A fixed Student t model cut mean joint loss for three US factors in 2005–2025, but the gain was uncertain with single annual blocks

We tested fixed Student t shapes for joint monthly forecasts of US market, size, and value factor returns. Twenty annual origins used official dated archives, 120 training months through July, and fixed forecasts for the next October through September. The test had 240 monthly vectors in 2005–2025. All shape comparisons held means and actual covariance fixed. The primary model had five degrees of freedom. It cut mean joint negative log density by 0.1614 nats against a normal model. The planned 95% paired interval with an expected block length of two years was 0.0035 to 0.3339. The interval from single annual blocks included zero. A separate 200,000-draw precision check confirmed this block sensitivity. Two known crisis blocks supplied 74.8% of net gain. With half correlations, the shape gain was 0.1352 nats. Against a normal model with 1.5 times the covariance, the gain was uncertain. Separate lower 1% and 5% quantile scores gave no clear gain. Larger joint region coverage improved but remained imperfect. Revision checks gave similar point gains. The test assumes each annual file preserves its stated historical version and was available by September 30. Labels use the earliest annual record in the collection, not first monthly releases. This is an extension on a previously used sample, not an independent replication or a trading test. The package preserves code, provenance, all forecasts and scores, resampling draws, negative results, figures, passed checks, exact replay records, and 77 unscored forecasts for November 2026 through September 2027.

return density forecasts · Student t distribution · annual data archives · point in time data · chronological tests · tail quantiles · block bootstrap · Fama French factors