Barillas-Shanken Model Comparison
A statistical method for ranking competing asset-pricing factor models against each other directly, without needing to test them against a separate set of "test asset" portfolios.
With dozens of competing factor models on the market (Fama-French three-, five-, and six-factor, q-factor, and many more), the traditional way to judge them was to see how well each explains the returns of a chosen set of test-asset portfolios — but that choice of test assets can itself tilt the horse race toward one model or another. Barillas and Shanken showed that comparing factor models actually doesn't require test assets at all: since a model's own factors are themselves tradable portfolios, you can compare models purely by how well each model's factors price the other models' factors.
Their method uses a Bayesian approach to compute the probability that each candidate model is the best one, given the data, producing a ranked list of models rather than a single reject/don't-reject verdict. This sidesteps the test-asset-selection problem entirely and lets researchers compare, say, six or seven competing multifactor models on equal footing.
Because factors are themselves portfolios, factor models can be ranked against each other directly — using each model's factors as the test assets for its rivals — removing the need to pick a separate test-asset menu that could bias which model looks best.
Worked example. Comparing the Fama-French five-factor model against the q-factor model, Barillas-Shanken's Bayesian procedure might assign a 78% posterior probability that the q-factor model is the better description of returns over the sample studied, versus 22% for the five-factor model — a direct, quantified comparison rather than two separate pass/fail test-asset regressions that might disagree with each other.
Practice in interviews
Further reading
- Barillas & Shanken, 'Comparing Asset Pricing Models'