Factor Regression

• CAPM, Fama-French 3-factor, Fama-French 5-factor, and Carhart 4-factor models
• Daily, monthly, and annual frequency options
• Residual diagnostics (autocorrelation, variance stability)
• Factor exposure confidence intervals
• Portfolio-level and single-asset regression

• What drove returns? The exposure chart plots each estimated beta with its 95% confidence interval against a zero line. It shows how far the portfolio moved with the factors in the selected model, and which exposures are distinguishable from zero. The coefficient table below it carries the exact estimates, standard errors, and p-values.
• Was performance just factor exposure? Alpha and residual diagnostics show how much return remains after the model accounts for the selected factors.
• How believable is the fit? R-squared, F-statistic, and residual dispersion indicate whether the factor model explains most of the observed behavior.

• The regression uses excess returns: portfolio returns minus the Fama-French risk-free series.
• Factor availability matters because each model has a different history. Later-starting models can shorten the usable sample window, and the tool surfaces that adjustment.
• Monthly mode compounds daily observations and excludes incomplete first and last months. Annual mode compounds daily observations into calendar-year returns and drops incomplete edge years.
• The portfolio configuration reuses the same typed portfolio model as the backtester, but the tool excludes cash flows because they distort return attribution.

• The tool accepts exactly one portfolio. Use the Portfolio Backtest allocation editor, but analyze one finished portfolio instead of a comparison set.
• This analysis does not support cash flows. For a DCA or withdrawal plan, first use Portfolio Backtest. Then, analyze the static portfolio configuration.
• Custom factors live in the advanced settings panel. Each custom factor is a long-short spread built from public ticker returns. Specify tickers and weights, which must sum to zero. The tool adds the custom factor return series as an additional regressor alongside the selected factor model.
• After the run, you can save, share, and reopen the analysis from your workspace just like other major tools.

Start with the factor-exposure chart. Each point is an estimated beta. Each horizontal line is its 95% confidence interval. Then read R-squared for the return variation that the model explains. Annualized alpha is the modeled return that the factors do not explain.

The coefficient table contains exact p-values and confidence bounds from the t-distribution. Use the F-statistic to evaluate joint significance. Use the fitted-versus-actual chart and residual series to identify persistent or regime-specific errors and errors that are mostly noise. The residual summary gives the mean, standard deviation, skewness, and excess kurtosis.

• P-values use the exact t-distribution with n - k - 1 degrees of freedom. Here n is the observation count and k is the factor count. Significance markers are *** p < 0.001, ** p < 0.01, and * p < 0.05.
• Confidence intervals are 95% two-tailed, computed from the same t-distribution critical values.
• F-statistic tests joint significance of all factor loadings (excluding the intercept). A large F with a small p-value means the factors collectively explain meaningful variation.
• Intercept diagnostics report standard error, t-stat, p-value, and confidence interval for the alpha estimate itself.
• Residual summary reports mean (should be near zero for OLS), standard deviation, min, max, skewness, and excess kurtosis. Heavy tails or skew may indicate the factor model is missing an important driver.

• CAPM is the simplest baseline when you only want market beta and alpha.
• Fama-French 3 factor is a strong default for broad equity portfolios with size and value tilts.
• Carhart 4 factor is useful when momentum may explain part of the return pattern.
• Fama-French 5 factor adds profitability and investment exposures to the 3-factor model.
• q-factor (Hou-Xue-Zhang) is an investment-based model with market, size, investment-to-assets, and return-on-equity factors. Use monthly frequency, because daily q-factor data is not publicly available.
• AQR multi-factor provides a comprehensive model with market, size, value, momentum, betting-against-beta, and quality factors. It is useful for portfolios that blend multiple style tilts.
• Fixed income factors provides term spread, default spread, and corporate bond excess return factors for fixed income attribution. Use this when the portfolio has significant bond exposure.

• CAPM and FF3 use data from July 1926 onward.
• Carhart 4 factor momentum data is available from November 1926 onward.
• Fama-French 5 factor daily data begins July 1963.
• q-factor monthly data is available from January 1967 onward.
• AQR multi-factor coverage varies by factor. Many US equity factor series start in the early 1970s. Check each factor's data window.
• Fixed income factors start in the mid-1960s for most series.
• When the requested date range extends beyond factor data coverage, the tool trims the regression window and surfaces a warning.

• Read Estimated factor exposures first. Large positive market beta means broad equity exposure. Negative SMB or HML betas indicate large-cap or growth exposure, respectively.
• Check p-values and confidence intervals to assess whether each factor loading is statistically distinguishable from zero at the sample size.
• Check Annualized alpha after the exposures. A small alpha with a high R-squared indicates that the selected factors explain most of the modeled return variation.
• Use the residual chart to look for clusters. If misses cluster in one crisis or regime, a missing driver matters.