Portfolio Beta Calculator
Weighted average beta for up to five holdings, with normalized weights and a market posture label.
What it does
Portfolio beta summarizes how a mix of investments has moved relative to a benchmark. A stock with a beta of 1.2 has tended to move 20 % more than the benchmark, up or down, while a stock with a beta of 0.8 has moved about 20 % less. The portfolio value is the weighted average of those individual betas.
The arithmetic is simple when the weights are clean: multiply each weight by its beta, add the products, and divide by the total weight. The division matters when weights do not add to 100 %. A portfolio that is only 90 % invested still has a beta that describes its invested sleeve, but the cash sleeve has a beta of zero and should be included when you want the beta of the whole account.
The default portfolio holds 50 % at beta 1.2, 30 % at beta 0.8, and 20 % at beta 1.5. The contributions are 0.60, 0.24, and 0.30, which add to 1.14. The weights already total 100 %, so normalization does not change the result.
Beta is usually estimated by regressing an asset's excess returns on a benchmark's excess returns over a chosen window. Different windows and benchmarks produce different betas, especially for funds that change strategy. A single published beta is a snapshot, not a fixed property.
Use portfolio beta to compare market sensitivity across allocations or to feed a CAPM estimate. Do not use it as a complete risk measure: it ignores company-specific risk, fees, taxes, currency, and changes in correlation. It also says nothing about whether the portfolio is suitable for your goals.
How to use
- Enter the percentage weight of each holding.
- Enter the beta for each holding using the same benchmark and time window.
- Leave unused holding rows at zero weight.
- Check that the weight total matches the account you are analyzing.
- Read the portfolio beta and the market sensitivity label.
- Rerun the mix with cash included if you want the beta of the full account.
Formula
- weight_i
- Weight of holding i in percent.
- beta_i
- Sensitivity of holding i to the benchmark.
- sum(weight_i)
- Total invested weight, used as the divisor.
The tool treats blank or zero weights as zero and rejects weights above 100 % or a total above 100.5 %. It does not estimate beta from price data. You must supply each holding beta from a source that uses the same benchmark you care about. A cash position has a beta of zero and lowers the portfolio beta when it is included.
Worked example
Example: three holdings with weights that total 100 %
The default weights and betas are already filled in the form.
- Holding 1 contribution: 0.50 x 1.20 = 0.60.
- Holding 2 contribution: 0.30 x 0.80 = 0.24.
- Holding 3 contribution: 0.20 x 1.50 = 0.30.
- Add the contributions: 0.60 + 0.24 + 0.30 = 1.14.
- Divide by the total weight: 1.14 / 1.00 = 1.14.
- The label reads Above market because 1.14 is above the 1.05 threshold.
Reference table
| Holding | Weight | Beta | Weight x beta |
|---|---|---|---|
| Holding 1 | 50 % | 1.20 | 0.60 |
| Holding 2 | 30 % | 0.80 | 0.24 |
| Holding 3 | 20 % | 1.50 | 0.30 |
| Total | 100 % | 1.14 | 1.14 |
Limits
- Beta is backward looking and changes with the estimation window and benchmark.
- The weighted average assumes the betas are measured on the same benchmark and frequency.
- It measures market sensitivity, not total risk, liquidity, fees, taxes, or currency exposure.
- Weights above 100 %, borrowed money, short positions, and derivatives need a more detailed model.
Common mistakes
- Mixing betas calculated against different indexes, such as one stock versus the S&P 500 and another versus a global fund.
- Leaving cash out of the weights and then treating the result as the beta of the whole account.
- Using a fund name instead of checking whether its strategy and benchmark changed.
- Interpreting a beta of 1.14 as a 14 % return advantage.
- Averaging betas without weighting them by position size.
Try it yourself
Quick checks. Answers sit tucked under each question.
A portfolio is 50 % in a fund with beta 1.4 and 50 % in a fund with beta 0.6. What is its beta?
0.50 x 1.4 + 0.50 x 0.6 = 0.70 + 0.30 = 1.00, labeled Near market.
A portfolio holds 40 % at beta 2.0 and 60 % at beta 0.5. What is its beta?
0.40 x 2.0 + 0.60 x 0.5 = 0.80 + 0.30 = 1.10, labeled Above market.
A portfolio holds 60 % at beta 1.2 and 40 % at beta -0.3. What is its beta?
0.60 x 1.2 + 0.40 x -0.3 = 0.72 - 0.12 = 0.60, labeled Below market.
Questions
What is portfolio beta?
A weighted average of the betas of the holdings. It estimates how sensitive the portfolio has been to moves in a benchmark.
What does a beta of 1 mean?
The portfolio has moved roughly in line with the benchmark over the estimation period.
What if my weights do not add to 100 %?
The tool divides by the entered total, so it returns the beta of the invested portion. Include cash at a beta of zero if you want the beta of the whole account.
Can beta be negative?
Yes. A negative beta means the asset has tended to move opposite the benchmark. Some hedges and inverse funds are built for that.
Is a high beta better?
No. A high beta means more market sensitivity in both directions. Whether that is desirable depends on your goals and risk tolerance.
How often should I update betas?
Review them when holdings or benchmarks change, and at least annually. Short windows react faster but are noisier.
Sources
- Modigliani and Pogue, an introduction to risk and return concepts and evidence (MIT DSpace)
- CFA Institute, Portfolio Risk and Return: Part II