Tranching and Collateralized Debt Obligations

Collateralized Debt Obligations

Investors can be divided into two broad classes:

• Those who seek a high degree of safety (minimal risk)
• Other investors seek high returns, and are willing to take risks to get it
• Third category, those demanding bonds of intermediate risk, is fairly small

From previous chapter, we have that the coupon payments are

$$c(p)=\frac{r+p(1-R)}{1-p(1-R)}$$

where $p$ is the probability of default, $R$ is the recovery rate, and $r$ is the risk-free rate.

Let’s say that the probability of default is 2% per annum. The problem here is, those seeking high risks cannot invest in these bonds, since the coupon rate is too low. Similarly, those seeking low risk cannot invest in high-risk bonds.

so basically, imagine as a bank, I buy two of these less interesting bonds. Then I can create two new bonds, one with high coupon rate, another with lower coupon rate, and those are more attractive!

So we do this like this. We slice our portfolio into two equal parts called tranches.

We name one “senior” and one “junior”. This refers to the cashflows, the senior tranche gets paid first, then the junior tranche. That means if one of our two bonds default, then the senior will get paid, the junior gets what is left.