Question

Pertaining to the solution of Ch. 8, problem 18fq for Options, futures, and other derivatives ; where does the 10.25% and 5.25% come from?

Options, Futures, and Other Derivatives (9th Edition)

Chapter 8, Problem 18FQ

Problem: In the ABS assets has been allocated in the ratio of 80% in Senior Tranche, 15% in Mezzanine Tranche and 5% in Equity Tranche. Getting Mezzanine Tranche is difficult so it is again allocated as ABS CDO in the ratio of 65% of 15% in AAA Tranche, 25% of 15% in BBB Tranche and 1- of 15% in Equity Tranche.

The way ABS CDO has constructed, Senior Tranche which is AAA rated can expect to receive its promised return and get its principal back if losses on the portfolio is less than 20%. Losses up to 20% get absorb by the Mezzanine which is BBB rated (15%) and Equity Tranches (5%).

However the AAA rate tranche of the ABC CDO is more risky. It will get promised return and get its principal back if losses on the underlying assets are up to 10.25%. This is because loss of 5% will be absorb by Equity Tranche and remaining loss of 5.25% will be borne by BBB tranche.

Since the Mezzanine Tranche has 15% share in total assets of the ABS, losses to Mezzanine Tranche will be 5.25%/15% or 35% of their principal.So up to loss of 10.25%, entire loss get absorb by Equity & Mezzanine Tranche and the Senior Tranche remain intact.

If the losses increase more than 10.25% then Senior Tranches of the ABS CDO suffer losses. If the loss is 18% on the underlying portfolio then loss of 5% will be borne by Equity Tranche of the ABS and remaining loss of 13% will be borne by the Mezzanine Tranche of the ABS.

Losses on the Mezzanine Tranches are therefore 13%/15% or 86.7% of their principal. Out of 86.7%, first 35% will be borne by the Equity & Mezzanine Tranches of the ABC CDO and remaining 51.7% or 51.7%/65% or 79.8% by the senior tranches of the ABS CDO.

Answer 1

Answer :

Let total ABS assets be 1,000

Hence, As per basic structure :

It divided as follows:

Particulars	%	Total
Senior Tranche	80%	=1,000 x 80% = 800
Mezzanine Tranche	15%	= 1,000 x 15% = 150
Equity Tranche	5%	=1,000 x 5% = 50

Here, it is further given that :

Getting Mezzanine Tranche is difficult so it is again allocated as ABS CDO in the ratio of 65% of 15% in AAA Tranche, 25% of 15% in BBB Tranche and 1- of 15% in Equity Tranche.

Particulars	Calculation	Total %
ABC CDO	=65% OF 15% =0.65 X 15%	9.75%
BBB Tranche	= 25% of 15% = 0.25 x 15%	3.75%
Equity Tranche	= 10% of 15% (but in total limited upto share in lossess of ABS Assets 5%)	1.5%

The way ABS CDO has constructed, Senior Tranche which is AAA rated can expect to receive its promised return and get its principal back if losses on the portfolio is less than 20%. Losses up to 20% get absorb by the Mezzanine which is BBB rated (15%) and Equity Tranches (5%).

Since the Mezzanine Tranche has 15% share in total assets of the ABS, losses to Mezzanine Tranche will be 5.25%/15% or 35% of their principal.So up to loss of 10.25%, entire loss get absorb by Equity & Mezzanine Tranche and the Senior Tranche remain intact.

Which means first losses are there then in total 5% will be allocated to Equity tranche. And remaining will be allocated to Mezzanine Tranche , But such loss can not be allocated to more than 5% to Equity Tranche in Total. Hence, In such case remaining loss of Equity tranche in Mezzanine Tranche will be born by BBB Tranche.

In such case the total BBB tranche share will be 35% (i. e. 25% + remaining of share of Equity tranche 10% = 35%)

Therefore The structure of losses born by Mezzanine Tranche and Equity Tranche to 20% when losses be up to in such case be:

Particulars	% of losses absorb
Equity Tranche	Assured up to 5% in total
BBB tranche	25% + 10% = 35% 0f 15% i.e. 5.25%
ABC CDO (AAA Rating)	65% of 15% = 9.75%

Hence, In total Equity tranche and BBB Tranche will born 10.25% of losses ( 5% + 5.25% )

There fore as per given explanation the given will be proved :

If the losses increase more than 10.25% then Senior Tranches of the ABS CDO suffer losses. If the loss is 18% on the underlying portfolio then loss of 5% will be borne by Equity Tranche of the ABS and remaining loss of 13% will be borne by the Mezzanine Tranche of the ABS.

Losses on the Mezzanine Tranches are therefore 13%/15% or 86.7% of their principal. Out of 86.7%, first 35% will be borne by the Equity & Mezzanine Tranches of the ABC CDO and remaining 51.7% or 51.7%/65% or 79.8% by the senior tranches of the ABS CDO.