Understand Bollinger Bands and squeezes

Core Intuition

WHY do we need them?
Price alone doesn't tell you if a move is "normal" or "extreme" for that stock. A ₹50 move means nothing for a ₹10,000 stock but is huge for a ₹200 stock. Bollinger Bands adapt to each stock's personality by measuring volatility, not just price.

WHAT are they measuring?
Statistical standard deviation from a moving average. 95% of "normal" price action stays within ±2 standard deviations if returns are normally distributed. When price hits the bands, it's in the outer5% of recent behavior—potentially extreme.

Mathematical Foundation

WHY these formulas?

Let's derive from scratch. We want to know: "Is today's price normal or unusual compared to recent history?"

Step 1: Define "normal" as the average price over recent days
→ This gives us the middle band $\text{MB}_t = \frac{1}{N}\sum P_{t-i}$

Step 2: Measure how much prices typically deviate from this average
→ For each historical price, compute deviation: $P_{t-i} - \text{MB}_t$
→ Square them (so negative deviations don't cancel positive ones): $(P_{t-i} - \text{MB}_t)^2$
→ Average these squared deviations: $\frac{1}{N}\sum(P_{t-i} - \text{MB}_t)^2$
→ Take square root to get back to price units: $\sigma_t = \sqrt{\text{variance}}$

WHY this measures volatility? If prices swing wildly, deviations are large → $\sigma$ is large → bands are wide. If prices barely move, $\sigma$ is small → bands are narrow.

Step 3: Create boundaries at "typical extreme" levels
→ Statistics tells us: for a normal distribution, ≈95% of data falls within ±2σ
→ So we place bands at $\text{MB} ± 2\sigma$ to capture "normal" range

WHY derive these?

• Bandwidth makes squeezes quantifiable: BW < 0.10 (or historical low) signals a squeeze
• %B normalizes position: now we can compare a₹100 stock to a ₹5000 stock using the same 0-1 scale

The Bollinger Squeeze

The Physics Analogy: Think of volatility as energy. Low volatility = energy stored (potential energy). High volatility = energy released (kinetic energy). Energy cannot stay compressed forever—it must release.

WHAT triggers a squeeze?

• Consolidation after a trend
• Uncertainty before major news (earnings, policy)
• Tight trading range where buyers and sellers are balanced

HOW to identify?

1. Calculate Bandwidth for last 6months
2. Current BW is in the lowest 5-10% of that range
3. Alternative: Use Bollinger Band Width indicator (most platforms have it)
4. Confirmation: Low volume often accompanies squeezes

WHAT happens after?

• Volatility mean-reverts: low volatility → high volatility
• Price breaks out of the range (direction uncertain)
• New trend often begins
• Bands "re-expand" rapidly

Trading Strategies

WHY volume matters: Breakout without volume = "false breakout" (likely to fail). Volume confirms conviction.

Common Mistakes & Fixes

Parameter Optimization

How to choose $N$ and $k$?

Default (20, 2) works for daily stock charts because:

• 20 days ≈ 1 trading month (reasonable "recent" window)
• 2σ captures 95% of normally distributed data

But adjust for:

• Timeframe: Intraday → shorter $N$ (10-15), weekly → longer $N$ (50)
• Volatility regime: High-vol stocks → increase $k$ to 2.5 or 3
• Strategy: Mean reversion → wider bands, breakout trading → tighter bands

Example Optimization:
Testing TSLA (high volatility stock):

• (20, 2): Price touches bands 15% of time
• (20, 2.5): Price touches bands 8% of time ← better for mean reversion
• (15, 2): Price touches bands 22% of time ← better for active trading

Active Recall Practice

Question: What are the three components of Bollinger Bands and what does each represent? :: 1) Middle Band = N-period SMA (the average/center), 2) Upper Band = MB + k×σ (upper boundary of "normal"), 3) Lower Band = MB - k×σ (lower boundary of "normal"). Standard is 20-period SMA with k=2 (2 standard deviations).

Connections

• 3.4.01-MovingAverages-SMA-EMA|Moving Averages: Middle band is a simple moving average—understanding SMA is prerequisite
• 3.4.03-RSI-and-Stochastic-Oscillators|RSI: Combine with BB for confluence—RSI divergence + band touch = stronger signal
• Average True Range: Both measure volatility; ATR is absolute, BB is relative to price
• Volume Analysis: Essential for confirming breakouts from squeezes
• Support & Resistance: Bands act as dynamic support/resistance, but not static levels
• 2.5.03-Standard-Deviation-and-Volatility|Standard Deviation: Core statistical concept—BB visualizes σ in price domain
• Trend Following: Walking-the-bands strategy works in trending markets
• Range Trading: Mean-reversion at bands works in ranging markets

#flashcards/stock-market

Concept Map

Hinglish (regional understanding)