Unwinding CDS’s

As pointed out several times by Steve Hsu recently, a major instigator of our current financial crisis is the Credit Default Swap (CDS). As far as financial instruments go, this one is almost understandable. Basically, it is an insurance policy that is exchanged between two firms. So, say you just loaned a bunch of money and you want to insure it. Well, you can buy a CDS for some fee from someone who will pay you some agreed upon amount if the loan goes bad. It is a zero sum game, which is why the amounts insured (notional amount) can be larger than the GDP of the entire world. Although the notional amounts of these CDS’s could be large, the big banks and hedge funds that traded them are often hedged so that the net gain or loss are manageable. The problem was that when Lehman Brothers went down, the whole network became unbalanced and some parties were exposed to huge losses. However, given that there is no market for these things, no one knows who is holding what. Steve drew a complex graph and an example to demonstrate how difficult it would be to unwind everything.

I like to visualize this as a problem of flux balance. For example, let be a CDS payout from party j to i. Then the total net gain or loss (i.e. flux) for party i is given by

We see that the sum over is zero verifying that it is a zero sum game. It actually would be a simple matter to unwind all the obligations if everyone agreed to do it all at once. This could even be done without anyone disclosing any of their trades. People may want to do this so others wouldn’t know how weak they were. The way you would do it is for everyone to compute their net flux and disclose this amount to a central clearinghouse. The clearing house then checks to see if the sum of all the fluxes is zero. If the sum is not zero then either someone made a mistake or tried to cheat. If it sums to zero then those with a negative flux would deposit that amount to the clearinghouse and those with a positive flux could then withdraw from it. It is possible to cheat if you collude with someone else so that the net change to the sum of your two fluxes is zero. However, that would not affect anyone else so it would be like a private deal between two parties.

Formal Proof

This month’s Notices of the American Mathematical Society is highlighting formal proof, which is a proof where every step is justified with respect to the axioms of mathematics so there is no chance of error. Generally, this would be extremely tedious to do by hand so people have been developing computerized proof assistants to help do the job. My good friend and former colleague at the University of Pittsburgh, Tom Hales penned one of the articles. I actually lured Tom from Michigan to Pittsburgh several years ago. At that time, Tom had recently finished his proof of the Kepler conjecture, which asserts that the densest arrangement of balls in three dimensional space is face-centered cubic (FCC) packing. He had been battling with the editors of the Annals of Mathematics to get his proof published. The problem was that Tom’s proof was quite long (300 pages) and used a computer. Tom’s strategy for the proof was to show that all possible packings in infinite space could be reduced to a finite number of arrangements, which needed to be tested individually. Tom and a student then wrote a program with about forty thousand lines that used interval arithmetic to show that none of these other arrangements was ever denser than FCC. A panel of experts worked on reviewing the proof and essentially gave up. They were pretty sure it was right but were unwilling to certify it. Eventually, the Annals published the proof with an asterisk that it was not fully checked by referees. I may have played a small part in helping Tom finally get the proof published. I remember going down to Tom’s office one day. He was slumped in his chair and declared that he was giving up on the Annals and writing a book instead. I convinced him not to give up and gave him some tips on the strategy to deal with the editors and referees. I’m not sure exactly what happened but the next time I saw Tom he was beaming that the work would finally be published.

Explanation versus narration

Noted Harvard economist Greg Mankiw wrote an op-ed last week for the New York Times and posted to his blog, a letter to the president-elect. One of his recommendations was to listen to economists. Following up on Steve Hsu’s post on intellectual honesty, I think this exhibits an element of hubris since the majority of economists did not foresee this current financial meltdown. There were certainly those that were warning about the collapse of the housing bubble, like Robert Shiller, but other than Nouriel Roubini, I didn’t hear too much about it causing the worst crisis since the Great Depression. Even Paul Krugman admits that this took him by surprise. I could see that there was a housing bubble back in 2004, which is why I haven’t bought a house yet, but I had no idea that the bursting of a bubble could cause so much damage. The bursting of the internet bubble caused a lot of pain to some people but did not destroy the financial system.

The current crisis first became public knowledge when Bear Stearns went under in March of this year. Federal Reserve Chairman Ben Bernanke quickly engineered a buy out of Bear by JPMorgan and the market calmed for a while. Then in quick succession starting in September came the bailout of Fannie Mae and Freddie Mac, the sale of Merrill Lynch to Bank of America, the bankruptcy of Lehman Brothers, and the bailout of A.I.G. Shortly afterwards, Treasury Secretary Hank Paulson went to Congress to announce that the entire financial system is in jeopardy and requested 700 billion dollars for a bail out. The thinking was that banks and financial institutions had stopped lending to each other because they weren’t sure which banks were sound and which were on the verge of collapse. The money was originally intended to purchase suspect financial instruments in an attempt to restore confidence. The plan has changed since then and you can read Steve Hsu’s blog for the details.

Dead Zones

Marine dead zones are regions of the ocean, usually near the mouths of rivers or waterways, which receive a large amount of nutrient (phosphorous and nitrogen) run off mostly from fertilizer. This causes a great phytoplankton and algae bloom that takes up carbon dioxide. However, when they die they sink to the ocean floor where other aerobic bacteria break them down with such vigor that they deplete the oxygen supply leaving an anoxic zone that cannot support marine life. The environmental movement is striving to curb fertilizer use in an attempt to mitigate these dead zones. There are also theories that the increase in the number of these dead zones are related to global warming.

I have a heretical thought on this regard and I haven’t been able to find any information on it so if anyone knows please enlighten me. The earth’s oxygen was originally created by cyanobacteria, which make up the algae that are causing the dead zones. So, could these dead zones actually be removing and sequestering carbon dioxide? Once the ocean bottom becomes anoxic, would the phytoplankton and algae fecal matter and remains pile upon the ocean floor and turn into fossil fuels in a few hundred million years? I don’t think we should necessarily encourage dead zones but is there any data out there that they could be mitigating global warming? I don’t want to be another one of those staunchly leftist youths going conservative in their old age so please set me straight if I’m wrong.

Rationality and politics

I’ve been trying to reconcile the current political environment in terms of a consistent framework. In particular, I’ve been interested in dissecting how issues have been divided between the so-called left and right in the United States. My premise is based on ideas set down in my previous post on the genetic basis of political orientation. In that post I proposed that the political thesis of the right is that the wealth should be distributed according to a person’s direct contribution while the left’s premise is that wealth should be distributed equitably regardless of standing in the community. I think these are fair definitions based on historical notions of the right and left. What I want to do now is to see how current issues should be divided between these positions in a perfectly rational world.

Let me first summarize some positions currently held by the US right: 1) low taxes, 2) small government, 3) deregulation of industries, 3) free trade, 4) gun rights, 5) strong military, 6) anti-abortion, 7) anti-gay rights, and 8 ) anti-immigration. I would say positions 1) through 4) seem consistent with the historical notion of the right (although regulation can be consistent with the right if it makes markets more transparent), position 5) is debatable, while positions 6) through 8 ) seem dissonant. The left generally but not always take the opposite positions except possibly on point 5), which is mixed. The strong military position was understood as a right wing position during the Cold War because of the opposition to communism. The rationale for a strong military waned after the fall of the Soviet Union but 9/11 changed the game again and now the military is justified as a bulwark against terrorism