Portfolio Beta Calculator (weighted beta, CAPM return & market-move test)

Understanding the portfolio beta calculator — concept and principle

Portfolio beta measures how sensitive a whole portfolio is to moves in the overall market. This calculator combines the betas of your holdings into one figure, estimates the CAPM expected return and shows how the portfolio might react to a given market move.

How it is calculated

• Portfolio beta βP = Σ wi × βi, where wi is each holding's share of total value.
• If the weights do not add up to 100%, they are scaled so that they do.
• Cash and short-term government bills have a beta of about 0.
• CAPM expected return = risk-free rate + βP × market risk premium.
• Expected portfolio move ≈ βP × market move.

The principle

Beta measures how much an asset tends to move when the market moves by 1%. Because a portfolio's return is the weighted average of its holdings' returns, its beta is the weighted average of their betas. That makes beta easy to adjust: adding cash or low-beta stocks lowers it, adding high-beta stocks raises it. Under the Capital Asset Pricing Model, only this market risk is rewarded with higher expected return, because other risks can be diversified away.

Worked example

Default inputs: weights 40, 25, 20, 15%; betas 1.2, 0.8, 1.5, 0; value 100,000 USD; risk-free 4%; market premium 5%; market move −10%.

1. Weights add up to 100%, so no scaling is needed.
2. βP = 0.40 × 1.2 + 0.25 × 0.8 + 0.20 × 1.5 + 0.15 × 0 = 0.98.
3. CAPM expected return = 4% + 0.98 × 5% = 8.9%.
4. Expected move for a −10% market = 0.98 × −10% = −9.8%, about −9,800 USD.
5. Weight in holdings with beta above 1 = 40 + 20 = 60%; number of holdings = 4.

How to read the result

A beta near 1 means the portfolio tends to move with the market; below 1, less; above 1, more. Beta only captures market-driven moves; individual stocks can still rise or fall for their own reasons, so actual results differ. Betas are estimated from past returns and change over time.

Common mistakes

• Using weights by number of shares instead of by value.
• Forgetting that cash has a beta of about 0 and lowers the total.
• Mixing betas measured against different market indices.
• Treating beta as the total risk of a portfolio.

Frequently asked questions

How do you calculate portfolio beta?

Multiply each holding's beta by its share of the portfolio value and add the results.

What does a beta of 0.98 mean?

The portfolio has tended to move about 0.98% for each 1% move in the market.

Can beta be negative?

Yes, for assets that tend to move opposite to the market, though this is uncommon for stocks.

Sources: Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance, 19(3). · Bodie, Kane & Marcus, Investments (portfolio beta and CAPM)