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Sharpe Single Index Model - Coggle Diagram
Sharpe Single Index Model
Introduction
Simplified Markowitz
Uses market index
Reduces calculations
Suitable for large portfolios
Risk Types
Systematic Risk
Cannot be reduced
Market risk
Affects all securities
Examples:
Inflation
Interest rate
Economic changes
Unsystematic Risk
Firm-specific
Can be reduced
Examples:
Strike
Management issues
Competition
Total Risk
Total = Systematic + Unsystematic
Diversification reduces only unsystematic
Characteristic Line
Relationship between Ri and Rm
Regression line
Formulas
Ri = α + βRm + e
α → excess return
β → systematic risk
σ² = β²σm² + σe²
σe² → unsystematic risk
Beta = market risk
Alpha = extra return
Diversification reduces risk
Model is simple and practical
Summary
Beta = market risk
Market sensitivity
Risk measure
Alpha = extra return
Extra return
Company performance
Error term (e)
Random factors
Usually assumed zero
Alpha Interpretation
α > 0 → good performance
α < 0 → poor performance
Beta (β) Meaning
β = 1 → normal risk
β > 1 → high risk
β < 1 → low risk
Advantages
Simple to use
Less data required
Easy calculation
Limitations
Assumes single factor (market)
Ignores multiple factors
Not 100% accurate
Assumptions
Only one factor (market) affects returns
Linear relationship between Ri and Rm
Residual error (e) has mean = 0
Securities are related through market index
Returns are normally distributed (basic assumption)
Applications / Uses
Portfolio selection
Estimation of expected return
Risk measurement
Helps in diversification decisions
Simplifies Markowitz model