A portfolio of assets is sold by the originators of the assets to a special purpose vehicle $($SPV$)$ and the cash flows from the assets are allocated to trances $($senior$,$ mezzanine and equity$).$ Financial engineers created an Asset$-$Backed Security $($ABS$)$ from the mezzanine trances of ABSs, known as ABS CDO. Suppose that the principals assigned to the senior, mezzanine, and equity tranches for the ABSs and ABS CDOs are $75\%,20\%,$ and $5\%.$ a$.$ Consider the losses to the portfolio of assets be equal to $15\%.$ Calculate the losses to Mezzanine Tranche of ABS and to Mezzanine Tranche of ABS CDO. b$.$ Consider now the losses to the portfolio of assets be equal to $20\%.$ Calculate the losses to Mezzanine Tranche of ABS and to Mezzanine Tranche of ABS CDO. c$.$ Explain the concept of waterfall in an Asset$-$Backed Security