The concept of Slope or Angle within an Indicator is vague and complex. Given that, generally there is no right answer as it depends upon the purpose of considering the slope. Will it just be a relative measure comparied to earlier measurements or is there comparison across charts & time frames.
The general idea is that on a dynamic scale
(your chart x,y axis) there is no relative way to measure angles, as it depends on the height and width of your chart window, and the minimum and maximum prices displayed within the visible area. In short, measuring angles or slopes is not possible in this context
[top]How Slope Can Be Used In Trading
It is absolutely correct, to obtain the "true" slope of an indicator is quite involved. You need to know the aspect ratio of the resolution of your monitor and then map that back accordingly to the y and x axis units.
But in trading close is close enough. It is possible to determine a slope of a plot based on price and the horizontal axis. The following works rather well:
slope_degree = (radToDegrees*(Math.Atan((Input-Input)/TickSize))) // for a lookback distance of 1
or more general
slope_degree = (radToDegrees*(Math.Atan((Input-Input[lookBackDistance])/lookBackDistance/TickSize)))
The divider of 1.5 you see in the source code of a number of indicators, for example in the linear regression indicator provided by Ninja Trader, means an odd lookback distance of 1.5.
In the end, you are really looking for a way to measure the change of the y axis to the x axis. We have come accustom to the concept of degrees or radians as the standard measure, but you could really use any ratio as long as it was consistent for your measure purpose.
Think about the tachometer in a car
- how accurate is it's reading? Does it really matter? Or is it more important to know at what value your car behaves the best at when shifting. It provides a consistent level of detail to allow you to make an informed decision.
What gets even more interesting is the change of the change. Given the above equation applied to a moving average, it will generate a value. It is possible to then calculate the change of that value 1 bar ago to the current bar. This provides the change of the slope. In mathematics the change of the slope is called the 1st derivative. Velocity is the measure of how fast something is moving. The 1st derivative of Velocity is Acceleration, how fast the Velocity is changing. If we have an accepted measure of the slope of a moving average and we then get the 1st derivative of that (the change of the change) we now know a measure of the change of the slope, sort of the Acceleration of the moving average increase or decrease in steepness. It is very interesting to see what a strong trend looks like with this type of an indicator - it does not need to be to the exact degree, just provide a consistent measure to make informed decisions by.
But with all this stated about slope, it is more important to know this concept does not drive the market. All indicators are representative of what has occurred. Price, greed and fear are the fule for the movement of the market - everything else simply illustrates what has already occurred.
[top]Links to Slope/Angle discussion
[top]What are you trying to accomplish?
When listening to traders discuss Angle/Slope it is clear they are trying to quantify something about the market. Given the relative nature of slope/angle, this is not a concept that will travel well to other charts/instruments. The above formula doesn't properly normalize the result. Normalizing by "TickSize" (that's what the formula does) is not very helpful. For example a tick for ES is something very different then a tick for CL and so are the results with above formula. Proper normalization needs to take volatility into consideration and thus needs more complicated processing. But is it really necessary?
The trader needs to ask, "What am I trying to accomplish?"
What they trader is likely trying to understand about the market is if it is trending or not. Fat Tails
offers a recommendation based upon Volatility and Momentum
Movement is momentum. Momentum can be compared to volatility.
If momentum is small compared to volatility, then we have barb wire market. If momentum is large relative to volatility then the market is trending.
Volatility is smaller time frame momentum, and can be measured via the average range, the average true range or standard deviation.
A little more detail can be found here:
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