RSI: alternative derivation

Most traders accept the Relative Strength Index (RSI) as a standard tool for measuring momentum. But what if RSI is actually a position indicator?

This script introduces an alternative derivation of RSI, offering a fresh perspective on its true nature. Instead of relying on the traditional calculation of average gains and losses, this approach directly considers the price's position relative to its equilibrium (moving average), adjusted for volatility.

While the final value remains identical to the standard RSI, this alternative derivation offers a completely new understanding of the indicator.

Key components:

• Price (Close)
  Utilizes the closing price, consistent with the original RSI formula.
  
• normalization factor
  Transforms raw calculations into a fixed range between -1 and +1.
  

  normalization_factor = 1 / (Length - 1)

• EMA of Price
  Applies Wilder’s Exponential Moving Average (EMA) to the price, serving as the anchor point for measuring price position, similar to the traditional RSI formula.
  

  myEMA = ta.rma(close,Length)

• EMA of close-to-close absolute changes (unit of volatility)
  Adjusts for market differences by applying a Wilder’s EMA to absolute price changes (volatility), ensuring consistency across various assets.
  

  CC_vol = ta.rma(math.abs(close - close[1]),Length)

Calculation Breakdown

1. DISTANCE:
   Calculate the difference between the closing price and its Wilder's EMA. A positive value indicates the price is above the EMA; a negative value indicates it is below.
   

   distance = close - myEMA

2. STANDARDIZED DISTANCE
   Divide the distance by the unit of volatility to standardize the measurement across different markets.
   

   S_distance = distance / CC_vol

3. NORMALIZED DISTANCE
   Normalize the standardized distance using the normalization factor (n-1) to adjust for the lookback period.
   

   N_distance = S_distance * normalization_factor

4. RSI
   Finally, scale the normalized distance to fit within the standard RSI range of 0 to 100.
   

   myRSI = 50 * (1 + N_distance)

The final equation:
RSI = 50 × [1 + (Price - EMA) / (Volatility × (n-1))]

What This Means for RSI

• Same RSI Values, Different Interpretation
  
• The standard RSI formula may obscure its true measurement, whereas this approach offers clarity.
  
• RSI primarily indicates the price's position relative to its equilibrium, rather than directly measuring momentum.
  
• RSI can still be used to analyze momentum, but in a more intuitive and well-informed way.