This is apparently the formula that got us into the credit mess in the US and now is threatening the entire world’s financial system. Developed by David Li, a Chinese-born New York banker, the formula came out of a “broken heart”. The hypothesis that David Li started with was this: People tend to die faster after the death of a beloved spouse. With this simple formula - called copulas - Li was able to relate different variables and measure the intensity of each variables’ effect on one another. A good example would be this: Let’s say you’re going to the supermarket. You look at an orange. In the normal world, you would see the price of the orange - let’s say 10USD (some expensive oranges from Japan - flown overnight, first-class, and straight from the orchards on the slopes of Mount Fuji… I am exaggerating). That’s a pretty big sum of money for the simple pleasure of eating an orange. There are risks involved in your purchasing that orange at 10USD: what if (1) when you get home, it’s not as great as you expected it to be? I’d call this the “satisfaction risk”; (2) when you get home, the orange tastes like a normal apple that you could have purchased at a lower price? I’d call this the “relativity risk” (3) in spite of it being orangey and brightly-orange, it actually is rotten inside? “Real-freshness risk” (4) you don’t get to eat it - and you had to postpone eating it… and this 10USD-orange will only last for only 12-24 hours after having been purchased? “Time-Effects Risks”. In the world of copulas and correlations, this apple would have taken into account the different risk aspects. So in this world, you will see not only the price - 10USD per orange - but also descriptions of the risks. The 10USD pricing takes into account not just the price of produce but also the risks involved in your purchasing the orange. Or better yet - and this is what happened with the CDOs, SIVs, and what-nots - you have different bunches of oranges priced differently to take into account their risk-profiles: 1. In this risk-world, you’ll have 10USD oranges - high-grade, minimal risks across all four risk-dimensions. 2. You’ll also have 8USD oranges - still high-grade, but perhaps there is a higher likelihood of it being not fulfilling the Real-freshness/Relativity Risks. 3. You’d also have 5USD oranges - which can guarantee risks on satisfaction, relativity, and real-freshness - but not necessarily the time-effects risks. 4. You’d also have 2USD oranges - which are “junk oranges” - high-risk, caveat-emptor, ‘junk’ oranges. The idea behind it is that, the risks have been ‘dimensionalized’ and have been ‘measured and priced’ accordingly. (This is what ratings agencies - such as S&P, Moody’s, and Fitch - do.) And another core tenet is that there is a market for these tranches of oranges - regardless of whether they are high-grade or junk. Why would anyone buy the junk ones? Well, remember the tenet “Without risks, there are no rewards” and that “The higher the risks, the higher the reward”. So even the junk ones can potentially reward a buyer with high returns. And another thing: Because you have the copulas, you can even segment the 2USD oranges when you have bought them into different segments: If I bought 100 of the junk oranges, I’d be able to sub-divide them even further - say into 5 more sub-division - based on their risk profiles and resell them for a profit. I could probably have 2USD oranges, 1.50USD oranges, 50cents, and 25cents. (Remember: there’s always a market for everything in the market!) This is what copulas have allowed financial engineers to do: peek into the risk profiles of each of the different oranges, put a dollar value into them, and sell (and resell) them. The formulas essentially created for us a way to put a number to the correlations and co-relations between different variables, which at first are seemingly unrelated, put a dollar value to that risk, and package them and sell it to others. I’d say this is pretty neat. But what’s happened in the credit-crunch is different: You see, you were not just buying oranges - you were buying people’s debts. And the assumption was that people are going to be rational when it comes to paying their debts - particularly their home mortgages. What was forgotten in the credit-crunch is that, people are not rational: we tend to move in herds - and we tend to move in response (logical or illogical) to news (real or unreal) that are broadcast in the media (which tend to be gloom and doom). Essentially, people are not oranges. And that’s where the financial engineers failed. (Disclosure and disclaimer: Much of this came from reading Wired.Com cover story. I am not an expert on risk management - I am currently studying risk management but I am not an expert. These are my interpretations - and my attempt to understand them. Copulas, having tried them in an exercise in a class, are I think a great tool. There is more to copulas than these, I am sure. Copulas are not - in themselves - good nor bad. They just are tools - and it is the people who use them and abuse them that make the difference - or not. Like the Black-Scholes Options-Pricing Model, it’s neither good nor bad. It is what it is - a set of formulas that can be used for good. Or for bad.) Re-blogged from Experimentalist.
Comments