## What is Beta?

Beta is a measure of volatility compared to a benchmark index like the S&P 500. It is also primarily used in the capital asset pricing model (CAPM).

Beta represents the systematic risk of each asset and the sensitivity of asset returns to the market return and is referred to as ‘Asset’s Beta’.

Investors use the beta calculation to determine if a stock moves in lockstep with the rest of the market.

## Example of Beta:

$ \beta _{i}\, = \, \frac{Covariance\, of\, asset\, is\, return\, with\, the\, market\, return}{variance\, of\, the\, market\, return}\, = \, \frac{Cov_{I,M}}{\sigma ^{2}}\, = \rho _{i,M}\, \times \frac{\sigma _{i}}{\sigma _{M}} $

Market beta = 1: Any security that moves in a one-to-one relationship with the market.

Beta > 1: Cyclical (e.g., luxury goods stock).

Beta < 1: Defensive (e.g., a utility stock).

An investor is looking to calculate Apple’s beta (AAPL) compared to the SPDR S&P 500 ETF Trust (SPY). Based on recent five-year data, the correlation between AAPL and SPY is 0.83. AAPL has a standard deviation of returns of 23.42%, and SPY has a standard deviation of returns of 32.21%

$ Beta\; = \; 0.83\; \times \; \left ( \frac{0.2342}{0.3221} \right ) \; = 0.6035 $

## Why is Beta important when making investment decisions?

Beta plays a significant role in understanding the market risk of the assets. It allows investors to understand the dynamics of assets’ relation with the market and information on investment decisions.