Analysing a Real Portfolio

Everything in this section is more useful once applied to a portfolio you actually hold. This article walks through running a factor regression on your own returns: what you need, how to read the output, and the errors that make the result meaningless. The exercise is worth doing because its conclusions are frequently surprising, and because it converts a vague sense of "my portfolio is diversified" into a measurement.

What you need

Your portfolio's periodic returns. Monthly is standard. These must be time-weighted returns that strip out the effect of your deposits and withdrawals, not the change in your account balance. Using balance changes is the most common way this analysis goes wrong.
The factor return series. Published free by the Kenneth R. French Data Library, which is the same source used throughout this dashboard. Match the region of your holdings and the frequency of your returns.
The risk-free rate. Supplied in the same files. Your returns must be converted to excess returns by subtracting it before regressing.
Enough observations. Sixty monthly returns is a common minimum. Fewer produces coefficients too imprecise to act on, and results from short samples should be treated as suggestive at best.

The regression

Regress your excess returns on the factor returns. Any statistics package, spreadsheet, or scripting language will do this.

Rp - Rf = alpha + b(Mkt-Rf) + s(SMB) + h(HML) + r(RMW) + c(CMA) + e

Each coefficient is the portfolio's sensitivity to that factor. Alpha is the average return unexplained by the set of factors used.

Reading the coefficients

The market coefficient (b) is usually close to 1 for a diversified equity portfolio. Materially above 1 means you are taking more market risk than the index, whether through concentration, high-beta holdings, or leverage. Materially below 1 usually indicates a meaningful cash or bond allocation.

The size coefficient (s) is positive for a small-cap tilt and negative for a large-cap tilt. Portfolios built from well-known large companies frequently show a negative loading their owners did not intend.

The value coefficient (h) is positive for a value tilt, negative for growth. This is the coefficient that most often contradicts expectations. Investors who consider themselves value-oriented regularly discover a negative loading, because the companies they regard as high quality at a fair price are classified as growth by book-to-market.

Profitability (r) and investment (c) capture quality and capital discipline. Portfolios of established, profitable, conservatively financed companies typically show positive loadings on both.

Judging alpha honestly: look at its statistical significance and the width of its confidence interval, not just its sign. With five years of monthly data the interval around alpha is usually wide enough to include zero comfortably. An alpha that is positive but insignificant is not evidence of skill, and treating it as such is the main way this exercise gets misused.

Mistakes that invalidate the result

Using money-weighted returns. Contributions and withdrawals contaminate the series and the regression measures your cash-flow timing rather than your portfolio.
Forgetting to subtract the risk-free rate. This biases alpha and is easy to miss.
Mismatching regions. Regressing an internationally diversified portfolio on US-only factors attributes genuine international exposure to alpha.
Ignoring changes in the portfolio. If your strategy changed partway through the sample, a single regression averages two different portfolios into a description of neither. Rolling regressions show how exposures have drifted.
Over-reading a short sample. Coefficients from two or three years of data move substantially with a single unusual month.

What to do with the answer

The purpose is diagnosis, not a trading signal. The useful questions are whether your actual exposures match what you intended, whether you are paying active fees for exposures available cheaply, whether several holdings are duplicating the same bet, and whether the portfolio's past results are explained by tilts rather than selection. Those answers are actionable in a way that a factor forecast is not.

This article is educational and is not investment advice.