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Miha Kralj
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128 lines
6.5 KiB
Markdown
128 lines
6.5 KiB
Markdown
# SUPER: SuperTrend
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> *It's not an indicator; it's a trailing stop with a marketing budget.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Dynamic |
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| **Inputs** | OHLCV bar (TBar) |
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| **Parameters** | `period` (default 10), `multiplier` (default 3.0) |
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| **Outputs** | Multiple series (UpperBand, LowerBand) |
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| **Output range** | Varies (see docs) |
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| **Warmup** | `> period + 1` bars |
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| **PineScript** | [super.pine](super.pine) |
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- SuperTrend is a trend-following overlay that uses ATR-scaled bands around the HL2 midpoint, switching between upper and lower bands based on close ...
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- **Similar:** [SAR](../../reversals/sar/Sar.md), [Ghla](../ghla/Ghla.md) | **Complementary:** ADX for trend strength | **Trading note:** SuperTrend; ATR-based trailing stop that flips direction. Popular in crypto and forex.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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SuperTrend is a trend-following overlay that uses ATR-scaled bands around the HL2 midpoint, switching between upper and lower bands based on close price breakouts. A ratchet mechanism prevents the active band from moving against the trend, creating a step-like trailing stop that adapts to volatility. The indicator is a two-state machine (bullish/bearish) with O(1) per-bar updates and zero allocations in the hot path.
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## Historical Context
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Olivier Seban created SuperTrend, which gained massive popularity in the retail trading community for its visual simplicity: a single line that is green during uptrends and red during downtrends. The construction combines Wilder's ATR volatility measurement (1978) with a breakout/ratchet mechanism. Unlike moving-average crossover systems that produce continuous values, SuperTrend outputs a binary trend state with a concrete stop level, making it directly actionable as a trailing stop-loss. The indicator does not repaint historical values, though the current bar's value can oscillate until the close is finalized.
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## Architecture & Physics
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### 1. Basic Bands
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The raw bands center on the HL2 midpoint, offset by ATR times a multiplier:
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$$\text{Upper}_{\text{basic}} = \frac{H_t + L_t}{2} + m \cdot \text{ATR}(N)$$
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$$\text{Lower}_{\text{basic}} = \frac{H_t + L_t}{2} - m \cdot \text{ATR}(N)$$
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where $m$ is the multiplier (default 3.0) and $N$ is the ATR period (default 10).
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### 2. Ratchet Logic
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The bands act as a one-way ratchet that prevents regression against the trend:
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**Upper band** (bearish stop) can only move down:
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$$\text{Upper}_{\text{final}} = \begin{cases} \min(\text{Upper}_{\text{basic}},\ \text{Upper}_{\text{prev}}) & \text{if } C_{t-1} \leq \text{Upper}_{\text{prev}} \\ \text{Upper}_{\text{basic}} & \text{otherwise} \end{cases}$$
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**Lower band** (bullish stop) can only move up:
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$$\text{Lower}_{\text{final}} = \begin{cases} \max(\text{Lower}_{\text{basic}},\ \text{Lower}_{\text{prev}}) & \text{if } C_{t-1} \geq \text{Lower}_{\text{prev}} \\ \text{Lower}_{\text{basic}} & \text{otherwise} \end{cases}$$
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### 3. Trend State Machine
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$$\text{Trend}_t = \begin{cases} \text{Bullish} & \text{if } C_t > \text{Upper}_{\text{final}} \\ \text{Bearish} & \text{if } C_t < \text{Lower}_{\text{final}} \\ \text{Trend}_{t-1} & \text{otherwise (hysteresis)} \end{cases}$$
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$$\text{SuperTrend} = \begin{cases} \text{Lower}_{\text{final}} & \text{if Bullish} \\ \text{Upper}_{\text{final}} & \text{if Bearish} \end{cases}$$
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The output is the active stop level. Crossing the active band flips the state.
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### 4. Complexity
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| Metric | Value |
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|:-------|:------|
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| Time | O(1) per bar |
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| Space | O(1) (ATR state + 2 band values + 1 trend boolean) |
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| Allocations | Zero in hot path |
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| Warmup | N bars (ATR stabilization) |
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## Mathematical Foundation
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### Parameters
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| Parameter | Type | Default | Constraint | Description |
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|:----------|:-----|:--------|:-----------|:------------|
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| atrPeriod | int | 10 | > 0 | ATR lookback period |
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| multiplier | double | 3.0 | > 0 | ATR multiplier for band width |
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### Band Behavior by State
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| State | Active Band | Ratchet Direction | Flip Condition |
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|:------|:------------|:------------------|:---------------|
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| Bullish | Lower (support) | Can only rise | Close < Lower |
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| Bearish | Upper (resistance) | Can only fall | Close > Upper |
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The step-like output results from the ratchet constraint: the band remains flat until a new extremum pushes it in the trend direction. Whipsaws occur in ranging markets where close repeatedly crosses both bands.
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## Performance Profile
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### Operation Count (Streaming Mode)
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Supertrend uses ATR-based bands with a state-machine ratchet: upper/lower bands only move in their respective directions, and the trend flips when price crosses the active band.
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**Post-warmup steady state (per bar):**
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| Operation | Count | Cost (cycles) | Subtotal |
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| :--- | :---: | :---: | :---: |
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| TR computation (SUB×3, ABS×2, MAX×2) | 7 | 1 | 7 |
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| FMA (RMA ATR update) | 1 | 4 | 4 |
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| MUL (ATR × multiplier) | 1 | 3 | 3 |
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| ADD + SUB (upper/lower basic bands) | 2 | 1 | 2 |
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| MAX/MIN (ratchet: clamp to prev band) | 2 | 1 | 2 |
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| CMP × 2 (trend flip conditions) | 2 | 1 | 2 |
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| CMP × 2 (final band selection) | 2 | 1 | 2 |
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| **Total** | **19** | — | **~22 cycles** |
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The ratchet logic adds branch overhead (~3 cycles average from the CMPs), but overall ~22 cycles per bar.
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### Batch Mode (SIMD Analysis)
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| Operation | Vectorizable? | Notes |
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| :--- | :---: | :--- |
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| TR + ATR (RMA) | **No** | Recursive RMA — sequential |
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| Band arithmetic | Yes | VADDPD + VSUBPD + VMULPD after ATR pass |
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| Ratchet clamp | **No** | State-dependent MAX/MIN — depends on prior band value |
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| Trend flip state machine | **No** | Branch-heavy flip logic depends on prior trend state |
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The ratchet and trend-flip logic create strong sequential dependencies. The ATR and band arithmetic sub-steps are vectorizable as intermediate passes.
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### Quality Metrics
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| Metric | Score | Notes |
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| :--- | :---: | :--- |
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| **Accuracy** | 9/10 | FMA ATR; ratchet logic exact |
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| **Timeliness** | 7/10 | ATR period warmup; ratchet responds immediately to band crosses |
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| **Smoothness** | 9/10 | One-way ratchet eliminates oscillation; clean directional band |
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| **Noise Rejection** | 8/10 | ATR-scaled bands self-adjust to volatility regime |
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## Resources
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- Seban, O. SuperTrend indicator documentation.
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- Wilder, J. W. (1978). *New Concepts in Technical Trading Systems*. Trend Research. |