How David Bowie nearly blew up Wall Street - Part 2

To recap from last time, courtesy of a clever idea from some financial wizards, sober bankers like Capt. George Mainwaring suddenly had a solution to the age-old problem of managing the risk of borrower default in their mortgage portfolios. They could suddenly do two things with their mortgage portfolios:
Firstly, they could "sell" their mortgages more easily, by putting them into a format which allowed economic interests in the mortgages to be transferred without the transfer of the mortgages themselves. This is "securitisation" - which means "turning into a debt security" - a debt security being banker jargon for a bond. Bonds are like bank notes: they are easily transferred: mere possession of a bond is enough to prove you own it.
Bonds are, in this way, very different from mortgages. A mortgagee lender not only has to prove the existence of the loan by means of signed, witnessed loan contracts, but also needs to register the mortgage with  the land transfer authorities.
Now the ability to sell mortgage portfolios by itself wouldn't be that big a deal, as any buyer would wind up with exactly the same problem that the seller had in the first place: a buried, impossible to predict, risk of borrower default. But securitisation enables many buyers to buy small  shares of the same portfolio. This permitted trick number two, which is the "special sauce".
Say you are Captain Mainwaring, and you manage a portfolio of a hundred mortgages for your bank. If you arranged these in a 10 x 10 grid, and marked the defaulted mortgages with an x, it might look a bit like this:

That is to say, defaults randomly dispersed all over the place, with no rhyme or reason to how they came about. Since you can't predict which loans will blow up, it doesn't really matter how you look at it: Captain Mainwaring has this risk. Assume that in normal economic times, about 5% of all the mortgages are likely to go bust.
But look what happens when two people share ownership of the portfolio: an ambitious investor can say: Tell you what, if you pay me three quarters of the total interest due on all the mortgages, I'll take all the defaulted loans into my share of the portfolio first. That way you'll get less interest, but you have much less risk: you'll get all your interest and principal back unless there are so many mortgage defaults that I lose my whole investment. So we can rearrange our mortgage portfolio to represent this:

Because Investor B has agreed to take all the first losses, Investor A is able to confidently say that, until Investor B is wiped out in full, it has no risk on its portfolio.  Investor A has a "second-loss" risk on the portfolio.

This technique of packaging a mortgage portfolio up into a securitisation and selling it into the capital markets as a bond instrument became to be known as the "Originate and Distribute" model of mortgage finance. Instead of lending money and keeping the "assets" represented by mortgage loans on its books for thirty or more years (the "Originate and Hold" model), a lending bank can immediately "sell down" its risk in the capital markets for a repayment in full, without bothering the borrower of the loan.

This is attractive because we are able to slice the portfolio into high risk "equity" part, and a very low risk "senior" part. In the example above, before Investor A (the "senior" investor) starts to lose any money, there would need to be a 20% default rate in the total portfolio (that is, all of Investor B's portfolio would have to have defaulted). This, the logic goes, is highly unlikely given the usual means of assessing probabilities, which put the risk of default in the portfolio at no more than 5%.

And so, were the usual means of assessing probabilities  to apply, it would be. The problem is that, for two reasons, usual rules of assessing probabilities (that apply a "normal" distribution to events) are a misleading guide. 

On of those reasons is fascinating, but complex, and I couldn't cover it in detail in this post without getting completely side-tracked. Suffice to say, where humans interactions are concerned, "normal" distributions are often misleading because human actions tend to influence each other (that is, once one person defaults, that makes it all more likely that others will too). A "normal" distribution assumes all events are independent of each other, and therefore have no influence on each other. 
Interdependent human events follow tend to follow a "power law" distribution, which has a much longer and fatter "tail" than a normal distribution. If you are interested in reading about this I heartily recommend a few books: The (MIS)Behaviour of Markets: A Fractal View of Risk, Ruin, and Reward by cassandra-like French Mathematician Benoit Mandelbrot, The Black Swan by Nassim Nicholas Taleb, and Critical Mass by Philip Ball.
The other reason is related, but subtly different: The very act of creating a securitisation and changing the to the "originate and distribute" model itself changes the probabilities, because it changes the parties' interests.
Mortgages tend not to default immediately. Usually even a poor creditor will manage to make payments for six months or a year. When you originate a loan you know you'll be stuck with for 30 years, you're very careful to pick borrowers whom you think unlikely to default at any time. Having a close and personal relationship with your borrowers enables you to make these assessments with a relatively high degree of comfort - hence the relatively low level of historical defaults on mortgage portfolios. Banks of Capt. Mainwaring's persuasion used to be prudent lenders, because it was in their interest to be prudent.
Note how that dynamic changes with the originate and distribute model:

• Firstly, Banks who expect to quickly "sell down" mortgages they originate have less interest in the long term creditworthiness of the borrowers: once the securitisation is completed it is "somebody else's problem" as they no longer have risk to the borrowers at all.
• Secondly, Securitisation investors have far less ability to assess the credentials of mortgage borrowers as, unlike originating banks who lend the money, securitisation bondholders have no direct relationship with borrowers at all, and far less information about each loan. Instead they tend to rely on general due diligence done by rating agencies who are retained by originators to provide a ratings valuation for the securitisations. Rating agencies are a fit subject for another whole post.
• Thirdly, Securitisation investors have less ability to do anything should mortgages start going bad: they are reliant on third party mortgage servicing companies, who, unlike originating banks, have no "skin in the game".

We know that mortgage lending standards "relaxed" markedly in the late 1990s, and the world was bequeathed concepts like "self-certifying mortgages"; acronyms like NINJA "no income, no job, no assets", and from personal experience I know it became a lot easier to borrow a much higher multiple of income. It also didn't help that interest rates were extremely low throughout the 2000s - in England, a rough and ready average of the rates was far lower than it had been in the preceding 25 years, not exceeding 6% at any stage:

This is significant because it becomes easier to make money out of property if your cost of financing that property drops: Simply put, if you borrow £100,000 at 10% per annum to buy a property, your property has to increase in value by £10,000 in a year for you to even break even. If you borrow at 0.5%, then it only has to increase in value by £500!
These lower interest rates and a greater availability of mortgage lending meant it became viable to invest in property as a sort of investment, and before long it became almost mandatory, to avoid "falling behind": 

By now, I hope, you'll see that a perfect storm was developing, and all these little developments were feeding into each other and egging each other on: Banks were now able to quickly sell their portfolios, and so were less incentivised to apply strict lending criteria. Rates were dropping, making it more compelling to invest in property. Given the returns to be had on property and the low interest rates, demand was picking up for residential property, which in turn caused property values to rise, creating more demand for mortgages, and more demand for securitised product. A classic bubble was developing. 

Foghorns, mist and grammar

But if each of us can see only our own segment of blackly shining asphalt, how can we extrapolate that to a common picture of the world to share with our fellow travellers? We need signposts, foghorns, landmarks, lighthouses – a map, in short – by which we can navigate the terrain.

Some like Steven Pinker see evidence for a lingua franca: a common grammar shared by all human languages which is pre-wired by evolution into the cognitive faculties all human beings. On this view language – and therefore the particular rendition of the universe it affords – is as much a product of our biology as our arms or eyes, and through the office of this grammar there is a universal means of perceiving the world. In other words, after all, there is a single common map by which we do orient ourselves and avoid colliding with each other, and by reference to which all uncertainties and misunderstandings can be resolved.

It is courtesy of just this innate universal grammar that we can “shape events in each other’s brains with exquisite precision”.

As we pass the 200^th anniversary of Charles Darwin’s birth, one might remark in the margin at the huge variety of social, political and philosophical literature which claims Darwin’s intellectual antecedence. Some might see this as evidence of the rude health in which Darwin’s Dangerous Idea finds itself a couple of centuries on – universal acid indeed, as Daniel Dennett termed it. Others might wonder whether such universal acidity is symptomatic of weakness in Darwin’s programme: a theory which can be all things to all people ends up being nothing to anyone; there’s a point where flexibility needed for multiple applications tips into ambiguity and incoherence.

For me, Pinker’s account or universal grammar, Darwin-certified or not, leaves something out. Even if it were sufficiently, exquisitely, precise as to permit only a single literal interpretation for a given statement (as far as I can tell, it isn’t), there would still be an infinite universe of possible figurative interpretations of the same statement, and grammar – the rules for constructing meanings from words – cannot help us with our vocabulary. When Lou Reed tells us, at the end of his exquisitely miserable single Perfect Day, “You’re going to reap just what you sow”, grammar is no help in determining whether or not he was talking about gardening, and whether it really was a “perfect day”, or perhaps there was just a little bit of irony interlaced. 

But – and here’s the thing – the ambiguity conferred by the possibility of metaphor is not an obstacle only for our poets and novelists. Exactly the same ambiguity, the susceptibility to figurative meaning, infests every statement, however strictly empirical or even mathematical. Indeed, that was the very problem with Bertrand Russell’s Principia Mathematica, so deftly exposed by Goedel. This is significant, because it suggests there is no difference between literature and science might not be as ontological as scientists tend to suppose.

So how are we meant to identify each time, from the infinite set of possible meanings, the right one? Like any natural language, English is no more and no less than a formal logical system, like Mathematics. In these technologically revolutionary times we are confronted, as never before, by the fact that English is a numeric system: Every character can in theory be and, for the purpose of electronic processing of data, is assigned its own digit – the ASCII code. A computer can only understand text by reducing it to numbers.

And in the same way that a mathematical system is, English is (non-viciously) circular (you can only validly define an English expression in terms of other English expressions: evidence: the Shorter Oxford Dictionary, a document which defines and explains the set of “every word in the English language” wholly in terms of words taken from that very same set).

Ultimately, the meanings we hang on the intricate latticework of words we create each day comes from beyond the formal set of symbols which comprise the English language. “Meaning in the world” when we apply our own respective vocabularies to the formal symbols in the language. Notwithstanding the Shorter Oxford Dictionary, the set of formal symbols in practical use in any single person’s language will almost certainly be unique, and the precise meanings which that person assigns to that set of symbols, being completely functional on that person’s individual life history, definitely will be.