Fama-French five-factor plus momentum regression
Which well-known sources of return the portfolio is exposed to, with honest standard errors.
What it does
The portfolio's daily return above the T-bill rate is regressed on six factor returns: the market, size (small minus big), value (high minus low book-to-market), profitability (robust minus weak), investment (conservative minus aggressive) and momentum (recent winners minus losers). The coefficients are the portfolio's exposures, or loadings.
Why it is used
Two portfolios with the same volatility can be exposed to completely different things. Factor loadings say what kind of stocks the portfolio behaves like, and how much of its return those exposures explain.
Inputs
- Daily portfolio returns over the last five years.
- Daily factor returns and the risk-free rate from the French library.
Formulas
Assumptions
- Loadings are constant over the window. The rolling chart shows how far that is from true.
- The relationship is linear.
- Newey-West (HAC) standard errors allow for autocorrelation and changing volatility in the residuals.
How to read the results
A market loading of 1 means the portfolio moves one-for-one with the market after other factors are accounted for. Loadings whose 95% interval includes zero are shown in grey: the data cannot tell them apart from no exposure. Alpha is the average return the factors do not explain; its interval is almost always wide. The variance inflation factor (VIF) flags factors that move together in this sample; above 5, their separate loadings are unreliable.
Limitations
- The factors are built from US stocks. For bonds, gold or foreign stocks the loadings are harder to interpret and R² is lower.
- Factor data is published with a one-to-two-month lag.
- Daily data can understate loadings for holdings that trade infrequently or in other time zones.
Where it can fail
- For portfolios with few stocks, the unexplained part is large and loadings move a lot from year to year.
Changes from the original version
DeanOS began as a personal tool. Rebuilding it for the public meant rechecking each model; these are the changes that came out of that.
- The original version regressed on six ETFs (SPY, IWM, IVE, MTUM, QUAL, QQQ). All hold large US stocks and move closely together, so their coefficients were unstable. The French factors are long-short portfolios designed to be close to independent.
- Newey-West standard errors and the VIF check are new.
Validation on current data
Fit and collinearity for the example portfolios from the current snapshot.
References
- Fama, E. and French, K. (2015). A five-factor asset pricing model. Journal of Financial Economics 116(1).
- Carhart, M. (1997). On persistence in mutual fund performance. Journal of Finance 52(1).
- Newey, W. and West, K. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55(3).
- Newey, W. and West, K. (1994). Automatic lag selection in covariance matrix estimation. Review of Economic Studies 61(4).