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Standard Deviation

Standard Deviation is a statistical measure of volatility. It measures the difference between the market’s closing price and its average price over a defined preceding period of time. The more the price ‘deviates’ from its average i.e. the larger the difference between the closing and average prices, the more volatile the price is said to be and the higher the Standard Deviation. The Bollinger Bands® indicator is based on Standard Deviation.


In times of high price volatility the Standard Deviation increases and in times of low volatility the Standard Deviation decreases.


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The Standard Deviation is based on the range of price movement relative to the Moving Average. The number of periods associated with the Standard Deviation, are used to calculate the moving average, and the number of deviations is used to calculate the Standard Deviation around the moving average.


The prices at each interval for the defined number of periods are used to determine the deviation values. One standard deviation represents 68.2% of the range of price movement relative to the moving average; two standard deviations represent 95.4% of the price movement relative to the moving average and therefore only excludes the extreme highs and lows during the period; three standard deviations represents 99.6% of the price movement.



Standard Deviation Formula

The expectation is that the price distribution around the Simple Moving Average forms a bell curve and that Standard Deviations can be used to establish if the price movement is within normal trading ranges. The following chart provides a visual representation of a classic bell curve with the Standard Deviations representing the range of price movement captured within each deviation:


Standard Deviation Distribution.png


where:

  • 1 Standard Deviation (1σ) = 68.2%
  • 2 Standard Deviation (2σ) = 95.4%
  • 3 Standard Deviation (3σ) = 99.6%


The Standard Deviation chart is calculated based on 1 Standard Deviation. Multiply the Standard Deviation by 2 or 3 to calculate it at vary deviations.


To calculate the Standard Deviation start by calculating the Simple Moving Average, where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle n} is typically 10 or 20 periods:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \text{Simple Moving Average} = \displaystyle \frac { \displaystyle \sum_{j=1}^n \text{CLOSE}j } { n } }


To calculate the Standard Deviation:


Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \text{Standard Deviation} = \displaystyle \sqrt { \frac { \displaystyle \sum_{j=1}^n (\text{CLOSE}j - \text{Simple Moving Average})^2 } { n } } }


Standard Deviation Indicator

The Standard Deviation indicator can be displayed on the TimeToTrade charts. To add the Standard Deviation indicator to the TimeToTrade charts, go to the chart settings and click on the 'Add Indicator' button. Click on the search box and type the name of the indicator that you are looking for, or for example type Standard Deviation and scroll through the results:


Generic Indicator Settings 1.png


After adding the Standard Deviation indicator, within the chart settings, click on it to set the parameters and change colours.



Standard Deviation Alerts

Alerts can be set up to provide an Email or SMS text message notification of when your Standard Deviation indicator chart conditions have been met, backtest trading strategies or execute demo trades. To learn more:



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The information and data provided is for educational and informational purposes only. Interpretation and use of the information and data provided is at the user's own risk. All information and data on this website is obtained from sources believed to be accurate and reliable. However, errors or omissions are possible due to human and/or mechanical error. All information and data is provided "as is" without warranty of any kind. We make no representations as to the accuracy, completeness, or timeliness of the information and data on this site and we reserve the right, in its sole discretion and without any obligation, to change, make improvements to, or correct any errors or omissions in any portion of the services at any times. Past performance is not a guarantee of future results. Trading carries a high level of risk to your capital and can result in losses that exceed your deposits. It may not be suitable for everyone so please ensure you fully understand the risks involved.


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