Typical Price

I. What is Typical Price

Typical Price (TP) is the arithmetic mean of the high, low, and close prices of each bar. It is one of the most important price transforms in technical analysis and serves as the core input for numerous classic indicators.

Historical Background

The concept of Typical Price can be traced back to the formative period of technical analysis in the mid-20th century. Its widespread adoption was driven by Donald Lambert’s invention of the Commodity Channel Index (CCI) in 1980, which explicitly uses Typical Price as its calculation basis. Subsequently, Gene Quong and Avrum Soudack also chose Typical Price as the core price input when they created the Money Flow Index (MFI) in 1989.

Propelled by these classic indicators, Typical Price became the standard representation of the “three-price average” in technical analysis, and virtually every technical analysis software platform includes it as a built-in price type.

Indicator Classification

• Type: Overlay indicator, plotted directly on the price chart
• Category: Other Overlay / Price Transform
• Default Parameters: No parameters; calculated independently for each bar
• Data Requirements: Requires High, Low, and Close data

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II. Mathematical Principles and Calculation

Core Formula

Typical Price is the arithmetic mean of three prices:

$TP_t = \frac{H_t + L_t + C_t}{3}$

Where:

• $H_t$ is the high price of bar $t$
• $L_t$ is the low price of bar $t$
• $C_t$ is the close price of bar $t$

Step-by-Step Calculation

1. Obtain three prices: Read the bar’s High, Low, and Close.
2. Sum: Add the three values $H_t + L_t + C_t$.
3. Divide by 3: Obtain the typical price.
4. Calculate independently per bar: No dependency on any historical data.

Weight Analysis

In Typical Price, each of the three prices accounts for $\frac{1}{3} \approx 33.3\%$ of the weight. Since Close typically falls between High and Low, Typical Price can be understood as:

$TP_t = \frac{H_t + L_t}{2} \times \frac{2}{3} + C_t \times \frac{1}{3} = MP_t \times \frac{2}{3} + C_t \times \frac{1}{3}$

That is, Typical Price is the weighted average of Median Price (weight 2/3) and Close (weight 1/3).

Deviation from Median Price

$TP_t - MP_t = \frac{C_t - MP_t}{3} = \frac{C_t - \frac{H_t + L_t}{2}}{3}$

• When $C_t > MP_t$ (close in the upper half of the bar range): $TP_t > MP_t$, typical price is above median price
• When $C_t < MP_t$ (close in the lower half of the bar range): $TP_t < MP_t$, typical price is below median price
• The deviation magnitude is $\frac{1}{3}$ of the distance the close deviates from the midpoint

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III. Python Implementation

import numpy as np
import pandas as pd

def typical_price(high: pd.Series, low: pd.Series,
                  close: pd.Series) -> pd.Series:
    """
    Calculate Typical Price

    Parameters
    ----------
    high : pd.Series
        High price series
    low : pd.Series
        Low price series
    close : pd.Series
        Close price series

    Returns
    -------
    pd.Series
        Typical price series
    """
    result = (high + low + close) / 3.0
    result.name = "TypicalPrice"
    return result


def typical_price_numpy(high: np.ndarray, low: np.ndarray,
                        close: np.ndarray) -> np.ndarray:
    """
    Calculate Typical Price using numpy
    """
    return (high + low + close) / 3.0


# ========== Usage Example ==========
if __name__ == "__main__":
    np.random.seed(42)
    dates = pd.date_range("2024-01-01", periods=120, freq="D")
    price = 100 + np.cumsum(np.random.randn(120) * 0.5)

    df = pd.DataFrame({
        "date": dates,
        "open":  price + np.random.randn(120) * 0.2,
        "high":  price + np.abs(np.random.randn(120) * 0.8),
        "low":   price - np.abs(np.random.randn(120) * 0.8),
        "close": price + np.random.randn(120) * 0.15,
        "volume": np.random.randint(1000, 10000, size=120),
    })
    df.set_index("date", inplace=True)

    # Calculate Typical Price
    df["tp"] = typical_price(df["high"], df["low"], df["close"])

    # Also calculate Median Price for comparison
    df["mp"] = (df["high"] + df["low"]) / 2

    # Deviation analysis between TP and MP
    df["tp_mp_diff"] = df["tp"] - df["mp"]

    print("=== Typical Price vs Median Price Comparison ===")
    print(df[["high", "low", "close", "tp", "mp", "tp_mp_diff"]].tail(10))

    # Use TP to calculate CCI (simplified version)
    period = 20
    df["tp_sma"] = df["tp"].rolling(window=period).mean()
    df["tp_mad"] = df["tp"].rolling(window=period).apply(
        lambda x: np.mean(np.abs(x - x.mean())), raw=True
    )
    df["CCI"] = (df["tp"] - df["tp_sma"]) / (0.015 * df["tp_mad"])

    print("\n=== CCI(20) Based on Typical Price ===")
    print(df[["close", "tp", "CCI"]].tail(15))

    # Use TP to calculate MFI (simplified version)
    df["mf"] = df["tp"] * df["volume"]  # Money Flow
    df["mf_positive"] = np.where(df["tp"] > df["tp"].shift(1), df["mf"], 0)
    df["mf_negative"] = np.where(df["tp"] < df["tp"].shift(1), df["mf"], 0)

    mfr = (df["mf_positive"].rolling(14).sum()
           / df["mf_negative"].rolling(14).sum().replace(0, np.nan))
    df["MFI"] = 100 - 100 / (1 + mfr)

    print("\n=== MFI(14) Based on Typical Price ===")
    print(df[["close", "tp", "volume", "MFI"]].tail(10))

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IV. Problems the Indicator Solves

1. Standard Input for Core Indicators

Typical Price is the “official” input source for many classic indicators:

Indicator	How TP is Used
CCI (Commodity Channel Index)	$CCI = \frac{TP - SMA(TP)}{0.015 \times MAD(TP)}$
MFI (Money Flow Index)	$MF = TP \times Volume$; positive/negative flow determined by TP change direction
VWAP	$VWAP = \frac{\sum TP \times V}{\sum V}$
Pivot Points	$Pivot = \frac{H + L + C}{3} = TP$

2. Provides a Balanced Price Representation

Typical Price achieves a good balance across three dimensions:

• Price range: Reflects intraday volatility range through High and Low
• Market consensus: Reflects the final pricing through Close
• Balanced weighting: Each factor accounts for 1/3, without overemphasizing any single element

3. Support/Resistance Calculation (Pivot Points)

The classic Pivot Points system directly uses Typical Price as the pivot:

$Pivot = TP = \frac{H_{prev} + L_{prev} + C_{prev}}{3}$ $R_1 = 2 \times Pivot - L_{prev}$ $S_1 = 2 \times Pivot - H_{prev}$

4. Money Flow Analysis

In money flow indicators such as MFI, the per-bar change direction of TP is used to determine capital inflow/outflow:

• $TP_t > TP_{t-1}$ indicates positive money flow (buyer-dominated)
• $TP_t < TP_{t-1}$ indicates negative money flow (seller-dominated)

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V. Advantages, Disadvantages, and Use Cases

Advantages

Advantage	Description
Multi-dimensional information	Simultaneously reflects the price range (H, L) and final consensus (C)
Industry standard	The standard input for CCI, MFI, VWAP, Pivot Points, and more
Simple computation	Requires only one addition and one division, no parameters
More stable than Close	Less affected by extreme closing prices than pure Close

Disadvantages

Disadvantage	Description
No open price information	Lacks Open data compared to Average Price
Equal weight assumption	H, L, C are each weighted at 1/3, though Close may be more important
No independent signals	Does not generate any buy/sell signals on its own
Long shadow sensitivity	Extreme High or Low values will skew TP

Use Cases

• CCI/MFI indicator calculation: These indicators explicitly require Typical Price as input
• Pivot Points systems: The foundation for day traders calculating support/resistance levels
• VWAP calculation: An institutional-grade price benchmark
• Custom indicator development: When a more balanced price input than Close is needed

Comparison with Other Price Types

Comparison	Typical Price	Average Price	Median Price	Weighted Close
Formula	(H+L+C)/3	(O+H+L+C)/4	(H+L)/2	(H+L+2C)/4
Close weight	33.3%	25%	0%	50%
Includes Open	No	Yes	No	No
Classic usage	CCI, MFI, VWAP	Heikin-Ashi Close	Channel midline	Close substitute