I have been musing for a while on how best to give insight into the returns of fairly safe instruments, like an asset swapped government or investment grade corporate bond. Here’s what I have come up with.
The first thing you need is to understand what the probability of default is. Now, in a precise sense this number is meaningless in that ‘probability’ implies that we have some (ideally large) population of things that we are sampling, and they are IID. This isn’t true with a typical bond – either it defaults or it doesn’t, and no two bond issuers have exactly the same return distribution. Still, let’s pretend that probability of default makes sense. For high quality bonds, survival probabilities (i.e. 1 – PD) are close to one, so showing full return distribution won’t tell us much; instead then let’s zoom in to the 90% to 100% area. Our first visual aid then is survival probability, graphed between 90% and 100%.
The second thing we want to know is how much we get back if default happens: the recovery. Again, we can’t know this, nor does it really make sense to talk about a distribution of recoveries. We have Knightian uncertainty rather than risk. However, if we make the (false) assumption that recoveries for similar types of issuer are similar, then one could (mis-) represent unknown recovery as a distribution of possible returns, which we can also separately picture.
A typical high grade corporate bond with PD = 1% and average recovery 45% would then look like this:
(By keeping the ‘doesn’t default’ part separate from the ‘does default’ we can at least see what is going on in the latter.)
Now consider a higher quality corporate bond, with PD = 0.5% but still with average recovery 45% and the same uncertainty in recovery. Comparing the two bonds, we would have
Here we can clearly see that the second bond is safer: it is less likely to default, and the average recovery is the same. Thus for the first bond, the expected loss (EL) is 0.55% (1% PD with 45% average recovery), while for the second it is 0.275% (0.5% PD, same recovery).
Now let’s turn to a typical high grade ABS. Here credit enhancement typically means that the PD is low, but if the credit enhancement doesn’t work, then the losses can be quite large. Recoveries, in other words, are often lower when ABS don’t pay in full*. Thus we might have the following comparison:
This shows that the ABS has the same PD as the corporate bond but if it defaults, you are likely to get less back. Intuitively, it is riskier, and indeed its EL is 0.72%, higher than the 0.55% for the corporate bond.
Now let’s look at an ABS with the same EL as the corporate bond, but with ABS-style low recoveries. It’s PD is 0.764% or in pictures:
Which of these bonds is riskier? The corporate bond is more likely to default, but if it defaults, the expected recovery is higher. The two bonds have the same EL. Riskiness isn’t easy to call; it really depends on your tolerance for large losses vs. your desire for 100% capital return. Depending on your rating system, you could justify rating either bond a notch over the other – and all that that demonstrates is how hard it is to compare things with multidimensional properties on a single linear scale.
In the next post we will use this tool to discuss ABS structuring and the recurrent topic of informationally insensitive assets.
*This is not necessarily true, but it is common especially in structures where reserve accounts are used. We will say more about this tomorrow.