CDS

[srinu2singaraju]

Question:
A pool of high-yield bonds is placed in an SPV and three tranches (including the equity tranche) of bonds are issued collateralised by the bonds to create a Collateralised Bond Obligation (CBO). Which of the following is true?

Choose one answer.

a. At fair value, the value of the issued bonds should be less than the collateral.

b. At fair value, the total default probability, weighted by size of issue, of the issued bonds should equal the default probability of the collateral pool.

c. The equity tranche of the CBO has the least risk of default.

d. The yield on the low risk tranche must be greater than the yield on the collateral pool.

The Answer is B. Please explain me why?

 

[David Harper CFA FRM]

Hi Srinu,

Neat question, I didn't write it

It means to query the idea that the tranches issued on the collateral pool (assuming no overcollateralization) must preserve cash flows and risk. (a sort of law of conservation: if the risk and cash cannot leak through other means, the must be preserved in aggregate)

In mathy terms:
Let A,B, & C = market values of senior/mezz/junior tranches and x, y, z = respective # of defaults expected in each tranche, such that market-value based PD(tranche A) = x/A.

What is "the total default probability, weighted by size of issue?"
= x/A * A/(A+B+C) + y/B * B/(A+B+C) + z/C * C/(A+B+C)
i.e., the sum of each tranche PD weighted by tranche
This = x/(A+B+C) + y/(A+B+C) + z/(A+B+C) = (x+y+z)/(A+B+C) = default probability of the collateral pool

Or just more intuitively, imagine the "violation" where you could carve up notes (tranches) that had a different aggregate PD. It would be a free lunch and imply an arbitrage prospect.

David

 

[srinu2singaraju]

Thank you David for quick responce.

Good explanation.