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How to Calculate Portfolio Beta 

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Written By
Dan Buckley
Contributor Image
Written By
Dan Buckley
Dan Buckley is an US-based trader, consultant, and part-time writer with a background in macroeconomics and mathematical finance. He trades and writes about a variety of asset classes, including equities, fixed income, commodities, currencies, and interest rates. As a writer, his goal is to explain trading and finance concepts in levels of detail that could appeal to a range of audiences, from novice traders to those with more experienced backgrounds.
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Updated
Mar 29, 2024

In this article, we give a step-by-step breakdown of how to calculate portfolio beta.

Understanding Beta

Beta measures the volatility of a portfolio compared to the overall market.

  • A beta of 1 means the portfolio moves in line with the market.
  • A beta greater than 1 indicates more volatility than the market (higher risk, higher potential return).
  • A beta less than 1 means less volatility than the market (lower risk, lower potential return).

 

Formula for Calculating Portfolio Beta

To calculate the beta of a portfolio, you use the weighted average of the betas of the individual securities within the portfolio.

The formula is:

 

Portfolio Beta = ∑(wi*βi)

 

Where:

  • wi = the weight of the ith asset in the portfolio (calculated as the value of the asset divided by the total value of the portfolio)
  • Β = the beta of the ith asset
  • The summation ∑ runs over all assets in the portfolio

 

Steps to Calculate Portfolio Beta

Identify the Assets in the Portfolio

List all the assets you have in your portfolio.

Find the Beta for Each Asset

Look up the beta for each asset.

This information can often be found on financial news websites, investment research tools, or from a broker.

Determine the Weight of Each Asset

Calculate the weight of each asset in the portfolio.

This is done by dividing the market value of each asset by the total market value of the portfolio.

Calculate the Weighted Beta for Each Asset

Multiply the beta of each asset by its respective weight in the portfolio.

Sum the Weighted Betas

Add up all the weighted betas calculated in step 4.

The result is the beta of the portfolio.

 

Example

Suppose a portfolio consists of three stocks:

  • Stock A: $10,000, Beta = 1.2
  • Stock B: $15,000, Beta = 0.9
  • Stock C: $25,000, Beta = 1.5

Total value of the portfolio = $10,000 + $15,000 + $25,000 = $50,000

Calculate Weights

  • Weight of A = $10,000 / $50,000 = 0.2
  • Weight of B = $15,000 / $50,000 = 0.3
  • Weight of C = $25,000 / $50,000 = 0.5

Calculate Weighted Betas

  • Weighted Beta of A = 0.2 * 1.2 = 0.24
  • Weighted Beta of B = 0.3 * 0.9 = 0.27
  • Weighted Beta of C = 0.5 * 1.5 = 0.75

Sum the Weighted Betas

  • Portfolio Beta = 0.24 + 0.27 + 0.75 = 1.26

This portfolio has a beta of 1.26, indicating it’s expected to be 26% more volatile than the market.

 

Notes

  • Time Period – The beta of stocks and portfolios can change over time. It’s important to use data points covering a period relevant to your investment strategy.
  • Online Calculators – There are several online calculators specifically for portfolio beta that can automate the process for you.
  • Diversification – Even with a high portfolio beta, diversification can help manage overall risk.