Hull & White on AAA Tranches of Subprime

John Hull and Alan White have published a working paper titled The Risk of Tranches Created from Residential Mortgages:

This paper examines, ex-ante, the risk in the tranches of ABSs and ABS CDOs that were created from residential mortgages between 2000 and 2007. Using the criteria of the rating agencies, it tests how wide the AAA tranches can be under different assumptions about the correlation model and recovery rates. It concludes that the AAA ratings assigned to the senior tranches of ABSs were not totally unreasonable. However, the AAA ratings assigned to tranches of Mezz ABS CDOs cannot be justified. The risk of a Mezz ABS CDO tranche depends critically on the correlation between mortgage pools as well as on the correlation model and the thickness of the underlying BBB tranches. The BBB tranches of ABSs cannot be considered equivalent to BBB bonds for the purposes of subsequent securitizations.

This paper won’t be popular amongst the Credit Ratings Agencies Are Evil crowd!

Credit derivatives models often assume that the recovery rate realized when there is a default is constant. This is less than ideal. As the default rate increases, the recovery rate for a particular asset class can be expected to decline. This is because a high default rate leads to more of the assets coming on the market and a reduction in price.

As is now well known, this argument is particularly true for residential mortgages. In a normal market, a recovery rate of about 75% is often assumed for this asset class. If this is assumed to be the recovery rate in all situations, the worst possible loss on a portfolio of residential mortgages given by the model would be 25%, and the 25% to 100% senior tranche of an ABS created from the mortgages could reasonably be assumed to be safe. In fact, recovery rates on mortgages have declined in the high default rate environment experienced since 2007.

The evaluation of ABSs depends on a) the expected default rate, Q, for mortgages in the underlying pool, b) the default correlation, ρ, for mortgages in the pool, and c) the recovery rate, R. Data from the 1999 to 2006 period suggest a value of Q less than 5% assuming an average mortgage life of 5 years. But, as has been mentioned, a different macroeconomic environment could be anticipated over the next few years. It would seem to be more prudent to use an estimate of 10%, or even higher. We will present results for values of Q equal to 5%, 10%, and 20%. The Basel II capital requirements are based on a copula correlation of 0.15 for residential mortgages.6 We will present results for values of ρ between 0.05 and 0.30. As already mentioned, a recovery rate of 75% is often assumed for residential mortgages, but this is probably optimistic in a high default rate environment. We will present results for the situation where the recovery rate is fixed at 75% and for the situation where the recovery rate model in the previous section is used with Rmin=50% and Rmax=100%.

ABS CDOs also depend on the parameter, α. Loosely speaking, this measures the proportion of the default correlation that comes from a factor common to all pools. A value of α close to zero indicates that investors obtain good diversification benefits from the ABS CDO structure. In adverse market conditions some mezzanine tranches can be expected to suffer 100% losses while others incur no losses. However, a value of α close to one indicates that all mezzanine tranches will tend to sink or swim together. We do not know what estimates rating agencies made for α. (Ex post of course, we know that it was high.) We will therefore present results based on a wide range of values for this parameter.

The meat of the matter – at least as far as the CRAs are concerned – is:

Table 2 shows that when a 20% default rate is combined with a high default correlation, and a stochastic recovery rate model, the AAA ratings that were made seem a little high. Also, the ratings are difficult to justify when the most extreme model (double t copula, stochastic recovery rate) is used. But overall the results in Table 2 indicate that the AAA ratings that were assigned were not totally unreasonable.

Very bad things happened to CDOs created from the mezzanine tranches of the structures – and here the CRAs can be faulted:

It should be noted that a CDO created from the triple BBB tranches of ABSs is quite different from a CDO created from BBB bonds. This is true even when the BBB tranches have been chosen so that their probabilities of default and expected losses are consistent with their BBB rating. The reason is that the probability distribution of the loss from a BBB tranche is quite different from the probability distribution of the loss from a BBB bond.

The authors conclude:

Contrary to many of the opinions that have been expressed, the AAA ratings for the senior tranches of ABSs were not unreasonable. The weighted average life of mortgages is about five years. The probability of loss and expected loss of the AAA-rated tranches that were created were similar to or better than those of AAA-rated five-year bonds.

The AAA ratings for Mezz ABS CDOs are much less defensible. Scenarios where all the underlying BBB tranches lose virtually all their principal are sufficiently probable that it is not reasonable to assign a AAA rating to even a quite thin senior tranche. The risks in Mezz ABS CDOs depend critically on a) the width of the underlying BBB tranches, b) the correlation between pools, c) the tail default correlation, and d) the relationship between the recovery rate and the default rate. An important point is that the BBB tranche of an ABS cannot be assumed to be similar to a BBB bond for the purposes of determining the risks in ABS CDO tranches.

In practice Mezz ABS CDOs accounted for about 3% of all mortgage securitizations. Our conclusion is therefore that the vast majority of the AAA ratings assigned to tranches created from mortgages were reasonable, but in a small minority of the cases they cannot be justified.

I think it’s fair to conclude that the problems of the sub-prime crisis were not with the rating agencies or, to a small degree, with investors who plunked down their money. The problem lay in concentration: the banks took the view that if one is good, two is better … and went the way of all those who fail to diversify sufficiently.

Update: For a review of what participants were thinking at the time, see Making sense of the subprime crisis. For more on subprime default experience, see Subprime! Problems forseeable in 2005?. I will admit, though, that what I’m really waiting for is an accounting of realized losses on subprime paper.

3 Responses to “Hull & White on AAA Tranches of Subprime”

  1. […] far as the CRAs are concerned, John Hull’s work on the ratings has been previously reported on PrefBlog – he concluded: It should be noted that a CDO created from […]

  2. […] in the sub-prime market; it just wasn’t used and – in some cases – the math was wrong. Additionally, firms were hired as collateral managers on the basis of – as far as I can tell […]

  3. […] mortgages). The rating is much more volatile, and loss given default is much more severe. See Hull & White on AAA Tranches of Subprime for more […]

Leave a Reply

You must be logged in to post a comment.