# R-Squared

> R squared shows how much of a portfolio's movement is explained by its benchmark or a model. Learn what it means, how to read it with beta and alpha, and its traps.

Source: https://learn.tradelabsai.com/portfolio/r-squared/  
Track: Portfolio and Performance · Level: Intermediate · Updated: 2026-10-03  
Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice.  
Cite as: TradeLabs Learn, "R-Squared", https://learn.tradelabsai.com/portfolio/r-squared/

R squared, also called the coefficient of determination, measures how much of the variation in one series is explained by another. In investing, it usually shows how much of a fund's or strategy's return movements are explained by its benchmark. A US index fund might have an R squared near 1.00 against the S&P 500; a market neutral hedge fund might have one near 0. R squared does not say whether performance was good. It says how much the benchmark comparison, and therefore beta and alpha, can be trusted.

## What it means

```
R squared = 1 - (Unexplained variation / Total variation)
```

For a simple regression on one benchmark, R squared equals the correlation between the two series, squared. See [Covariance and Correlation](https://learn.tradelabsai.com/math/covariance-and-correlation/) and [Regression Analysis](https://learn.tradelabsai.com/math/regression-analysis/).

| R squared | Interpretation for a fund versus its benchmark |
|---|---|
| 0.90 to 1.00 | Moves very closely with the benchmark; beta and alpha estimates are reliable |
| 0.70 to 0.90 | Mostly explained by the benchmark |
| 0.40 to 0.70 | Partly explained; other factors matter |
| Below 0.40 | The benchmark explains little; beta and alpha estimates are weak |

**Example: Reading R squared with beta and alpha**
A fund's correlation with its benchmark is 0.90, so its R squared is 0.81: about 81% of its return variation is explained by the benchmark. Its beta is 1.1 and its annual alpha is 2%. Because R squared is high, the beta is meaningful and the alpha is measured against a relevant benchmark. A second fund reports alpha of 5% against the same benchmark, but its R squared is 0.25. Its "alpha" is measured against a benchmark that explains only a quarter of its movement, so the figure says little; a different benchmark or factor model would be needed. See [Alpha and Beta](https://learn.tradelabsai.com/portfolio/alpha-and-beta/).

## Uses of R squared

| Use | How |
|---|---|
| Judging benchmark fit | Low R squared suggests the wrong benchmark |
| Detecting closet indexing | A high fee active fund with R squared above 0.95 may be little more than an index fund. See [Active vs Passive Investing](https://learn.tradelabsai.com/portfolio/active-vs-passive-investing/) |
| Diversification | Assets with low R squared to your portfolio add more diversification. See [Diversification](https://learn.tradelabsai.com/portfolio/diversification/) |
| Hedging | High R squared means index futures will hedge the portfolio well. See [Hedging](https://learn.tradelabsai.com/markets/hedging/) |
| Evaluating factor models | Higher R squared means the factors explain more of the returns. See [Factor Models](https://learn.tradelabsai.com/portfolio/factor-models/) |

## R squared in model building

In forecasting, R squared measures how much of the target's variation a model explains. In trading, out of sample R squared values for return forecasts are usually tiny, often below 1%, yet can still be economically valuable when applied across many bets. An in sample R squared that looks high is often a sign of overfitting. See [Overfitting and Curve Fitting](https://learn.tradelabsai.com/research/overfitting-and-curve-fitting/) and [Information Ratio and Tracking Error](https://learn.tradelabsai.com/portfolio/information-ratio/).

## Traps

1. **High R squared is not good performance:** an index fund has R squared near 1 and zero alpha before fees.
2. **Trending series:** regressing one trending price series on another can give a high R squared with no real relationship, a spurious regression. Use returns, not prices. See [Stationarity, Differencing and Unit Roots](https://learn.tradelabsai.com/math/stationarity/).
3. **Adding variables always raises in sample R squared:** use adjusted R squared or out of sample tests.
4. **Outliers:** a few extreme points can create or destroy R squared. See [Outliers and Robust Statistics](https://learn.tradelabsai.com/math/outliers-and-robust-statistics/).
5. **Non linear relationships:** option strategies may relate strongly to the market in a non linear way that a linear R squared understates.

## Adjusted R squared

Adjusted R squared penalises extra explanatory variables:

```
Adjusted R squared = 1 - (1 - R squared) × (n - 1) / (n - k - 1)
```

where n is the number of observations and k the number of explanatory variables. It rises only when a new variable improves the model more than expected by chance.

## Frequently asked questions

### What does R squared mean in investing?

The share of a portfolio's return variation explained by its benchmark or a model, from 0 (none) to 1 (all).

### What is a good R squared for a mutual fund?

It depends on the goal. Index funds should be near 1; active funds with R squared above about 0.95 may be closet indexers, and low values suggest the benchmark is a poor fit.

### Does a high R squared mean a good investment?

No. It only measures how closely returns follow the benchmark, not whether they were high or low.

Next, move from measuring performance to building portfolios in [Portfolio Construction](https://learn.tradelabsai.com/portfolio/portfolio-construction/).

## Continue learning

- Next lesson: [Portfolio Construction](https://learn.tradelabsai.com/portfolio/portfolio-construction/)
- Previous lesson: [Treynor Ratio](https://learn.tradelabsai.com/portfolio/treynor-ratio/)
- Related: [Treynor Ratio](https://learn.tradelabsai.com/portfolio/treynor-ratio/): The Treynor ratio divides excess return by beta to measure reward for market risk. Learn the formula, a worked comparison and how it differs from the Sharpe ratio.
- Related: [Regression Analysis](https://learn.tradelabsai.com/math/regression-analysis/): Regression models how one variable relates to others. Learn linear regression, beta, R squared, multiple regression for factors, hedge ratios and common pitfalls.
- Related: [Alpha and Beta](https://learn.tradelabsai.com/portfolio/alpha-and-beta/): Beta measures how much a portfolio moves with the market; alpha is the return beyond what that exposure explains. Learn formulas, CAPM, regression and pitfalls.
- Related: [Covariance and Correlation](https://learn.tradelabsai.com/math/covariance-and-correlation/): Covariance and correlation measure how two assets move together. Learn the formulas, how to read them, why correlations change in crises and their portfolio role.
- Related: [Information Ratio and Tracking Error](https://learn.tradelabsai.com/portfolio/information-ratio/): The information ratio divides active return by tracking error to measure how consistently a portfolio beats its benchmark. Learn the formulas, values and uses.
- Related: [Factor Models](https://learn.tradelabsai.com/portfolio/factor-models/): Factor models explain asset returns with common drivers such as the market, size, value and momentum. Learn CAPM, Fama French and how to run a factor regression.