Definition of R-Squared

R-squared (R²) is a statistical measure that indicates how well an investment’s returns correlate with a benchmark index. It ranges from 0 to 1 (or 0% to 100%), and a higher R² means a stronger correlation. Thus, it helps investors determine how much of a fund’s performance is influenced by the market.

For example, if a mutual fund has an R² of 90% against the S&P 500, the index's performance explains 90% of the fund’s movements.

Purpose of R-Squared in Finance and Investing

R² is used for:

• Measuring how closely an investment follows its benchmark.
• Assessing the reliability of beta in risk analysis.
• Identifying diversification benefits in portfolio management.
• Comparing actively managed funds against passive index funds.
• Evaluating stock performance in relation to market trends.

How R-Squared Is Calculated

R-Squared Formula

R² = 1 - (Sum of Squared Errors / Total Sum of Squares)

Example Calculation

• A mutual fund’s returns are compared against the S&P 500 index.
• If the fund has an R² of 85%, it means 85% of its performance is due to the index’s movements, while 15% is influenced by other factors.

Interpreting R-Squared in Investing

High R-Squared (70% – 100%)

• The investment closely tracks the benchmark index.
• Example: A large-cap index fund with an R² of 98% moves almost identically to the market index.

Moderate R-Squared (40% – 70%)

• The investment has some correlation but is also influenced by other factors.
• Example: A sector-specific fund with an R² of 60% has partial market dependence.

Low R-Squared (0% – 40%)

• The investment does not significantly follow the benchmark.
• Example: A hedge fund with an R² of 20% has little correlation with the broader stock market.

R-Squared vs. Beta

Feature	R-Squared	Beta
Definition	Measures how closely an asset follows its benchmark	Measures an asset’s volatility relative to the market
Indicates	The percentage of movement explained by the benchmark	The level of risk compared to the market
Example	A fund with an R² of 95% moves in sync with the index	A stock with a beta of 1.5 is 50% more volatile than the market

Example: A mutual fund with high R² but low beta closely tracks the market but is not significantly more volatile than the index.

Advantages and Disadvantages of R-Squared

Advantages

• Helps investors choose funds based on correlation with benchmarks.
• Assists in evaluating fund manager performance in active vs. passive strategies.
• Identifies the degree of diversification in a portfolio.

Disadvantages

• Does not indicate profitability or risk-adjusted returns.
• High R² funds may not offer diversification benefits.
• Does not account for external factors affecting investment returns.

Related Terms

• Beta – Measures volatility relative to the market.
• Alpha – Measures excess returns beyond benchmark performance.
• Standard deviation – Evaluates investment volatility.

Interesting Fact

Studies show that actively managed funds with low R² tend to have higher risk and less predictable returns, making passive index investing a preferred strategy for many long-term investors.

Statistic

According to Morningstar, over eighty percent of actively managed equity funds have an R² above 90%, meaning they largely follow their benchmark index despite aiming for excess returns.

Frequently Asked Questions (FAQ)

1. What does an R-squared of 100% mean?

An R² of 100% means an investment perfectly follows its benchmark, with no independent movements.

2. Is a high R-squared always good?

Not necessarily—high R² indicates a strong correlation but does not guarantee high returns or risk-adjusted performance.

3. How is R-squared used in portfolio diversification?

A low R² asset may provide diversification benefits since its returns are less dependent on the overall market.

4. Can R-squared be used alone to evaluate investments?

No, R² should be combined with other metrics, such as beta and alpha, for a full risk-return assessment.

5. What is considered a good R-squared value for an index fund?

An R² above 90% is ideal for index funds, as it indicates strong tracking of the benchmark.