# Formula for Calculating Portfolio Beta

by Dennis Hartman ; Updated April 19, 2017A portfolio is any group of investment assets that an individual or organization holds. As with individual assets, understanding the risk and possible returns of a portfolio is key to making informed investment decisions. Measurements such as portfolio beta provide data that can help an investor reshape a portfolio in changing economic times or ensure that a group of investments has a high probability of performing as expected.

## Asset Beta

An asset's beta refers to how likely it is to change in value as broader financial markets change. When an asset has a beta of zero, it changes independent of fluctuations in the market. A positive value indicates that an asset rises in value when the markets rise, and falls when markets fall. Conversely, a negative beta indicates that an asset moves in the opposite direction of the financial market.

## Basic Formula

To calculate the beta of a portfolio, you must first use a formula to calculate the beta of each asset it contains. The basic formula for an asset's beta is, covariance divided by variance. Covariance refers to change, or variations, over time in the difference between the value of an asset and the value of an index that represents the broader market that contains the asset. Variance refers to the degree of change in just that index over the same period of time.

## Portfolio Beta

To determine portfolio betas, you must weight individual asset betas to produce a beta that reflects the proportion of each asset. The first step is to multiply the beta of each asset by that asset's proportion of the portfolio, expressed as a percentage. The formula for weighted portfolio beta is the sum of these values.

For example, if a stock portfolio includes 20 shares of a stock with a beta of 1, 40 shares of a stock with a beta of 2 and 40 shares of stock with a beta of 1.5, the first step reveals values of .2 (20 percent times 1), .8 (40 percent times 2) and .6 (40 percent times 1.5). The sum of these, and the portfolio beta, is 1.6.

## Results

Portfolio beta shows how closely a portfolio follows more general market trends. This allows an investor to take advantage of projected market growth, or hedge against market downfalls by making investments with negative betas that will love contrary to a market. Portfolio beta also provides a reference point for comparing projected returns for markets, individual assets and portfolios.

For example, if every major financial journal expects a gain of between 2 and 4 percent for the Dow Jones index over the next three months, but the manager of a portfolio that includes stocks that are part of the Dow index and has a beta of -1, projects a 5 percent return for the portfolio over the same time period, the manager's estimation is called into question. In this case the negative beta suggests that the portfolio will move in the opposite direction of the Dow, losing value instead of gaining high returns as the manager predicts.