Calculate portfolio beta from holdings
Enter each holding's portfolio weight and beta against the same benchmark and lookback period. Weights are normalized automatically.
Private by design: values stay in your browserWhat You'll Learn
- The two equivalent portfolio beta formulas (statistical and weighted-average)
- A worked example with illustrative stock betas across a 5-holding portfolio
- How to interpret beta values (defensive vs aggressive)
- The difference between portfolio beta, total risk, and alpha
- Why beta calculated on different time windows can give very different answers
What Is Portfolio Beta?
Portfolio beta (βp) measures how sensitive a portfolio's returns are to movements in a market benchmark, typically the S&P 500. It is the slope of the regression line of portfolio returns against market returns.
A portfolio with a beta of 1.20 is expected to rise 12 percent when the market rises 10 percent and fall 12 percent when the market falls 10 percent. A beta of 0.70 means the portfolio moves about 70 percent as much as the market in either direction. Beta is the standard measure of systematic risk (the risk you cannot diversify away).
The Portfolio Beta Formula
Method 1: Statistical Formula (from returns)
| Cov(Rp, Rm) | Covariance between portfolio returns and market returns |
| Var(Rm) | Variance of the market's returns |
| Rp, Rm | Periodic returns of the portfolio and the market (typically daily, weekly, or monthly) |
| βp | Portfolio beta (dimensionless) |
Method 2: Weighted-Average Formula (from holdings)
For a portfolio of individual stocks or funds whose betas are already known, portfolio beta is a simple weighted average:
| wi | Weight of holding i in the portfolio (market value of i / total portfolio value) |
| βi | Beta of holding i against the chosen benchmark |
| βp | Portfolio beta |
The two methods agree, but use different inputs
The statistical method (Method 1) computes beta directly from the portfolio's actual return history. The weighted-average method (Method 2) uses each holding's published beta. They give the same answer if the published betas were computed against the same benchmark over the same window. In practice, Method 2 is faster; Method 1 is more accurate for portfolios with concentrated or unusual positions.
How to Calculate Portfolio Beta: Step-by-Step Example
Example: 5-Holding Portfolio Beta Calculation
Benchmark: S&P 500 (β = 1.00 by definition)
Holdings (illustrative 5-year betas):
NVDA: weight 25%, beta 1.70 · AAPL: weight 20%, beta 1.20
JPM: weight 20%, beta 1.10 · JNJ: weight 20%, beta 0.55
BND (US Aggregate Bonds): weight 15%, beta 0.05
NVDA: 0.25 × 1.70 = 0.425
AAPL: 0.20 × 1.20 = 0.240
JPM: 0.20 × 1.10 = 0.220
JNJ: 0.20 × 0.55 = 0.110
BND: 0.15 × 0.05 = 0.0075
βp = 0.425 + 0.240 + 0.220 + 0.110 + 0.0075
The portfolio has roughly the same market-risk sensitivity as the S&P 500. The high-beta tech positions (NVDA, AAPL) are offset by the low-beta defensive and bond positions (JNJ, BND), producing a market-matching beta. If the S&P 500 returns +10% over a year, this portfolio is expected to return about +10% from market exposure alone, before any stock-specific (idiosyncratic) effects.
If you replace BND with 15% more NVDA: new weights are NVDA 40%, AAPL 20%, JPM 20%, JNJ 20%, no bonds.
New beta = (0.40 × 1.70) + (0.20 × 1.20) + (0.20 × 1.10) + (0.20 × 0.55) = 0.68 + 0.24 + 0.22 + 0.11 = 1.25
A 25 percent shift from bonds to NVDA increased portfolio beta from 1.00 to 1.25, meaning expected portfolio swings are now 25 percent larger than market swings.
How to Interpret Portfolio Beta
| Beta Value | Interpretation | Typical Example |
|---|---|---|
| β < 0 | Moves opposite the market (rare for long-only portfolios) | Gold during equity bear markets; short-equity ETFs |
| β = 0 | No correlation to market moves | Cash; short-term T-bills |
| 0 < β < 1 | Defensive: moves less than the market | Bond-heavy portfolios; utilities-heavy portfolios |
| β = 1 | Market-matching | S&P 500 index fund; balanced large-cap portfolio |
| 1 < β < 1.5 | Aggressive: moves more than the market | Concentrated tech portfolios; small-cap heavy portfolios |
| β > 1.5 | Very aggressive; large amplification of market moves | Single-name growth stocks; leveraged ETF holdings |
Beta is window-dependent
A stock's beta calculated over the last 1 year can differ substantially from its beta over the last 5 years. Companies change. Apple's beta was below 1.0 for several years before climbing above 1.2 as the stock matured. Always check what window a published beta was computed over before using it in a portfolio calculation.
Portfolio Beta vs Total Risk vs Alpha
Beta, standard deviation, and alpha measure different things and are often confused:
| Metric | What It Measures | Formula Summary |
|---|---|---|
| Beta (β) | Sensitivity to market moves (systematic risk) | Cov(Rp, Rm) / Var(Rm) |
| Standard Deviation (σ) | Total volatility, both systematic and idiosyncratic | √(wTΣw) at the portfolio level |
| Alpha (α) | Excess return beyond what beta would predict | Rp − (Rf + βp(Rm − Rf)) |
| R-squared | Share of portfolio variance explained by the market | Correlation(Rp, Rm)2 |
Beta alone is incomplete
A portfolio with beta 1.0 against the S&P 500 but R-squared of only 0.30 has a lot of risk that is not explained by market moves. Beta tells you about market sensitivity. R-squared tells you whether beta is the right lens. Use both.
From Portfolio Beta to a Broader Risk Check
This calculator answers one narrow question using the beta values you provide. It does not fetch security betas, choose a benchmark, estimate R-squared, or measure stock-specific risk. For a broader view, Guardfolio analyzes synchronized portfolio holdings across concentration, ETF overlap, allocation drift, volatility, diversification, and portfolio health.
The free portfolio risk check requires no connected account and helps examine:
- Portfolio concentration and diversification
- Volatility and drawdown context
- ETF overlap and repeated underlying exposure
- Portfolio health signals beyond benchmark sensitivity