A factor model of monthly returns shows a Durbin-Watson of 0.9, residual variance rising with market volatility (Breusch-Pagan p = 0.01) and variance inflation factors of 12 on two value factors. Which assumption does each break, what happens to the coefficients and t-statistics, and what is the fix?

All three leave the coefficients roughly unbiased and all three make the t-statistic unreliable, so the 2.4 does not survive as reported. A Durbin-Watson of 0.9 means residual autocorrelation near 0.55, which understates standard errors; fix with Newey-West errors. The Breusch-Pagan result means non-constant variance; use robust errors. Variance inflation factors of 12 mean the value factors overlap by 92%; combine them. Corrected, the t-statistic falls to about 1.8.

A Durbin-Watson statistic near 2 means each month's residual is unrelated to the last; it is roughly 2 x (1 - rho), where rho is the residuals' first-order autocorrelation. A value of 0.9 implies rho of about 0.55: misses come in runs, which breaks the assumption that errors are independent. Think of a cricket batter's form. If a good innings makes the next one more likely good, ten innings tell you less about true ability than ten unrelated ones would. The coefficients are still roughly unbiased, but the usual standard errors assume every month is fresh information. If the factor itself is autocorrelated, say 0.5 month to month, the true standard error is about sqrt((1 + 0.55 x 0.5)/(1 - 0.55 x 0.5)) = 1.33 times the reported one. The fix is Newey-West standard errorsStandard errors that allow residuals to be correlated over several lags and to have changing variance, so t-statistics stay honest when the usual assumptions fail., or modelling the dynamics if a lagged term belongs in the model.

The test regresses squared residuals on candidate variables; a p-value of 0.01 says their variance moves with market volatility. That breaks the constant-variance assumption, which again leaves coefficients unbiased but makes the textbook standard errors wrong, usually too small when the volatile months are also the months when the factors move most. The fix is heteroskedasticity-robust standard errorsWhite standard errors: they estimate each coefficient’s uncertainty without assuming the residual variance is the same in every observation.; Newey-West already includes this, so one correction handles both problems. Weighted least squares, down-weighting the volatile months, is the alternative if you also want more precise estimates.

A variance inflation factor is 1/(1 - R-squared) from regressing one factor on all the others. A value of 12 means 91.7% of book-to-price is explained by the other factors, mostly earnings yield, so the regression cannot tell the two apart and each coefficient's standard error is sqrt 12 = 3.46 times what it would be with unrelated factors. This one is not a lie in the standard error; it is a true lack of information. The symptom is coefficients that swing, even flip sign, when a few months are added, and two value factors that are each insignificant though jointly strong. The fix is to combine them into one value composite, drop one, or test them jointly with an F-test rather than one at a time.

Apply the autocorrelation correction alone: 2.4 / 1.33 = 1.81, below the usual 1.96. Once the standard errors are made honest, book-to-price is no longer significant on its own, and the collinearity means the regression could not have separated it from earnings yield anyway. What you tell the committee is that value as a group may matter, which a joint test or a single composite factor can check, but the claim about book-to-price specifically does not stand. The limitation: the 0.5 autocorrelation of the factor is an assumption, so rerun with Newey-West errors on the actual data before quoting the corrected figure.