Trading Using ATR Normlise trigonometric angle of EMA 50 slope

Where:

• ​EMA_{current} - EMA_{n}: The vertical change (rise) over n bars.

• ​\text{ATR}: The Average True Range (typically 14 periods) used to normalize the price distance.

• ​n: The lookback period for the slope (often 1 bar for immediate slope or 5-10 bars for trend).

• ​180/\pi: Converts the result from radians to degrees.

​Implementation Steps

1. ​Calculate the EMA 50: Determine the current value and the value n bars ago.

2. ​Calculate the ATR: Use a standard 14-period ATR to gauge the "unit of movement" for that specific asset.

3. ​Normalize the Slope: Divide the EMA difference by the ATR. This tells you how many "volatility units" the average moved per bar.

4. ​Apply Arctangent: Use the formula above to get a degree between -90^\circ and +90^\circ.

​Why Use ATR for This?

• ​Scale Independence: An EMA rising 10 points on a \$50 stock is massive, but on a \$50,000 asset, it is negligible. ATR-based angles treat both relatively.

• ​Trend Strength: A 45^\circ ATR-normalized slope indicates that the EMA is moving up by exactly 1 ATR per bar—a very strong, high-momentum trend.

• ​Filtering Noise: If the price is moving but ATR is also very high (high volatility), the angle will appear "flatter," warning you that the trend is messy rather than clean.

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