Style Analysis R-squared measures how much of a portfolio’s performance can be explained by systematic factors like market, value, size, and momentum. It reveals whether returns come from factor exposures or genuine stock selection.
Beginner
What It Means
R-squared tells you what percentage of your portfolio’s returns are explained by known factors. Higher R-squared means your returns mostly come from factor exposures, not unique stock picking.
Portfolio Examples
| Portfolio | R-Squared | Interpretation |
|---|
| Index Fund | 99% | Almost entirely explained by market factor |
| ”Active” Fund A | 95% | Closet indexer - paying active fees for passive exposure |
| Active Fund B | 70% | Mix of factor exposure and stock selection |
| Hedge Fund | 40% | Mostly unique strategies, less factor-driven |
Why It Matters
R-squared helps identify “closet indexers” - funds charging active fees but delivering passive-like returns. If 95% of returns are explained by factors you could get cheaply through ETFs, why pay active management fees?
Advanced
Mathematical Definition
R-squared = 1 - (SS_residual / SS_total)
= Variance explained by factors / Total return variance
From regression:
Rp = α + Σ(βi × Fi) + ε
R-squared = 1 - Var(ε) / Var(Rp)
Interpreting R-Squared with Alpha
| R-Squared | Alpha | Interpretation |
|---|
| High | Low | Closet indexer - consider cheaper alternatives |
| Low | High | Genuine skill creating value |
| Low | Low | Active bets not adding value |
| High | High | Skilled factor timing (rare) |
Factor Models Used
Common models for style analysis:
| Model | Factors Included |
|---|
| CAPM | Market only |
| Fama-French 3 | Market, Size, Value |
| Carhart 4 | + Momentum |
| Fama-French 5 | + Profitability, Investment |
R-squared depends on which factors you include. Adding more factors typically increases R-squared. Use a consistent model for fair comparisons.
Typical R-Squared Values
| Fund Type | Typical R-Squared |
|---|
| Index Funds | 98-99% |
| Enhanced Index | 95-98% |
| Large-Cap Active | 85-95% |
| Small-Cap Active | 75-90% |
| Long/Short Equity | 50-80% |
| Market Neutral | 10-40% |
Detecting Closet Indexers
Warning signs of closet indexing:
| Metric | Concern Level |
|---|
| R-squared above 95% | High concern |
| Tracking error under 2% | High concern |
| Holdings overlap above 80% | High concern |
| Active share under 20% | High concern |
If a fund has R-squared above 90%, you’re likely paying active fees for returns you could replicate with cheap factor ETFs.
R-Squared vs. Active Share
| Metric | Based On | Measures |
|---|
| R-Squared | Returns | How much return variance factors explain |
| Active Share | Holdings | How different holdings are from benchmark |
| R-Squared | Active Share | Manager Type |
|---|
| High | Low | Closet indexer |
| High | High | Factor bettor |
| Low | Low | Diversified stock picker |
| Low | High | Concentrated stock picker |
Practical Applications
Due Diligence Process:
- Run style regression on manager returns
- If R-squared above 90%: Question if active fees justified
- Examine factor loadings for style consistency
- Compare R-squared over rolling windows to detect style drift
- Combine with active share analysis
Style Drift Detection
Changes in R-squared over time may indicate:
- Strategy changes
- Manager turnover
- Capacity constraints forcing index-like positions
- Deliberate shift in investment approach
Data Requirements
| Requirement | Details |
|---|
| Minimum | 36 months for stable estimate |
| Preferred | 60+ months |
| Factor Data | Need factor return series |
| Model Choice | Results depend on factors included |
