R-Squared (R²)

Risk & Portfolio

Updated Apr 2026 • Has calculator

The proportion of a fund's return variation explained by its benchmark, from 0 (no relationship) to 1 (perfect fit).

What is R-Squared?

R-Squared (the coefficient of determination) is the square of the Pearson correlation between a fund's returns and its benchmark's returns. It tells investors how much of the fund's volatility is attributable to movements in the benchmark. An R-squared of 0.95 means 95% of the fund's return variation is explained by the benchmark, suggesting the fund closely tracks it. A low R-squared (below 0.70) means the fund behaves very differently from its benchmark, which may indicate active management, style drift, or a benchmark mismatch. R-squared is most useful when interpreting beta: a fund's beta is only meaningful if its R-squared is high.

Formula

R² = ρ² = [Σ(Aᵢ−Ā)(Bᵢ−B̄)]² / [Σ(Aᵢ−Ā)² × Σ(Bᵢ−B̄)²]

Worked Example

Annual returns 2019–2023

Step 1 VFIAX annual returns (%): 31.4, 18.3, 28.6, −18.2, 26.2

Step 2 S&P 500 annual returns (%): 31.5, 18.4, 28.7, −18.1, 26.3

Step 3 Correlation ρ ≈ 1.000 (index fund tracks its benchmark almost perfectly)

Step 4 R² = 1.000² ≈ 1.00

Step 5 → Nearly 100% of VFIAX's return variation is explained by the S&P 500

Source: Vanguard — VFIAX Fund Overview (2024-01-31)

Calculate R-Squared

Fund Returns (%)

Enter comma-separated fund period returns

Benchmark Returns (%)

Enter comma-separated benchmark returns (same number of periods)

R-Squared

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Not investment advice.

How to Interpret R-Squared

< 0.4

Low — fund diverges significantly from benchmark

0.4 – 0.7

Moderate — partial benchmark exposure; active component

0.7 – 0.9

High — largely tracks the benchmark

> 0.9

Very High — near-index fund behavior

📚 Risk Metrics — Complete the path

Sources