There is at least a little bit of interesting bath math
\nto learn from in the whole financial mess going on now. A couple
\nof commenters beat me to it, but I’ll go ahead and write about
\nit anyway.<\/p>\n
One of the big questions that comes up again and again is: how did they get away with this? How could they find any way of
\ntaking things that were worthless, and turn them into something that could be represented as safe? <\/p>\n
The answer is that they cheated in the math.<\/p>\n
<\/p>\n
The way that you assess risk for something like a mortgage bond is based on working out the probability of the underlying loans failing, and using that to compute the likelihood of the
\nentire bond package to end up losing.<\/p>\n
The biggest problem is that the whole system of ratings and
\ninsurance for mortgage (and other) bonds is based on probability
\ncomputations of how likely it is for the underlying loans to
\ndefault. The problem is in how they computed the probability of
\ndefault. They made the same mistake that we constantly see
\ncreationists making in some of their stupid arguments: false
\nindependence. They build up assessments of risk based on the the
\nassumption that for a given set of loans, the probabilities of
\ndifferent loans failing are completely independent of one another.<\/p>\n
Quick refresher on probability. Take two events – like It’s easiest to describe how this works by using an example. Now, suppose that these were really lousy loans – they expected By assuming that the probability of default for each of the loans is independent of the probability of default for any other loan, they can say that the probability of any particular loan defaulting is 10%. Assuming that defaults for loans are all independent, they can build an argument that probability predicts that only 10% of the loan will fail, and that it’s incredibly unlikely for the rate of failure to reach higher than 20%. But the probability of defaults aren’t independent. Sure, there’s random failures, where someone gets sick and can’t work, and ends up defaulting on a loan. That kind of default generally But without doing anything complicated, I can<\/em> say that they did it wrong. As I argued above, when you’ve got a huge collection of high-risk loans with variable interest rates, the pattern of default isn’t going to be independent. While the probability of any given loan defaulting, looked at individually, is only around 10%, the probability of 50% of the loans defaulting As a result of this, tranching didn’t work. They set up the tranches so that they partitioned things so that the top tranch was safe given the assumption of independence. But if independence Plenty of people knew that this was wrong. But they were able to write up impressive looking risk assessments, full of pretty math showing how unlikely it was for anything bad to happen. The math was dreadful – but it looked good. And the fact that it looked good provided enough<\/em> of an excuse for everyone to pretend that they believed it. (And for lots of people to actually really believe it; there’s no shortage of people who invested in this stuff without understanding it, who assumed that a “AAA” rating actually meant that someone had really checked to make sure that it was safe.)<\/p>\n","protected":false},"excerpt":{"rendered":" There is at least a little bit of interesting bath math to learn from in the whole financial mess going on now. A couple of commenters beat me to it, but I’ll go ahead and write about it anyway. One of the big questions that comes up again and again is: how did they get […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[71],"tags":[],"class_list":["post-685","post","type-post","status-publish","format-standard","hentry","category-bad-economics"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4lzZS-b3","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/685","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/comments?post=685"}],"version-history":[{"count":0,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/685\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/media?parent=685"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/categories?post=685"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/tags?post=685"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\ntwo loans defaulting. If the probability of the first
\nloan defaulting is p0<\/sub>, and the probability of the second
\nloan defaulting is p1<\/sub>. If the two events are independent, then the probability of both occuring – the probability of both loans defaulting – is p1<\/sub>×p2<\/sub>. But if they’re not<\/em>
\nindependent, that doesn’t work. Then the computation gets a
\nlot messier – because you need to work out the math describing
\nthe relationship – which generally involves lots of analysis,
\nand lots and lots of use of Bayes’ theorem.<\/p>\n
\nSuppose we’ve got a package of 100 mortgages, each of which
\nborrowed $100,000. So we’ve got 10 million dollars worth of
\nmortgages. Suppose, for simplicity, that the total interest earned
\non the loans was going to be 150% – so at the end of the 30 year
\nterm of the loan, the bonds were expected to pay $25 million. <\/p>\n
\nthat each loan had a 10% probability of defaulting, and that they’d lose the entire amount of the loan on a default.<\/p>\n
\nBased on that, they say that by using tranching to separate risk, they can claim that they’re being extra careful, and put 80% of
\nthe mortgage bonds into a top tranch fund, which is supposed to be
\nsuper safe.<\/p>\n
\nreally is an independent event. But that’s not the story behind most<\/em> defaults in low-quality loans. The garbage loans are almost always variable interest rate, and the most common cause of default is interest rate changes, which cause the loan payments
\nto become too large for the borrowers to pay. When that happens,
\nthey’re not independent events. The same thing that causes one
\nloan to fail causes others to fail. Huge numbers fail at the same time, for the same cause. Depending on how the numbers work out,
\nyou can get very different results for what’s likely to happen.
\nIt’s not simple – there’s no one answer. And I don’t have the information that I would need to do the math. This isn’t back of
\nthe envelope stuff.<\/p>\n
\nisn’t 1 in 10something really big<\/sup> – because the same condition that causes one loan to fail is likely to cause many others to fail.<\/p>\n
\ndoesn’t hold – and it doesn’t in these – then even an extremely conservatively structured tranching package doesn’t guarantee
\nthe safety of the top tier.<\/p>\n