portfolios.tools

Portfolio Beta Calculator

Calculate a weighted portfolio beta and view linear scenarios for benchmark changes using comparable holding beta estimates.

Holdings

Enter the holding beta estimate yourself or select a Yahoo ticker suggestion when a reported numeric beta is available. Confirm the source and method before comparing estimates.

Enter each holding weight as a percentage from 0 to 100. The accepted total must be within 0.01 percentage points of 100%.

Enter a finite beta estimate. Zero and negative values are valid; negative values point opposite to the benchmark in the linear model.

Enter the holding beta estimate yourself or select a Yahoo ticker suggestion when a reported numeric beta is available. Confirm the source and method before comparing estimates.

Enter a ticker, weight, and beta to calculate a portfolio result.

How it works

For each holding, enter a ticker, portfolio weight as a percentage, and beta estimate. The calculator multiplies each beta by its share of the accepted total weight, then adds the weighted values. The result is one coefficient for the portfolio relative to the estimates you supplied.

The weight total must be 100% within 0.01 percentage points. The calculator normalizes a total inside that tolerance. It rejects repeated tickers, incomplete rows, weights outside 0% to 100%, and nonfinite results. Beta may be zero or negative. The displayed coefficient bands are below 0.8, 0.8 through 1.2, and above 1.2; these labels do not judge suitability or total risk.

The scenario table multiplies the portfolio beta by benchmark changes from negative 20% to positive 20%. The custom slider applies the same linear calculation to a selected change. Negative beta produces a modeled move in the opposite direction. Neither output predicts what the portfolio will actually return.

For a meaningful comparison, use beta estimates built from the same benchmark, observation window, return frequency, and return basis. The calculator does not retrieve historical price series or recalculate individual betas. It stores the ticker, weight, and beta values in this browser; current prices are not part of its inputs.

Step by step

  1. Enter a distinct ticker, weight, and beta for each holding.
  2. Check that weights total 100% and the beta estimates are comparable.
  3. Review the weighted coefficient and linear benchmark scenarios.

Worked example

Enter one holding with a 60% weight and beta 1.10, and another with a 40% weight and beta 0.30. The weighted beta is 0.78: 0.60 × 1.10 plus 0.40 × 0.30. In the linear scenario, a benchmark rise of 10% maps to a portfolio change of 7.8%, while a benchmark fall of 20% maps to a change of negative 15.6%.

The displayed sensitivity relative to beta 1 is negative 22%. If the second holding beta changes from 0.30 to 0.60, the weighted beta becomes 0.90. These are arithmetic scenarios, not forecasts of portfolio returns.

When to use this calculator

Use this calculation to combine holding beta estimates into one portfolio coefficient when checking allocation changes or comparing proposed mixes against the same benchmark. The result is interpretable only when the underlying beta estimates are comparable.

Use drawdown or volatility measures when the question concerns observed loss depth or total variation. Use concentration and overlap measures when repeated exposures matter. Portfolio beta is one benchmark sensitivity measure, not a complete risk assessment.

Common input errors

Do not combine estimates measured against different benchmarks, periods, frequencies, or return bases without noting the mismatch. Enter weights as percentages, such as 60 rather than 0.60. Check that every row has a distinct ticker and that all weights add to 100% within the stated tolerance.

Do not treat a beta of 0.78 as a promise that every decline will be 22% smaller. It is a coefficient used in a linear scenario. Review drawdowns, volatility, concentration, liquidity, and nonlinear exposures separately. A negative beta can imply a large modeled move in the opposite direction.

Formula

Portfolio Beta = Σ((weight_i ÷ total weight) × beta_i)

Sensitivity relative to beta 1 = (Portfolio Beta − 1) × 100

Linear scenario change = Portfolio Beta × benchmark move

Weights must total 100% within 0.01 percentage points. The calculation normalizes the accepted total. Beta estimates should use the same benchmark, observation window, return frequency, and return basis.

Limits and assumptions

The model assumes a linear relationship to one common benchmark and treats supplied beta estimates as comparable and stable. Historical estimates depend on benchmark, observation window, return frequency, return basis, and data quality. The tool does not estimate alpha, a risk free return, total volatility, residual risk, liquidity, credit risk, fees, taxes, or nonlinear exposure. Correlations and beta can change, especially during market stress. Negative beta is permitted and does not mean low total risk.

Key terms

Portfolio beta
Portfolio beta is the weighted average of the beta estimates entered for the holdings.
Weighted average
The weighted average multiplies each holding beta by its weight divided by the accepted total weight, then sums the results.
Sensitivity relative to beta 1
Sensitivity relative to beta 1 is portfolio beta minus 1, multiplied by 100. It compares coefficients and does not measure borrowing or leverage.

Compare related measures

Portfolio beta summarizes benchmark sensitivity. Maximum Drawdown measures the depth of observed losses, while Sharpe Sortino Ratio compares returns with volatility or downside deviation. These measures describe different properties.

Use Portfolio Rebalancer to estimate trades for a target allocation, or ETF Overlap Detector to identify repeated fund holdings. Those tools examine allocation and overlap, not the beta calculation itself.

FAQ

What does portfolio beta measure?

Portfolio beta is the weighted average of the beta estimates entered for each holding. A coefficient of 1 means the model maps a 1% benchmark move to a 1% portfolio move. A coefficient of 0.78 maps that benchmark move to 0.78% in the same direction under the linear scenario. It describes sensitivity to the chosen benchmark, not total portfolio risk or volatility.

How is the weighted beta calculated?

The calculator multiplies each holding beta by its weight and sums the results. Weights are percentages and must total 100% within a tolerance of 0.01 percentage points. The accepted total is normalized in the weighted average. Every holding needs a distinct ticker and a finite beta. A beta of zero is valid, and negative beta values are allowed.

What do the coefficient bands mean?

The labels use fixed coefficient bands: below 0.8, from 0.8 through 1.2, and above 1.2. They are descriptive bands, not risk grades or recommendations. Negative beta falls below 0.8 and means the entered estimate points in the opposite direction from the benchmark. Its magnitude can still be large.

Are the market move scenarios forecasts?

No. The sensitivity table multiplies portfolio beta by a selected benchmark change. It omits alpha, a risk free return, residual movements, changing correlations, and nonlinear exposures. A result is a linear scenario, not a return forecast, maximum loss, or probability estimate.

Does beta describe total portfolio risk?

No. Beta describes a relationship with one benchmark and does not summarize all sources of risk. It may miss company specific events, interest rate changes, liquidity, credit, concentration, and nonlinear outcomes. A low or negative beta does not establish that a portfolio is low risk.

Related tools

Maximum Drawdown summarizes the depth of observed losses. Sharpe Sortino Ratio compares return with volatility or downside deviation. Portfolio Rebalancer estimates trades for a target allocation, and ETF Overlap Detector identifies repeated fund holdings.