## The Wild Prologue

Semigroups are like groups but semigroup elements don’t always have inverses, necessarily.

Semigroups obey the associative law:

• a then b, then c       =       b then c, after a.

but not necessarily the commutative law (3+14=14+3). Aristotle observed that time obeys the associative law.

It is commonly agreed that time moves forward only and not backward. Not invertible means you can’t always undo what was done. (Both groups and semigroups can be noncommutative; order sometimes matters, like whether you put the couch down first or pour the concrete first.) So, John Rhodes says, we should model time with semigroups.

` `

Speaking in terms of sets and sequences, (a,b,c,d,e) is equivalent to (a, ab, abc, abcd, abcde). The two representations (let’s call them events and timelines) serve different functions mathematically but are isomorphic. With this identification in hand, Rhodes launches into a tornadic discussion of groups, commutative and noncommutative:

1. groups have fundamental constituent parts;
2. we have found all of them;
3. we know how they combine to form larger actions;
4. so we essentially know everything about every group;
5. and this bears on Life, The Universe, and Everything.

Rhodes co-invented the wreath product , which explains how to combine the fundamental units of semigroups into any semigroup at all.

` `

If semigroups represent all the logical options that anyone can do with anything, then the total classification of finite simple groups is an achievement with epic implications. It would mean a mathematical theory of all the things that can be done. “Do” and “thing”, that is breaking it down pretty much to the basics.

I read some of The Wild Book at a friend’s house a couple months ago (I haven’t bought a copy yet). Skimming throughout the text, it looks like a really fun read — jumping from abstract algebra to (mathematical) cellular automata to the Krebs cycle to religion.

` `

However, Rhodes draws some unwarranted conclusions, or otherwise demonstrates overly simplistic thinking.

• He equates “religion" with beliefs about the afterlife.

And he’s an Egyptologist or something?
• His example of a semigroup loses all knowledge right away rather than things being gradually more covert depending on ingenuity.
• Does the semigroup therefore model our understanding or the progress of the physical world?
• He says that scientific understanding is equivalent to the introduction of spacetime coordinates. Um, dissection & anatomy? Synthesis of urea? Germ hypothesis, periodic table, polio vaccine?

Also, by existence I think he means experience. Existence does not imply feedback.
• Just because there are many different “models” of time or space, doesn’t reduce the credibility of any religion. Unless the religion specifically stated “The body moves around in ³ forever — throughout time, which is ¹.” I can’t remember reading that in Scripture.
• And semigroups are supposed to be unpopular because they controvert religion? I assume it’s just because they’re abstruse.

Has it really been proven that information is lost when a person dies and is buried or cremated? The smoke from the funeral pyre is in a lower entropic state than the atoms of the nervous system were, but doesn’t the specific configuration parametrise the smoke which affects the wind and so on? Information may be chaotically scrambled but is that the same thing as lost?

` `

I’m not insulting what John Rhodes produced: a rare jewel that looks at scientific and philosophical questions through the lens of abstract algebra. These questions are meant to provoke further discussion of his ideas.

Utopia. Class struggle. Liberty. Tyranny. Property. Natural law. Human rights. Rousseau, Locke, Paine, Plato, Spinoza, The Federalist Papers, Marx, Rawles, and the rest. What is a “good” society and how can “we” make our society better?

For me there was a time (age 18) when these things seemed very important. I’m a socially minded guy, and political problems seem to always be f**king things up for people who don’t need their lives f**ked with. If you fancy yourself compassionate and intelligent, it’s natural to be drawn to political problems. For me it was an ego draw — the appeal of “doing good” with my mind.

After a while, though, I started to feel like I was going in circles, endless debates that seemed to dance around — but never solve — certain fundamental problems (and meanwhile Idi Amin killing his countrymen, Bosnians and Serbians tearing each other apart, etc). Schools of thought seemed to coalesce around personalities (not facts) and I felt this pursuit was going nowhere.

I wanted a way out…

## The Median Voter Theorem

Imagine 10,000 people were voting on which of 2 congressional candidates to elect. Each candidate is represented merely by a real number* which indicates liberal -vs- conservative. Once elected, the candidate implements policies robotically. “I am 23% liberal and 77% conservative, therefore I will do exactly what a 23% liberal would do.”

If voters have single-peaked, symmetrical preferences over the same real number* spectrum and everyone knows the formulas and figures involved, then there is only one Nash equilibrium strategy: run to the middle. Campaigning on a policy that pleases the median voter is the only Nash equilibrium and therefore what rational, winning politicians would do.

* or element of any measurable space, like a sig-algebra

Interpretation

This result is niche famous. People whose friend took a game theory class in college might have heard a version of this as a “proof” that the 2-party system is better or more centrist than multi-party systems.

I’m telling the more mathematical version because, when “popular accounts” try to relate an important result like the median voter theorem while taking the math out, they end up making no sense or accidentally lying.

I ain’t gonna talk down to you. You’re smart enough to look up what a Nash equilibrium is. And you can decide for yourself what it means if a mathematical model sounds somewhat like human reality but isn’t exactly like it.

The median voter theorem doesn’t say that 2-party systems are better, it suggests something — or maybe it doesn’t. It’s just a piece of math that may be relevant to real life, may serve as a mental model, may serve as a basis for intuition, or … may be misleading.

## "Political Philosophy" from a different perspective

The Median Voter Theorem naturally brings up questions — questions that you wouldn’t think of if you framed your thinking in response to Rousseau, Locke, and other famous writers.

• Are these preferences symmetric?
• Are these preferences 1-dimensional?
• Are these preferences stable over time?
• Do these preferences map onto the real numbers? (or something isomorphic to R)
• Are these preferences single-peaked?
• Are these preferences symmetrical?
• Can you represent a congressional representative’s behaviour in office by a single number?
• What about after they’re elected? Won’t they deviate from what they said they would do?
• What about party politics? Won’t the party whips keep them in line?
• Back to the voters; what if the politicians don’t know what they want?

(This last point turns out to be very important in Persson & Tabellini’s theory, which explains that George W. Bush could be re-elected not because the hateful simpletons who voted for him were numerous, but because they are predictable.)

More sophisticated would be to ask: “to what degree or in what ways / cases are the above things true or false?” And those questions tend to be more answerable.

Other kinds of questions you might want to add to the mathematical framework begun here:

• Is this in just one district? How do inter-district politics factor in?
• What about fact X about Country A's constitution vis-a-vis Country B's constitution?
• What about cultural fact Y? How could we take account of that mathematically?

I could go on and on, and in fact many people have. I think this is how fields of research get started. This one is called “spatial voting theory”.

But this is ridiculous. People are not one-dimensional.

One surprising result, due to Rosenthal & Poole, about the unidimensionality question, is that — yes! — politicians are pretty well represented as just a number on a one-dimensional scale — like maybe 85% of their votes can be characterized this way.

Also surprising. Judges are even more unidimensional than politicians. However, voters are decidedly not uni-dimensional.

Not what I would have assumed, although I can make up a story to “explain” these findings post hoc. Actually I could make up lots of different stories and am just left with more questions. But. At least I’ve moved outside of the narrative of political philosophy handed down to me in college.

## Wrap Up

• politics = relevant  +  math = logical
• application of math to something more interesting than bridge engineering
• sorry engineers, but all the engineering in the world isn’t going to solve global poverty — that’s a political problem
• and it would be sweet if logical thinking could lead to an optimal constitution (if such a thing exists).

• didn’t know enough math at the time I read it to think deeply or broadly about what they were saying
• as far as I know, no practical applications (yet)

Too long, didn’t read: Variations on a theme, the theme being the Median Voter Theorem. Game theory leads to a framework for political analysis called “spatial voting theory” which is alternative to the “pure-humanities” approach from my college political philosophy courses.

hi-res

## Vector fields

Vector fields pervade. I think about them every time I throw a frisbee in wind.

In a social context, I think about vectors of intent attached to people talking at a party — vectors of flirtation, vectors of eye movement and attention, and more abstract vectors representing jokes, topics of discussion, dance moves, or songs that are playing.

Also when I’m thinking about international trade or just the local flows of money in my community, it’s natural to use the vector-field metaphor to “see” the flows.

I also think of history (at different scales) using vector fields. Wars are like nation-states or soldiers aiming weapon vectors at each other. Commerce has many more dimensions since goods and money are both multi-dimensional. Ideas and culture also transmit in a vector-field-like way. Epidemics — well, there’s a reason mosquitoes are referred to as disease vectors.

Information flows, thoughts, internet bits — anything that can be characterised as a vector, you can expand that thought into a more complicated vector-field thought. Turbulent versus laminar flows of ideas and culture? Maybe it wouldn’t deserve a research grant but it’s fun to think about.

There are pretty obvious physical examples of vector fields — rivers, wind, geological eroding forces, magnetism, gravity, flying machines, bridge engineering, parachute design, weather patterns, your entire body as it does martial arts or dances. Being measurable, these are the source of most of the neat vector-field pictures you can find online.

(Or you find programmatically simple theoretical vector fields like the above: a vector facing [−y,x] is attached to every point (x,y). So for instance the point (3,4) has a pointer going out −4 south and 3 east, which equals a total force of 5.)

The same metaphors and visualisations, though, are open to interpretation as social or economic variables too. For example a profitable business is more of a “sink” or attractor for 1-D money flows, while a benefactor is a “source”. Likewise a blog that receives lots of links and traffic is a 2-D attractor on the graph of the web — and Google recognises that as PageRank.

I know of at least one paper that tries to best economists’ utility theory models by imagining a person on a 1-D vector field, trying to avoid minus signs and find a path to plus signs in the space.

There is also a game theory connection. Basins of attraction can draw you into a locally optimal place that is not globally optimal. You can imagine examples in the evolution of animals, in company policies or business practices, or in whole economic systems.

On the one hand it may seem frivolous or crackpottical to generalise these concrete physical concepts to the social or psychological. On the other hand — that’s the power of the generality of mathematics!

Vector fields are surfaces or spaces with a vector at each point. That’s the mathematical definition.

The radiolab story “It’s Alive” made vivid the claim of Geoffrey West and Luis Bettencourt that a city’s size determines how fast people walk in that city.

West & Bettencourt have written that people earn more in large cities, waste less, file more patents, and commit more crimes — and that city size is the main determinant of all these things.

The charming Cosma Shalizi has recently published a 15-page paper that rebuts them. From the abstract:

Re-analysis of the gross economic production and personal income for cities in the United States, however, shows that the data cannot distinguish between power laws and other functional forms … and that size predicts relatively little of the variation between cities.

The striking appearance of scaling in previous work is largely artifact of using extensive quantities (city-wide totals) rather than intensive ones (per-capita rates).

(Sorry if that’s hard to read. Horizontal axis = log( city population ). Vertical axis = pedestrian speed in m/s, give or take a standard dev. Solid & dashed lines are two fits proposed by Bettencourt & West.

## Do-It-Yourself MFE

or, The Reading List That Will Make You Rich.

What follows is very much a field report of one particular DIY Masters in Financial Engineering. That brings drawbacks (like idiosyncrasy and personal narrative) — and advantages (I’ve actually read the stuff I’m going to tell you about). The report is half why-I-didn’t-get-an-MFE and half what-I-did-instead.

Like a good postmodern, I’ll just present the story and let you make up your own mind.

### DON’T SMART PEOPLE GO TO GRADUATE SCHOOL?

When I took a graduate-level economics class (optimal control) in my final year of school, I noticed a few things:

(a) the deeper the math, the worse the professor
(b) nobody in my class really understood the lectures
(c) my favorite math professor (who was teaching himself molecular biology at the time) said he never went to class, he just taught himself from textbooks
(d) at least half of my classmates were in graduate school to avoid the real world

and most important, to me:
(e) classes and exams after age 22 were grinding the creativity out of all those who had it to start with.

All of my own ideas, too, smelled like a sausage-grinder that puréed together fuzzy logic, equilibrium / optimization models, and vector calculus with whatever talk I had most recently gone to. Fuzzy lexical preference orderings in convex optimization" actually sounded like a good idea to me, I sh*t you not. Also, the meat-grinder never gets cleaned. (because I never went anywhere without a book in hand or an idea in my head).

WHY SHOULD I PAY FOR THAT?

I said to myself:

"I don’t learn much in lecture. I could do just as well by getting course syllabi from the Internet and reading the books myself."

And that is what I did.

### TYPICAL MFE COURSEWORK

Here is a typical course list for a money mint, I mean MFE program.

0. ‘Remedial’ math
1. Probability theory / stochastic processes
2. Numerical methods; Finite element method and Monte Carlo
3. Time series
4. Functional analysis
5. VAR, cVAR, CAPM, Greeks
6. The Heat Equation a.k.a. Black Scholes Parabolic PDE
7. Programming
8. Financial stuff like defining what various product areas are. If you DIY you can focus on the area you want to do.
9. Meeting practitioners.
Well DIY really can’t do that, so (9) might be a reason to enrol in a course. Maybe if you live in NYC or London you can show up at some parties and act like you belong. "My name is Paul Allen" kind of thing.

AUTODIDACTISM

We live in the age of the Internet. That means free sh^t. Not even counting the open-source educational efforts by tip-top universities like MIT, Yale, and Stanford, there are 𝓞(1 bazillion) papers on xxx.lanl.gov. If you want to be on the cutting edge of machine learning, numerical methods, or time series analysis, you should be reading preprints, not textbooks.

If I can’t teach these things to myself, it’s because ultimately I lack either the interest or the aptitude. In both cases, I’ll be better off finding that out BEFORE spending two years of my life and \$100,000, rather than after.

HUMILITY

Yet another reason to self-educate is that fresh graduates are always over-confident in the power of their mathematical methods.

Emanuel Derman asks MFE graduates why they believe they can get a price for a particular security and (lamentably) they answer, “Girsanov’s theorem.”

Mark Joshi’s “So you want to be a quant?” also says that fresh graduates usually propose a needlessly complicated math solution rather than use common sense, better evidence/research, or a quick, satisfactory math solution. And Sylvain Raines notes that quants who bring up matrices during sales talks are more likely to close doors than to close deals.

Finally — here is something I’ve never understood about the putative value of an MFE. So you’re trying to get a job where you face the market everyday and disagree with it. In other words you have to think for yourself, think differently, and come to a different conclusion than the average bettor. But you pay someone to indoctrinate you with exactly the same methods and formulae that all of your competitors are using. Then you expect to come to not just a different conclusion, but a market-beating conclusion?

That just sounds dumb.

### AUTOEPISKEPSIS

I’m not just skeptical of graduate school, I’m also skeptical of my own skepticism of graduate school. So I did actually talk to admissions staff at MFE programs and the Wilmott CQF people.

I even applied to the CQF and took their test. It was hard enough to make you feel smart for knowing that the third moment of a distribution is its skewness, but easy enough that many many people could pass and win the prize of paying \$23,000 to 7city Learning.

### ANSWER MY QUESTION BEFORE I FORK OVER 100 G’s

Whenever I pressed admissions staff for actual data on the earnings of graduates, they demurred.

My criterion was that the lowest decile of graduates should be using their degree (directly) and earning a salary that would justify the time and money expense of the degree. In other words I wanted a guarantee that paying \$150k would get me an interesting, high-paying job with excellent growth prospects. But I was met with (a) excuses / obfuscation, (b) possibly massaged figures, and (c) questions as to whether I was in fact smart enough for the program.

My conclusion is that there are enough gullible people with physics degrees, that the admissions staff don’t really have to work hard to fill the ranks. Just design good flyers and website, and let the tao-of-not-selling do your selling for you.

Maybe I’m wrong and everybody from the MFE programs I talked to does really well. Baruch College actually brags about its 88% placement rate, as if that’s a good number when you’re forking over several years’ salary for the purchase of more work.

If the MFE is legit, then it was a good trade and I missed the opportunity. I’m preparing for a career characterized by missed opportunities. But learning from Jesse Livermore, I’m not going to make that trade unless I’m confident; the evidence does not make me confident. I can see how the sellers of the degree will make money, but not how the buyers will.

BOOKS, BOOKS, BOOKS

OK, here is what you probably came here for. Not narrative but data. The reading list that will make you rich.

Here’s the course I assembled for myself, as well as what I learned. I have read part or all of the following works.

MATH

• Ito Calculus at MIT. Rigorous. Necessary.
• Exploratory & Robust Data Analysis. Robust data analysis is the sh*t. Just ask yourself, would your method of analysis break if just one of the data you feed into the computer had an extra digit at the front? If the answer is yes, check yourself before you wreck yourself.
• Gilbert Strang, Advanced Calculus for Engineers. These are some fun videos aimed at working engineers. You can brush up on linear algebra and differential equations by learning something new about them, while also picking up some numerical methods. Have you noticed how many job postings require Finite Elements Method? Bonus: the calculus of variations is how your computer solves an OLS regression. You probably want to understand that.
• John Kruschke, Bayesian Data Analysis. Well, you’ve gotta keep your mind open and not be bound to least-squares land. Everyone has to leave the Shire at one time or another. Kruschke’s book is aimed at lab scientists but he teaches you to Actually Do Bayesian Data Analysis, using R and BUGS. He also lambastes p-values quite heavily.
• Angrist & Pischke. Now that you’re doubting everything you ever learned in econometrics class, it’s time for some reassurance. Things you can legitimately, robustly conclude from your regressions.
• Time Series by John Cochrane. This is written for MBA students so it’s quite easy to read. Lays out basic time series analysis in plain English.
• Cosma Shalizi, Intro to Complex Systems Science. Shalizi draws parallels between machine learning, statistical mechanics, and econometrics. It’s not his best work stylistically but Cosma is still a charmer. He also covers overfitting, V-C dimension, penalization.
• Nonlinear Dynamics and Chaos. MIT OCW. It’s about weather but we all know the similarities between meteorology and economics. Useful. And if the finance thing doesn’t pan out, maybe I can try fluid dynamics. (I also read a geophysics text from MIT OCW … same story, I want to keep the petro options open. Maybe I’ll trade oil futures and have an understanding of geology as well as finance.)
• Terence Tao, Functional Analysis. Short and good.
• Ed Leamer, Let’s Take the Con Out of Econometrics. Classic, just plain fun. There is lots of good Ed Leamer stuff to find while you visit.
• Brad Osgood, Fourier Analysis. The signal processing perspective is not really valid for financial data in my opinion, but it’s good to see the same mathematical object analyzed from a totally different perspective. Also you’ll get a better sense of generalized functions and along with that come tools for manipulating probability distributions and MGF’s.
• Roger Penrose, The Road to Reality. Even though this is a physics book, it’s a great reference to give you the basics on a mathematical object. Also a handy, short calculus review.
• Solid Shape by Jan Koenderink. Just to get a little deeper into algebra and geometry, a.k.a. Wisdom, and give yourself a break from the diff eq’s.
• Wikipedia. I like Wikipedia better than Mathworld because they use simpler language, especially with algebraic geometry (and when they don’t I change it). It’s the right level of depth for non-mathematicians. Also, academics frequently promote themselves on Wikipedia via links to relevant papers, for example look at the nodes around “Chirplets”. Wikipedia hunts can get too broad though, so it’s important to close the laptop from time to time and look at physical paper (books, printouts) to get the depth.

FINANCE

• Liar’s Poker. Don’t read it, it’s merely OK.
• When Genius Failed. Don’t read it, I have no idea why anybody recommends this except they must not have read it themselves.
• Black Swan. Also not really necessary. It’s just a trendy book. Do you want to think like everybody else?
• My Life As A Quant. I didn’t read this and I’m not going to. The very existence of this book is what made me doubt that an MFE would get me anywhere (it signifies that many math people must try to enter Wall Street and make millions with their smarts).
• Commodities and Commodity Derivatives by Helyette Geman. Covers weather, oil, nat gas, electricity, emissions, and precious metals. Nassim Taleb’s thesis advisor opens with a volley of Black-Scholes theory for mean-reverting processes and then she hands it off to some real traders. Also covers real options theory (just think about that jargon for a second).
• Beat the Forex Dealer by Agustin Silvani. I got the feel of a modern trader’s mindset from this. I don’t know if the trading ideas still work but the KINDS of trading ideas he puts forward gave me a realistic idea of what kinds of trades to look for. As the title suggests, some of the trades are for retail forex traders to screw over their dealers. He aims to be half-academic and half-practical.
• Volatility Trading by Euan Sinclair. Just started this. It’s decent so far. Volatility trading seems like a good thing to be aware of in cross-asset strategies or even if you’re just looking to shield your strategy from cross-asset destruction.
• Robust Portfolio Optimization and Management. Really easy math and it actually takes taxes and trading costs into account. It’s “robust” in the sense I outlined above for Robust Statistics. That’s very good. This was the best portfolio management book out of several from the nearby university’s library. Also Frank Fabozzi is the guy who puts his imprimatur on all the fixed income stuff so if you’re into fixed income that’s another reason to read this.
• Beyond the J Curve. You don’t really need this but I read it because I used to work in venture capital.
• Financial Economics course by Bob Shiller. Easy introduction to dealers, bankers, brokers, shorts, futures, options, etc. Includes interviews with Andrew Redleaf, Carl Icahn, and Steve Schwartzmann. (!)
• New York Supreme Court Case no. 603839/03. Renaissance Technologies Corporation versus Millennium Partners, LP (Pavel Volfbeyn and Alexander Belopolsky, Defendants). In the spirit of Reminiscences, some real-life gunfire to complement the academic stuff.
• Blogs by traders, stat arbs, chartists, more. These are your opponents and if they choose to mouth off their thought process then that will only help you predict their trading choices. Plus you can get plain old useful info like practical considerations that traders actually think about.
• Wilmott Magazine. Kent Osgood’s articles on “Iceberg Risk”.
• Wilmott Magazine. “A Quant in King Arthur’s Court.”
Reading Wilmott magazine isn’t necessary. I just enjoyed the sense that I was reading the same thing stuff as real, paid quants.
• Algorithmic Trader magazine. Same deal.
• Janet Tavakoli. Get the skinny on synthetic CDO’s from someone who structured them. Didn’t go to school for finance (so not doctrinaire).
• Benjamin Graham. Warren Buffett and a handful of other investors have become billionaires by following Benjamin Graham’s method over their lifetimes. Charlie Munger <link> says that the techniques they used are no longer valid but you can get an idea of how these guys picked winners from the public market. Very anti-EMH stance. If you decide to play equities this is one school of thought of your opponents.
• Andrew Lo. A non-random walk down Wall Street. Just perused this bad boy. It’s very academic, by which I mean it addresses the Efficient Markets Hypothesis all the time and is clearly written by a statistician rather than a trader. His trading ideas have the flavor of Applied Quantitative Research — statistical anomalies.
• Wikipedia is so-so for finance. You can find out some dubious or some comprehensive details. Usually not very in depth but it can be. Compare article on the CME to the list of S&P 500 companies.

My financial reading list is really personal to my interests. For example I’m intrigued by commodities just because it’s associated with the salt-of-the-earth. Volatility trading seems like a good thing to mix with cross-asset arbitrage strategies.

PROGRAMMING

• C++ Design Patterns for Derivatives Pricing by Mark Joshi (comes with a forum where Joshi responds quickly and helpfully to reader questions)
• reddit.com/r/CarlHProgramming is a good introduction to C and then … you’ll need something else for the object-oriented features of C++ and I don’t have a good recommendation
• Bearcave. This goes more under finance but this is the story of a programmer who took the signal + noise view of the market, thought he could use wavelets to pull out the noise, and ultimately failed. Good story.
• Wikipedia is not a really good source for a beginning programmer. You can skim and find out what a term means, but not find tutorials and often the language is too technical. Remember that Wikipedia is made and maintained by geeks.

Plus I’ve done lots of googling and read various library sources (none really superb) on the following topics:

• Bash / shell scripting
• R
• another programming language if you feel like going there. Python and VBA seem to be popular but who really knows. Jason Victor Dartmouth wrote a trading software that you can program in Ruby. You can interface R with iBrokers now. No right answers as far as I can tell.

"REMEDIAL"
If you didn’t major in math, maybe you can get what you want out of two lecture series from MIT:

• Arthur Mattuck, Ordinary Differential Equations
• Gilbert Strang, Linear Algebra

and a statistics course. You can get notes to my econometrics class (Bill Becker’s) at indiana.edu/~e471.

Two good, difficult books that cover the calculus-and-linear-algebra combo that marks the beginning of erudition in mathematics, are:

• Advanced Calculus by C H Edwards
• Calculus 2: Linear and Nonlinear Functions by Flanerty and Kazdan

If you get more curious about complex numbers in the process, read Tristan Needham’s “Visual Complex Analysis”.

The above list is not a comprehensive list of everything that I read in my DIY MFE. You will no doubt stumble across things that interest you and those will give you a different background than me and everybody else. Just wait until my strategy kills yours because I read a paper on a Lp metric that takes into account the sequential nature of time series.

And, why am I calling it The Reading List That Will Make You Rich? I’m poking fun at myself. I have this stupid belief, not explicitly stated, but that if I simply learn these things, that I will get a high-paying job.

Other materials that I haven’t read but want to:

• Paul Wilmott on Quantitative Finance I, II, III
• L C Evans, Partial Differential Equations
• L C Evans, Stochastic Differential Equations lecture notes
• Evidence-based Technical Analysis
• Elements of Statistical Learning
• Strogatz. Nonlinear Dynamics and Chaos.
• A.W. van de Vaart. Time Series.
• J P May. A concise course in algebraic topology.
• Master the Markets by Tom Williams of TradeGuider Systems.
It’s not easy to distinguish validity of a trading technique simply by the pedigree of the person who writes it. I read stuff outside of the approved sphere to get a different perspective. Also, how is a quant supposed to model real traders if the quant only reads quant books by quants, for quants? The Turtle Traders book is another book that exemplifies the way non-quant traders think. Do I need to say this? You have to be able to predict what non-quants will do for your algo to beat them.
• El Aleph por Jorge Luis Borges, in the original Spanish.
• Random Walks and Diffusion. MIT OCW
• Intro to Numerical Methods. MIT OCW
• Infinite Random Matrix Theory. MIT OCW
• Wavelets, filter banks, and applications. MIT OCW
• Statistical Learning Theory, MIT OCW
• Nonparametric statistics, MIT OCW
• Several books on the Theory of Distributions
• Several books on Wavelets
• Several books on Machine Learning
• Andrew Ng lectures on machine learning AcademicEarth.org
• Intro to Python on AcademicEarth.org
• Danny Duffy programming book
• dbphoenix’s epic post on EliteTrader
• The Volatility Surface
• Iceberg Risk
• The Blank Swan

WHAT EMPLOYERS SAY THEY WANT

Of course you need to meet people to actually get a job, but you can do that without paying \$150k for a masters degree, if you’re clever and personable. I got into an SPSS conference this fall by saying that my company was considering buying SPSS software. Then I met a bunch of statisticians. Just one example.

Anyway you will find similar book lists as the above coursework if you look at, e.g., DRW’s careers page or google for various quant reading lists.

Some employers are only interested in math / CS PhD’s, or more specifically people with a numerical methods background. That’s another reason to be skeptical about the value of an MFE.

The best reason to be skeptical of its value, though, is that as much money as was made by mathematicians in the markets over the last 20 years, the career opportunity may have been gone as soon as Emanuel Derman’s book hit the shelves.

WHAT INSIDERS SAY ABOUT THE JOBS MARKET

To quote a founding member of NuclearPhynance:

the job market is competitive and tight at the junior level and almost non-existent at the senior level compared to several years ago, likely to not return anytime soon. The quality people are staying put / being retained and the less-than-quality people are free and exponentially increasing their linkedin connections. Think long and hard about why you really want to move to this space.

WHAT OUTSIDERS SAY ABOUT THE JOBS MARKET

To paraphrase some random guy on /r/physics:

If you’re good at math, companies will hire you and teach you all the finance stuff.

Actually that is a paraphrase of literally quadrillions of people who have never traded or even thought much about finance. Quant-fin is just some stuff that’s trivial for mathematicians and physicists, but if they sink so low as to want to earn tens of millions of dollars per year, the money is there for the taking.

Yeah, right.

If you think I’ve missed something, leave a comment with book or paper title, a link to it, and your justification for why we should read it. If I agree with you I’ll add it to the list. If I disagree I’ll just taunt you in the comments.

YO, PEOPLE WHO ARE CRITICIZING ME

1. I am not claiming that this book list is good or complete. It’s just what I have read.
2. I don’t know for sure that the M.F.E. is a ripoff. But would you bet on a security with the payoff characteristics of these degrees? It’s just too risky.
3. I am not claiming that what I did was the right thing to do. It’s just what I did and therefore what I can talk about.

UPDATE

I now believe that programming know-how is much more important than mathematical erudition or familiarity with quant models. The job postings I have seen have all been for computer scientists, numerical programmers, people who can speed up existing strategies or at least program their own ideas.

I also found it worthwhile to do some paper trading. (I used ThinkOrSwim because iBrokers requires \$10k minimum to use the system for fake trading or otherwise. ToS / TD Ameritrade lets you play around in the past.) The job I’m shooting for is research rather than trading, but I found it too easy to get lost in theory-land by reading paper after book after course notes. The Greeks, basic combinations of options, spreads, “psychology” or “emotions”, are much more meaningful after feeling the market whip my fake \$100,000 up and down. Theoryspace is a probabilistic realm; live markets (even live past markets) are an actual realisation.

Also, it makes sense that jobs on the buy-side will want to see positive results of successful strategies that worked in the real world, not just GPA’s and theses. (Paper trading falls short here but is better than theory.)

UPDATE 2

Here’s the job requirements list for one “quantitative strategist” job (at Tradeworx). From what I’ve seen this is typical:

• PhD maths/physics/ee/econ/finance/and so on
• knowledge of machine learning
• knowledge of unix / linux / bsd
• c/c++ stl and, ideally, two of the following languages: python, bash, awk, tcl/tk, perl
• interpersonal skills
• experience in finance is not required

(Source: nuclearphynance.com)

## Circles

A circle is made up of points equidistant from the center. But what does “equidistant” mean? Measuring distance implies a value judgment — for example, that moving to the left is just the same as moving to the right, moving forward is just as hard as moving back.

But what if you’re on a hill? Then the amount of force to go uphill is different than the amount to go downhill. If you drew a picture of all the points you could reach with a fixed amount of work (equiforce or equiwork or equi-effort curve) then it would look different — slanted, tilted, bowed — but still be “even” in the same sense that a circle is.

Here’re some brain-wrinkling pictures of “circles”, under different L_p metrics:

p = ⅔

The subadditive “triangle inequality” A→B→C > A→C no longer holds when p<1.

p = 4

p
= ½
. (Think about a Poincaré disk to see how these pointy astroids can be “circles”.)
p = 3/2

The moves available to a knight ♘ ♞ in chess are a circle under L1 metric over a discrete 2-D space.

## Half a Year of Blogging

I’ve been writing for half a year now. It’s been an instructive and fulfilling experience. I’m a little better than I was in June.

Writing is hard. Not being pedantic writing about math is hard. Concision is hard.

Here are some of the posts I’m proud of:

I think I have a few more original posts in me. I’ve been surprised to see how "big ideas" that were taking up a lot of space in my head, don’t look that big written out.

Well, I didn’t think this book was that funny. It was interesting to peep inside Salomon Smith Barney as bond trading was becoming lucrative. John Gutfreund was the first of many to take his firm public

• to the dismay of the partners he took it over from;
• to his vast personal gain;
• to begin an era of rapacity in finance, according to Michael Lewis.

What is funny, is how many people, instead of hearing Lewis’ message, take away: "Wow, cool! Those guys got sooo rich.”

The guy who recommended this book to me also told me to read The 48 Laws of Power and watch Boiler Room.  Same deal with Boiler Room; it’s a movie about young guys who don’t understand the movie Wall Street, that the “Greed is good” monologue is a villain’s perspective speech.

To paraphrase Michael Lewis’ own summary of Liar’s Poker: “Hey! I was wet behind the ears! An art history major, for goodness’ sake. This business was dysfunctional, even fraudulent; and my co-workers were pathological.”

hi-res

So is it going to happen again? Another crippling financial maelstrom, I mean.

I guess we haven’t yet reached the period of complacency that was said would follow the “subprime crisis” or the “financial mess” or whatever you want to call it. People are still angry at bankers. But the news yaps less about finance than it did 1 or 2 years ago.

Anyway, the US stock market has been up and down—but more uppish for about two years now:

Everybody said during the heat of the crisis that “the real problem” was not necessarily this moment — but would depend upon vigilance enduring for years.

Well, have people forgotten about the bonuses? the leverage? the national debt? the foreclosed homes? the bailouts?

Part of me says no, but I do sense a waning in American anger.

Let me quote from the Amazon Preview of The Big Short, which is all I read:

What’s strange … is that pretty much all the people from both sides of the gamble left the table rich. … Wing Chau’s CDO business went bust, but he, too, left with millions of dollars … he had lost billions of dollars of other people’s money.  Howie Hubler lost more money than any trader in the history of Wall Street—and yet he [kept] the tens of millions of dollars he had made. The CEO’s of every major Wall Street firm were also on the wrong side of the gamble. All of them, without exception, either ran their public corporations into bankruptcy or were saved from bankruptcy by the United States government. They all got rich, too.

What are the odds that people will make smart decisions if they don’t need to make smart decisions—if they can get rich making dumb decisions? The incentives on Wall Street were all wrong; they’re still all wrong.

So there you have it. EconTalk said all along that we should have let the baddies fail, eat the pain, and then it wouldn’t happen again. The news was talking about Goldman’s congressional hearings a few months ago. That seemed related to the incentive to rip one’s customers off. And there was definitely a furore. But that happened after the ‘87 crash too. And there was enough public interest in the LTCM disaster to justify books and articles. But still the incentives didn’t change. And according to Lewis’ book, they still haven’t changed.

Other themes of the book:

• partnerships bet with their own money; corporations bet with other people’s money
• stock analysts are expected to lie or at least find a muted way to say “Your company sucks”

hi-res

### Volatility

Volatility, in finance, refers to the wiggliness of the time series. You observe the price of a security go up and down over time. If it changes a lot, that’s high vol: unstable, unpredictable. If it changes only a little, that’s low vol: stable, consistent.

There are many ways to define volatility, just as there are different ways to measure distance. Portfolio variation should be measured with a quasimetric (unidirectional metric).

But for all those definitions, it should mean roughly: the magnitude of change in the price, during some time interval.

hi-res