Hi everyone!
I will be presenting my project on May 14 at UNS Energy-Tucson Electric Power (88 E Broadway Blvd). The presentations start at 6 pm.
Thanks for reading this blog, and I hope to see you there! :)
Saturday, May 10, 2014
Sunday, April 20, 2014
Week 11?
Hey guys! Just a quick update here. Obviously everyone's projects are basically done by this point (including mine) and I'm super excited to report that I finally finished my draft for the final paper and have sent it to my advisers for review. I'll probably add to and edit it throughout this coming week, and hope to have it completely polished by next Monday. (I'm also working on figuring out a way to share it to this blog, so that anyone who wants to read it can.) It ended up being the longest paper I've written in my high school career, so that's exciting.
I also have my first presentation rehearsal tomorrow, during which we'll see how successful I was at trimming everything down to fit the time limit. I hope to see you all at my final presentation. (date still TBD, but I'll let you know!)
I also have my first presentation rehearsal tomorrow, during which we'll see how successful I was at trimming everything down to fit the time limit. I hope to see you all at my final presentation. (date still TBD, but I'll let you know!)
Saturday, April 12, 2014
Week 10: End Stretch
Hey guys! I'm going to apologize in advance for a briefer blog post. As it turns out, I've already talked about everything I'm planning to include in my final paper; there might be a bit more detail, but these blogs should give you an idea of the topics I'm going to cover and the arguments I'm planning to make.
Unfortunately, the final paper is a lot harder than I was expecting it to be! I've finished an outline and the skeleton of the paper, but right now I'm struggling to fill it in so that I can create a persuasive argument that isn't too repetitive; (you'd be surprised how many times I've used the word "Econophysics" in the first three pages alone...) not to mention citations, which are close to the top of my list of least favorite things.
Everything else about my project is winding down; I'm meeting with Dr. Frieden as usual next Tuesday, but most likely for the last time, and of course I've also begun work on my final presentation. Due to scheduling conflicts, I didn't go into the lab this past week like I thought I was going to, but I'm planning to make up that time this coming week, in addition to finishing my final paper and presentation draft.
I actually have family in town this weekend, so I haven't had time to do much of anything (hence the really short blog post), but I'll resume what's left of my project on Monday. Have a great week, everyone!
Unfortunately, the final paper is a lot harder than I was expecting it to be! I've finished an outline and the skeleton of the paper, but right now I'm struggling to fill it in so that I can create a persuasive argument that isn't too repetitive; (you'd be surprised how many times I've used the word "Econophysics" in the first three pages alone...) not to mention citations, which are close to the top of my list of least favorite things.
Everything else about my project is winding down; I'm meeting with Dr. Frieden as usual next Tuesday, but most likely for the last time, and of course I've also begun work on my final presentation. Due to scheduling conflicts, I didn't go into the lab this past week like I thought I was going to, but I'm planning to make up that time this coming week, in addition to finishing my final paper and presentation draft.
I actually have family in town this weekend, so I haven't had time to do much of anything (hence the really short blog post), but I'll resume what's left of my project on Monday. Have a great week, everyone!
Saturday, April 5, 2014
Week 9: Mixing Metaphors
As I'm reading everyone's blog posts, and seeing how everything is beginning to wind down, I keep having to go take a few deep breaths and think calming thoughts. It's crazy how fast this project has gone!
I'm still doing some work with the sandpiles (next week I will be working to determine if their dynamics behave differently at different frequencies projected by a speaker system) but I don't think the actual experimental results will play a role in my final product or presentation. (Rather, the things I've learned about sandpiles and avalanche dynamics will be larger factors.) On the reading front, I still have one-and-a-half more books to read (one-half about sandpiles and the markets; one about fractals and the markets) and I've started work on my final paper and presentation!
On that front, I'm planning to have my final paper rough draft finished by this coming Thursday, and then after that I'll start on the presentation. (I'm hoping that having everything already outlined in the paper will make the presentation easier, but I guess we'll see.)
And then... I'll be done?
As long as we're talking about things giving me anxiety issues, fitting my presentation into twenty minutes is going to be a bit of a bear. I'm guessing I'll be talking about as fast as those prescription drug commercial narrators, where they try to tell you the side effects as fast as possible so you don't have time to wonder why you'd take headache medicine if it's going to give you diarrhea, nausea, and dizziness.
This week, I will be discussing the work of Nassim Taleb, who I mentioned a few weeks ago. I read his book The Black Swan, which concerns unpredictable events, both in and outside the markets.
Taleb argues that events that are considered by most to be extremely rare (for example, a black swan) are actually more common than would be expected. He goes on to detail different events that he considers to be black swans; most of them take place in the financial markets. (It turns out that his "black swans" become metaphors for the fat-tailed distributions I've been going on about for the last few weeks.)
However, what distinguishes Taleb's work is that he argues that these events are not only extreme (and therefore occur more often than a typical bell curve would have us believe) but he also argues that these events are inherently unpredictable.
This is where a friend of Taleb's, a French physicist named Didier Sornette, comes in. Sornette, who has background in geophysics and other modeling involving critical events, agrees with Taleb about extreme events being a more common occurrence than the traditional bell curve would lead us to believe. However, he argues that rather than being silent-but-deadly black swans, these events would be better-represented by Dragon Kings; if you "listen" the right way, you can hear them coming.
Sornette can back his claim up; he's actually predicted the last few financial crises (and made quite a bit of money off of it, too.) If you guys are interested, you can watch his Ted Talk here. It's really interesting, and in my opinion, makes a better case for Dragon Kings than for Black Swans.
Hope you all are having a great week!
I'm still doing some work with the sandpiles (next week I will be working to determine if their dynamics behave differently at different frequencies projected by a speaker system) but I don't think the actual experimental results will play a role in my final product or presentation. (Rather, the things I've learned about sandpiles and avalanche dynamics will be larger factors.) On the reading front, I still have one-and-a-half more books to read (one-half about sandpiles and the markets; one about fractals and the markets) and I've started work on my final paper and presentation!
On that front, I'm planning to have my final paper rough draft finished by this coming Thursday, and then after that I'll start on the presentation. (I'm hoping that having everything already outlined in the paper will make the presentation easier, but I guess we'll see.)
And then... I'll be done?
As long as we're talking about things giving me anxiety issues, fitting my presentation into twenty minutes is going to be a bit of a bear. I'm guessing I'll be talking about as fast as those prescription drug commercial narrators, where they try to tell you the side effects as fast as possible so you don't have time to wonder why you'd take headache medicine if it's going to give you diarrhea, nausea, and dizziness.
This week, I will be discussing the work of Nassim Taleb, who I mentioned a few weeks ago. I read his book The Black Swan, which concerns unpredictable events, both in and outside the markets.
Taleb argues that events that are considered by most to be extremely rare (for example, a black swan) are actually more common than would be expected. He goes on to detail different events that he considers to be black swans; most of them take place in the financial markets. (It turns out that his "black swans" become metaphors for the fat-tailed distributions I've been going on about for the last few weeks.)
However, what distinguishes Taleb's work is that he argues that these events are not only extreme (and therefore occur more often than a typical bell curve would have us believe) but he also argues that these events are inherently unpredictable.
This is where a friend of Taleb's, a French physicist named Didier Sornette, comes in. Sornette, who has background in geophysics and other modeling involving critical events, agrees with Taleb about extreme events being a more common occurrence than the traditional bell curve would lead us to believe. However, he argues that rather than being silent-but-deadly black swans, these events would be better-represented by Dragon Kings; if you "listen" the right way, you can hear them coming.
Sornette can back his claim up; he's actually predicted the last few financial crises (and made quite a bit of money off of it, too.) If you guys are interested, you can watch his Ted Talk here. It's really interesting, and in my opinion, makes a better case for Dragon Kings than for Black Swans.
Hope you all are having a great week!
Sunday, March 30, 2014
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!
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!
Saturday, March 22, 2014
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:
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:
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...."
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:
Sunday, March 16, 2014
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.
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:
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 |
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!
Sunday, March 9, 2014
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:
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:
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.
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!
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:
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."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)
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!
Sunday, March 2, 2014
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.
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.
Saturday, February 22, 2014
Week 3: Avalanches, Rockslides, and Sandpiles, Oh My!
Hello everyone!
If you've been following me up to this point, you're probably starting to wonder what the details of my project are. I realized this week that while I've been busy talking about the gloriously cool things I've been finding, I have yet to mention what I'm doing on a day-to-day-basis.
So let's do that!
So far, my project has two parts; for the first part, I am working with Dr. Roy Frieden (at the U of A), who has done econophysics research in the past. He has been directing me to the materials I should read next, in addition to helping explain some of the gnarly statistics.
Dr. Frieden's research (econophysics-related and otherwise) deals primarily in the field of Fisher information, which I feel like I know quite a lot about by this point and plan on sharing with you all in the very near future.
For the second part of the project, I am working with Dr. Srin Manne (also at the U of A). Dr. Manne is helping me to design an experiment about avalanche dynamics, because as it turns out, the inner workings of avalanches somewhat resemble the inner workings of economic collapses.
I should point out that I'm not referring to snow-based avalanches here, which seem to be the first thing to leap to everyone's mind. As cool (and terrifying) as those are, they are rather tough for a high school student to model quickly and cheaply.
(While I'm all for Grant's suggestion that I just build a mountain of Eegee's for observation, there's still the melting problem to consider. And then we'd have a waste of perfectly good Eegee's on our hands, and that's not even justifiable in the name of scientific progress.)
So the avalanches I will be working with are rock-based, rather than snow-based. This distinction doesn't matter too much, because rock-based avalanches (sometimes called rockslides) actually behave really similarly to snow-based models as long as they "flow" fast enough.
(Avalanches are part of a field called granular physics, which is distinctive because materials following granular behavior behave differently from other "standard" forms of matter, e.g. solid, liquid, and gas. For example, a rockslide can behave as a liquid entity even though its individual components are solid.)
There are lots of ways to model rocks falling down a hill, it turns out. One paper I came across actually used fragmented blocks of coal. The most famous (and best-explored) model, though, is the sandpile model, which is (surprise, surprise) basically a pile of sand.
Sandpiles (and, by extension, avalanches) are systems that obey self-organized criticality (SOC). That's a fancy way of saying that the system is attracted to a certain critical point. For example, if building a sandpile from scratch (as in the above picture), it would collapse in on itself at some critical angle, and stop growing taller.
Classic (non-SOC) examples of "critical points" are defined by an exact parameter. For example, a phase transition, like liquid turning to gas, occurs at some exact temperature. However, in SOC systems, the parameters are not exact-- we have no way of knowing which grain of sand will be the one to tip the pile over; it's different for every trial.
In the same way, when dealing with forecasting economic predictions, we might not know exactly which news, action, or other variable will tip the market downwards. However, we can (hopefully) have some idea of when such a downward spiral might occur, by looking at the patterns. (Consider the 2008 housing bubble; it followed a familiar and predictable economic pattern. If we were to somehow repeat the situation, we would still expect some form of market collapse, but it could be from an entirely different variable.)
Obviously, I still have a lot of work to do, as right now I'm working on actually designing the experiment. I have some ideas; for example, while considerable work has been done with the standard sandpile, which consists of point particles (the grains of sand), Dr. Manne and I are both curious what happens if we were to make a "sandpile" of string particles instead-- e.g. many beaded chains.
Not to worry, though, as soon as I get past the developmental phase and actually start gathering supplies and building the models, I'll be sure to keep you all updated. Including real live pictures!
Hope you're all having a good week. Feel free to comment below if you have anything to say!
If you've been following me up to this point, you're probably starting to wonder what the details of my project are. I realized this week that while I've been busy talking about the gloriously cool things I've been finding, I have yet to mention what I'm doing on a day-to-day-basis.
So let's do that!
So far, my project has two parts; for the first part, I am working with Dr. Roy Frieden (at the U of A), who has done econophysics research in the past. He has been directing me to the materials I should read next, in addition to helping explain some of the gnarly statistics.
Dr. Frieden's research (econophysics-related and otherwise) deals primarily in the field of Fisher information, which I feel like I know quite a lot about by this point and plan on sharing with you all in the very near future.
For the second part of the project, I am working with Dr. Srin Manne (also at the U of A). Dr. Manne is helping me to design an experiment about avalanche dynamics, because as it turns out, the inner workings of avalanches somewhat resemble the inner workings of economic collapses.
I should point out that I'm not referring to snow-based avalanches here, which seem to be the first thing to leap to everyone's mind. As cool (and terrifying) as those are, they are rather tough for a high school student to model quickly and cheaply.
(While I'm all for Grant's suggestion that I just build a mountain of Eegee's for observation, there's still the melting problem to consider. And then we'd have a waste of perfectly good Eegee's on our hands, and that's not even justifiable in the name of scientific progress.)
 |
| Way to go, Grant. Now I really want some. |
(Avalanches are part of a field called granular physics, which is distinctive because materials following granular behavior behave differently from other "standard" forms of matter, e.g. solid, liquid, and gas. For example, a rockslide can behave as a liquid entity even though its individual components are solid.)
There are lots of ways to model rocks falling down a hill, it turns out. One paper I came across actually used fragmented blocks of coal. The most famous (and best-explored) model, though, is the sandpile model, which is (surprise, surprise) basically a pile of sand.
Sandpiles (and, by extension, avalanches) are systems that obey self-organized criticality (SOC). That's a fancy way of saying that the system is attracted to a certain critical point. For example, if building a sandpile from scratch (as in the above picture), it would collapse in on itself at some critical angle, and stop growing taller.
Classic (non-SOC) examples of "critical points" are defined by an exact parameter. For example, a phase transition, like liquid turning to gas, occurs at some exact temperature. However, in SOC systems, the parameters are not exact-- we have no way of knowing which grain of sand will be the one to tip the pile over; it's different for every trial.
In the same way, when dealing with forecasting economic predictions, we might not know exactly which news, action, or other variable will tip the market downwards. However, we can (hopefully) have some idea of when such a downward spiral might occur, by looking at the patterns. (Consider the 2008 housing bubble; it followed a familiar and predictable economic pattern. If we were to somehow repeat the situation, we would still expect some form of market collapse, but it could be from an entirely different variable.)
Obviously, I still have a lot of work to do, as right now I'm working on actually designing the experiment. I have some ideas; for example, while considerable work has been done with the standard sandpile, which consists of point particles (the grains of sand), Dr. Manne and I are both curious what happens if we were to make a "sandpile" of string particles instead-- e.g. many beaded chains.
Not to worry, though, as soon as I get past the developmental phase and actually start gathering supplies and building the models, I'll be sure to keep you all updated. Including real live pictures!
Hope you're all having a good week. Feel free to comment below if you have anything to say!
Wednesday, February 12, 2014
Week 2: Drunken Meanderings, Fat Tails, and the Markets
Hey guys! I hope you are all having a fun and productive time at your internships. This week, I thought I would address some of the earliest research in econophysics. (Buckle in for another unnecessarily long blog post, everyone!)
Econophysics, it turns out, isn't nearly as innovative as it sounds. As I mentioned last week, the term was coined almost twenty years ago, (in 1995) but the field's central tenants have been around for much longer than that. In this blog post I'm going to be talking about Louis Bachelier and his Theorie de la Speculation, or in English, Theory of Speculation. My onsite adviser, Dr. Frieden, suggested that I start with his work, since it has greatly influenced economic and econophysical theory since its rediscovery in the mid 1950s.
Bachelier, originally trained as a physicist, published his Theory in 1900, dealing principally with the movements of stock prices. (As data, Bachelier analyzed numbers from the Paris Bourse, then France's principal financial exchange, where he worked for several years in order to pay for his schooling.)
Bachelier's work had two parts that are significant to modern econophysics; I'll explain them both below. First of all, he derived the mathematical expression of Brownian motion. Second, he found that the motion of prices in a stock market follows a statistical random walk model.
Since neither of those probably meant very much to you, I'll explain. Brownian motion is the seemingly random motion of particles suspended in a fluid. (Liquid or gas.) A common and easily visualized example is the motion of dust molecules in the air. This gif (credit to Wikipedia) shows a big particle (e.g. dust particle) colliding with a lot of smaller ones (e.g. gas molecule) and producing random, Brownian motion.
(For those of you who worked with Mr. Young in Multivariable Calc this year, I actually talked to him about this, and it turns out that his work in mathematical modeling is similar to modeling Brownian motion; however, he assumes that the particles or objects he is dealing with have some initial velocity that can impact their final positions.)
When Einstein published a paper in 1905 describing Brownian motion, he didn't know that he was five years too late. Actually, no one did, as Bachelier's work languished in obscurity for decades despite the fact that he invented a lot of probability theory that was years before its time.
While it is interesting to note that a physicist derived a way to understand our natural world by looking at the economy (which perhaps belies an intrinsic connection), Bachelier's work had a more important side effect that lay in the expression of Brownian motion; if given an infinite amount of time, Brownian motion begins to follow a statistical random walk model.
What's a random walk?
Imagine an incredibly drunk man trying to find his hotel room in a long hall. Since he's stumbling around, blindly intoxicated and completely clueless, he has an equal probability of stepping forward as stepping backwards. If he steps forward with his first step, he could step either forward or backward with the next. You might even say that he's walking... randomly.
It turns out that these random walks follow our buddy the normal curve! This makes intuitive sense; if our drunk friend starts at hotel room number 50, in principle he could end up at room 10 or room 100 by taking a whole lot of drunk steps forward, or a whole lot backwards. These "extreme" events are just a lot more unlikely because they would require a certain result (stepping only forward or backwards) many times in a row, similar to flipping a coin 50 times and getting 50 heads.
If you'll recall, though, Bachelier's work was not originally about Brownian motion or random walks at all-- it was about stock prices. Essentially, Bachelier found that the motion of stock prices follows a random walk. (It was only as he explored the mathematics of random walks that he "accidentally" solved Brownian motion. Oops.)
This should be fairly intuitive to us also; we would expect a stock price to fluctuate, but not very much. What Bachelier was arguing was that small fluctuations in price were much more likely than large ones; statistically speaking, a stock jumping from $1 to $1000 overnight would be incredibly rare; much more rare than the same stock jumping from $1 to $1.05 overnight. (This becomes important when dealing with something called the Efficient Market Hypothesis, which states that the market is a perfect synthesis of all available information about the value of a stock. Therefore, the fluctuations would center around a price that was the inherently "correct" value. I might deal with this more in a future post.)
Also important in his work was the implication that stock markets are inherently random. After all, if they are truly random, they follow statistical rules... and they can be predicted with statistical tools. This was (and is) revolutionary.
It turns out that, unfortunately, Bachelier was wrong, in 2 important ways. As Maury Osborne discovered in 1959, it is not the prices of stocks that are random, but the relative price changes in stocks. This makes sense, since investors really care about the percent increase in the value of their stocks more than simply the change in price. This problem is easily solved by describing the motion of the markets with geometric Brownian motion, which uses the log-normal distribution. (Taking the logarithm of the difference in prices makes a Gaussian curve.)
Even Osborne didn't have the complete picture; Benoit Mandelbrot (mostly known for discovering fractal geometry) found the next piece of the puzzle, the one that has the biggest implication for modern econophysics.
If we look at the normal curve, we can see that statistical anomalies should not occur very often. That is, price fluctuations should be relatively stable, with outliers occurring very rarely. This is not the case in actual market dynamics. Stocks over a single day typically change less than 2%; a movement of ten standard deviations therefore means a movement of at least 20%. While Gaussian statistics tells us that such movements should happen once every 10^22 days (longer than the age of the universe) market data shows us that it happens at least once a week. Something is clearly wrong with our model.
Mandelbrot, while analyzing cotton prices, found that they follow a distribution with fat tails. Fat-tailed distributions are similar in shape to the normal curve, except that instead of approaching zero probability, their "tails" remain positive for a long time.
This means, in essence, that improbable events in the markets happen a lot more often than we would imagine. (Fat tails pop up in physics all the time, incidentally; I'll probably also deal with that in a future post.)
So Bachelier was essentially wrong in his most important argument-- that markets are like random walks. (To his credit, the data that he analyzed at the Paris Bourse did actually follow a random walk model-- perhaps it was especially stable at that time.) However, he's still relevant to the field, because he established one of the first relationships between physics and the economy, fixed a precedent for analysis of statistical data in the economy, and argued that markets are random. Economists mostly agree that he got that part right, and that since the markets are random, we can predict their (overall) behavior. He also laid the groundwork for Mandelbrot to discover the market's fat tails, and thus put us one step closer to understanding some of the latest economic crises.
Sorry again for the pedantic rant, guys. Have a great week, and feel free to comment!
Econophysics, it turns out, isn't nearly as innovative as it sounds. As I mentioned last week, the term was coined almost twenty years ago, (in 1995) but the field's central tenants have been around for much longer than that. In this blog post I'm going to be talking about Louis Bachelier and his Theorie de la Speculation, or in English, Theory of Speculation. My onsite adviser, Dr. Frieden, suggested that I start with his work, since it has greatly influenced economic and econophysical theory since its rediscovery in the mid 1950s.
Bachelier, originally trained as a physicist, published his Theory in 1900, dealing principally with the movements of stock prices. (As data, Bachelier analyzed numbers from the Paris Bourse, then France's principal financial exchange, where he worked for several years in order to pay for his schooling.)
Bachelier's work had two parts that are significant to modern econophysics; I'll explain them both below. First of all, he derived the mathematical expression of Brownian motion. Second, he found that the motion of prices in a stock market follows a statistical random walk model.
Since neither of those probably meant very much to you, I'll explain. Brownian motion is the seemingly random motion of particles suspended in a fluid. (Liquid or gas.) A common and easily visualized example is the motion of dust molecules in the air. This gif (credit to Wikipedia) shows a big particle (e.g. dust particle) colliding with a lot of smaller ones (e.g. gas molecule) and producing random, Brownian motion.
When Einstein published a paper in 1905 describing Brownian motion, he didn't know that he was five years too late. Actually, no one did, as Bachelier's work languished in obscurity for decades despite the fact that he invented a lot of probability theory that was years before its time.
While it is interesting to note that a physicist derived a way to understand our natural world by looking at the economy (which perhaps belies an intrinsic connection), Bachelier's work had a more important side effect that lay in the expression of Brownian motion; if given an infinite amount of time, Brownian motion begins to follow a statistical random walk model.
What's a random walk?
Imagine an incredibly drunk man trying to find his hotel room in a long hall. Since he's stumbling around, blindly intoxicated and completely clueless, he has an equal probability of stepping forward as stepping backwards. If he steps forward with his first step, he could step either forward or backward with the next. You might even say that he's walking... randomly.
It turns out that these random walks follow our buddy the normal curve! This makes intuitive sense; if our drunk friend starts at hotel room number 50, in principle he could end up at room 10 or room 100 by taking a whole lot of drunk steps forward, or a whole lot backwards. These "extreme" events are just a lot more unlikely because they would require a certain result (stepping only forward or backwards) many times in a row, similar to flipping a coin 50 times and getting 50 heads.
This should be fairly intuitive to us also; we would expect a stock price to fluctuate, but not very much. What Bachelier was arguing was that small fluctuations in price were much more likely than large ones; statistically speaking, a stock jumping from $1 to $1000 overnight would be incredibly rare; much more rare than the same stock jumping from $1 to $1.05 overnight. (This becomes important when dealing with something called the Efficient Market Hypothesis, which states that the market is a perfect synthesis of all available information about the value of a stock. Therefore, the fluctuations would center around a price that was the inherently "correct" value. I might deal with this more in a future post.)
Also important in his work was the implication that stock markets are inherently random. After all, if they are truly random, they follow statistical rules... and they can be predicted with statistical tools. This was (and is) revolutionary.
It turns out that, unfortunately, Bachelier was wrong, in 2 important ways. As Maury Osborne discovered in 1959, it is not the prices of stocks that are random, but the relative price changes in stocks. This makes sense, since investors really care about the percent increase in the value of their stocks more than simply the change in price. This problem is easily solved by describing the motion of the markets with geometric Brownian motion, which uses the log-normal distribution. (Taking the logarithm of the difference in prices makes a Gaussian curve.)
Even Osborne didn't have the complete picture; Benoit Mandelbrot (mostly known for discovering fractal geometry) found the next piece of the puzzle, the one that has the biggest implication for modern econophysics.
If we look at the normal curve, we can see that statistical anomalies should not occur very often. That is, price fluctuations should be relatively stable, with outliers occurring very rarely. This is not the case in actual market dynamics. Stocks over a single day typically change less than 2%; a movement of ten standard deviations therefore means a movement of at least 20%. While Gaussian statistics tells us that such movements should happen once every 10^22 days (longer than the age of the universe) market data shows us that it happens at least once a week. Something is clearly wrong with our model.
Mandelbrot, while analyzing cotton prices, found that they follow a distribution with fat tails. Fat-tailed distributions are similar in shape to the normal curve, except that instead of approaching zero probability, their "tails" remain positive for a long time.
 |
| Probability of large fluctuations is greater in fat-tailed distributions |
So Bachelier was essentially wrong in his most important argument-- that markets are like random walks. (To his credit, the data that he analyzed at the Paris Bourse did actually follow a random walk model-- perhaps it was especially stable at that time.) However, he's still relevant to the field, because he established one of the first relationships between physics and the economy, fixed a precedent for analysis of statistical data in the economy, and argued that markets are random. Economists mostly agree that he got that part right, and that since the markets are random, we can predict their (overall) behavior. He also laid the groundwork for Mandelbrot to discover the market's fat tails, and thus put us one step closer to understanding some of the latest economic crises.
Sorry again for the pedantic rant, guys. Have a great week, and feel free to comment!
Wednesday, February 5, 2014
Week 1: Why Do We Care?
Hi guys!
I hope everyone had a lovely time at Disneyland; if you didn't go, consider yourselves at least a little bit lucky, because I guarantee you got more sleep than I did.
So I'd like to start out by explaining why my project is even relevant in the first place. Why study Econophysics? How is it different from or applicable to "normal" economic theory?
When I first started this project way back in October, I found basically an overwhelming number of resources on the Internet that related to this field of study. One of the things I found was a news editorial by Vincent Fernando about Econophysics, which can be found at
http://www.businessinsider.com/failed-economists-concoct-new-econophysics-2010-8
(I spent about a half hour trying different variations of Google searches before I thought to look in my browser history. D'oh.)
For those too lazy to read the whole thing, the most important sentence is probably,
"[Econophysics is flawed] because economics is a social phenomenon, like politics, or social development. It's not physics, and it's not chemistry."
The idea being that we cannot predict the behavior of humans (and thus the markets) using laws derived to predict the behavior of particles and other physical phenomenon like earthquakes. This is by virtue of the fact that, unlike electrons, humans make decisions that are emotion-based, occasionally illogical, and that depend on limited information.
(Let's forget for just a moment that most modern macroeconomic theory is based on rational choice, which states that people make decisions that are the most prudent, logical, and likely to provide them with the greatest benefit in their own self-interest. How much more particle-like and/or oversimplified can we get here?)
(If you can't tell, I'm not the biggest fan of rational choice theory, mostly because the only place I've ever seen people act 100% in their own self-interest is in the BASIS parking lot.)
Mr. Fernando's claim, however, completely misunderstands the nature and purpose of Econophysics.
Let's look at a definition by Dr. Roy Frieden, my onsite-advisor, who has analyzed this topic with regard to optical statistics:
"[The basic premise of econophysics] is that the same mathematical and phenomenological insights that are used to provide unification for complex physical systems can now apply to problems of economics and finance." (Frieden and Gatenby, 2007, p. 43).
Dr. Frieden is not claiming that people are atoms, or that we should expect them to behave rationally and logically all the time. He is claiming that the overall behavior of markets and economic systems can be compared with behaviors in the natural sciences. He is claiming that the same tools (e.g. statistical models, physical models and theories, etc.) can be applied to understand markets better.
It is important to make the distinction, as Mark Buchannon does quite well, that "The most important lesson of modern physics is that it is often not the properties of the parts that matter most, but their organization, their pattern and their form." (Buchannon, 2007, p. 10). He goes on to say that "no study of soil or stones could perfectly explain [the circular patterns that form due to weather and earth movements] just as no study of air molecules on their own could help anyone understand a hurricane." (p. 12)
In much the same way, while humans as individuals are very complex and ruled by emotion and unpredictability, that doesn't mean that their actions as a whole can't be predicted or at least understood. Current Macroeconomic theory aims to do exactly that, after all-- there is no reason that physics, a field dedicated to unifying and modeling smaller parts of a whole, cannot at least attempt it.
Perhaps the one thing that Mr. Fernando got completely correct in his article was that current macroeconomic theory, bluntly put, isn't working very well. As the economic consultancy London Economics, led by John Kay, points out, "It is a conventional joke that there are as many different opinions about the future of the economy as there are economists. The truth is quite the opposite. Economic forecasters... all say more or less the same thing at the same time... The differences between forecasts are trivial compared to the differences between forecasts and what actually happens... what they say is almost always wrong... the consensus forecast failed to predict any of the most important developments in the economy over the past seven years."
What I hope to evaluate with this project is not only the usefulness of these comparisons to physics but also the extent to which they can be applied. So far, it seems to me that a further study into econophysics can, at worst, only broaden our knowledge of current economic workings, and at best, can be used to permanently change our view of the markets, especially given the current misunderstandings going on in economics.
(Note: Mr. Fernando is also incorrect in his assumption that the field of econophysics is somehow "new." While the term was coined fairly recently-- in 1995, still roughly fifteen years before his editorial was published-- the field has been around for much longer than that, and has influenced modern economic theory in several important ways. I will hopefully cover those in the near future.)
Sorry this is a bit long...
Have a great week everyone! Please feel free to comment!
I hope everyone had a lovely time at Disneyland; if you didn't go, consider yourselves at least a little bit lucky, because I guarantee you got more sleep than I did.
So I'd like to start out by explaining why my project is even relevant in the first place. Why study Econophysics? How is it different from or applicable to "normal" economic theory?
When I first started this project way back in October, I found basically an overwhelming number of resources on the Internet that related to this field of study. One of the things I found was a news editorial by Vincent Fernando about Econophysics, which can be found at
http://www.businessinsider.com/failed-economists-concoct-new-econophysics-2010-8
(I spent about a half hour trying different variations of Google searches before I thought to look in my browser history. D'oh.)
For those too lazy to read the whole thing, the most important sentence is probably,
"[Econophysics is flawed] because economics is a social phenomenon, like politics, or social development. It's not physics, and it's not chemistry."
The idea being that we cannot predict the behavior of humans (and thus the markets) using laws derived to predict the behavior of particles and other physical phenomenon like earthquakes. This is by virtue of the fact that, unlike electrons, humans make decisions that are emotion-based, occasionally illogical, and that depend on limited information.
(Let's forget for just a moment that most modern macroeconomic theory is based on rational choice, which states that people make decisions that are the most prudent, logical, and likely to provide them with the greatest benefit in their own self-interest. How much more particle-like and/or oversimplified can we get here?)
(If you can't tell, I'm not the biggest fan of rational choice theory, mostly because the only place I've ever seen people act 100% in their own self-interest is in the BASIS parking lot.)
Mr. Fernando's claim, however, completely misunderstands the nature and purpose of Econophysics.
Let's look at a definition by Dr. Roy Frieden, my onsite-advisor, who has analyzed this topic with regard to optical statistics:
"[The basic premise of econophysics] is that the same mathematical and phenomenological insights that are used to provide unification for complex physical systems can now apply to problems of economics and finance." (Frieden and Gatenby, 2007, p. 43).
Dr. Frieden is not claiming that people are atoms, or that we should expect them to behave rationally and logically all the time. He is claiming that the overall behavior of markets and economic systems can be compared with behaviors in the natural sciences. He is claiming that the same tools (e.g. statistical models, physical models and theories, etc.) can be applied to understand markets better.
It is important to make the distinction, as Mark Buchannon does quite well, that "The most important lesson of modern physics is that it is often not the properties of the parts that matter most, but their organization, their pattern and their form." (Buchannon, 2007, p. 10). He goes on to say that "no study of soil or stones could perfectly explain [the circular patterns that form due to weather and earth movements] just as no study of air molecules on their own could help anyone understand a hurricane." (p. 12)
In much the same way, while humans as individuals are very complex and ruled by emotion and unpredictability, that doesn't mean that their actions as a whole can't be predicted or at least understood. Current Macroeconomic theory aims to do exactly that, after all-- there is no reason that physics, a field dedicated to unifying and modeling smaller parts of a whole, cannot at least attempt it.
Perhaps the one thing that Mr. Fernando got completely correct in his article was that current macroeconomic theory, bluntly put, isn't working very well. As the economic consultancy London Economics, led by John Kay, points out, "It is a conventional joke that there are as many different opinions about the future of the economy as there are economists. The truth is quite the opposite. Economic forecasters... all say more or less the same thing at the same time... The differences between forecasts are trivial compared to the differences between forecasts and what actually happens... what they say is almost always wrong... the consensus forecast failed to predict any of the most important developments in the economy over the past seven years."
What I hope to evaluate with this project is not only the usefulness of these comparisons to physics but also the extent to which they can be applied. So far, it seems to me that a further study into econophysics can, at worst, only broaden our knowledge of current economic workings, and at best, can be used to permanently change our view of the markets, especially given the current misunderstandings going on in economics.
(Note: Mr. Fernando is also incorrect in his assumption that the field of econophysics is somehow "new." While the term was coined fairly recently-- in 1995, still roughly fifteen years before his editorial was published-- the field has been around for much longer than that, and has influenced modern economic theory in several important ways. I will hopefully cover those in the near future.)
Sorry this is a bit long...
Have a great week everyone! Please feel free to comment!
Wednesday, January 29, 2014
Hi Everyone!
So here we are.
Welcome, everybody, to my blog! The theme should be pretty self-explanatory-- I will be discussing my work on my Senior Research Project (henceforth SRP).
I will be exploring the field of Econophysics, or the use of patterns and models in physics to improve economic and market models. Thus the blog title.
Enjoy!
Welcome, everybody, to my blog! The theme should be pretty self-explanatory-- I will be discussing my work on my Senior Research Project (henceforth SRP).
I will be exploring the field of Econophysics, or the use of patterns and models in physics to improve economic and market models. Thus the blog title.
Enjoy!
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