For a specific coupon, if TBA TOAS is greater than a Specs TOAS, does that imply that the Specs are trading too rich to TBAs (given liquidity risk, payup risk, etc)? I realize relative value comparisons in Specs are usually done against Specs, but am trying to understand what this could mean. Could there be another explanation for why this could be the case?
Added later The first answer I came up with was embarrassingly incorrect; I have pointed out why. Please feel free to uncheck it.
Technically, this should be impossible: the Spec pool is always deliverable into the TBA, so the TBA OAS is a floor for the Spec pool valuation. This is plain wrong -- the TBA price is a lower bound on the price of the Spec pool, but there is no such constraint on the respective OASs of the two instruments. We can definitely ask the question as to why one would hold a Spec Pool at a richer valuation than TBAs and the discussion below offers some sanity checks to first ensure that this relationship really holds.
Is there an issue with the prepayment model? The model may not be recognizing the prepayment protection offered by the Spec pool and/or the true callability of the TBA
Are the correct collateral characteristics of the TBA being input into the OAS model? This can be tricky to get right: Dollar rolls, float, issuance patterns, and Fed purchase activity all play a role (among other factors).
Is there a pricing error? It is hard to get TBA prices wrong but Spec pool payups can sometimes be stale because of an absence of deep markets (or because the pricing source does not have an accurate idea of the market).
In the unlikely event that the OAS anomaly still persists after these factors are accounted for, the only somewhat contrived scenario in which Spec Pool OASs are lower than TBA OASs that I can think of is if there is a strong bid for Spec Pools from the CMO desk for a particular settlement month. Even this would be pretty irregular because CMOs are generally created from cheap not rich collateral, but occasionally there could be a short squeeze.