RSI Formulations

The Relative Strength Index (RSI) measures momentum by comparing the magnitude of recent upward price movements against recent downward movements. Two common calculasion variants are widely used.

Summation Approach (SMA-based)

For a chosen look-back period N:

• G = Sum of all positive daily price changes over the interval
• L = Sum of absolute values of all negative daily changes over the interval
• RSI = G / (G + L) × 100

Smoothed Aproach (Wilder's Method)

• Average Gain = Smoothed moving average of positive changes using smoothing factor α = 1 / N
• Average Loss = Smoothed moving average of absolute negative changes using α = 1 / N
• Relative Strength (RS) = Average Gain / Average Loss
• RSI = 100 − 100 / (1 + RS)

The smoothed approach is the convention used by most professional charting platforms.

Dataset Prerequisites

The implementations below expect a DataFrame containing at minimum a close column of numeric prices. A date column is optional but recommended for chronological alignment. The default look-back is 14 periods, though horizons such as 6 or 21 are also common.

Implementation: Summation Method

import pandas as pd

def rsi_sma_variant(prices: pd.DataFrame, period: int = 14) -> pd.DataFrame:
    frame = prices.copy()

    if "date" in frame.columns:
        frame["date"] = pd.to_datetime(frame["date"])
        frame = frame.sort_values("date").reset_index(drop=True)

    # Daily price deltas
    delta = frame["close"].diff()

    # Isolate upward and downward moves
    advances = delta.clip(lower=0)
    declines = (-delta).clip(lower=0)

    # Aggregate over the look-back window
    sum_gains = advances.rolling(window=period, min_periods=period).sum()
    sum_losses = declines.rolling(window=period, min_periods=period).sum()

    # Compute oscillator
    frame["rsi"] = 100.0 * sum_gains / (sum_gains + sum_losses)

    return frame

Implementation: Smoothed Average Method

import pandas as pd
import numpy as np

def rsi_smoothed_variant(prices: pd.DataFrame, period: int = 14) -> pd.DataFrame:
    frame = prices.copy()

    if "date" in frame.columns:
        frame["date"] = pd.to_datetime(frame["date"])
        frame = frame.sort_values("date").reset_index(drop=True)

    # Compute daily returns
    delta = frame["close"].diff()

    up = delta.clip(lower=0)
    down = (-delta).clip(lower=0)

    # Wilder's exponential smoothing: alpha = 1 / period
    avg_up = up.ewm(alpha=1 / period, min_periods=period, adjust=False).mean()
    avg_down = down.ewm(alpha=1 / period, min_periods=period, adjust=False).mean()

    # Guard against zero average loss
    rs = avg_up / avg_down.replace(0, np.nan)

    # Apply RSI formula
    frame["rsi"] = 100.0 - (100.0 / (1.0 + rs))

    # When no losses exist, RSI is defined as 100
    frame.loc[avg_down == 0, "rsi"] = 100.0

    return frame

Consistency Notes

The smoothed implementation generally reproduces values displayed in retail and institutional trading terminals because standard RSI defaults to Wilder's exponential smoothing rather than a simple rolling summation. Where average loss equals zero, the formula naturally converges to the upper bound of 100.