Sizing the Structure
Order is heaven’s first law, and this confessed, Some are, and must be, greater than the rest . . .
In the liability waterfall model previously introduced, bond allocations and spreads were given as inputs. Spreads are determined by the market. For example, there is a general consensus among traders as to the bid-ask spreads of A-rated bonds backed by diversified pools of subprime mortgages (or other assets). However, the optimal size or number of bonds of each rating in a new structure (called the allocation) is not obvious.
Where did each bond’s rating come from? The rating is granted by an agency if the bond passes certain requirements specific to that rating and asset class. Key to the requirements is a credit enhancement constraint. This constraint may state that for a bond to be granted a certain rating, the bonds subordinate to it must absorb all losses of principal and all deferrals of interest over the life of the bond, given some particular assumption of asset losses, prepayments, and other characteristics. To get a higher rating, assumed asset losses need to be higher, among other things. For a given asset type, the agencies present the market with mappings between ratings and stress assumptions. The mappings are not equivalent among the agencies, so it can be that over periods of time one rating agency is more binding than another; that is, one agency is more conservative and its mappings require more credit enhancement ...