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gateway/knowledge/trading/strategies/stocks/support-and-resistance.md

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+---
+description: "Derives support and resistance levels from the previous day's pivot point and trades breakouts or reversals relative to these computed price levels."
+tags: [stocks, technical-analysis, support-resistance, pivot-point]
+---
+
+# Support and Resistance
+
+**Section**: 3.14 | **Asset Class**: Stocks | **Type**: Technical Analysis
+
+## Overview
+This strategy uses "support" (S) and "resistance" (R) levels computed from the previous day's high, low, and closing prices via a "pivot point" (center) C. The trader establishes or liquidates positions based on whether the current price crosses the center, reaches the resistance, or falls to the support level.
+
+## Construction / Signal
+Using the previous day's high `P_H`, low `P_L`, and closing `P_C` prices:
+
+**Pivot point (center)**:
+```
+C = (P_H + P_L + P_C) / 3                                 (325)
+```
+
+**Resistance level**:
+```
+R = 2 * C - P_L                                           (326)
+```
+
+**Support level**:
+```
+S = 2 * C - P_H                                           (327)
+```
+
+**Trading signal** (P is the current price):
+```
+Signal = { Establish long position if P > C
+          { Liquidate long position if P >= R
+          { Establish short position if P < C
+          { Liquidate short position if P <= S              (328)
+```
+
+## Entry / Exit Rules
+- **Long entry**: Current price P crosses above the pivot center C.
+- **Long exit**: Current price P reaches or exceeds the resistance level R (take profit at resistance).
+- **Short entry**: Current price P crosses below the pivot center C.
+- **Short exit**: Current price P falls to or below the support level S (take profit at support).
+
+## Key Parameters
+- **Price inputs**: Previous day's High (P_H), Low (P_L), Close (P_C)
+- **Pivot definition**: Standard: `C = (P_H + P_L + P_C) / 3` (other definitions exist)
+- **Holding period**: Very short-term (intraday to 1 day); pivot levels are reset daily
+
+## Variations
+- **Open-price pivot**: Some definitions use the current day's open price instead of the prior close P_C
+- **Higher/lower support-resistance levels**: Extended pivot systems define multiple support/resistance levels (S2, S3, R2, R3)
+- **Breakout mode**: Instead of reverting at S/R, treat a break through R as a new long entry (trend-following variant)
+
+## Notes
+- Support and resistance levels are reset daily using the previous day's OHLC data.
+- The strategy is primarily intraday or very short-term (daily bar).
+- There is substantial literature on support/resistance strategies but academic evidence for profitability is mixed.
+- Can be combined with volume confirmation: signals are more reliable when price breaks through S/R levels with increased volume.
+- The pivot point methodology has many variants (using open price, weekly pivots, Fibonacci ratios, etc.).