Residuals when you don't expect to see them

Most folks in our industry are aware that if you employ a holdings-based model for attribution, you're subject to residuals creeping in. Residuals are the unexplained differences between the excess return (portfolio return minus benchmark return) and the sum of the attribution effects. Because holdings-based models don't capture intraperiod cash flows, they're subject to residuals. And so, our research confirms that most asset managers prefer to use a transaction-based model to be more accurate.

However, if you're using a monthly return formula (e.g., Modified Dietz), then you may still end up with residuals, because the transaction-based approach is capturing an exact return, while the Modified Dietz arrives at an approximation to the true, TWRR. Ideally, you should be using a daily return method so that you will eliminate the residual.

Note: you can still have what might be called a longitudinal or intertemporal (occurring across time) residual, unless you employ an appropriate linking method.

p.s.,  I believe I'm the first to use the term "intertemporal" to describe this form of a residual. I believe it's a handy way to distinguish between single-period residuals which can arise from using a holdings-based model, and residuals across time, when using an arithmetic approach.