Factor Regression with 36 Observations

The OLS coefficients may be unbiased, but the standard errors and prediction interval are not reliable. The Breusch-Pagan p-value of 0.03 rejects homoskedasticity, so OLS standard errors are inconsistent; White or Newey-West standard errors are needed. The Durbin-Watson statistic of 1.08 is far below 2, indicating positive first-order serial correlation, which understates standard errors and makes t-statistics too large. Newey-West HAC standard errors address both problems.

VIFs of 5.8 and 6.1 for value and momentum indicate moderate-to-high multicollinearity. Individual t-statistics are unstable, although the joint model may still be useful. The 2020 strategy change is a structural break; pooling 36 months can mix different regimes, and more observations are not better if the relationship changed. Daniel should use a Chow test or regime dummy, or estimate on the post-change period if enough data exist. The 95% interval of 1.2% to 5.8% is likely too narrow because it assumes homoskedastic, serially independent, stable errors. With 36 observations and selected factors, parameter uncertainty is also understated. Finally, choosing the best of 20 factor combinations by R-squared is data snooping; the reported fit is optimistic and must be validated out of sample.

Momentum should not be dropped solely because its t-statistic is -1.6. First, the t-statistic is unreliable under heteroskedasticity, serial correlation, and multicollinearity; Daniel should compute a Newey-West t-statistic and a joint F-test for value and momentum. Second, multicollinearity means the coefficient is imprecisely estimated, not necessarily zero. Third, economic rationale matters: momentum has a documented risk premium and a relation to returns; dropping it could cause omitted-variable bias and distort the other coefficients.

Fourth, check the correlation between value and momentum. If they are nearly collinear, consider combining them or using orthogonalized factors. Fifth, evaluate out-of-sample forecast performance: drop momentum only if it does not improve out-of-sample forecasts and has no economic justification. A negative coefficient can be plausible if the fund is contrarian or if the sample includes a momentum crash. The decision should rest on robust inference, stability, and forecast usefulness, not on a single t-statistic.

Use a holdout or walk-forward design: estimate on an initial window, forecast the next month, roll forward, and compare forecast errors such as RMSE and MAE with a simple benchmark. Test parameter stability with rolling regressions and Chow tests around 2020. Report Newey-West standard errors and robust prediction intervals. Check factor definitions and data timing to avoid look-ahead bias.

Account for the 20-combination search by using an information criterion that penalizes model selection, cross-validation, or a pre-registered selection rule. Stress test forecasts under alternative factor returns and regimes. Compare the model's asset-allocation recommendations with equal-weight and risk-parity benchmarks after transaction costs. Document limitations: 36 observations is short, the fund is small-cap and may have liquidity and selection biases, and value and momentum are correlated. The committee should rely on the model only after out-of-sample evidence and a clear regime-stability assessment.