R-Squared (R²)

What is R-Squared (R²)?

R-Squared (R²) is a statistical measure that shows how much of a portfolio’s or asset’s performance can be explained by movements in a benchmark index. It indicates the strength of the relationship between two variables — often used in finance to measure how well a stock’s returns track the market.

Key takeaway: An R² close to 1 means strong correlation with the market, while a low R² indicates weak or no correlation.

Why It Matters

R² helps investors determine whether a fund’s performance is driven by market trends or independent management decisions. It’s crucial in assessing diversification, benchmarking, and the reliability of performance metrics like Beta and Alpha.

Key Features

• Expressed as a percentage (0–100%).
• Indicates correlation strength between asset and benchmark.
• Complements Beta and Alpha in performance analysis.
• High R² means performance is benchmark-driven.
• Low R² means returns are largely independent.

How It Works

1. Select Data: Compare asset returns with market returns over time.
2. Run Regression Analysis: Fit a line of best fit to returns data.
3. Calculate R²: R² = (Explained Variation ÷ Total Variation).
4. Interpret Results:
   • R² > 0.85 → Highly correlated with benchmark.
   • R² < 0.70 → Low correlation, independent performance.
   • R² = 1 → Perfect fit.

Types

• Fund R²: Measures how much fund movement aligns with its benchmark.
• Model R²: Used in regression to explain dependent variable behavior.
• Adjusted R²: Corrects for sample size and variable count.

Comparison Table

Feature or Aspect	R-Squared (R²)	Beta (β)
Measures	Correlation strength	Sensitivity to market movement
Value Range	0–1 (or 0%–100%)	Any real number
Interpretation	Fit quality	Volatility relative to market
Use Case	Model reliability	Risk assessment

Examples

• Example 1: A mutual fund with R² = 0.95 → 95% of returns explained by market movement.
• Example 2: Hedge fund with R² = 0.40 → Independent from market trends.
• Example 3: Passive index fund → R² near 1.0; actively managed fund → lower R².

Benefits and Challenges

Benefits

• Helps assess portfolio diversification.
• Clarifies dependency on market trends.
• Useful in verifying Beta reliability.
• Aids in performance attribution.

Challenges

• High R² doesn’t always mean good performance.
• Can be misleading if benchmark poorly chosen.
• Doesn’t measure causation, only correlation.

Related Concepts

• Beta (β): Volatility compared to the market.
• Alpha (α): Performance beyond expected returns.
• Correlation Coefficient (r): Statistical measure of relationship strength.

FAQ

What is a good R-Squared value?

For market-tracking funds, 85–100% is ideal. For hedge or alternative funds, lower values show desirable independence.

How is R² used with Beta and Alpha?

R² validates whether Beta and Alpha are meaningful — if R² is too low, those metrics are less reliable.

What’s the difference between R² and correlation (r)?

R² is the square of the correlation coefficient (r) and shows the proportion of variance explained.

Can R² predict future performance?

No, it only describes how well past data fit the model — not future outcomes.

Sources and Further Reading

• Investopedia: https://www.investopedia.com/terms/r/r-squared.asp
• CFA Institute: Statistical Tools for Financial Analysis
• Morningstar: Understanding R-Squared and Fund Correlation

Quick Reference

• R² (Coefficient of Determination): Explains variation strength.
• Regression Analysis: Statistical technique linking variables.
• Benchmark: Market index used for comparison.