Math & Analytics

R-Squared

Statistical measure (0–100) of how much of a portfolio's movements are explained by the benchmark index.

S65S66CFP

R-squared (R²) measures what percentage of a portfolio's or security's return variability is explained by the movements of its benchmark index. It ranges from 0 to 100 (or 0% to 100%).

Interpretation:

| R-squared | Meaning | |---|---| | 100 | 100% of returns explained by the benchmark — perfect tracking | | 85–100 | Highly correlated; fund closely mirrors the index | | 70–85 | Moderate correlation | | <70 | Low correlation; returns largely independent of the benchmark |

R-squared and beta relevance: - High R² → beta is a reliable indicator of the fund's market risk. - Low R² → beta is NOT meaningful; the fund's returns aren't well explained by the market.

Example: A mutual fund with R² = 95 vs. S&P 500 behaves very much like an index fund; its beta is a reliable measure of sensitivity. A fund with R² = 20 vs. S&P 500 marches to its own drummer — beta is largely meaningless.

R-squared vs. correlation: - R² = Correlation² (for simple linear regression). - Correlation = 0.9 → R² = 0.81 = 81%.

Active vs. passive management: - Index funds: R² close to 100. - Active managers: Aim to have lower R² (higher active share) to justify higher fees.

> Exam tip: Low R-squared = beta is unreliable. High R-squared = returns well explained by market movements. On the CFP® and Series 65, know that you cannot trust a fund's beta as a risk measure if R-squared is below 70.

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