|
|
Sort of a bad title, but here are the stages, courses, and best textbooks that I find are necessary to advance oneself through the world of finance. Mastery of a stage can be assumed by passing certain standardized tests or through the more obvious path of passing the class in school. Standardized tests have the advantage of being uniform where academic standards can be different between schools or professors, while school or work provides a better structure to prove your competence or find a niche. Most university curricula are centered around pushing students through each level in a year or so. Students are expected to develop their learning capacity and discipline so as to accommodate the more difficult and larger workloads that higher levels require.
This is really just for me to create a structure for myself and hopefully lay the groundwork for a neat tree diagram which will make my goals clearer. It borrows heavily from a guide to being a pure mathematician, Amazon, and a variety of other sources on Google. I’ll use the level system to provide a basis for difficulty. Level E is fresh out of high school level, going up to A, which would be doctorate level. There will also be level S for those extraordinarily difficult subjects that are unnecessary unless you’re a masochist, an inventor, or a fraud.
Level E/D – Elementary stuff: calculus, probability, economics
This is for the intro level courses where professors are correcting bad habits learned from high school, where reasoning was usually just a lot of hand-waving and magic. For most students, this means taking a modestly formal class that teaches complex numbers, systems of equations, limits, delta-epsilon proofs, exponential functions, independence, conditional probability, expectation, and the basics of supply and demand. For people who want to learn programming, discrete math will lay the foundation for logical thinking. Learning these topics is crucial later on – gaps in knowledge about calculus or probability will really hurt when the math gets much heavier.
Standardized tests: SAT, AP exams
Spivak – Calculus (probably the best and most rigorous book out there)
Stewart – Calculus: Early Transcendentals (the standard with pretty pictures and lots of problems, but not the most rigorous mathematically)
Hardy – A Course of Pure Mathematics (if you really want to sharpen your logical skills)
Anton and Rorres – Linear Algebra with Applications (first few chapters)
Chung – Elementary Probability Theory (the best, although Ross is also good)
Mankiw – Principles of Economics (good standard text, but lots are pretty good)
Halmos – Naive Set Theory (very difficult but good for proofs and set theory)
Graham, Knuth, and Patashnik – Concrete Mathematics: A Foundation for Computer Science
Level C – Beginning the Education: linear algebra, multivariable calculus, statistics, micro/macro-economics
Most universities structure their math requirements to encourage students to choose their specialty, but this allows them to neglect portions that may be important. A balance should be struck between finding one’s strengths to choose a major and building a proper foundation for higher education. This is the area that is most dangerous, because a lot of authors and professors like to go back to the bad habit of hand-waving rather than making students take the difficult transition to rigorous and formal thinking. If you got the books from Level E that I suggested, most of them are good enough to carry you through here too. Topics to focus on are vectors, linear transformations, matrix algebra, orthogonality, double/triple integrals, Green’s theorem, Fourier series, basic hypothesis testing, distributions, maximum likelihood estimators, marginal cost/revenue/benefit, market structure, business cycles, and exchange rates.
If you’re programming (and sooner or later you’ll have to learn this), you should be learning how to use Excel, Access, and maybe a programming language; you should be able to know what programs and components are good and bad for your computer and how to fix minor problems.
Standardized tests: real estate exams, GRE/GMAT (math portion)
Apostol – Calculus Vol 2 (very dry and technical, but very good – better than Stewart, which will get you here too)
Boyce and DiPrima – Elementary Differential Equations and Boundary Value Problems (the standard text along with Anton and Rorres)
Freedman, Pisani, and Purves – Statistics (excellent overview of all topics in probability and statistics)
Ott and Longnecker – Statistical Methods and Data Analysis (good overview of statistics with a hands-on approach)
Ross – A First Course in Probability (pushes you farther than Chung)
Varian – Microeconomics (not the most intense but the best conceptually)
Mas-Colell – Microeconomic Theory (the most intense, for serious economists only)
Mankiw – Macroeconomics (the easiest to read and understand)
Level B – Mature education: analysis, statistical inference/computing, finance, accounting
This is it. The honest start of your education. Don’t expect “plug and chug” to work any more, because you have to know what you’re doing and why. This is an intense part of the field, because finance and accounting involve cramming a LOT of stuff into your brain. At this point, authors will often skip steps and calculations with the dreaded note “trivial proof left to reader”. It sounds mean but the serious student will spend the time understanding why it’s trivial by filling in the gap. It is a tool that will serve well later on when presented with new ideas, which must be critically regarded. If you have been, you should stop being impressed with resumes and school names, because you do not want to be brow-beaten into beliefs just because someone from Harvard treats you like an idiot. If their ideas don’t flow logically, then you should learn to identify it and point it out. Mastering this level would provide a strong foundation for graduate school and most likely marks the end of an undergraduate career. Topics covered are metric spaces, compactness, measure theory, Markov chains, parametric and non-parametric tests, time value of money, financial ratios, capital budgeting, managerial decisions, and derivative products.
On the programming side, you should know how to build and maintain a network, how the internet works, and feel comfortable with a programming language and/or software packages such as R. You want to be very strong at C++, Java, Matlab, or R. Don’t spread yourself thin learning a little bit about all of them.
Standardized tests: CMA (first 2 levels), Actuarial exams P and FM, Series 7
Ross – Introduction to Probability Models (a more thorough version of his other book, esp. introducing stochastic processes)
Rice – Mathematical Statistics and Data Analysis (lots of good illustrations and lots of gaps in proofs – if you do not have a good grounding in statistics, you will get hammered)
DeGroot and Schervish – Probability and Statistics (detailed explanations and points out common misconceptions)
Rudin – Principles of Mathematical Analysis (Baby Rudin, but still not for the faint of heart)
Brealey – Principles of Corporate Finance (a Bible in the field for MBAs and finance students)
Hull – Options, Futures and Derivatives (a common text, weak on math but a good introduction to derivatives)
Joshi – Concepts and Practice of Mathematical Finance (best intro book out there)
Horngren and Harrison – Accounting (another great intro book, but this is a wide open field)
Garrison, Noreen, and Brewer – Managerial Accounting (best budgeting text out there)
Level A – Grad school/Pro: regression, time series, martingales, modeling
These are the bread and butter tools that analysts and bankers use to make financial decisions. It can be mathematically rigorous but the real skill is to turn these advanced concepts into readable facts by the average person or more importantly, convenient packets of numbers for accounting purposes. These are extremely powerful in the right hands, as can be seen with examples like Enron and the housing bust, and if you didn’t follow my advice before about being impressed with resumes, it’s easy to be convinced that what you’re doing is very profitable, very effective, and very safe. The necessity for rigorous thinking here is absolute, because the translation from tremendous mathematical data into simple fact means that there’s a lot of room for error, misconception, and poor understanding. Remember that if statistical results seem to fly in the face of common sense, they’re probably wrong. Always moderate your faith in science with a healthy dose of non-mathematical skepticism. But if you’ve reached this level, you’ll have a graduate degree and/or a well-paying job.
The topics I listed above are the ones that best relate to advanced statistics and mathematical finance, but it’s very possible to have gone the less mathematical route through business school or law school. If you’re still programming at this point, you should build your own start-up or sell your programs.
Standardized tests: CPA, CFA, EA, NASD Series exams, bar exam
Casella and Berger – Statistical Inference (text used widely in grad school)
Kutner, Nachtscheim, Neter, and Li – Applied Linear Statistical Models (THE book on regression)
Tsay – Analysis of Financial Time Series (not easy, but a great book)
Chung – A Course in Probability Theory (the adult version of his elementary work)
Williams – Probability with Martingales (not an intro prob book, but an intro martingales book)
Chung – Introduction to Stochastic Integration (read and digest Williams first, or you will regret it)
Level S – Mathematicians/Physicists with a career change: interest rate modeling, credit derivatives, numerical techniques
The list is pretty much over, and you’d only learn this stuff if you were a quant, Einstein, or trying to commit suicide with math. At this point, you would be beyond exams because you would almost certainly have a PhD. Proving yourself at this point is a matter of accomplishment, publications, or millions of dollars. If you wanted to swindle the investing public, it is probably not difficult for you to scare up billions of dollars. You don’t fear Congressional subpoenas or the Supreme Court of the United States. Even for the so-called Masters of the Universe on Wall Street, the prospect of seeing those things makes their testicles shrivel into their abdomen.
Just remember that nothing hits harder than the ground. If something goes wrong and you melt down the US financial system, your career is effectively over and you should plan to die before you ever see the inside of a federal penitentiary (e.g. Ken Lay).
Brace – Engineering BGM (Brace is the “B” in BGM, because he invented the LIBOR market model that forms the basis for global capital flows. Brace believes in “less is more” when it comes to explaining things, which is why he’s smarter than you are.)
Schonbucher – Credit Derivatives Pricing Models: Models, Pricing and Implementation (an explanatory text for pricing credit derivatives, a booming industry before the financial system went belly-up, so either it’s all junk or everyone was doing it wrong)
Glasserman – Monte Carlo Methods in Financial Engineering (definitive reference on Monte Carlo methods in finance)
Level 0 – Nonessential reading and movies
If you want to know about the trials and tribulations of working in finance, here are some great books. A lot of these are cautionary tales about taking mathematical models too far and the excess of both work and play in the financial world.
Derman – My life as a quant: reflections on physics and finance (takes you through his career in physics and finance, and he lived through some very interesting times and was an interesting character. You see the egos in Wall Street and the vicious schadenfreude.)
Lewis – Liar’s Poker (shows the excess of Wall Street in the 1980s. Read by everyone who’s ever wanted to get in the money game)
Lowenstein – When Genius Failed: The Rise and Fall of Long Term Capital Management (story of statistical models blowing up a hedge fund. Not an exact sequel but a lot of overlap with characters from Liar’s Poker)
Taleb – Fooled by Randomness/Black Swan (two books, first details that most skill is masking extraordinary luck, second shows you that most mathematical theory and science is a house of cards built on sand. Writing is turgid and repeats itself ad nauseum, but it’s worth reading if nothing else to provide an exercise in why you think Taleb is an incredible douchebag)
Enron: Smartest Guys in the Room (documentary about the end of Enron. You get to see that incredible assholes are common in finance and how tenuous the system is between statistics, economics, and law when placed in the hands of very smart and very greedy people. The money game attracts sharks and most regulators and lawmakers are just blubber)
President Obama held a press conference last night to shore up support for his health care reform bill. I thought he did a great job politically of managing the questions and getting people enthusiastic about the issue. However, I did notice a couple things, like the fact that his answers to hard questions ramble on until he forgets what was asked in the first place and that he knows absolutely nothing about economics. Also, his speeches are very formulaic. They’re effective and make people think he’s a genius, but there is a formula to it. So I unveil to you, the anatomy of an Obama speech:
1) “I’m your knight in shining armor. I saved America with hope”
Now, six months ago, I took office amid the worst recession in half-a-century. We were losing an average of 700,000 jobs per month, and our financial system was on the verge of collapse.
As a result of the actions we took in those first weeks, we’ve been able to pull our economy back from the brink. We took steps to stabilize our financial institutions and our housing market. And we passed a Recovery Act that has already saved jobs and created new ones, delivered billions in tax relief to families and small businesses, and extended unemployment insurance and health insurance to those who’ve been laid off.
Of course, we still have a long way to go. And the Recovery Act will continue to save and create more jobs over the next two years, just like it was designed to do.
2) Hate the rich, they made America fat and lazy
I realize this is little comfort to those Americans who are currently out of work. And I’ll be honest with you: New hiring is always one of the last things to bounce back after a recession.
And the fact is, even before this crisis hit, we had an economy that was creating a good deal of wealth for those folks at the very top, but not a lot of good-paying jobs for the rest of America.
It’s an economy that simply wasn’t ready to compete in the 21st century, one where we’ve been slow to invest in clean-energy technologies that have created new jobs and industries in other countries, where we’ve watched our graduation rates lag behind too much of the world, and where we spend much more on health care than any other nation, but aren’t any healthier for it.
3) The common man has suffered, or If you don’t like Obama, you want everyone to die writhing in agony
That’s why I’ve said that, even as we rescue this economy from a full-blown crisis, we must rebuild it stronger than before. And health insurance reform is central to that effort.
This is not just about the 47 million Americans who don’t have any health insurance at all. Reform is about every American who has ever feared that they may lose their coverage if they become too sick, or lose their job, or change their job. It’s about every small business that has been forced to lay off employees or cut back on their coverage because it became too expensive. And it’s about the fact that the biggest driving force behind our federal deficit is the skyrocketing cost of Medicare and Medicaid.
So let me be clear: If we do not control these costs, we will not be able to control our deficit. If we do not reform health care, your premiums and out-of-pocket costs will continue to skyrocket. If we don’t act, 14,000 Americans will continue to lose their health insurance every single day.
These are the consequences of inaction; these are the stakes of the debate that we’re having right now.
4) Promises – Elaborate promises that are the adult version of coke in every drinking fountain
If you have health insurance, the reform we’re proposing will provide you with more security and more stability. It will keep government out of health care decisions, giving you the option to keep your insurance if you’re happy with it.
It will prevent insurance companies from dropping your coverage if you get too sick. It will give you the security of knowing that, if you lose your job, if you move, or if change your job, you’ll still be able to have coverage.
It will limit the amount your insurance company can force you to pay for your medical costs out of your own pocket. And it will cover preventive care like check-ups and mammograms that save lives and money.
Now, if you don’t have health insurance or you’re a small business looking to cover your employees, you’ll be able to choose a quality, affordable health plan through a health insurance exchange, a marketplace that promotes choice and competition.
And, finally, no insurance company will be allowed to deny you coverage because of a pre-existing medical condition.
5) Token gesture. His plan will cost trillions of dollars, but look, he saved a couple pennies!
Already we’ve estimated that two-thirds of the cost of reform can be paid for by reallocating money that is simply being wasted in federal health care programs. This includes over $100 billion of unwarranted subsidies that go to insurance companies as part of Medicare, subsidies that do nothing to improve care for our seniors. And I’m pleased that Congress has already embraced these proposals.
6) Slap Republicans. Imply they’re the cause of the problem.
I understand how easy it is for this town to become consumed in the game of politics, to turn every issue into a running tally of who’s up and who’s down. I’ve heard that one Republican strategist told his party that, even they may want to compromise, it’s better politics to “go for the kill,” another Republican senator that defeating health reform is about “breaking” me.
So let me be clear: This isn’t about me. I have great health insurance, and so does every member of Congress. This debate is about the letters I read when I sit in the Oval Office every day and the stories I hear at town hall meetings.
7) Tears. Tell sad anecdotes
This is about the woman in Colorado who paid $700 a month to her insurance company only to find out that they wouldn’t pay a dime for her cancer treatment, who had to use up her retirement funds to save her own life.
This is about the middle-class college graduate from Maryland whose health insurance expired when he changed jobs and woke up from the emergency surgery that he required with $10,000 worth of debt.
As an aside, what percent of his anecdotes do you think are fake? He doesn’t say names or use any way to verify their identity, so it wouldn’t be hard to fabricate. I have a friend in New Jersey who’s a doctor, and he thinks medicine should focus solely on underlying problems and not just treating the symptoms. His own practice has been extremely successful doing just that. Yeah, his name is Dr. Gregory House. See how easy that is? I could even plausibly say I wasn’t lying.
But check out any of his speeches and you’ll see all of these elements in there.
Just for kicks, here is a brief layout of financial employers.
-Commercial banks (i.e. B of A, Citibank)
Commercial banks tend to ask less of their employees, pay less, and give them less interesting work. The plus side is that they offer better job security and there’s more room for shifting around the banking industry to find a better fit.
-Investment banks (i.e. Goldman Sachs, Morgan Stanley)
Investment banks are considered the gold-plated jobs in the financial industry. They pay extremely well and offer some of the most interesting work in the industry. However, they also demand the most of their employees and aren’t afraid to fire anyone who isn’t top quality. Expect to work 15+ hour days and get laid off if you have a bad week.
-Hedge funds
Hedge funds are the cowboys of the financial industry. It is a very volatile industry and most employees can expect to be looking for another job within 6 months. In the meantime, they can make an obscene amount of money. And/Or be investigated by the SEC.
-Accounting firms
Accounting firms often have consulting or financial arms that offer work. Like most accounting jobs, they pay well, have good job security, and are often willing to pay for continuing education. The downside is that you are far from the action and since the top notch are in the previous three areas, it’s difficult to find someone good to learn from.
-Software companies
With a growing focus on complex mathematical models and thus increasingly fewer people who understand finance, statistics, economics, mathematics, and computer programming at the requisite level, financial companies have been outsourcing their computational needs to software companies. They have the same qualities as accounting firms. Software companies also tend to be small so there is even less room for upward movement.
The rule of thumb is that the closer you are to the money changing hands, the better and more interesting the job. Naturally, being close to the action necessarily means the job is very intense and employers demand a lot in time and quality. It should be noted that starting salary and bonuses are not a good measure of the quality of a job, at least not compared to the type of experience one gets, upward mobility, turnover, and the quality of the team. In the financial industry, if you’ve been in the same place for more than 2-3 years and haven’t moved up, you’ve been pigeon-holed and are in danger of stagnating.
A primer on quantitative easing and what the Fed is trying to do:
http://www.ft.com/cms/s/0/8ada2ad4-f3b9-11dd-9c4b-0000779fd2ac.html
It’s a video, so here are the highlights if you can’t or don’t want to watch it:
-normally central banks set interest rates to regulate monetary policy
-interest rates cannot be below zero (it makes no sense for banks and would force people to stuff money in mattresses)
-so the Fed creates new money, increasing its own credit which is backed by the government
-it buys every asset in sight, increasing the price and yield of bonds and other assets
-this should encourage greater demand (and reduce bad assets), giving banks an incentive to lend and picking the economy out of recession
now the risks:
-the Fed could lose money on its purchases, and remember that the taxpayer is on the hook for the government’s losses
-this increases consumer prices, which could spiral into unstoppable inflation and destroy the value of the dollar
-this strategy depends entirely on market confidence, it can be counterproductive if people don’t think things are better
-must be done extremely aggressively or it won’t work, this is why it’s very risky and the central bank only does it as a last resort
-because it’s a last resort, it is necessarily rare, which means we have no empirical evidence how much is enough
I read a very interesting solution this morning to create de facto negative interest rates and spur spending. The Treasury could randomly pick a number 0-9 and say that every bill ending with that number will be worthless. That would create a massive game of hot potato as people tried to shed themselves of the dreaded bills, speeding transactions in the country. I don’t think it will happen, but it’s a fascinating idea.
From today’s Wall Street Journal:
Public relations disaster of the year: The three CEOs of America’s car industry, for flying private jets to Washington to beg for a bailout because they’re running out of money. What better way to illustrate how out of touch they are with the American public? Runner-up: John Thain, CEO of Merrill Lynch. He was hailed as a hero for saving his firm with bailout money, only to blow it by demanding his bonus.
Swimming naked award: This refers to a joke by Warren Buffett that anybody can succeed in finance when times are good, but you find out who’s been swimming naked (taking stupid risks) when the tide rolls back. The winner is Iceland, whose entire economy exploded because a few people in America defaulted on their mortgages.
Fight of the year: Dick Fuld versus his own employees. Fuld presided over Lehmen’s demise and an anonymous employee attacked him in the office gym. Fuld was knocked the fuck out with a single punch, ironically mirroring his firm’s problem of having a glass jaw.
Best letter of the year: Congressman Henry Waxman with unmasked schadenfreude when he demanded that all Wall Street firms bailed out by the government publicly list their top earners, their bonuses, and how this was calculated.
Flop of the year: Sovereign wealth funds. Earlier in the year, they were the new financial monster as government-backed funds from China and Dubai were anticipated to simply buy the entire world. Then they were going to buy our financial system when it was in peril. Now the Chinese and Arabs are counting their massive losses and wondering what happened to the money. Turns out economies dependent on cheap manufactured products and oil have a massive gap in their strategy when consumers stop buying.
Client of the year: Eliot Spitzer, aka Client Number Nine. Wall Street didn’t have much to cheer in 2008, but the fall of New York’s most hated regulator in a sex scandal was one of them.
Worst abbreviation: The early winner was structured investment vehicle, or SIV. The new winner is TARP, troubled asset relief program. Someone needs to re-think these names and find out if they could have terrible ramifications like these are having now.
Poorly timed nickname: joint winners are Whole Foods Market and Starbucks. They earned their nicknames of Whole Paycheck and Fourbucks, and true to that, consumers stopped going when the economy got rocky. Both have stocks that are down more than 50% for the year with even uglier forecasts for 2009.
Saved the Universe award: Warren Buffett. His timely investments saved General Electric and Goldman Sachs from the humiliation of requiring a bailout. Masters of the Universe breathed a sigh of relief.
Comeback kid: Cash, which is once again king. Others thought this might be the year when oil, China, environmentalism, or hope and change might be the new hottest commodity. But at the end of the day, cash is indisputably still the only commodity that matters. Runner-up: Bank of America, which now has enough of the US government’s cash to deserve the name.
I want to be more active on my blog beyond just tracking my daily habits, so I decided to add a new financial section where I plan on commenting on economic news. As I get more knowledge, hopefully my ability to predict and comment on current events will become more sophisticated. For now, here’s a classic post on economic history.
Today’s history lesson takes place at the height of the Great Depression, when the American public blamed greedy Europeans for World War I and the renewed gold standard for their deflation problems. A collection of Democrats, politicians from silver mining states, and currency speculators called for a return to bimetallism and using the silver standard to help stabilize the dollar. The gold standard was failing because too many countries were incorrectly pegged without a way to correct it; changes to currency pegs badly damaged a country’s reputation, as Argentina learned when it tried despite the warnings and ended up with massive bank runs as well as being shunned like a leper by the British Empire in trade (which made up more than 80% of Argentina’s trade).
The result of the ill-conceived new gold standard was hyperinflation in Germany (with the famous story of a guy running around with a wheelbarrow full of money to buy a loaf of bread, then being chased by a mob trying to steal his wheelbarrow) and wild deflation in Britain and the US. This is where a deep recession turns into the Great Depression because of the Federal Reserve. The Fed at the time believed that deflation could be turned if people had more disposable income from savings and decided to raise the interest rate. Incidentally, the idea of printing more money was rejected because the government was “committed” to trading gold for cash if demanded and feared bank runs if too much money circulated. Of course, the result of high interest rates was the ruin of society because people could not afford to pay the high interest rates on loans, especially in the farm sector. Employers laid off most of their workers to avoid the need to borrow more money, damaging their productivity and leaving many people without incomes.
The silver bimetallism people had been around since William Jennings Bryan nearly won the presidency on that issue in 1896, but the Great Depression was the ultimate failure of the gold standard. While silver had languished at a trading rate of 86 oz to 1 oz of gold, the silver politicians wanted it to trade at the “traditional” rate of 16 to 1 (it was traditional in the sense that this was the price written in the Constitution – like today, some thought the rule of the Constitution was absolute and the founding fathers never intended to change that price). With influential support, a bill to buy silver to the traditional rate passed in 1933 and the Fed started buying silver. President Roosevelt supported the silver legislation in a deal to push many of his New Deal reforms through an unwilling Congress. While times were great for silver between 1933-1937, the demand for silver plummeted after this short-run gain and effectively ended silver’s role as a meaningful currency because nobody wanted silver at such a high price in gold.
Where does China fit into all this? Well, China was among the few countries in the world that used a silver standard to peg its currency, since most of its gold supplies had been drained by Europeans in the unequal treaty era and many Europeans were only willing to pay for Chinese goods in silver (ironically, one reason that Europe went to the gold standard and abandoned bimetallism was the silver drain in paying for Chinese tea and silks, even with adjustments from the opium trade). When the Chinese heard that the US was paying premium prices for silver, there was a mad rush to sell every bit of silver in the country. People went so far as to melt their silver currency to sell to Americans. This crazed outflow of silver drained China of much of its reserves and caused severe deflation in that country, because now nobody had the proper silver to pay for anything in China. Of course, silver had been adjusted and pegged by the American market to be very expensive, so the Chinese government could not afford to buy back enough silver to fill its reserves.
By 1937, the Nationalist Chinese government was desperate for money because of the new Japanese and Communist threats. So they decided to abandon silver as a peg and print paper money, and just like every other n00b to print paper money from the 1778 Continental Congress in America to the Weimar Republic in Germany, they went crazy on the printing press and tried to outpace inflation by printing money faster. Even though the Chinese risked hyperinflation, it was clear in the late 1930s both that the Japanese intended to invade China and that the Chinese could not win with their current forces. The combination of brutal losses to the Japanese and the ugly effects of hyperinflation on Chinese society lost all credibility for Chiang Kai-Shek’s government and gave credence to Mao and the Communist cause.
So there you have it, FDR ruined the Chinese.
|
|
