Credit Risk & Credit Derivatives

[Swarnendu Pathak]

Can anybody please explain why the value of the subordinate debt will increase & value of senior debt will decrease when the firm is under financial distress? It is explained that under the financial distress the subordinate debts will act like equity but please highlight on how the value of the same would increase.

Thanks in advance.

 

[ashanks]

Hi Swarnendu,

Under low probability of default and low correlation, it is very unlikely that there will be more than a few defaults. Thus under these conditions, the equity tranche suffers all the losses, and the mezzanine (subordinate tranche) will be basically safe - just like senior tranche.

Now, if probability of default increases significantly (but correlation stays low), the losses will spill over from equity tranche to mezzanine tranche, and hence it will lose value.

But if the correlation increases significantly to a high value also (along with PD), then increasing correlation actually increases the equity value because it is more likely that in half the cases, none of the underlying loans will default (along with half the cases where all underlying loans will default). This reduces the expected loss from before, when the correlation was a little lower.

During times of financial distress, it is observed that correlation sharply rises.

The key point is: while keeping PD constant, increasing correlation will have one of the following two effects at the mezzanine tranche:

1] at high correlation, it will increase the mezzanine tranche value (mezzanine behaves like equity tranche)​

2] at low correlation, it will decrease the mezzanine tranche value (mezzanine behaves like senior tranche)​

Hope that helps.

 

[Tania Pereira]

Hi, could someone explain more about it? What to say about convexity effect in this case?

 

[bpdulog]

Hi, could someone explain more about it? What to say about convexity effect in this case?

Mezz tranche is convexity can vary because it can take on characteristics of senior debt or equity depending on circumstances, and equity is positive convex. So, traders assumed they were hedged w/ the mezz.


It is similar to contango and backwardation effects on hedging from Part 1

 

[Tania Pereira]

Thank you!

 

[David Harper CFA FRM]

In case it's helpful, I copied below a response from recent discussion here at https://forum.bionicturtle.com/thre...-stulz-applying-merton-model.7677/#post-50045 which is a snippet of our recently updated Stulz notes. This concerns the OP question about subordinated debt in a firm: basically, it acts like debt if firm value is high and default probability is "typical" (so it's value is mostly a function of interest rates, as usual, and to a lessor extent firm volatility). But if firm value is low and solvency is jeopardized, interest rates are less important and volatility is more important (here, the subord debt is more like equity).

@FrmL2_Aspirant we recently published (to the SP) the study note for Stulz which includes actual Excel spreadsheet implementation of Stulz' subordinated debt concept. See below. Basically, in the "high-value" firm (green line) where default is reasonably unlikely, SD behaves like debt as you would expect. But, in the low-value firm (orange line), the optionality that is sensitive to volatility overwhelms and the SD behaves more like equity. I hope that's helpful!

We're more likely to see "convexity" in the context of junior/mezz tranches in structured credit; e.g., Malz Chapter 9

"There are several important patterns in the results we see in the example, particularly with respect to the interaction between correlation and default probability:
Increases in the default rate increase bond losses and decrease the equity IRR for all correlation assumptions. In other words, for any given correlation, an increase in the default rate will hurt all of the tranches. This is an unsurprising result, in contrast to the next two.
Increases in correlation can have a very different effect, depending on the level of defaults. At low default rates, the impact of an increase in correlation is relatively low. But when default rates are relatively high, an increase in correlation can materially increase the IRR of the equity tranche, but also increase the losses to the senior bond tranche. In other words, the equity benefits from high correlation, while the senior bond is hurt by it. We will discuss this important result in more detail in a moment.

The effect on the mezzanine bond is more complicated. At low default rates, an increase in correlation increases losses on the mezzanine bond, but decreases losses for high default rates. In other words, the mezzanine bond behaves more like a senior bond at low default rates, when it is unlikely that losses will approach its attachment point and the bond will be broken, and behaves more like the equity tranche when default rates are high and a breach of the attachment point appears likelier.

Convexity. At low correlations, the equity value is substantially positively convex in default rates. That is, the equity tranche loses value rapidly as default rates increase from a low level. But as default rates increase, the responsiveness of the equity value to further increases in the default rate drops off. In other words, you can’t beat a dead horse: If you are long the equity tranche, once you’ve lost most of your investment due to increases in default rates, you will lose a bit less from the next increase in default rates.

For low correlations, the senior bond tranche has negative convexity in default rates; its losses accelerate as defaults rise. The mezzanine tranche, again, is ambiguous. It has negative convexity for low default rates, but is positively convex for high default rates. At high correlations, all the tranches are less convex; that is, they respond more nearly linearly to changes in default rates."