What Is the Average True Range (ATR)?

The average true range (ATR) is a technical analysis indicator introduced by market technician J. Welles Wilder Jr. in his book New Concepts in Technical Trading Systems that measures market volatility by decomposing the entire range of an asset price for that period.

The true range indicator is taken as the greatest of the following: current high less the current low; the absolute value of the current high less the previous close; and the absolute value of the current low less the previous close. The ATR is then a moving average, generally using 14 days, of the true ranges.

Traders can use shorter periods than 14 days to generate more trading signals, while longer periods have a higher probability to generate fewer trading signals.

The Average True Range (ATR) Formula

The formula to calculate ATR for an investment with a previous ATR calculation is :

$\begin{aligned}&\frac{ \text{Previous ATR} ( n – 1 ) + \text{TR} }{ n } \\&\textbf{where:} \\&n = \text{Number of periods} \\&\text{TR} = \text{True range} \\\end{aligned}$​nPrevious ATR(n−1)+TR​where:n=Number of periodsTR=True range​

If there is not a previous ATR calculated, you must use:

$\begin{aligned}&\Big ( \frac{ 1 }{ n } \Big ) \sum_{i}^{n} \text{TR}_i \\&\textbf{where:} \\&\text{TR}_i = \text{Particular true range, such as first day’s TR,} \\&\text{then second, then third} \\&n = \text{Number of periods} \\\end{aligned}$​(n1​)i∑n​TRi​where:TRi​=Particular true range, such as first day’s TR,then second, then thirdn=Number of periods​

You must first use the following formula to calculate the true range:

$\begin{aligned}&\text{ TR } = \text{ Max } [ ( \text{H} – \text{L} ), | \text{H} – \text{C}_p |, | \text{L} – \text{C}_p | ] \\&\textbf{where:} \\&\text{H} = \text{Today’s high} \\&\text{L} = \text{Today’s low} \\&\text{C}_p = \text{Yesterday’s closing price} \\&\text{Max} = \text{Highest value of the three terms} \\&\textbf{so that:} \\&( \text{H} – \text{L} ) = \text{Today’s high minus the low} \\&| \text{H} – \text{C}_p | = \text{Absolute value of today’s high minus} \\&\text{yesterday’s closing price} \\&| \text{L} – \text{C}_p | = \text{Absolute value of today’s low minus} \\&\text{yesterday’s closing price} \\\end{aligned}$​ TR = Max [(H−L),∣H−Cp​∣,∣L−Cp​∣]where:H=Today’s highL=Today’s lowCp​=Yesterday’s closing priceMax=Highest value of the three termsso that:(H−L)=Today’s high minus the low∣H−Cp​∣=Absolute value of today’s high minusyesterday’s closing price∣L−Cp​∣=Absolute value of today’s low minusyesterday’s closing price​

How to Calculate the ATR

The first step in calculating ATR is to find a series of true range values for a security. The price range of an asset for a given trading day is its high minus its low. To find an asset’s true range value, you first determine the three terms from the formula.

Suppose that XYZ’s stock had a trading high today of $21.95 and a low of $20.22. It closed yesterday at $21.51. Using the three terms, we use the highest result:

$( \text{H} – \text{L}) = \$21.95 – \$20.22 = \$1.73$(H−L)=$21.95−$20.22=$1.73

$| ( \text{H} – \text{C}_p ) | = | \$21.95 – \$21.51 | = \$0.44$∣(H−Cp​)∣=∣$21.95−$21.51∣=$0.44

$| ( \text{L} – \text{C}_p ) | = | \$20.22 – \$21.51 | = \$1.29$∣(L−Cp​)∣=∣$20.22−$21.51∣=$1.29

The number you’d use would be $1.73 because it is the highest value.

Because you don’t have a previous ATR, you need to use the ATR formula:

$\begin{aligned}\Big ( \frac{ 1 }{ n } \Big ) \sum_{i}^{n} \text{TR}_i\end{aligned}$(n1​)i∑n​TRi​​

Using 14 days as the number of periods, you’d calculate the TR for each of the 14 days. Assume the following prices from the table.

What Is the Arithmetic Mean?

The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series. For example, take the numbers 34, 44, 56, and 78. The sum is 212. The arithmetic mean is 212 divided by four, or 53.

People also use several other types of means, such as the geometric mean and harmonic mean, which comes into play in certain situations in finance and investing. Another example is the trimmed mean, used when calculating economic data such as the consumer price index (CPI) and personal consumption expenditures (PCE).

How the Arithmetic Mean Works

The arithmetic mean maintains its place in finance, as well. For example, mean earnings estimates typically are an arithmetic mean. Say you want to know the average earnings expectation of the 16 analysts covering a particular stock. Simply add up all the estimates and divide by 16 to get the arithmetic mean.

The same is true if you want to calculate a stock’s average closing price during a particular month. Say there are 23 trading days in the month. Simply take all the prices, add them up, and divide by 23 to get the arithmetic mean.

The arithmetic mean is simple, and most people with even a little bit of finance and math skill can calculate it. It’s also a useful measure of central tendency, as it tends to provide useful results, even with large groupings of numbers.

Limitations of the Arithmetic Mean

The arithmetic mean isn’t always ideal, especially when a single outlier can skew the mean by a large amount. Let’s say you want to estimate the allowance of a group of 10 kids. Nine of them get an allowance between $10 and $12 a week. The tenth kid gets an allowance of $60. That one outlier is going to result in an arithmetic mean of $16. This is not very representative of the group.

In this particular case, the median allowance of 10 might be a better measure.

The arithmetic mean also isn’t great when calculating the performance of investment portfolios, especially when it involves compounding, or the reinvestment of dividends and earnings. It is also generally not used to calculate present and future cash flows, which analysts use in making their estimates. Doing so is almost sure to lead to misleading numbers.

Arithmetic vs. Geometric Mean

For these applications, analysts tend to use the geometric mean, which is calculated differently. The geometric mean is most appropriate for series that exhibit serial correlation. This is especially true for investment portfolios.

Most returns in finance are correlated, including yields on bonds, stock returns, and market risk premiums. The longer the time horizon, the more critical compounding and the use of the geometric mean becomes. For volatile numbers, the geometric average provides a far more accurate measurement of the true return by taking into account year-over-year compounding.

The geometric mean takes the product of all numbers in the series and raises it to the inverse of the length of the series. It’s more laborious by hand, but easy to calculate in Microsoft Excel using the GEOMEAN function.

The geometric mean differs from the arithmetic average, or arithmetic mean, in how it’s calculated because it takes into account the compounding that occurs from period to period. Because of this, investors usually consider the geometric mean a more accurate measure of returns than the arithmetic mean.

Example of the Arithmetic vs. Geometric Mean

Let’s say that a stock’s returns over the last five years are 20%, 6%, -10%, -1%, and 6%. The arithmetic mean would simply add those up and divide by five, giving a 4.2% per year average return.

The geometric mean would instead be calculated as (1.2 x 1.06 x 0.9 x 0.99 x 1.06)^1/5 -1 = 3.74% per year average return. Note that the geometric mean, a more accurate calculation in this case, will always be smaller than the arithmetic mean.

Notional Value vs. Market Value: An Overview

The notional value and market value both describe the value of a security. Notional value speaks to how much total value a security theoretically controls—for instance through derivatives contracts or debt obligations. Market value, on the other hand, is the price of a security right now that can be bought or sold on an exchange or through a broker.

Market value is also used to refer to the market capitalization of a publicly traded company and is determined by multiplying the number of outstanding shares by the current share price.

Notional Value

The notional value is the total amount of a security’s underlying asset at its spot price. The notional value distinguishes between the amount of money invested and the amount of money associated with the whole transaction. The notional value is calculated by multiplying the units in one contract by the spot price.

For example, assume an investor wants to buy one gold futures contract. The futures contract costs the buyer 100 troy ounces of gold. If gold futures are trading at $1,300, then one gold futures contract has a notional value of $130,000.

Notional value can be used in futures and stocks. But it is more often seen and used in the following five ways: through interest rate swaps, total return swaps, equity options, foreign currency exchange and foreign currency derivatives, and exchange-traded funds (ETFs).

With interest rate swaps, the notional value is used to come up with the amount of interest due. With total return swaps, the notional value is used as part of several calculations that determine the swap rates. With equity options, the notional value refers to the value that the option controls. With foreign currency exchange and foreign currency derivatives, notional value is used to value the currencies.

Market Value

Market value is very different from notional value. Market value is the price of a security that buyers and sellers agree on in the marketplace. The security’s market value is calculated by determining the security’s supply and demand. Unlike the notional value, which determines the total value of a security based on its contract specification, the market value is the price of one unit of the security.

For example, assume that the S&P 500 Index futures are trading at $2,700. The market value of one unit of the S&P 500 Index is $2,700. Conversely, the notional value of one S&P Index futures contract is $675,000 ($2,700*250) because one S&P Index futures contract leverages 250 units of the index.

A company’s market value is a good indication of investors’ perceptions of its business prospects. The range of market values in the marketplace is enormous, ranging from less than $1 million for the smallest companies to hundreds of billions for the world’s biggest and most successful companies.

Market value can fluctuate a great deal over periods of time and is substantially influenced by the business cycle. Market values may plunge during the bear markets that accompany recessions, and often rise during the bull markets that are a feature of economic expansion.

The Bottom Line

Market value and notional value each represent different sums that are important for investors to understand. The notional value is how much value is represented by an obligation or contract—for instance, an options contract that controls 1,000 bushels of wheat or a corporate bond with a face value at maturity of $1,000. The market value of these obligations, however, will vary due to supply and demand and prevailing market conditions. For instance if the options contract is very far out of the money, its market value may be close to zero, or if interest rates rise substantially the market value of the bond will be for less than $1,000.