Intractability of Financial Derivatives
freedom-to-tinker.com
freedom-to-tinker.com
There's an old saying on wall street, the harder it is to understand the deal the bigger the profit. The truth of this should be self evident. Add to that the fact that the people gambling weren't gambling with their own money. That way if they won then got big bonuses, and if they lost they simply didn't get bonuses. Clearly the only rational action in this situation is to go all in with other people's money.
Is it really that complicated? You wouldn't give your money to someone else and send them to Vegas, tell them to gamble if they win you split the profits, if they lose you lose your money.
You shouldn't invest in things you don't understand, and mind that old wall street saying.
But people do invest in things they don't understand, and pyramid schemes, and tulips, none of this is new. Sure some fancy math was involved this time, but that's only tangential.
I think everyone is concentrating on the fancy math because it's like magic, and then it's not their fault, it's not the same old story of everyone just being stupid again like in .COM 1.0, oh no - It's magic!
I think an analogy to medicine is appropriate - for many years the desperation and naivete of the sick was exploited by frauds selling patent medicines. Many makers of these bogus cures undoubtedly sincerely believed in their efficacy. Watching this history would make you suspicious of anyone who claimed that they could cure your illness with a drug. Despite this sordid reputation, there really are wonder drugs. If medicine can be made scientific so can finance.
Uh, one thing to be careful with in such a statement is reasoning by analogy.
Consider if someone says:
"If physics can be made scientific, so can pertual-motion-machine-construction"
Or
"If chemistry can be made scientific, so can alchemy!"
Or
"If astronomy can be made scientific, so can astrology!"
The problem is clearer. Not every "field" is subject to valid innovation since some fields are inherently bogus. It is a hard problem determining which fields can "scientifized" so you might not be wrong. But I personally think that the real scientific economists are those that have argued that you're not ever going to find a "financial innovation" which adds value to the economy as a whole.
Throughout history physics has had experiments whose results were incompatible with current models, which eventually lead to new theories (relativity, etc) but how do you know when contradicting information disproves your theory or will expand it.
Definition 1: A field that can't be can't make falsifiable predeictions. By this definitino, astrology is certainly a real science.
Definition 2: A field that makes false predictions. By this definition, most peoplle thing astrology is a pseudo-science.
If you're interested in this problem, this is a great reference: http://plato.stanford.edu/entries/pseudo-science/
Let me reiterate since it seems that my message was a little unclear - the purpose of the medicine and finance analogy was say that even though there were many bogus financiers making false promises about their products by using simple models where they don't apply - this doesn't mean that there could never be non-bogus financiers that take a more rigorous and transparent approach to their use of models. We should demand the construction of financial instruments which cannot be "booby trapped". This is a case for more and better financial innovation, not less of it.
Of course this takes a broad view of financial innovation to include such things as auction design, election methods, etc.
I will also retract my statement that the valuation models were pseudo-science - to the extent that they made real predictions they were scientific. But they were undoubtedly cynically exploited.
Sadly there are still no regulations preventing this from happening again.
However this doesn't remove the irresponsibility of taking a mortgage that you cannot afford to pay, which may be your point. Sorry if I misunderstood.
But finance is different in the sense that any investor has to understand things down to where the money is coming from. You correctly reason that "innovation" in finance is simply a system for gambling with other people's. That's indeed more or less fraud by your reasoning.
But the tricky part is that an investor in technology has to know where the substantial engineering technology ends and the insubstantial "financial technology" begins. It's OK not to understand the first but deadly, over time, not to understand the second. So the problem can get tricky despite the underlying situation being simple.
There's an interesting difference between assuming perfect information and perfect rationality -- idealizations of existing scenarios -- and essentially assuming P=NP; the former makes the math easier at no real penalty (provided you remember not to confuse the map with the territory) but until P is proven to be equal to NP (which probably won't happen) the latter is more like sprinkling pixy dust to make it go.
The only school that really takes something like tractability seriously are the Austrians, but their math phobia leaves their approach unrigorous and not very useful outside of as an anti-central-planning argument.
The claim that a market will converge on an accurate price (!) for an "intractable" financial asset is pretty dubious; the price-discovery process is supposed to depend on lots of agents running their #s and taking positions depending on if they think current price is different than it ought to be...over time this process will push the market price toward an accurate price.
In the case of an intractable asset there'd be no reason to believe that any outside agents crunched accurate #s, which means that even if the price converged there'd be no reason to believe that the converged-to price had any accuracy, which isn't usually the case in most other classes of financial assets.
As noted towards the end they need to do some work about estimating "lemon cost" and otherwise establishing how close you can estimate with approximate methods.
(!) In general there's not much sense in talking about true or accurate prices for some good; price is what it gets, full stop.
In the case of most financial products the notion of accurate price is more justified: a product entitles the owner to some sequence of future cash flows, which can be assigned a value in some straightforward manner. When a financial asset's current price deviates from the value of the underlying sequence of payments in some substantial way it's usually due to some easily-understood dynamic (eg: inflation expectations, doubts about some of the payments coming through) which makes a minor correction to the price it fetches.
An "inaccurate price" would be one with no apparent relation to the underlying cash flows.
Well, if the price is not above the costs of production, you're going to have a hard finding the product in stores for very long. Oppositely, the price and availability of food, say, isn't at a certain level, the whole society may cease to function.
While arguments about intractability, chaos and uncertainty are great and interesting, it's worth considering that if an economy doesn't have a number of important, predictable elements, things stop working.
so he says that a buyer cannot determine that a CDO has been maliciously packed with bad assets because this is equivalent to finding the densest subgraph. Is there a reason why an approximate solution to the dense subgraph problem could not allow one to conclude that a CDO was more likely to have been stuffed with garbage?
clearly if the problem is truly like encryption as Appel says then an approximate solution is worthless (an approximate encryption key would still give you garbage)
I'd guess that even if you can't solve the problem exactly you could find a tractable probabilistic solution that works x% of the time and traders spend their time finding such solutions. The real problem is that for the (1-x)% of the time when it doesn't work it wrecks major havoc.
I haven't read the paper either ;] (just skimmed bibliography to get a sense, as I usually do first) but Arora (one of the authors) is an expert on probabilistic approximations, and they do cite 2001 paper by Feige which is standard ref. on approximations to dense subgraph. Also, what they reduce their model to is a "planted" hidden clique variant of dense subgraph, a problem which is hard "on average" and not only in worst case (propety used in crypto protocols also).
With poloynomial time problem reductions (which is what is usually used with showig a problem is NP complete, though I too haven't read the paper) equivilent just means something like "an exact solution in A translates to an exact solution in B." Unfortunatly, in general, an approxmimate solution to A doens't translate to an approxmiate solution to B.
Note: This part is me really guessing so please don't take it at face falue.
If I had to guess, I'd say that this is like densest subgraph in the sense that:
The mortgages are the nodes.
High correlation --> Edge connections.
So there might be a straightforward translation of approxmiate solutions. Like I said, just a guess.
there's actually another layer of abstraction involved. a mortgage backed security, or collateralized mortgage obligation (CMO), is formed by packaging together a large group of home mortgages. a CDO is made by packaging together hundreds of MBS obligations or CMOs.
For example, some originators encouraged their borrowers to lie more, and now post-meltdown some servicers are less willing to agree to loan modifications / short-sales.
At first traders didn't place much emphasis on the originator, servicer, or bank, because they focused on the loan stats (FICO score, loan type, interest rate, etc).
Post-meltdown, the smart players see obvious systematic patterns between originators and servicers, even given the same paper stats. But again, to see it before it happened, it's less a computer problem and more an unscalable human due diligence problem.