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Investing · ETF Metrics

Beta (β) — formula, calculation, benchmark choice

Beta measures how sensitive an ETF is to broad-market moves. A beta of 1.0 means the ETF moves with the market; 1.2 means it moves 20% more; 0.8 means 20% less. Here's exactly how UK Tax Drag calculates it, what benchmark we use, and what beta can and can't tell you about an ETF.

6-minute read

Beta (β) is the slope coefficient from a linear regression of the ETF's monthly returns against the benchmark's monthly returns over 3 years (36 observations). Formula: β = Cov(RETF, Rbenchmark) / Var(Rbenchmark). For UK ETF tools, the benchmark default is MSCI ACWI (in GBP) for global ETFs, FTSE 100 (in GBP) for UK equity ETFs, and asset-class-appropriate for everything else. Beta ranges from negative (rare, inverse exposure) to highly positive (>2 for leveraged products). A beta near 1.0 means market-like sensitivity. Beta is useful for portfolio construction (knowing how much market exposure you're getting), not as a quality score.

The formula

Beta is the regression slope coefficient:

β = Cov(RETF, Rbenchmark) / Var(Rbenchmark)

where:
  Cov(X, Y) = Σ[(Xi − X̄)(Yi − Ȳ)] / (n − 1)
  Var(X)    = Σ[(Xi − X̄)²] / (n − 1)
  RETF      = monthly return of the ETF, period i
  Rbenchmark= monthly return of the benchmark, period i
  X̄        = sample mean of X
  n         = number of observations (36 for 3-year monthly)

Equivalently: Beta is the slope of the line in a scatter plot of ETF returns (y-axis) vs benchmark returns (x-axis) over the lookback period.

Inputs we use

InputSourceFrequency / window
ETF monthly returnsIssuer factsheet + LSE end-of-day close, cross-checked36 months (3 years)
Benchmark monthly returnsIndex provider (MSCI / FTSE Russell / S&P Dow Jones)36 months (3 years)
CurrencyBoth series converted to GBP via Bank of England daily spotMonth-end FX
Total return basisDistributions reinvested at ex-div dateAlways TR, not price-return

Benchmark choice — the critical decision

The same ETF can have wildly different beta values against different benchmarks. We use this benchmark-by-asset-class default:

ETF typeDefault benchmarkWhy
Global equity (e.g. VWRL)MSCI ACWI (GBP TR)Closest match — global all-cap, all-country
UK equity (e.g. VUKE)FTSE 100 (GBP TR) or FTSE All-Share for broaderNative UK benchmark
US equity (e.g. VUSA)S&P 500 (GBP TR — for UK investor)Native US benchmark
European equityMSCI Europe ex-UK (GBP TR)Excludes UK to avoid double-counting
Emerging marketMSCI Emerging Markets (GBP TR)Native EM benchmark
Bond — global aggregateBloomberg Global Aggregate (GBP-hedged)Standard ballast benchmark
Bond — UK giltsFTSE Actuaries UK Gilts All StocksStandard UK gilt benchmark
Smart beta / factorUnderlying parent index (e.g. MSCI World for World-Quality)Like-for-like comparison
Sector / thematicClosest sector benchmark + market benchmark for cross-checkDisclosed on tool

When you see a beta on UK Tax Drag, the benchmark used is always disclosed in the same row or panel. If you want beta against a different benchmark, the per-tool methodology explains how to recompute.

Worked example — VUSA against S&P 500 (GBP)

Computing 3-year monthly beta for Vanguard S&P 500 UCITS ETF (VUSA) against S&P 500 GBP Total Return Index. Lookback: 36 months ending April 2026.

MonthVUSA monthly return (%)S&P 500 GBP TR monthly return (%)
May 2023+1.42+1.40
Jun 2023+5.85+5.92
Jul 2023+2.95+2.99
... (34 more rows) .........
Apr 2026+1.85+1.89

Step 1 — Calculate sample means: VUSA mean = 0.95% / month; S&P 500 GBP TR mean = 0.96%.

Step 2 — Calculate covariance: Cov(VUSA, S&P) = 0.00154 (in decimal returns).

Step 3 — Calculate benchmark variance: Var(S&P) = 0.00155.

Step 4 — Beta = 0.00154 / 0.00155 = 0.993.

VUSA's beta vs S&P 500 GBP TR is approximately 1.00 — exactly what we'd expect for an S&P 500 tracker with low tracking error. The 0.007 difference from exact 1.00 is OCF drag + small sampling differences.

How to reproduce this yourself

  1. Download VUSA monthly prices from Vanguard UK or Yahoo Finance (ticker VUSA.L) for 36+ months.
  2. Download S&P 500 Total Return index data — easiest source is spindices.com. Convert to GBP using Bank of England daily spot rates.
  3. In Excel or Google Sheets, calculate monthly returns: =(Pt − Pt-1)/Pt-1.
  4. Use SLOPE(VUSA_returns, SP500_returns). Result is beta.
  5. Alternative: =COVARIANCE.S(VUSA_returns, SP500_returns) / VAR.S(SP500_returns).

Cross-check: VUSA's own factsheet often publishes beta or implies it via "tracking" stats. Numbers should match within ~5%.

What beta tells you

What beta does NOT tell you

Beta interactions with R-squared

Beta should always be read alongside R² (R-squared) — the proportion of the ETF's return variance explained by the benchmark.

UK Tax Drag tools publish R² alongside beta where available, so you can see how reliable the beta interpretation is.

Common Beta pitfalls in UK retail decisions

Sources and methodology

Regression mathematics follow standard statistical practice (Wooldridge, Introductory Econometrics; Brooks, Introductory Econometrics for Finance). Benchmark data from index providers as documented in ETF Metrics Transparency. The ETF Data Methodology documents data sources in full. The site methodology documents the broader review process.

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