The problem with assessing bond return distributions February 1, 2012 at 1:24 pm

Yesterday we saw that one good way of visualizing bond returns is to look separate at the survival probability and the distributions of returns given default (also known as the LGD distribution).

(A minor technical point – in the prior post I used normal LGD distributions, whereas in fact something like a beta distribution might be more suitable.)

We noted too that once we look at the distribution, subtler differences between bonds than just probability of default are obvious. Another example of this is how much uncertainty in recovery there is. Consider this example:

Visualizing bonds 5

These two bonds have the same PD, the same average recovery and hence the same expected loss. But one has more uncertainty in recovery than the other, and hence can reasonably be called riskier.

Now, a plain vanilla tranched security supported by a diverse pool of collateral assets might well have quite a benign return distribution. Losses come from the bottom up, and if the loss distribution of the collateral is fat tailed, and our tranche is not the bottom of the stack, then we might well find something roughly like this (although of course the precise form is subject to considerable debate):

Visualizing bonds 6

In other words, even if you do get a loss, it will likely not be large. The problem though is that this assumption is rather sensitive both to the collateral loss distribution, and to the structure of the securitization. Something like this is entirely possible too:

Visualizing bonds 7

Now, remember first that it is really hard to know what the real loss distribution is – there is a lot of model risk – and second, its shape really effects the expected loss. For instance, for the first tranched ABS above, the expected loss (EL) is only 0.25%, whereas the EL for the second bond is 0.65%. Assessing the real world return distribution of these securities is difficult.

This brings us nicely to informationally insensitive assets. What people want is something with PD = 0 (and so EL = 0). There isn’t any such thing. What is available are assets with small PDs, and unknown loss distributions. Sovereign recoveries are typically low and uncertain: 30 to 40 isn’t a bad guess for an average. AAA ABS, on the other hand, can be structured to have whatever loss distribution the issuer wants. What we learn from this is that it is a serious error looking just at PD or EL in assessing credit quality; you need to get several different views of what the whole return distribution might be like. Moreover, a crisis in the securitized funding markets is caused not just by a reassessment of PDs, but also by a realization that the loss distribution is likely to be more like the third graph above than the second.

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