What is Portfolio / Index Beta?
Beta is a measure of the volatility or systematic risk of a portfolio or individual asset relative to a benchmark index, typically a broad market index like the S&P 500. It shows how much the portfolio’s returns move in relation to the overall market. A beta value greater than 1 indicates the portfolio is more volatile than the market, while a beta less than 1 suggests it is less volatile.
Beta Calculation: Beta is calculated as the covariance of the portfolio's returns with the market's returns, divided by the variance of the market’s returns. The formula is:
Beta = Cov(Portfolio, Market) / Var(Market) Where:
Beta = 0.02 / 0.015 = 1.33 This means the portfolio is 33% more volatile than the market. If the market rises by 10%, the portfolio is expected to rise by 13.3%.
Beta Calculation: Beta is calculated as the covariance of the portfolio's returns with the market's returns, divided by the variance of the market’s returns. The formula is:
Beta = Cov(Portfolio, Market) / Var(Market) Where:
- Cov(Portfolio, Market): The covariance between the portfolio's returns and the market's returns
- Var(Market): The variance of the market’s returns
Understanding Beta
Beta helps assess the market-related risk of a portfolio:- Beta > 1: Indicates that the portfolio is more volatile than the market. If the market rises by 1%, a portfolio with a beta of 1.2 is expected to rise by 1.2%.
- Beta < 1: Suggests that the portfolio is less volatile than the market. A beta of 0.8 means the portfolio would increase by 0.8% for every 1% rise in the market.
- Beta = 1: Implies the portfolio moves in line with the market. If the market rises by 1%, the portfolio is expected to rise by 1% as well.
- Negative Beta: Indicates that the portfolio moves inversely to the market. A negative beta can provide diversification benefits, as the portfolio may gain when the market declines.
Example Calculation
Suppose a portfolio’s returns have a covariance with the market of 0.02, and the variance of the market’s returns is 0.015. Using the formula:Beta = 0.02 / 0.015 = 1.33 This means the portfolio is 33% more volatile than the market. If the market rises by 10%, the portfolio is expected to rise by 13.3%.