Interviewer: "Have you ever thought your ideas may by wrong?"

Maldacena: "Yeah, this is possible; however the mathematical structure is probably going to be useful for whatever theory is the correct theory. And, what we do … at least is generate good interesting mathematics that is useful for other things in physics, and I think if it’s not string theory, it will be probably something similar to it."

And so it is with modern finance, which fully expects the yet unknown risk solution to be built out of the mathematical edifice already created, because the elegance and power of what has been created seems not just capable, but necessary to be any reasonable solution. The stochastic discount factor approach encapsulating CAPM is surely not a coincidence to these researchers. As Mark Rubinstein states about the Capital Asset Pricing Model (aka CAPM Betas):

More empirical effort may have been put into testing the CAPM equation than any other result in finance. The results are quite mixed and in many ways discouraging…At bottom…the central message of the CAPM is this: the prices of securities should be higher (or lower) to the extent their payoffs are slanted towards states in which aggregate wealth is low (or high)…The true pricing equation may not take the exact form of the CAPM, but the enduring belief of many financial economists is that, whatever form it takes, it will at least embody this principle.

The problem is, as the data have become clearer, the theory has become less clear. This is not a sign of a successful theory. Risk started out as merely nondiversifiable volatility, and now assets with really high nondiversifiable volatility presumably have low risk via some spooky risk factor, and behavioral biases are applied piecemeal to various anomalies (anchoring, preferring positive skew, or negative skew).

## 8 comments:

This is true of physics, too. Newton's theory on gravity, for example. I was inundated with teaching in high school and college on theories of gravity and light, and only now am I finding out that we aren't close to the basic truths.

Newtonian physics probably isn't the best analogy here, because it still works and has predictive value for most practical purposes. Maybe it didn't explain seeming anomalies such as the orbit of Mercury, but great works of engineering were built on the basis of classical mechanics.

hey eric, how about my C(x)-C(x+dx) question? I wrote you a more detailed explanation on that post. yes/no/maybe?

I was inundated with teaching in high school

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"the data have become clearer" cause we've added 10 more years???

Fischer Black "Noise" (1986) journal of finance

Thanks for taking the time to discuss this, I feel strongly about it and love learning more on this topic. If possible, as you gain expertise, would you mind updating your blog with more information? It is extremely helpful and beneficial to your readers.

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What is C(x)-C(x+dx)? Did I miss something on this post?

Earlier this week I spontaneously chose string theorists (in an argument about AGW on collide-a-scape) as an example of people who have a uniquely strong defense for screwing around with math without making connection (while claiming it's "without making connection *yet*") to physical reality.

Arguably Maxwell, then certainly Einstein, then Dirac, then Feynman, Schwinger, and Tomonaga were (eventually) able to triumphantly connect to reality by first staring at mathematical inconsistencies between successful incomplete physical theories, then Thinking Real Hard, then coming back with a mathematically elegant theory which managed to resolve those inconsistencies while remaining consistent with the older successful incomplete theories. Because that approach has paid off so well four times in a row in high energy physics, it's natural to try for a fifth. And since the inconsistencies between GR and QM are extremely mathematically gnarly, the string theorists can mess with it for a very long time returning only technical mathematical results, and still claim with some plausibility that what they're doing is analogous to Einstein messing with Mach's principle or Feynman messing with "it's all the same electron."

Thus, I don't think the analogy to string theorists makes a particularly telling criticism of economists unless you carefully put it alongside a supporting argument like "but while advanced math has been famously effective in theories of physics which achieve real-world success, in real-world theories of economics it's been more like a famous distraction."

(More precisely, advanced math related to the physicists' armamentarium of PDEs and tensors and perturbation theory and such hasn't been very important to economic theories which are useful in the real world. However, if math is sufficiently broadly defined to include other topics like game theory and information theory, then arguably the math needed merely to clearly specify the meaning of some usefully simple models (e.g., various kinds of bounds on rationality) is at least a little bit heavy by many people's standards. And it seems to me from looking at work in AI and CS on analyzing and optimizing systems involving multiple independent artificial actors, my opinion is that heavy math strongly tends to be important when analyzing the class of problems which includes economics. It's just that the useful heavy math doesn't look much like the usual physicists' math.)

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