Why r-squared matters
In investment analysis it indicates how closely a portfolio’s returns fit a benchmark or factor model, helping assess whether beta and estimated alpha are meaningful in that context.
How it is applied
Analysts regress portfolio returns on benchmark or factor returns, inspect sample frequency and period, and evaluate R-squared alongside coefficients, residuals, significance, stability, and economic logic. Run a regression of portfolio returns on benchmark returns over a stated frequency and window. R-squared equals the fraction of sample return variance explained by the fitted model. The benchmark, currency, net-or-gross return basis, and treatment of missing observations must be consistent.
Portfolio example
A fund regression has R-squared of 0.85, meaning the model explains 85% of observed return variation in that sample, while 15% remains unexplained by it. If total variation around a fund’s mean is 100 units and regression residual variation is 25, R-squared is 1 minus 25 divided by 100, or 75%. The remaining 25% is unexplained by that particular model, not necessarily manager skill.
How to interpret it
High R-squared means close historical model fit, not superior performance or causation. Low R-squared can signal differentiated exposure, noise, nonlinear behavior, or a poor benchmark. High R-squared indicates the selected benchmark explains much of historical variation. It does not prove the benchmark is appropriate or that beta is stable. Low R-squared can reflect alternative exposures, noise, illiquidity, or a poor benchmark.
Limitations and common misconceptions
R-squared usually rises when irrelevant variables are added and can be misleading with nonstationary, autocorrelated, smoothed, or nonlinear returns. Results are sample and benchmark dependent. R-squared is sample dependent and says nothing about causation, alpha quality, downside protection, or future fit. Smoothed returns can distort it. Adding factors mechanically increases model fit, so adjusted measures and economic reasoning remain important. Benchmark selection should precede statistical calculation. A global equity fund regressed only against a domestic index may show low fit because currency and regional exposures are missing, not because returns are uniquely idiosyncratic. Review residuals for changing variance and structural breaks, and pair R-squared with beta, alpha, tracking error, and qualitative holdings analysis before drawing conclusions about active management.
Sources and further reading
- Portfolio Performance EvaluationCFA Institute
- Quantitative MethodsCFA Institute