4 Easy Steps
- Population vs. Sample Variance and Standard Deviation

## Skewness

Skewness measures the **symmetry of the distribution** – most importantly it compares relative frequency of extreme low (left tail) and extreme high (right tail) values. Normal distribution, which is perfectly symmetric, has skewness of zero. Positive skewness means that extremely high values are *relatively* more common (right tail is fat), while negative skewness means that extremely low values are more common (left tail is fat). In finance and investing (and even more so in options pricing and trading), knowing skewness of return distributions is very useful, as it may indicate frequency or probability of huge gains and (more importantly) huge losses.

The **calculation of skewness** may look complicated at first, but as soon as you get the underlying logic, it is quite straightforward. It is not unlike calculating variance and standard deviation. Skewness too has slightly different formula for population and sample. Here you can see a detailed explanation and derivation of skewness formula.

In Excel, you can calculate **sample skewness** using the built-in SKEW function. There is no built-in function for population skewness, but you can easily calculate it through a small adjustment of the SKEW function (see how). In the calculator skewness is in the cell D13.

## Kurtosis

Kurtosis measures the **peakedness of the distribution** of the values in a data set. High kurtosis means that there are many values very close the the mean and (more importantly) many values very far from it (if you drew a chart of the distribution, there would be a sharp peak in the middle and fat tails). Conversely, low kurtosis means that most values are neither too close, nor too far from the mean.

Kurtosis is often quoted in the form of **excess kurtosis**, which equals kurtosis less 3. The lowest possible value of excess kurtosis is negative 2; the highest is infinite. Normal distribution has excess kurtosis equal to zero (that’s why excess kurtosis is used rather than the “basic” kurtosis). As with skewness, there is a little difference in calculation of population and sample kurtosis.

See detailed explanation of formulas for sample and population kurtosis and excess kurtosis.

In Excel, the function for **sample excess kurtosis** is KURT. There is no built-in Excel function for population kurtosis (you need to calculate it manually by adjusting from KURT – see how to do it here). You can calculate either population or sample excess kurtosis in the Descriptive Statistics Calculator in cell D14.

## Percentiles

Percentiles are used to describe the structure of the data in greater detail. They use the **same logic as median** (above on this page), which in fact is the 50th percentile, as there are 50% values in a data set greater and 50% values smaller than median. Analogically, for 5th percentile there are 95% values greater and 5% smaller, for 99% percentile there are 1% values greater and 99% smaller – and **for Nth percentile there are 1-N% values greater and N% values smaller**.

The Excel function for percentiles (exclusive or inclusive) is PERCENTILE.EXC and PERCENTILE.INC. In the Descriptive Statistics Calculator, percentiles are in cells C18-C28.

## Minimum and Maximum Value

The **extreme values** – **minimum** and **maximum** provide a very useful information that the other summary statistics don’t. In many cases (and especially in finance and investing), it is very useful to know the actual smallest and largest value (e.g. portfolio return in a period). Nevertheless, if your data set is only a sample (e.g. past returns), you should still be prepared for the population (which also includes unknown future returns) to contain even more extreme values.

In Excel, the functions are MIN and MAX. In the Descriptive Statistics Calculator, maximum value is at the top of the percentiles table (cell C17) and mimimum at the bottom (cell C29).

## Download the Calculator

You can find screenshots and download the calculator and the pdf guide here.