R-Squared

IntermediateRisk Management2 min read

Quick Definition

A statistical measure (0-100%) indicating how much of a portfolio's performance can be explained by movements in its benchmark index.

What Is R-Squared?

R-Squared (R²) measures the percentage of a fund's returns that can be attributed to movements in its benchmark index. It indicates how closely a fund tracks its benchmark.

Interpreting R-Squared:

R² ValueInterpretationExample
95-100%Very high benchmark dependencyIndex funds, closet indexers
85-95%High correlation to benchmarkMost large-cap active funds
70-85%Moderate — some active managementSector-focused funds
40-70%Low — significantly differentHedge funds, alternatives
0-40%Very low — minimal relationshipMarket-neutral strategies

Using R-Squared with Beta:

  • High R² makes beta meaningful (the relationship is reliable)
  • Low R² makes beta unreliable (too much unexplained variation)
  • Rule: only trust beta when R² > 70%

R-Squared for Fund Selection:

If You WantLook ForR² Range
True index trackingPassive index fund98-100%
Genuine active managementActive fund70-90%
Diversification benefitAlternative strategy< 50%
Closet indexer detectionActive fund charging high fees> 95% (warning sign)

Closet Indexer Alert: If an active fund has R² > 95% and charges 0.8%+ in fees, you're essentially paying for index-like returns. Switch to a real index fund at 0.03-0.10% fees.

Formula: R² ranges from 0 to 1 (or 0% to 100%). It equals the square of the correlation coefficient between the portfolio and benchmark returns.

Formula

Formula

R² = (Correlation)² = 1 - (SS_residual / SS_total)

R-Squared Example

  • 1An S&P 500 index fund has R² of 99.9% — nearly all its movement is explained by the S&P 500
  • 2A market-neutral hedge fund with R² of 15% offers genuine diversification from stock market movements