A while ago, I bought Complexity: A Guided Tour by Melanie Mitchell in the Kindle store and read it. This book covers all kinds of crazy things, like network theory and information theory, Von Neumann machines, and feedback loops. It was a fascinating book, and Mitchell mentioned that Douglas Hofstadter had inspired her and had become her mentor.

I had come across Hofstadter’s book I Am a Strange Loop in the bookstore, but it wasn’t until Mitchell mentioned it again that I actually bought it. Hofstadter, it seems, has been captivated by feedback loops and self-reference his whole life. I just started reading I Am a Strange Loop, and needless to say, I’m enthralled so far.

One of the early chapters brings up self-referencing sentences, like “This statement is false.” Is the statement true or false? Well, if the statement is false, then the statement is true, not false. Likewise, if the statement is true, then it’s false. It’s an unsolvable paradox, all because it references itself.

Hofstadter goes on to talk about Bertrand Russell and how he attempted to create a comprehensive tome of mathematics, but he ran into some trouble with set theory. Something about not being able to solve the set that contains all sets that do not contain itself, or something. Anyway, Russell was stumped, and instead of coming up with some creative answer, he “avoided” the problem by explicitly defining a set of definitions where a word could not reference itself. Hofstadter called this a timid theory of types, and rightly so.

Hofstadter ponders for a bit why some people shy away from this idea of self-reference. Indeed, it seems to offend or cause anxiety for some people. Like Hofstadter, I asked myself why this was.

My first idea was that most people tend to mentally categorize things. In fact, Nassim Taleb has a new book out called The Bed of Procrustes: Philosophical and Practical Aphorisms that examines people’s propensity to categorize things, including things that defy categorization. So my first impression was that self-reference leads to paradoxes that can’t be solved, and people don’t like that because they want to categorize things as true or false.

My second idea had to do with cognitive complexity. As I understand it, cognitive complexity means that you are able to look at something from all kinds of directions, and you are usually good at creative problem-solving. However, this looking-at-things-from-all-directions slows down the decision-making process, and cognitively simple people tend to make decisions more quickly. Anyway, I was told recently that I am cognitively complex, so this idea has also been on my mind as I start to grasp just what it means exactly.

So my second idea was that cognitively simple people don’t like self-reference because of its complexity. A sentence like “This statement is false” needs to be examined and looked over, and it’s impossible to take a glance and immediately understand what it’s saying. My thought was that cognitively complex people can appreciate the complexity of self-reference, but cognitively simple people can’t.

Then my third idea followed from the second, and it had to do with fact that a paradox like “This statement is false” can’t be solved. There’s no correct answer. It’s undecidable, unsolvable, does not compute. This brought to my mind some of my favorite images on the internets, namely dividing by zero:

Nothing like some math/nerd humor to liven things up. I’ll always love the first image because I think the “You son of a bitch” part in big block letters is hilarious, but I also like the infinity loop in the third, as it ties in nicely to what I’m discussing here.

Anyway, the point is that my third idea for why some people just don’t like self-reference is because of the undecidability or unsolvablility or does-not-compute-edness it creates. Go out and read Gödel’s Proof (a fascinating book in its own right) and see if your head doesn’t want to explode at some point. It’s like your mind is trying to compute something, but it just can’t. Some people, like Hofstadter and myself, find this idea intriguing. Others, like Bertrand Russell, turn away. I just wonder if these people basically fear the undecidability and the uncertainty it creates. I think they do. Hell, Taleb has made a career out of pointing out how people misunderstand uncertainty, and how some academics fear this type of unpredictable uncertainty.

My point with all this is that I Am a Strange Loop has all the makings of an incredible book, and hopefully I’ll provide an update when I finish it. I mean, just a few paragraphs on self-reference and why some people don’t like it by Hofstadter and my mind was spinning with all these ideas.

Maybe I really am cognitively complex.

How many bands do you know of who have a lead signer with a PhD? These guys have been rocking out since 1980, when they were 16 years old, and they haven’t slowed down. They have the unrelenting power and energy of punk, to which they add beautiful harmonies, and mix at all up with incredible intelligence, creativity, and lyricism.

I have seen these guys live once, and it was great. They mix up their new songs with their old songs, and their live shows have great energy. I’m seeing them again soon when they come into Seattle, which is why I’ve been listening to them a lot lately, and I can’t wait.

I present you with “New Dark Ages,” from the New Maps of Hell
album. This may not be in my top 5 all-time songs for this band, but it’s certainly one of their best recent songs.

Note: I’m pretty sure this is not an official video, but I think it’s pretty good.

Here are the lyrics:

Yeah can you hear the call in our rambling land susurrations,
That can expand beyond all hope of light and plunge us into unrelenting night

A pall on truth and reason,
It feels like hunting season
So avoid those lines of sight and we’ll set this right

Welcome to the new dark ages
I hope you’re living right
These are the new dark ages
And the world might end tonight

Now come ye children one and all – let’s heed Ezekiel’s call,
And bide until the word is good and ripe and get plucked clean out of sight

The world will be erased our kin will be
Immaculate ejaculate in space
Before the kind of king’s love, he’ll snatch us
From above, brothers help me sing it

Welcome to the new dark ages
I hope you’re living right
These are the new dark ages
And the world might end tonight

So how do you sleep
There’s nothing to keep
This is deep

Because we’re animals – with golden rules
Who… who can’t be moved by rational views

Welcome to the new dark ages
I hope you’re living right
Welcome to the new dark ages
And the world might end tonight

But I love music. I could talk about it hours. I love having a good-natured debate about it. I love sharing it with other people, exposing them to bands they’ve never heard of. Most of all, I love discovering new music. It is one of my true passions in life.

So I want to start a new feature on this blog, from the very beginning, because it will make me happy. And it’s my blog, so it’s my rules.

From now on, barring laziness or other acts of God, I will feature some band or song that I am currently enjoying in a feature called “Music Mondays.” I hope you enjoy the songs and bands that I share, because most likely I really like them. If you don’t, that’s cool, too. Taste in music, like any art, is a subjective thing.

By decree, this feature will begin today, starting immediately. Look for it in the next post.

/rant, and let the music begin.

When I tell people that I’m thinking of doing this, I often get a surprised reaction, like, “Wow, really?” The implication is almost, “Who on earth would want to do that? Wouldn’t that be a lot of work, and really hard?” Well, yes. It would take at least four or five years.

My short answer to the question of why is this: I find the idea of getting a PhD in finance intriguing, and I like a good challenge. This would certainly be a challenge.

Here is what I came up with for a long answer:

For ten years, I have been learning about the financial markets, particularly from the perspective of an investor and/or trader. I jumped into the stock market in 2000 when I was a freshman in college, at the very peak of the dot-com bubble, and I lost a lot of money (percentage of total assets-wise). I decided I better learn what I’m doing, and I’ve been learning ever since.

I started reading any book I could find on trading and investing. I switched my major from linguistics to business to economics, and I’m glad I did. I found economics to be fascinating, and it has led me to all kinds of other areas of study, including psychology, politics, behavioral finance, and philosophy. I was, and have been, captivated and fascinated by the financial markets.

All of this study, most of it self-directed and self-taught, has given me a pretty full, broad, deep, and intuitive (in my eyes, at least) understanding of the financial markets from the perspective of a trader, of a practitioner. My college experience of studying economics supplemented this understanding. Over the past year, I have further supplemented this understanding with a graduate study program that has included a lot of exposure to academic theory of finance.

So far the past year and into this year, I have looked at a lot of academic theory on finance. I also took to heart the ideas of Nassim Taleb, whom I will talk much more about in future posts, and who has been very critical of the same academic financial theories I have been learning about.

What do I mean when I talk about academic financial theory? The primary theory is the efficient market hypothesis, which basically states that no one can beat the market because the market fully reflects all available information. There are further refinements, including strong-form, semi-strong-form, and weak-form efficiency, but I won’t go into those distinctions. The implication is that you can’t beat the market, so don’t even try; just invest passively by going with an index such as the S&P 500.

I believe the efficient market hypothesis (EMH) is the primary and most important financial theory out there, but there are others. There is the random walk theory, which states that market price movements are random and not predictable in any way. There is the capital asset pricing model (CAPM), which states that return is directly related to risk and this relationship is characterized by something called beta, which reflects how a stock moves in relation to the overall market. There is the Black-Scholes Option Pricing Model, which uses things like the normal distribution to come up with a price for call and put options.

Please note that I haven’t yet studied these theories at the doctoral level, and my understanding of them is fairly informal and may be incomplete.

My current view of all these academic financial theories is that they are lacking and that they rely on many assumptions that do not hold up in the real world. They are important to understand because they cover a lot of important concepts in finance. But I think they are incomplete. And I think they can cause a lot of damage when relied upon too heavily, as the financial crisis of 2007-2008 would seem to indicate.

This view that I have developed plays into my desire to pursue a PhD in finance. Yes, over a period of four or five years (or more), I will have to delve into these theories and learn more about them than I care to admit. But I truly believe that I can develop a full understanding of them, including their positive aspects and their limitations. I am even bold enough to believe that I can improve upon them, either directly or by proposing an alternative theory.

As I have been thinking about the possibility of pursuing a PhD recently, I naturally gave some thought to what I would want to study, including possible dissertation topics. Some of the possibilities that have come to mind include the following:

• I believe that the structure of the market has changed in recent years, much more quickly and thoroughly than most people realize, and I believe this has important implications for all investors. Disparate markets are trading in lock-step (increased correlation between markets and between individual stocks), and this could have serious consequences. Potential reasons for this phenomenon include the increased use of exchange-traded funds (ETFs) and the predominance of high-frequency trading (HFT). All of these structural changes can have serious consequences, as the flash crash of May 6th, 2010 indicates. I would want to study these structural changes and hopefully improve people’s understanding so that they can safeguard themselves from potential dangers.
• I have been captivated by the ideas of Nassim Taleb, including his Black Swan Theory and his ideas of Mediocristan and Exstremistan. I really think Taleb is on to something, and I want to develop a fuller understanding of his ideas. He himself has a PhD, and has also worked as a Wall Street trader and hedge fund adviser. I know he has released some academic papers that have expounded on his theories, and I would want to study those and see if I could add anything.
• As a follow-up to the previous point on Taleb, I also want to look at Taleb’s answer to the problem of negative Black Swan events, namely his “barbell” strategy. Taleb believes that people have a poor understanding of the “middle” of available investments, meaning mid- and large-cap stocks. These stocks can be much more risky than people think, as indicated by the 40% decline during the recent financial crisis, and should therefore be avoided. Taleb’s advice is to invest the majority of your assets, from 70 to 90%, in “ultrasafe” investments like T-bills (although these are looking much less safe these day), and to invest the remainder in bets that are risky but have a huge potential payoff, such as out-of-the-money options or very-small-cap stocks. This will protect your assets while keeping you exposed to positive Black Swan events. Taleb has used this strategy to produce a huge return during the financial crisis, and I think it makes sense. I would want to conduct an academic study to see if this “barbell” strategy has merit and to see how it compares to more traditional investment strategies.

So these are the ideas that I have come up with for areas of future research, and may even lead to a possible dissertation topic. All of these ideas interest me, but part of me thinks they don’t go far enough. As I mentioned above, I believe that current academic financial theory falls short and can potentially be dangerous if relied upon too heavily. I want to shake things up a little. I want to propose something drastic and attention-grabbing, while still having merit and being defensible.

I love the maverick, the person who has no problem doing something unconventional or proposing an idea that no one has thought of before. As a strong proponent of the sanctity of the individual and a proud independent thinker, I would love to take that role as someone who wants to shake things up. Sometimes the status quo needs to be challenged.

So I wanted to come up with something that went farther. Last night, I had somewhat of an epiphany, and an idea came to me that I think may fit what I just talked about. As I said, the efficient market hypothesis seems to be the dominant financial theory out there, and I think it has its problems, and is incomplete at best.

I was thinking about what I thought was wrong with the EMH, and some things that came to mind include the idea of a “equilibrium” price and that the market can’t be beat. Maybe the market can be beat, at least sometimes. I think some hedge fund managers, like Jim Simons, George Soros, or Ken Griffin, would indicate that this is at least a possibility. So if the EMH is wrong, what is a possible idea that could do a better job of explaining how the markets work?

My contention is that market prices are driven solely by investors’ perceptions, their perceived true market value, which in aggregate determines the current market price. The idea of heterogeneous expectations is not enough. There’s too much that goes into making those expectations heterogeneous, including differences in models, frameworks, and assumptions used, investment horizons, investment styles, outlooks on the economy, the market, and individual stocks, views on what other market participants are doing, level of information available, and level of sophistication, among other things. All of these factor into an individual investor’s perception of what the true market value is. External factors also need to be considered, from market structure issues (think flash crash) to the regulatory and political environments. The effect that all of these factors have on the market price depends on the investor’s perception of them, as well as the investor’s perception of the perceptions of other investors, which I think creates a recursive feedback loop that needs to be examined. These types of feedback loops fascinate me, and I want to study them further.

All of this may seem pretty complicated, and it is. But I think it’s pretty representative of what actually happens in the market, and my hope is to develop a model that can somehow represent all this. I want to integrate all of my self-taught knowledge related to trading with any relevant academic theories, and synthesize the whole thing into a defensible and representative theory. Ambitious, I know, but what the hell. Fortune favors the bold.

There’s more to my new theory, but I don’t want to present it all here because it still needs to be fleshed out. I have no idea if any of this is feasible, but I’m going to pursue it until I find out one way or another. I’m excited by this idea, and I hope there’s something to it.

I realize that not many people are going to read this entire article, but I wrote it for my own purposes, to force myself to think all of this though, to flesh out the ideas, and to put it all on paper. All of this mostly just to help out my own sense of clarity around the issue. If you’ve made it this far, congratulations. You’ve just made it through 1,904 words related to my thinking about PhDs in finance, problems with modern academic financial theory, and possible solutions.