How to Calculate Portfolio Beta with an Example

To find a portfolio’s beta, multiply each holding’s beta by its weight in the portfolio, then sum. A portfolio that is 60% Stock A (beta 1.1) and 40% Stock B (beta 0.8) has a portfolio beta of 0.98—a single number capturing the portfolio’s overall sensitivity to market moves. This article walks through the math with concrete examples.

The basic formula

Portfolio beta is straightforward:

Portfolio Beta = (Weight₁ × Beta₁) + (Weight₂ × Beta₂) + … + (Weightₙ × Betaₙ)

Each weight must be expressed as a decimal (0.6 for 60%) and must sum to 1.0 across all holdings. Each beta is the individual asset’s beta relative to the same benchmark (usually the S&P 500 for U.S. equities).

Worked example: a three-stock portfolio

Suppose you own three stocks with the following market values and betas (all relative to the S&P 500):

Step 1: Calculate total portfolio value

$30,000 + $20,000 + $50,000 = $100,000

Step 2: Calculate weight of each stock

• Apple: $30,000 ÷ $100,000 = 0.30 (30%)
• Walmart: $20,000 ÷ $100,000 = 0.20 (20%)
• Tesla: $50,000 ÷ $100,000 = 0.50 (50%)

(Check: 0.30 + 0.20 + 0.50 = 1.00 ✓)

Step 3: Multiply each weight by its beta

• Apple: 0.30 × 1.25 = 0.375
• Walmart: 0.20 × 0.70 = 0.140
• Tesla: 0.50 × 1.80 = 0.900

Step 4: Sum the products

Portfolio beta = 0.375 + 0.140 + 0.900 = 1.415

Interpretation: This portfolio swings 41.5% more than the S&P 500. If the S&P 500 rises 10%, the portfolio is expected to rise about 14.15%. If the index falls 10%, the portfolio is expected to fall about 14.15%.

Including cash and bonds

If your portfolio contains cash or bonds, apply the same method. Cash typically has a beta near zero (it doesn’t move with the market), and bonds have lower betas than equities (usually between 0 and 0.5).

Example with bonds:

Weights: 0.80, 0.15, 0.05 (sum = 1.00 ✓)

Portfolio beta = (0.80 × 1.10) + (0.15 × 0.20) + (0.05 × 0.00) = 0.88 + 0.03 + 0.00 = 0.91

This portfolio moves 91% as much as the S&P 500—less volatile because bonds and cash cushion the equity exposure.

Using index funds or ETFs

If your holdings are index funds or ETFs rather than individual stocks, use the same method. For example, a portfolio of 60% S&P 500 index fund and 40% bond ETF would be:

Portfolio beta = (0.60 × 1.00) + (0.40 × 0.15) = 0.60 + 0.06 = 0.66

(An S&P 500 index fund has a beta of essentially 1.0 by definition, since it is the index. A typical bond fund might have beta around 0.15.)

Dynamic rebalancing: beta drift

Portfolio beta changes over time as two things happen:

1. Asset betas change: A company’s systematic risk can increase or decrease. A stable utility might have beta 0.9 today and 1.1 after a major acquisition.

2. Weights drift: As prices move, the dollar value of holdings shifts, changing their percentage of the portfolio. If Tesla doubles while Walmart flatlines, Tesla’s weight rises automatically, pulling the portfolio beta higher.

Example of drift:

Starting portfolio (from earlier): Apple 30%, Walmart 20%, Tesla 50%, portfolio beta = 1.415.

Six months later, prices have moved:

• Apple rose 15% → now worth $34,500
• Walmart rose 5% → now worth $21,000
• Tesla rose 30% → now worth $65,000
• New total: $120,500

New weights:

• Apple: $34,500 ÷ $120,500 = 0.286 (28.6%)
• Walmart: $21,000 ÷ $120,500 = 0.174 (17.4%)
• Tesla: $65,000 ÷ $120,500 = 0.540 (54.0%)

If betas remain unchanged: New portfolio beta = (0.286 × 1.25) + (0.174 × 0.70) + (0.540 × 1.80) = 0.358 + 0.122 + 0.972 = 1.452

The portfolio beta rose from 1.415 to 1.452 simply because the highest-beta holding (Tesla) grew in value. This is why investors who want a stable beta rebalance periodically—selling winners and buying losers to restore original weights.

Comparing portfolios by beta

Portfolio beta is useful for comparing risk profiles:

A beta of 1.0 means the portfolio moves exactly like the market. Below 1.0 is more stable. Above 1.0 is more volatile. An aggressive hedge fund might have a beta of 0.3 (low correlation to markets, due to active positions), while a simple 100% U.S. stock portfolio has a beta near 1.0.

Assumptions and limitations

Portfolio beta assumes:

• Historical stability: The individual betas used are based on past data and may not predict future sensitivity.
• Benchmark consistency: All betas are calculated against the same benchmark.
• Linear relationship: Beta assumes the relationship between a stock and the market is linear. In extreme market crashes, this breaks down.
• No leverage: The calculation ignores borrowing. A leveraged portfolio needs an adjusted method.

For a leveraged portfolio (using margin or derivatives), multiply the unlevered beta by the leverage ratio. If you use $150,000 of stocks with $100,000 of capital (1.5× leverage), and the stock portfolio’s beta is 1.0, the leveraged portfolio beta is 1.5.

Quarterly recalculation

Professional portfolio managers recalculate beta quarterly or whenever allocations shift materially. As individual asset betas change (companies’ volatility and correlation with markets shifts), and as weights drift due to price moves, the portfolio beta evolves.

This is especially important for mutual funds and hedge funds, which publish beta in their fact sheets. Investors rely on these figures to understand how much market risk they’re taking on relative to the risk-free rate or their own tolerance.

Practical use: calculating required return

Portfolio beta feeds into the capital asset pricing model (CAPM), which calculates the return an investor should demand:

Expected return = Risk-free rate + (Beta × Market risk premium)

If risk-free rate = 3%, market risk premium = 6%, and portfolio beta = 1.2:

Expected return = 3% + (1.2 × 6%) = 3% + 7.2% = 10.2%

The portfolio’s higher beta (1.2 vs. 1.0) justifies demanding a higher return (10.2% vs. 9%). This calculation is central to cost of equity estimation and portfolio performance evaluation.

See also