R-Squared
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 Value | Interpretation | Example |
|---|---|---|
| 95-100% | Very high benchmark dependency | Index funds, closet indexers |
| 85-95% | High correlation to benchmark | Most large-cap active funds |
| 70-85% | Moderate — some active management | Sector-focused funds |
| 40-70% | Low — significantly different | Hedge funds, alternatives |
| 0-40% | Very low — minimal relationship | Market-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 Want | Look For | R² Range |
|---|---|---|
| True index tracking | Passive index fund | 98-100% |
| Genuine active management | Active fund | 70-90% |
| Diversification benefit | Alternative strategy | < 50% |
| Closet indexer detection | Active 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
Related Terms
Beta (β)
A measure of a stock's volatility relative to the overall market, where a beta of 1.0 means the stock moves in line with the market, above 1.0 means more volatile, and below 1.0 means less volatile.
Alpha (α)
The excess return of an investment relative to a benchmark index, representing the value added (or lost) by active management or stock selection.
Correlation
A statistical measure ranging from -1 to +1 that describes how two investments move in relation to each other.
Tracking Error
The standard deviation of the difference between a portfolio's returns and its benchmark returns, measuring how closely a fund follows its index.
Standard Deviation
A statistical measure of how spread out returns are from the average, quantifying investment volatility and risk.
Risk Management
The systematic process of identifying, assessing, and mitigating financial risks to protect portfolio value and achieve investment objectives.
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