Beta Index Calculator

Formula

The formula to calculate the Beta Index (Beta) is:

\[ \beta = \frac{\text{Cov}(R_m, R_i)}{\text{Var}(R_m)} \]

Where:

\(\beta\) is the Beta Index
\(\text{Cov}(R_m, R_i)\) is the covariance between the return of the market and the return of the individual security
\(\text{Var}(R_m)\) is the variance of the return of the market

Beta Index Definition

A Beta Index, or simply Beta, is a measure used in finance to determine the volatility or systematic risk of a security or portfolio in comparison to the market as a whole. It is used in the capital asset pricing model (CAPM), which calculates the expected return of an asset based on its beta and expected market returns. A beta of 1 indicates that the security’s price moves with the market, a beta less than 1 means it is less volatile than the market, while a beta greater than 1 indicates it is more volatile than the market.

Example Calculation

Let's assume the following values:

Covariance Between Market Return and Security Return (Cov(R_m, R_i)) = 0.02
Variance of Market Return (Var(R_m)) = 0.01

Using the formula to calculate the Beta Index (Beta):

\[ \beta = \frac{0.02}{0.01} = 2 \]

The Beta Index (Beta) is 2.