Scientists Prove Toxic Assets are Impossible to Regulate
dailykos.com
dailykos.com
I would like to remind you people that we are not talking about abstract problem spaces where you can count on the problems being essentially "randomly selected" for some suitable definition of random. We are talking human-created financial instruments, being created by agents with every incentive to game the system. Complexity analysis is a whole different kettle of fish when you have to assume a malicious agent generating the problems! Everything you think you know about approximation may or may not apply, and probably doesn't apply, because approximation algorithms never (or virtually never) start out with "Assume a hostile malicious agent has constructed your problem instance..."
The correct mindset here is probably the security mindset, where no matter how small or trivial the "arbitrary command execution as root" vulnerability is, you damn well better close it, because in the computing world the smallest crack can be easily widened large enough to drive a truck through.
I wonder if some sort of game theory and/or randomized algorithms can help...
In any event, the root problem was still giving loans to people who shouldn't have gotten them. Regulation really needs to focus on that...
Everything in the real world is impossible, but we can try and get good results anyway.
A regulator trying to preempt unfair dealings with rules may have no chance, no matter how wise and disinterested, but people trying diverse strategies over time eventually settle on something that's good enough. (And some scams and business cycles are an inevitable part of that discovery process.)
http://www.cs.princeton.edu/~rongge/derivativeFAQ.html
And also his response to RJ Lipton who believes approximation ought to work (but then again Lipton believes P=NP, so for him nothing is impossible):
http://rjlipton.wordpress.com/2009/10/22/helping-wall-street...
These are mostly practical reservations, carefully stated as to convince of intractability in the real-world case (which they do) but not prove in theory. Excerpt:
current pricing and rating algorithms use monte carlo methods
and would not solve densest subgraphs even for moderate parameters.
So at the very least those should be changed.
The paper relies upon a stronger form of "P not equals NP", namely,
that the planted dense subgraph problem does not have an efficient
algorithm. (In fact it is conjectured that there is no algorithm
to even compute any approximate solutions to this problem).It is not impossible, merely Hard.
But approximation techniques are being used all the time to obtain near-optimal solutions to NP-hard problems. If you can obtain a valuation for a complex bundle of derivatives that's within 10% of the true value, then it seems silly to claim that they whole practice should be tossed out the window. This is like saying salesmen should no longer be able to travel because we cannot solve the traveling salesman problem.
just because there's no way to prove which CDOs have been tampered with doesn't mean that you can't figure it out. there are local search algorithms that may be able to give you a pretty good answer, even if you don't know for sure. there's some extra risk in CDOs because of this, fine, but it doesn't mean that the market would be locked up, or that no one would have any clue if there was misconduct.
regulators also have extra tools to detect fraud. maybe the buyer can't tell, but if the buyer suspects, and the regulator can check the seller's internal records, examine their processes, and in general, investigate whether the seller did any tampering.
The biggest I take from this (apart from it being an interesting analysis in itself) is that if there is an assumption of randomness in creation of CDO's that should be verified at creation.
Let's consider a house. Clearly the amount of money that someone would pay for said house varies from person to person. Which value is "correct"?
Before you jump in with some clever aggregation function, suppose that the owners want to sell said house. Will they agree to the value that your aggregation function produces? (They can choose to delay the sale, so if they don't agree, your function may well deprive someone of the ability to buy said house at a price that its acceptable to said someone.)
Ah, but you say that stock is stock. That's true, but again, different people have different priorities. I probably weight dividend paying history differently than you do. I have different expectations on inflation. I need to go liquid at different times. The end result is that we disagree about the value of the same share of Microsoft stock.
The one that actually results in a deal happening, which often means the highest amount on offer. The more standardized a good is and the more it's traded, the more well-defined its price is. If deals don't happen, there's no market-clearing price, e.g. no way to price sex with Mother Theresa.
Before you jump in with some clever aggregation function, suppose that the owners want to sell said house. Will they agree to the value that your aggregation function produces?
Yes they will, by my definition above :-)
BTW - Folks who don't participate in a deal often complain that the price at which it occurred was "wrong". Folks who can't find someone to buy from them at the price they want have an analogous complaint.
If I make 10 CDOs and I think 5% of the underlying assets are bad, if I share them out equally the top tranch takes all the damage for each CDO - if the top tranch is 5% then I make nothing basically. If I make one CDO with 50% bad assets, and 9 with 100% good assets, then some of those losses go to other people deeper into the bad CDO tranch, suddenly 90% of my assets pay off instead of 0%.