Risk & Performance
Beta
A measure of how sensitive an asset's returns are to market movements, indicating systematic risk exposure.
Formula
β = Cov(Rₐ, Rₘ) ÷ Var(Rₘ)
Variables
Cov(Rₐ, Rₘ)- Covariance of asset and market returns
Var(Rₘ)- Variance of market returns
Worked Example
Scenario: Stock with covariance 0.018 and market variance 0.012 has beta = 0.018 ÷ 0.012 = 1.50.
Steps:
- Calculate covariance between stock returns and market returns
- Calculate variance of market returns
- Divide covariance by variance
When to Use This Formula
- Measure systematic risk relative to market
- Evaluate portfolio contribution to market correlation
- Compare risk levels of different securities
Limitations & Assumptions
- Backward-looking; historical relationship may not persist
- Benchmark choice is critical—wrong benchmark misleads
- Assumes linear relationship; may miss nonlinear or tail risk
Common Questions
What does beta > 1 mean?
The asset is more volatile than the market; it moves more than the market in the same direction on average.
Does beta of 1.5 guarantee a 1.5× move?
No. Beta is a regression estimate across many observations, not a prediction for a single period.
Measuring return and risk
- Alpha formulaFormula
- Sharpe ratioDefinition
- Sortino ratioDefinition
- Maximum drawdownDefinition
- Treynor ratioDefinition
Reference note: This is an educational mathematical reference. The formula's applicability depends on assumptions, market conditions, and use case. Always verify results independently and consult domain experts for decisions.