Week 8: Beware of Geeks Bearing Formulas

Hi everyone!  Welcome to another Sunday Night Blog Post from Maddie the Procrastinator.
It's crazy how fast time is going... we're almost getting to that point where we have to start working on our final products!  I've decided that, in the interest of time, my final product will be a haiku about econophysics.  Here's a sample of my rough draft:

Econophysics
Oh, how you explain it all
More people should know.

Okay, just kidding.  My final product will not be a haiku, even though that would make my life significantly easier.  Instead, I'll be writing a paper that analyzes the claims of econophysics in the context of various investment strategies, trying to decide if it's worth its salt as a theory.  I'm super excited about it, but I definitely have a bit of an overflow of information, so my challenge will be organizing it in a way that creates an effective argument.

This week, I'll be talking about another allegation that is leveled at econophysics, claiming it is ineffectual or even harmful to the economy when applied improperly.  I don't think these allegations have a lot of substance, as I'll explain in a minute.

As I've mentioned before, the idea that tools from physics can be applied in the economy is not somehow novel.  Wall Street has been hiring physicists for decades, given their unique abilities in math, computer science, and problem solving.  They joined hedge funds and together with PhDs in finance, armed themselves with formulas and computer programs telling them exactly how options and stocks should be priced.  These scientists were referred to as "quants", short for quantitative finance.

However, in August 2007, hedge fund portfolios, run by quants, tanked.  Positions that were supposed to go up went down.  Positions that were supposed to go up even if everything else went down also went down.  As presitigious firms like Morgan Stanley and Goldman Sachs lost anywhere from 500 million to 1.5 billion dollars, every stock they had bet against actually rallied-- the DOW Jones overall went up 150 points.

Even as the crisis of the summer of 2007 (known as the "quant crisis") stabilized, the 2008 housing meltdown followed.  Again, models showing how subprime mortgages could be treated as bonds collapsed, leaving the entire housing market vulnerable.  (And we're arguably still recovering from the afteraffects.)

Many policymakers and regulators, seeing the disastrous results that the quants wreaked on the economy, are inclined to distrust any such models.  As Warren Buffett famously said, "Beware of geeks bearing formulas."  It seemed that using science on Wall Street was nothing more than a dream.

I disagree, however, and I certainly don't advocate the cessation of doing science on Wall Street, for several reasons.

1) Speculative bubbles are not a new thing.  While the housing craze and subsequent crash of 2008 may have been a result of the meddling of quants, such bubbles go much farther back to well before the dawn of computers.  (Remember the Dutch tulip frenzy from European history?  A single bulb could sell for the worth of a house, at least until the bubble popped.)  It's unfair to entirely blame quants for a crisis that could just as easily have been the Dot-Com crisis of the early 2000s.

2) The quants were doing "bad science."  Criticism of quants as scientists only works if you believe they were acting as scientists would.  The problem wasn't that the quants were using the scientifically-derived models to price options; rather, the problem was that they were relying too heavily on the models.  Any good scientist will recognize that there may be inherent holes in their model, and as such, will not treat it as infallible, but rather continue to look for the holes and be wary of its failings.  The quants of 2007, though, were not checking their models properly.

3) Not every hedge fund was hit by the crisis.  The Renaissance fund, run by Jim Simons (a well-known theoretical physicist), is staffed entirely by physicists, mathematicians, and statisticians.  None of them have gotten their start at traditional investment banks.  In 2008, when every other hedge fund was losing millions of dollars, Renaissance's Medallion Fund actually gained an 80% return.  This suggests that whatever models that Renaissance created were somehow "better" than those of their competitors; perhaps because they were created based on pure mathematical and scientific principles, that is, the principles that econophysics purports to advocate.

Therefore, we should not be skeptical of using mathematical and physical tools in the economy; people have proven that it is possible to do so successfully.  Rather, we should ensure that we are doing so in a manner that follows the scientific method, and continue to check ourselves for our mistakes.

I really enjoyed seeing many of you at the senior meeting!  For those of you who are out of town, I look forward to talking to you when you get back.  I hope this week brought good news to all waiting to hear from colleges. :)
Have a great week, and comment below if you have any questions/concerns.

Since I don't have any project-related pictures for you this week, here is a shot of an adorable baby animal!

Week 7: Can't We All Just Get Along?

This week, since it was Spring Break at the U of A and so my adviser Dr. Manne was out of the lab, I didn't get very much done with regards to my experimental work.  I did, however, still meet with Dr. Frieden; our discussions have started to branch out to other applications of statistics and statistical physics, which I find incredibly interesting.  Of the (many) things I've gotten out of this project so far, one of them is a new curiosity about statistics-- it's definitely on my list of things to try in college.  (Along with yoga, water polo, and Portuguese.  Go figure.)

This week, I thought I would bring some perspective into the project.  After all, my goal was to analyze the effectiveness and applicability of Econophysics' claims.  So it's about time, after 6 weeks of praising it, that I try to argue from the other perspective.

The thing is, though, that I genuinely think the claims of econophysics are correct.  They fit with experimental data, they find interesting correlations between our natural world and the markets, and they provide a similar or even more accurate view of economics models.  There are two main problems that I can see with econophysics so far, though.
For one, econophysicists, while they have shown myriad applications of physics and tools from physics in the economy, have yet to present a unified theory of macroeconomics that can trump our current ideas.  It's one thing to claim that macroeconomics is flawed; it's another thing to present a solution.
The second problem, though, I think is a lot more serious, and it has to do with the people advocating these ideas.

Physicists and other "hard" scientists have, traditionally, held a lot of animosity towards economics.  They mock it as an expression of "science" while ignoring its intellectual and mathematical roots.  They feel that their work is more important and applicable, conveniently ignoring the fact that markets impact our day-to-day lives much more than cosmology.

When physicists decide to get involved in economics, many of them don't familiarize themselves with the field beyond what is absolutely necessary.  This means that an physicist criticizing current macroeconomic theory might not even understand a simple supply-and-demand curve.  It means that a physicist may triumphantly show that income distribution follows a power law; he just may not know that economists have been aware of that for years.  Then he'll turn around and mock those same economists for not using his methods.

This isn't to say that economists don't suffer from institutional biases as well!  Many economists refuse to consider that the markets are anything less than perfectly efficient, or that equilibrium based on rational expectations doesn't always occur in real life.  Refusal to consider these claims has made trouble for them during the last few economic meltdowns, and econophysicists are quick to trumpet their methods as a fix for a corrupt, inept field.  These econophysicists are forgetting three essential things, though.
1) Just because an assumption of equilibrium economics or the Efficient Market Hypothesis is wrong, doesn't invalidate the whole field of economics or all the methods of economists
2) Econophysicists, while they have demonstrated impressive correlations and applications of their methods in the markets, have yet to come up with an alternative, all-encompassing macroeconomic theory of their own, and
3) Physicists criticizing institutional biases are hilarious examples of the pot calling the kettle black. 

Meanwhile, the quality of discussion is rapidly deteriorating as both sides resort to name-calling and patronizing epithets.  Just for fun, let's take a look at some of the rhetoric used by both econophysicists and economists.  Here are some quotes from different blogs dedicated to arguing about, criticizing, and defending economic theory:

• "If you want to know how the average Freshwater-y DSGE-slinging macroeconomist thinks about his place in the cosmos, read Yates' post."
• "So the only people qualified to judge the value of an activity are those being paid by the government to do it?  How convenient.  Snark snark."
• "Noah is extremely sceptical of microfoundations.  So much so that he requests a post to explain why they might have any merit at all.  So, he should be saying:  NO NO GET RID OF ALL THE MOTHER&&&&&&G MICROFOUNDATIONS WHILE YOU ARE AT IT."
• "The discussion about how to do macro often neglects that there are serious people trying to work out the details of how to do policy when you don’t understand how the world works."
• "What on earth is he saying?  And marvel at the confidence with which it is said."
• "Wonderful. Economists are no longer stuck with their RE straitjacket, but can readily begin exploring the kinds of things we should expect to see in economies where people act like real people."
• "Kind of obvious when you say it like that, but this is economics.... people have tried very hard to deny the obvious...."

This is just a few select blog posts.  The snippets of the books I've been reading really aren't too much better.

Now, don't get me wrong, I'm all about sarcastic rhetoric.  (Look at these blog posts!)  But the constant mud-slinging has to stop at some point.  If econophysicists ever want economists to take them seriously, they should invite them to their conferences.  Show respect for the ideas that economists have built their careers on.  Recognize that there's more than one way to skin a cat.  Present alternative solutions, rather than just claiming that the current methods don't work.  There has to be a real, intelligent exchange of ideas at some point, or the status quo will remain unchanged.  (Cue High School Musical "status quo" music in my head...)

I have no idea how to cite blog posts properly, but the links to the posts I quoted above can be found here, here, here, here, and here.  Hope you all had a great quasi-Spring Break.  I can't believe how quickly these projects are progressing... let me know in the comments if you have any questions!

P.S. In case all that negativity up there made you depressed, and as an apology for another lengthy blog post that's all words, here's a shot of a hedgehog cuddling a raspberry:

Week 6: I Learn What "Ubiquitous" Means

You know those words that you've seen a hundred times while reading, looked up fifty times, and can't remember to save your life?  The ones you dread seeing on the SAT, because you should remember them, but you don't?
For me, "ubiquitous" has always been one of those words.  Until recently, when my research led me to see the word so many times that eventually I no longer had any excuse to not remember it.

"Ubiquitous" is a fancy word for "found everywhere."  And apparently scientists won't use a simpler word when a fancy one will do, so I've been reading a lot about how power laws are ubiquitous.  So far, I've found it's a pretty accurate statement.

What's a power law?
I touched on this very briefly last week, but power laws are probability distributions that generate fat tails.  Specifically, the probability law p(x) follows the form p(x)=Cx^-a, where C and a are constants.  (The value of the constant a is the most important, as it determines how "fat" the fat tails will be.)

As a quick refresher, "fat tails" in a probability distribution mean that extreme events are far more probable (and remain more probable) than in systems with normal, Gaussian probability distributions, where the probability of extreme events quickly decreases to zero.

This image from a few weeks ago shows the fat tails in price
fluctuation probabilities, but could be a representation of the
probability of many different values

A power law is sometimes called a "scale-free" distribution because the distribution looks the same no matter what scale we use to look at it.  (If we change the scale or units by which we measure x, the overall shape of the distribution stays unchanged, except for some multiplicative constant.)

To understand scale-free distributions on a more descriptive level, we can go back to Pareto's law of income distribution from last week.  Sometimes called the 80-20 rule, or Pareto's Principle, Pareto found that 80% of the wealth of the world is held by only 20% of the people.
However, if we look at those top 20%, we'll see that 80% of their wealth is held by the top 20% in that group (and so forth).  Hence, no matter what scale you are looking at it, the distribution rule remains the same.  (Incidentally, income distribution follows a power law.)

So why are power laws considered ubiquitous?
I talked about this a bit in the comments section of my fat tails post from a few weeks ago, but I thought I'd do a quick recap here.  Examples of power-law distributions in nature include, but are not limited to:

• Magnitude of earthquakes and avalanches
• Diameter of moon craters
• Intensity of solar flares
• Models of Van der Waals forces
• Volume of water flowing through river branches
• Initial Mass Function of stars

Power laws are also very prevalent in economics, showing up in:

• Intensity of economic recessions
• Income and wealth distribution
• Stock market indices (and price fluctuations)
• Population of cities
• Urban areas of cities
• Company size
• Number of books sold in U.S.

Heck, they even show up in disciplines that seem fairly unrelated, including:

• Emails received
• Frequency of word usage 
• Frequency of family names
• Hits on websites
• Intensity of wars

It's important to note that these are just some of the applications of power law probability distributions.  They really are-- to use my new favorite word-- ubiquitous, and we should perhaps begin to pay more attention to their interesting properties.  (In particular with regards to the markets.)

Also interesting is that power laws are often found in systems that follow the self-organized criticality that I talked about a few weeks ago; so, these power law distributions are actually really relevant to my work with the sandpiles.

In related news: this week, I read a book called The Black Swan: The Impact of the Highly Improbable by Nassim Taleb.  I didn't enjoy it very much (I'm hoping to do an in-depth comparison in a few weeks with more market-related books I've been reading, so I'll explain more then) but the basic premise was that extreme events occur more frequently than we would expect them to.  Which, given the ubiquity (heh) of power laws and fat tails, shouldn't really come as much of a surprise.

Hope everyone is having a great week.  Comments are welcome!

Week 5: Econothermodynamics, and Other Words My Spell-Checker Doesn't Like

Hello hello!
This week, I will be talking largely about the efforts of physicists to make concrete parallels between the laws of thermodynamics and the behavior of the economy.
Thermodynamics is one of my weak spots, as for some reason I never studied it for longer than a day or two in Physics or Chemistry, so let me know if I've made any mistakes here!

The nice thing about thermodynamics is that it does not concern itself with the nature of interactions on a micro-level, but rather the behavior as a whole.  This makes it ideal to apply in macroeconomics, because then we don't have to justify studying the individual behaviors; instead, we can look at overall movement, as I've discussed quite a bit in previous blog posts.

Vilfredo Pareto was an Italian civil engineer-economist famous for discovering that income distribution follows a power law.  (Distributions that follow power laws have the fat tails that I discussed a few weeks ago.)  Pareto's work with income distribution is another example of fat tails cropping up in nature and economics alike, but in this case they also apply in econothermodynamics as well.

It turns out that you can model the relative fraction of people possessing some range of wealth with an equation that is eerily similar to the Boltzmann-Gibbs-Maxwell equation.  The B-G-M equation defines the relative fraction of gas molecules with some temperature T, within some range of energy.
Perhaps what makes the two equations commutative is the fact that they both depend on conservation laws.  (In an economic transaction, someone gains a specific amount of money and someone loses the same amount of money.  This is sometimes called conservation of cash flow.)

Here, we appear to be modeling economic interactions as if they were an interaction between two gas molecules; one agent gains, another loses.  However, most economists object to this idea, because no individual would freely enter into an arrangement where they knew themselves to be losing; after all, the theory of rational expectations states that in any given transaction, everyone should "win."

Econothermodynamic advocates decided that to solve this problem, they would rewrite laws of economics in terms of calculus, so that all economic interactions (which required some driving energy) ended up exploiting a third party-- nature.

Jurgen Minkes, one of the aforementioned advocates, took this theory a step further and wrote the laws of thermodynamics in terms of economic terms like capital growth, value added, and labor costs, rather than conventional physical quantities like heat, work, and energy.

Of course, we can't claim that the two fields are equatable simply because some equations are analogous.  The field of econothermodynamics endeavors to answer many questions, including:

• Should an economy be considered an open or closed thermodynamic system?
• Could entropy, as a measure of system disorder, be used to indicate the state of an economy?
• What are the macroscopic values that could give stability to an economy? (keep it in a state of thermodynamic equilibrium?)
• If economies are closed systems, are they at risk for a "thermal death"?
• What are more possible analogous values for magnetic field, pressure, temperature, volume, etc.?
• What is the role of phase transitions in an economy?
• How should the activity of a (macro)economy best be organized for it to be successful?

The best paper by far that I've found on the subject can be found here.  It answers all of the questions that I posed above (some of the above questions are  actually word-for-word from the text), and tries to do so in a manner accessible to physicists and economists both.  (It's about 25 pages long, which is why I didn't try to cram everything I learned into one blog post.)
I think my favorite quote from it, however, is the following:

"We do not claim (and it would be somewhat strange if we did) that a business community can only develop according to the laws of nature. Macroeconomic systems (like the real activity of individual large companies) are very complex, and since it is impossible to acquire completely comprehensive information about them, it is not possible to postulate formulas for their development. But we suggest taking these natural laws into account in the macro-economy. The possibility of their application should by all means be checked and tested scientifically, but we cannot afford to ignore them."  (p. 13)

This quote is actually applicable beyond econothermodynamics, to my project as a whole.  While it would be a mistake to rely fully on natural laws when developing laws regarding the economy, they can still be taken into account and tested scientifically to make our current understanding more complete.

That's all I've got for now.  In other news, I ended up ordering some of the materials for my sandpile experiment.  One of the things that I had to go on a scavenger hunt for (and found, thanks to the help of our very own Mr. Winkelman) was glass powder.  It turns out that "regular" (beach) sand is too variable in size and shape to be much use in consistent experimentation with basic sandpiles.  (I'm not sure if that's ironic or not.)  The glass powder is the same material as sand, but ground to a more uniform shape.

Glass powder (above) is much more uniform than normal
sand (below)

Fun fact: glass powder is generally added to paint to make it reflective.  Who knew?

If you have any questions, or one of the above questions I posed stood out to you and you'd like me to try to explain it (so you don't have to read the whole paper) let me know in the comments!
Have a lovely week everyone!

Week 4: Fishing for Information

Hi all!  Hope everything is going well and that you guys don't catch this stupid sickness that's been going around.
I have to admit, I was all proud of myself for coming up with a punny blog title, and then I saw that everyone else also came up with punny titles this week.  I suppose that's what I get for waiting until Sunday to post.

This week, I will be talking about Fisher Information (one of the main research components of my onsite adviser, Dr. Frieden) and its applications in econophysics.
Fisher information is a statistical tool developed by Ronald Fisher in the 1920s.  He was one of the chief inventors of modern information theory, which of course plays a large role in many different sectors of our lives.  (Computers science, physics, chemistry, and economics, to name a few.)

The basic idea behind Fisher information is to tell us how easy it is to learn about a probability distribution by sampling from it.  Say we have a probability density p that depends on some parameter (traditionally theta; I'll use t), so the density function is p(t).

(If you're interested in the mathematical equation for Fisher information, tell me in the comments and I will try to approximate it with this awful HTML formatting.  I'm focusing more on conceptual understanding here.)

The important result, though, is that the variance in any estimate of the parameter t is equal to 1/I.  
Therefore, the more Fisher information "I" that we have, the better our estimate of t, so it becomes possible to make more precise estimates from data.

(For systems of multiple parameters, this still works, but you have to use something called the Cramer-Rao inequality and the Fisher information matrix, so it's a bit uglier.)

Dr. Frieden's research is a bit of a deviation from standard Fisher Information; he claims that when  that when we observe a system, we do in fact measure some information "I."  However, due to a variety of factors, this value we observe can never be the exact value; rather, the exact, platonic value of the information is given by the letter J.

In any given system, we would want to minimize "I-J"; that is, make the perceived value of the system as close to the real value of the system as possible.  In other words, we are optimizing the information flow by minimizing the Fisher information.

Now, we can begin to apply this theory (called "Extreme physical information, or EPI, because I-J is a minimum/extremum) to financial markets.  After all, finance is completely dependent on information; the intrinsic value of a stock is believed to incorporate all available information about its value.  Stock traders fight each other for clues; in fact, this dependence on information is what makes insider trading such a big deal.  (And why people still attempt it, even though it's illegal.)

To summarize the applications in Fisher information, the probability density function is considered to be the probability of price fluctuation of some given stock, and can be generalized to include the entire market.  The trade price is considered to be the "measurement" in the EPI process.  It turns out that we can construct equilibrium distributions (including yield curves, which measure the volatility of the value of a stock) as well as more dynamic constructions.

There are also some interesting parallels; for one thing, the derived expression for economic valuation has the same general solution as that for stationary quantum mechanics.  (Both obey the Schrodinger equation.)  Also, interest rate dynamics are shown to be analogous to the Fokker-Plank expression for diffusion processes.

Ultimately, Fisher information is a statistical tool that is generally applied in the natural sciences; however, it can also be applied in economics, resulting in similar expressions to other physical properties.  Therefore, it is an interesting example of the range of tools available to those pursuing econophysics.

This coming week, I'm planning to start the grand scavenger hunt for supplies for my experimental work.  I'll be sure and keep you all updated about that, but until then, enjoy your week, and feel free to comment.