Let's say the credit-senstive asset pool (e.g., mortgages) has a value of $100. If the SPE pays $80 (this is Culp's example) and issues $80 in tranched notes to investors. Now there is $20 of O/C that provide the credit enhancement to the notes (i.e., OC = Assets - Liabilities, when Assets > Liabilities); even the riskiest note holder is "protected" by the $20 which is the equity tranche...btw, in the Ashcraft case study (recommended!), that is a classic example: the equity tranche (X) constituted 1.4% of overcollaterlization in the subprime securitization. Translation: the total collateral pool of mortgages had a value of +1.4% over the total debt (notes) issued to investors
Direct equity is similar from a capital structure perspetive. Here if value of assets = $100, SPE pays $80 then finds an outside investor who wants to invest $20, so now external investor owns the $20 equity tranche rather than it being implicity funded by the originator (in the O/C case, the originator sold $100 for only $80 so it must initially have the equity, which is likely then transferred to the SPV)
...there is an equity tranche is both cases, "direct equity" refers to finding an outside investor to pay for the tranche. We can work it from the other direction, though it's more academic than practical: assume we want to issue $100 MM in par value of liabilities, but the highest risk debt (credit linked note) needs 5% equity subordination. In the one case, we pool assets of $105; $105 collateral > 100 MM liabilities = $5 MM O/C. But what if we only have asset pool = $100. Then we go get an investor to fund $5 MM in "direct equity" for the equity tranche...
...the first is: assets (collateral) of 105 = liabities of 100 + equity of $5
...the second is: loan collateral of 100 + $5 (cash) funds = $100 liabilities + outside investor of $5
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