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| '''Average true range''' ('''ATR''') is a [[technical analysis]] [[Volatility (finance)|volatility]] indicator originally developed by [[J. Welles Wilder, Jr.]] for [[commodities]].<ref>{{cite book | author=[[J. Welles Wilder, Jr.]] | title=New Concepts in Technical Trading Systems | publisher=Trend Research |date=June 1978 | isbn=978-0-89459-027-6 |location=Greensboro, NC}}</ref> The indicator does not provide an indication of price [[Market trend|trend]], simply the degree of price volatility.<ref name=investopedia>[http://www.investopedia.com/terms/a/atr.asp ATR Definition - investopedia.com]</ref><ref>
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| {{cite book
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| | title = International encyclopedia of technical analysis
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| | author = Joel G. Siegel
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| | publisher = Global Professional Publishing
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| | year = 2000
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| | isbn = 978-1-888998-88-7
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| | page = 341
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| | url = http://books.google.com/books?id=IjuoD5yJs8YC&pg=PA341
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| }}</ref>
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| The average true range is an N-day [[moving average (finance)#Exponential moving average|exponential moving average]] of the '''true range''' values. Wilder recommended a 14-period smoothing.<ref>This is by his reckoning of EMA periods, meaning an α=2/(1+14)=0.1333.</ref>
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| == Calculation ==
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| [[File:ATR Indicator Chart.png|thumbnail|right|[[MetaTrader 4|MetaTrader]] EUR/USD chart showing ATR indicator (cyan line) with period 14.]]
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| The range of a day's trading is simply <math>\mbox{high} - \mbox{low}</math>. The '''true range''' extends it to yesterday's closing price if it was outside of today's range.
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| : <math>\mbox{true range} = {\max[(\mbox{high} - \mbox{low}), \mbox{abs}(\mbox{high} - \mbox{close}_\mbox{prev}), \mbox{abs}(\mbox{low}-\mbox{close}_\mbox{prev})]}\,</math>
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| The '''true range''' is the largest of the:
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| * Most recent period's high minus the most recent period's low
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| * Absolute value of the most recent period's high minus the previous close
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| * Absolute value of the most recent period's low minus the previous close
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| The ATR at the moment of time ''t'' is calculated using the following formula:<ref>[http://www.earnforex.com/articles/average-true-range#Average_Value Average True Range calculation]</ref>
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| :<math>ATR_t = {{ATR_{t-1} \times (n-1) + TR_t} \over n}</math>
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| The first ATR value is calculated using the arithmetic mean formula:
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| :<math>ATR = {1 \over n} \sum_{i=1}^n TR_i</math>
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| The idea of ranges is that they show the commitment or enthusiasm of traders. Large or increasing ranges suggest traders prepared to continue to bid up or sell down a [[stock]] through the course of the day. Decreasing range suggests waning interest.
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| == Applicability to futures contracts vs. stocks ==
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| Since true range and ATR are calculated by subtracting prices, the volatility they compute does not change when historical prices are back-adjusted by adding or subtracting a constant to every price. Back-adjustments are often employed when splicing together individual monthly [[futures contract]]s to form a continuous futures contract spanning a long period of time. However the standard procedures used to compute volatility of stock prices, such as the [[standard deviation]] of logarithmic price ratios, are not invariant (to addition of a constant). Thus futures traders and analysts typically use one method (ATR) to calculate volatility, while stock traders and analysts typically use another (SD of log price ratios).
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| == Use in position size calculation ==
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| Apart from being a trend strength gauge, ATR serves as an element of position sizing in financial trading. Current ATR value (or a multiple of it) can be used as the size of the potential adverse movement ([[Order_(exchange)#Stop_orders|stop-loss]] distance) when calculating the trade volume based on trader's risk tolerance. In this case, ATR provides a self-adjusting risk limit dependent on the market volatility for strategies without a fixed stop-loss placement.<ref name="atr-pos">http://www.earnforex.com/blog/position-sizing-rules/#atr-based-position-sizing</ref> A less volatile market has a larger trading position in comparison to a more volatile market in a portfolio.
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| ==References==
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| {{reflist}}
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| == External links ==
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| * [http://www.investopedia.com/articles/trading/08/average-true-range.asp ''Measure Volatility With Average True Range''] at investopedia.com
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| * [http://www.investopedia.com/articles/trading/08/ATR.asp ''Enter Profitable Territory With Average True Range''] at investopedia.com
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| * [http://stockcharts.com/help/doku.php?id=chart_school:technical_indicators:average_true_range_a Average True Range (ATR)] at stockcharts.com
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| {{technical analysis}}
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| [[Category:Technical indicators]]
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