Coppock Curve

I. What is the Coppock Curve

The Coppock Curve (also known as the Coppock Indicator) is a long-term momentum indicator that applies a Weighted Moving Average (WMA) to the sum of two Rate of Change (ROC) values with different periods, in order to identify major market bottoms and the beginning of long-term bull markets. It was designed as a monthly-timeframe indicator, primarily used to determine when the market is recovering from a significant decline.

Historical Background

The Coppock Curve was invented by Edwin Sedgwick Coppock in 1962 and first published in Barron’s magazine. Interestingly, Coppock consulted bishops of the Episcopal Church and asked about the average time people need to recover from the loss of a loved one (11–14 months). He applied this “mourning period” to the market — believing that the market’s recovery from a bear market bottom follows a process similar to human psychological recovery. This is why he chose 11 months and 14 months as the ROC periods.

Indicator Classification

• Type: Oscillator, displayed in a separate panel
• Category: Momentum — long-term indicator
• Default Parameters: WMA period $= 10$, long ROC $= 14$, short ROC $= 11$
• Value Range: Unbounded, oscillates around the zero line
• Original Design Timeframe: Monthly

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II. Mathematical Principles and Calculation

Core Formula

Step 1: Calculate two ROC values with different periods

$ROC_{14,t} = \frac{C_t - C_{t-14}}{C_{t-14}} \times 100$

$ROC_{11,t} = \frac{C_t - C_{t-11}}{C_{t-11}} \times 100$

Step 2: Sum

$Sum_t = ROC_{14,t} + ROC_{11,t}$

Step 3: Calculate Weighted Moving Average (WMA)

$Coppock_t = WMA(Sum, 10)_t = \frac{\sum_{i=0}^{9} (10-i) \cdot Sum_{t-i}}{\sum_{i=0}^{9} (10-i)}$

The WMA weights are: $w_0 = 10, w_1 = 9, w_2 = 8, \ldots, w_9 = 1$, with a denominator of $10+9+8+\cdots+1 = 55$.

Step-by-Step Calculation Logic

1. Calculate ROC(14): Percentage change between current price and price 14 periods ago
2. Calculate ROC(11): Percentage change between current price and price 11 periods ago
3. Add them together: ROC(14) + ROC(11)
4. WMA(10): Apply a 10-period weighted moving average to the sum

Why Use WMA?

WMA (Weighted Moving Average) assigns greater weight to recent data, providing better responsiveness to recent changes while maintaining smoothness. Compared to SMA, WMA turning points appear earlier.

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III. Python Implementation

import numpy as np
import pandas as pd


def wma(series: pd.Series, period: int) -> pd.Series:
    """Calculate Weighted Moving Average (WMA)"""
    weights = np.arange(1, period + 1, dtype=float)
    return series.rolling(window=period, min_periods=period).apply(
        lambda x: np.dot(x, weights) / weights.sum(), raw=True
    )


def coppock_curve(close: pd.Series,
                  wma_period: int = 10,
                  long_roc: int = 14,
                  short_roc: int = 11) -> pd.Series:
    """
    Calculate Coppock Curve

    Parameters
    ----------
    close : pd.Series
        Close price series (monthly data recommended)
    wma_period : int
        WMA period, default 10
    long_roc : int
        Long ROC period, default 14
    short_roc : int
        Short ROC period, default 11

    Returns
    -------
    pd.Series
        Coppock Curve values
    """
    roc_long = ((close - close.shift(long_roc)) / close.shift(long_roc)) * 100
    roc_short = ((close - close.shift(short_roc)) / close.shift(short_roc)) * 100

    roc_sum = roc_long + roc_short

    return wma(roc_sum, wma_period)


# ========== Usage Example ==========
if __name__ == "__main__":
    np.random.seed(42)

    # Simulate monthly data (5 years = 60 months)
    dates = pd.date_range("2019-01-01", periods=60, freq="ME")
    # Simulate a decline-then-recovery market cycle
    decline = np.linspace(0, -30, 20)
    recovery = np.linspace(-30, 20, 40)
    trend = np.concatenate([decline, recovery])
    noise = np.cumsum(np.random.randn(60) * 2)
    price = 100 + trend + noise

    df = pd.DataFrame({
        "date": dates,
        "close": price,
    })
    df.set_index("date", inplace=True)

    # Calculate Coppock Curve
    df["Coppock"] = coppock_curve(df["close"])

    print("=== Coppock Curve Results ===")
    print(df[["close", "Coppock"]].dropna().to_string())

    # Buy signal: Coppock turns up while below zero
    df["prev_coppock"] = df["Coppock"].shift(1)
    buy_signal = (
        (df["Coppock"] > df["prev_coppock"]) &  # Turning up
        (df["Coppock"] < 0)                       # Still below zero
    ) & (
        (df["prev_coppock"] <= df["Coppock"].shift(2))  # Previous period was declining
    )

    print("\n=== Buy Signals (Turning Up Below Zero) ===")
    print(df.loc[buy_signal, ["close", "Coppock"]].to_string())

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IV. Problems the Indicator Solves

1. Identifying Major Market Bottoms

The Coppock Curve’s core use case is identifying the bottom area of major bear markets. When the curve turns upward while below the zero line, it suggests the market is recovering from a deep decline.

2. Long-term Buy Signals

Classic buy signal:

• Coppock Curve is below the zero line (market has experienced a significant decline)
• The curve’s direction changes from declining to rising (turns upward)
• This signal indicates long-term momentum is recovering from the bottom

3. Bull Market Confirmation

When the Coppock Curve crosses above the zero line from negative territory, it confirms the long-term trend has shifted from bearish to bullish.

4. Sell Reference

Although Coppock originally designed the indicator as a buy-only tool, traders also use it in reverse:

• Curve turns down while above the zero line -> sell warning
• Curve crosses below zero -> long-term trend may be turning bearish

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V. Advantages, Disadvantages, and Use Cases

Advantages

Advantage	Description
Focused on major bottoms	Designed specifically to capture major market bottoms, historically validated
Very few false signals	Low-frequency signals naturally filter out most market noise
Unique logic	Design philosophy based on human psychological recovery cycles
High historical win rate	Buy signals on the S&P 500 monthly chart have a very high historical win rate

Disadvantages

Disadvantage	Description
Very few signals	May produce only one signal every several years, low daily utility
Monthly only	Originally designed for monthly charts; daily use requires major parameter adjustments
Significant lag	Long-period ROC + WMA results in severely lagging signals
Not a sell indicator	Original design only provides buy signals; selling requires additional judgment

Use Cases

• Long-term investors: Suitable for strategic position-building decisions measured in years
• Index investing: Works best on broad-based indices (e.g., S&P 500, CSI 300)
• Supplementary macro judgment: As a reference tool for judging major market cycle turning points

Comparison with Related Indicators

Comparison	Coppock	MACD	RSI
Time scale	Monthly/yearly	Daily/weekly	Daily/weekly
Signal frequency	Very low	Medium	High
Best for	Long-term positioning	Swing trading	Short/medium-term
Best asset type	Broad indices	Stocks/indices	Stocks/ETFs