Beta -> PROFABIGHI_CAPITAL

🌟 Overview

The Beta → PROFABIGHI_CAPITAL indicator calculates the systematic risk measurement of any asset relative to a chosen benchmark using statistical correlation analysis and variance decomposition methodology. It combines return calculation, covariance analysis, and variance measurement across (Asset Returns, Benchmark Returns, Correlation Analysis) with rolling window calculations. The indicator features automated beta coefficient calculation, zero-division protection, and benchmark comparison analysis for enhanced systematic risk assessment and market correlation identification.

⚙️ General Settings

– Lookback Period: Number of bars for calculating rolling statistics and correlations (1-500 bars, default: 30).
– Benchmark Symbol: Reference market index for beta calculation (default: CRYPTO:BTCUSD).
– Overlay Setting: False - displays as separate pane oscillator for clear beta visualization.

📊 Beta Calculation Components & Methods

The indicator calculates systematic risk metrics using advanced statistical methods:
- Asset Returns: Rate of change calculation for current asset percentage movements per bar
- Benchmark Returns: Rate of change calculation for benchmark percentage movements per bar
- Mean Asset Returns: Simple moving average of asset returns over lookback period
- Mean Benchmark Returns: Simple moving average of benchmark returns over lookback period
- Covariance Calculation: Manual computation measuring how asset and benchmark move together
- Benchmark Variance: Manual calculation of benchmark return volatility and dispersion
- Beta Coefficient: Systematic risk measure derived from covariance divided by benchmark variance

📈 Advanced Statistical Features

Correlation Analysis Framework:
- Return Decomposition: Separation of asset returns into systematic and unsystematic components
- Market Sensitivity: Measurement of asset responsiveness to benchmark movements
- Risk Attribution: Identification of market-related versus asset-specific risk factors

Rolling Window Analysis:
- Dynamic Lookback: Continuously updated statistics over specified period for current relevance
- Adaptive Calculation: Real-time recalculation with each new bar for evolving correlation analysis
- Statistical Smoothing: Moving average application for return volatility reduction

Mathematical Protection:
- Zero-Division Safety: Built-in protection preventing calculation errors when benchmark variance equals zero
- Error Handling: Returns appropriate values when statistical calculations become undefined
- Robust Framework: Maintains functionality across all market conditions and correlation scenarios

📏 Signal Levels & Interpretation

– Beta = 1 (Gray Dash): Asset moves in perfect correlation with benchmark (same volatility)
– Beta > 1 (Above Line): Asset exhibits higher volatility than benchmark (amplified movements)
– Beta < 1 (Below Line): Asset exhibits lower volatility than benchmark (dampened movements)
– Beta = 0 (Zero Line): No correlation between asset and benchmark movements
– Negative Beta: Inverse correlation - asset moves opposite to benchmark direction

📋 Beta Interpretation Framework

Systematic Risk Analysis:
- Beta > 1.0: High Beta Asset - greater systematic risk and volatility than market
- Beta = 1.0: Market Beta - moves in line with benchmark volatility
- Beta < 1.0: Low Beta Asset - lower systematic risk and volatility than market
- Beta ≈ 0: Market Neutral - minimal correlation with benchmark movements
- Negative Beta: Hedge Asset - provides portfolio diversification through inverse correlation

Portfolio Management Applications:
- Risk Assessment: Understanding asset's contribution to portfolio systematic risk
- Diversification Analysis: Identifying correlation patterns for portfolio construction
- Hedging Strategy: Utilizing beta relationships for risk management
- Asset Selection: Choosing assets based on desired beta characteristics

🎨 Visual Features

– Beta Line: Blue line plot with 2-pixel thickness showing beta coefficient evolution
– Reference Line: Horizontal dashed gray line at beta = 1 for market correlation reference
– Separate Pane Display: Independent oscillator visualization for focused beta analysis
– Dynamic Scaling: Automatic y-axis adjustment to accommodate beta value ranges

🔍 Advanced Features

– Multi-Asset Compatibility: Works across all asset classes and market instruments
– Benchmark Flexibility: Any tradable symbol can serve as correlation benchmark
– Real-Time Updates: Continuous beta recalculation with each new price bar
– Statistical Accuracy: Manual covariance and variance calculations ensuring precision
– Rolling Window Methodology: Maintains specified lookback period for all calculations
– Correlation Sensitivity: Responsive to changing market relationships and correlations

🔔 Beta Applications & Signals

– High Beta Identification: Assets with beta > 1.2 indicating high market sensitivity
– Low Beta Recognition: Assets with beta < 0.8 indicating defensive characteristics
– Beta Stability Analysis: Monitoring beta consistency over time for reliability assessment
– Correlation Breakdown: Identifying periods when historical correlations change
– Risk Management: Using beta values for position sizing and portfolio risk control
– Market Regime Detection: Beta changes often signal shifting market conditions

By utilizing precise statistical correlation analysis and systematic risk measurement, the Beta → PROFABIGHI_CAPITAL indicator provides mathematically robust market sensitivity analysis, offering accurate identification of systematic risk exposure through rigorous covariance calculation, variance analysis, and benchmark correlation assessment.