Vortex Indicator (VI)

I. What is the Vortex Indicator

The Vortex Indicator (VI) was first published in 2010 by Swiss engineer Etienne Botes and market analyst Douglas Siepman in the Technical Analysis of Stocks & Commodities magazine.

The Vortex Indicator belongs to the Trend Direction class of indicators. It identifies the direction and turning points of a trend by comparing Positive Vortex Movement (+VM) and Negative Vortex Movement (-VM). The default period is $n = 14$.

The indicator draws its inspiration from Austrian naturalist Viktor Schauberger (1885—1958) and his research on vortex movements in water. Schauberger observed that water flow contains both positive and negative vortex forces. Botes and Siepman applied this natural phenomenon as an analogy to financial market price movements: the forces of rising and falling prices behave like two intertwined vortex streams.

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II. Mathematical Principles and Calculation

2.1 Vortex Movement (VM)

Positive Vortex Movement (+VM):

$$+\text{VM}_t = |H_t - L_{t-1}|$$

Negative Vortex Movement (-VM):

$$-\text{VM}_t = |L_t - H_{t-1}|$$

Where $H_t$ is the current high, $L_t$ is the current low, and $H_{t-1}$ and $L_{t-1}$ are the previous bar’s high and low respectively.

2.2 True Range (TR)

$$\text{TR}_t = \max\bigl(H_t - L_t,\; |H_t - C_{t-1}|,\; |L_t - C_{t-1}|\bigr)$$

2.3 Vortex Indicators (+VI / -VI)

Sum +VM, -VM, and TR over $n$ periods respectively:

$$+\text{VI}_t = \frac{\sum_{i=0}^{n-1} +\text{VM}_{t-i}}{\sum_{i=0}^{n-1} \text{TR}_{t-i}}$$ $$-\text{VI}_t = \frac{\sum_{i=0}^{n-1} -\text{VM}_{t-i}}{\sum_{i=0}^{n-1} \text{TR}_{t-i}}$$

2.4 Calculation Steps Summary

1. Calculate +VM = |current high - previous low| for each bar
2. Calculate -VM = |current low - previous high| for each bar
3. Calculate the True Range for each bar
4. Sum +VM, -VM, and TR over period $n$ respectively
5. +VI = Sum(+VM) / Sum(TR)
6. -VI = Sum(-VM) / Sum(TR)

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III. Python Implementation

import numpy as np
import pandas as pd

def vortex(high: pd.Series, low: pd.Series, close: pd.Series,
           period: int = 14) -> pd.DataFrame:
    """
    Calculate the Vortex Indicator.

    Parameters:
        high   : Series of high prices
        low    : Series of low prices
        close  : Series of closing prices
        period : Rolling sum period, default 14

    Returns:
        DataFrame containing plus_vi, minus_vi columns
    """
    # Vortex Movement
    plus_vm = (high - low.shift(1)).abs()
    minus_vm = (low - high.shift(1)).abs()

    # True Range
    prev_close = close.shift(1)
    tr1 = high - low
    tr2 = (high - prev_close).abs()
    tr3 = (low - prev_close).abs()
    tr = pd.concat([tr1, tr2, tr3], axis=1).max(axis=1)

    # Rolling sums
    sum_plus_vm = plus_vm.rolling(window=period).sum()
    sum_minus_vm = minus_vm.rolling(window=period).sum()
    sum_tr = tr.rolling(window=period).sum()

    # Vortex Indicators
    plus_vi = sum_plus_vm / sum_tr
    minus_vi = sum_minus_vm / sum_tr

    return pd.DataFrame({
        'plus_vi': plus_vi,
        'minus_vi': minus_vi
    })


# ============ Usage Example ============
if __name__ == '__main__':
    np.random.seed(42)
    n_days = 120

    # Generate simulated OHLCV data with alternating trends
    trend = np.concatenate([
        np.linspace(0, 8, 40),     # Uptrend
        np.linspace(8, 3, 40),     # Downtrend
        np.linspace(3, 10, 40)     # Uptrend
    ])
    noise = np.cumsum(np.random.randn(n_days) * 0.2)
    base_price = 50 + trend + noise

    df = pd.DataFrame({
        'open':   base_price + np.random.randn(n_days) * 0.2,
        'high':   base_price + np.abs(np.random.randn(n_days) * 0.5),
        'low':    base_price - np.abs(np.random.randn(n_days) * 0.5),
        'close':  base_price,
        'volume': np.random.randint(1000, 10000, n_days)
    })

    # Calculate Vortex Indicator
    vi = vortex(df['high'], df['low'], df['close'], period=14)
    df = pd.concat([df, vi], axis=1)

    print("=== Vortex Indicator Results (Last 10 Rows) ===")
    print(df[['close', 'plus_vi', 'minus_vi']].tail(10).round(4).to_string())

    # Crossover signal detection
    df['signal'] = np.nan
    valid = df.dropna(subset=['plus_vi', 'minus_vi'])
    for i in range(1, len(valid)):
        idx = valid.index[i]
        prev_idx = valid.index[i - 1]
        if (valid.loc[idx, 'plus_vi'] > valid.loc[idx, 'minus_vi'] and
            valid.loc[prev_idx, 'plus_vi'] <= valid.loc[prev_idx, 'minus_vi']):
            df.loc[idx, 'signal'] = 1   # Bullish crossover
        elif (valid.loc[idx, 'minus_vi'] > valid.loc[idx, 'plus_vi'] and
              valid.loc[prev_idx, 'minus_vi'] <= valid.loc[prev_idx, 'plus_vi']):
            df.loc[idx, 'signal'] = -1  # Bearish crossover

    signals = df.dropna(subset=['signal'])
    print(f"\n=== Crossover Signals (Total: {len(signals)}) ===")
    for _, row in signals.iterrows():
        direction = "Bullish (+VI crosses above -VI)" if row['signal'] == 1 else "Bearish (-VI crosses above +VI)"
        print(f"  Price={row['close']:.2f}  +VI={row['plus_vi']:.4f}  -VI={row['minus_vi']:.4f}  {direction}")

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IV. Problems the Indicator Solves

4.1 Trend Direction Identification

The Vortex Indicator directly reflects trend direction through the relative position of +VI and -VI:

• +VI > -VI: uptrend dominates, positive vortex force is stronger
• -VI > +VI: downtrend dominates, negative vortex force is stronger
• +VI approx -VI: market direction is unclear, possibly in consolidation

4.2 Trend Reversal Signals

Crossovers of +VI and -VI provide early signals of trend reversals:

• +VI crosses above -VI: bullish signal, a potential shift from downtrend to uptrend
• -VI crosses above +VI: bearish signal, a potential shift from uptrend to downtrend

4.3 Trend Strength Assessment

The wider the gap between +VI and -VI, the more defined the trend:

Condition	Interpretation
+VI and -VI gap is large (> 0.2)	Strong and well-defined trend
+VI and -VI gap is small (< 0.1)	Weak trend or trend transition in progress
Two lines intertwined	Range-bound market, no clear trend

4.4 Typical Trading Strategies

1. Basic Crossover Strategy: go long when +VI crosses above -VI; go short when -VI crosses above +VI
2. Threshold Filter Strategy: only confirm a bullish signal when +VI exceeds a threshold (e.g., 1.10)
3. Multi-Indicator Confirmation Strategy: enter when Vortex crossover + moving average direction agree + ADX > 25
4. Stop-Loss Strategy: use the swing low/high before the crossover point as the stop-loss level

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V. Advantages, Disadvantages, and Use Cases

Advantages

Advantage	Description
Simple and intuitive calculation	Only requires summation and division; no complex recursive smoothing
Clear signals	+VI and -VI crossovers provide unambiguous trend change signals
Captures gaps	Normalized through True Range, correctly reflects the impact of price gaps
Good symmetry	The calculation structure of +VI and -VI is perfectly symmetric, treating both bullish and bearish directions equally

Disadvantages

Disadvantage	Description
Many false signals in range-bound markets	Frequent crossovers during sideways action, low signal reliability
Does not quantify trend strength	Unlike ADX, it does not provide a 0—100 strength reading
Period sensitivity	Too short a period increases noise; too long reduces responsiveness
Lacks built-in filtering mechanism	Requires additional indicators for confirmation

Use Cases

• Best suited for: capturing trend direction and reversals in clearly trending markets
• Well suited for: serving as a directional confirmation component in multi-indicator systems
• Not suited for: low-volatility, range-bound markets

Comparison with Similar Indicators

Indicator	Signal Method	Characteristics
Vortex Indicator	+VI/-VI crossover	Simple calculation; inspired by natural vortex movement
ADX/DMI	+DI/-DI crossover + ADX strength	More comprehensive (direction + strength); but more lagging
Aroon	Aroon Up/Down crossover	Based on position of highs/lows; faster response
MACD	Signal line crossover	Based on moving average difference; more momentum-focused