We have used the assumptions of independence and randomness of variables while forming the theoretical foundations of statistical analysis. Real-life conditions are more complex, and we have encountered situations wherein these premises go out of the window due to hidden confounding factors. One such – a very costly – example is the financial meltdown of 2008.
To understand the crisis of 2008, you need to understand what is known as mortgage bonds. These are packages of basically mortgages that an investment bank floats (secured from commercial banks that had lent to their customers). These share-like entities are now available to investors to buy. To cut the story short: once an investor buys a unit, she buys a portion of all the mortgages in that “special purpose entity”. Now, the assumptions regarding the strength of these bonds, e.g. a highly rated unit.
A seller promises two things within an AAA-rated package – the most trustworthy (high credit rating) borrowers and independence of default. When an investment bank informs you that they have bunched five mortgages into a pool and will pay you unless all the mortgages default. They made you believe the following,
1) Each of them has the lowest probability of failure because of the AAA rating
2) One mortgage failure does not impact the chances of the second – the assumption of independence.
These packages of mortgages may have names such as mortgage-backed securities (MBS) or collateralized debt obligations (CDO), depending on the exact composition of what is inside.
So, what’s wrong?
Suppose each of the units inside the pack has a default chance of 0.05 (5%); if you assume independence, the probability of everything defaulting becomes 0.055 = 0.0000003125 (0.00003%) – a negligible prospect. But what if the risks are perfectly aligned? Then a 5% chance will make all of them collapse. Suddenly, the 0.00003% becomes 160,000 -fold to 5%. On top of this, what if the credit agency erred in their estimate of 5% default risk, which was 10 or 20 per cent? The result caused the perfect storm of 2008.
MDS and CDO: Investopedia
2008 Housing Bubble: New Money
