Style Analysis R-Squared

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.

Metric	Based On	Measures
R-Squared	Returns	How much return variance factors explain
Active Share	Holdings	How different holdings are from benchmark

Both together give a complete picture:

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

Alpha

What remains after factor adjustment

Beta

Key factor exposure

Factor Investing

The factors being measured

​Beginner

​What It Means

​Portfolio Examples

​Why It Matters

​Advanced

​Mathematical Definition

​Interpreting R-Squared with Alpha

​Factor Models Used

​Typical R-Squared Values

​Detecting Closet Indexers

​R-Squared vs. Active Share

​Practical Applications

​Style Drift Detection

​Data Requirements

​Related Terms

Alpha

Beta

Factor Investing

Beginner

What It Means

Portfolio Examples

Why It Matters

Advanced

Mathematical Definition

Interpreting R-Squared with Alpha

Factor Models Used

Typical R-Squared Values

Detecting Closet Indexers

R-Squared vs. Active Share

Practical Applications

Style Drift Detection

Data Requirements

Related Terms