# Five ways to improve quantitative finance curricula

Two of the best things about writing a book are the people you meet and the things you learn when you send drafts around for comments. My new book, Red-Blooded Risk: The Secret History of Wall Street, was no exception. I expected to get the most controversy over the historical material about how Wall Street quantified in the 1980s, as there were a lot of strong personalities involved and credit for virtually every innovation has multiple claimants. However other than some minor corrections, everyone liked this part. While some of that no doubt results from passions cooling after a quarter century, my impression is it has more to do with having the complete story in one place.

No one cared who was the first person to think of a CMO, or pairs trading or VaR; lots of people had related ideas around the same time; and lots of people worked together to turn these ideas into profits. What participants wanted to tell the world is this was a cooperative project by smart researchers motivated by curiosity and adventure. Of course they wanted to be paid for their work, but they all had easier ways to make money. Participants also liked the message that quants were the driving force of the change. Wall Street did not change by itself in a way that induced it to go out and hire more quants. And maybe most important, participants liked a story that emphasized quants were engaged in a rational reengineering of the financial system, not foolishly building a disaster-generation system because they couldn’t understand anything other than equations. There were mistakes, of course, and some big ones. But innovation entails some failure, and quants were quick to learn from errors.

I had similar results with most of the rest of the material. Probability theorists had some comments about the material on that subject, economists differed in some details on my history of money and historians pointed out some minor issues in my history of risk. Finance professors and behavioral psychologists made suggestions to improve the material in their fields. Practitioners provided insights to add to my discussion of quant trading strategies and risk management principles. One diligent mathematician checked all the calculations and found some errors. But almost everyone found the material important, the basic arguments sound and the exposition clear (no doubt there is selection bias at work, the people I like and respect enough to send drafts to, and who are willing to do the work for me, are more likely to think the way I do; but a book that does not appeal even to like-minded people will probably not succeed when offered to the general public).

The one major exception was the second-to-last chapter, five pages in a 432 page book. In it I discussed risk management degree programs and sketched out what I consider to be an ideal curriculum. That ideal differs considerably from what is offered today. This generated passionate comments, some positive and others less so. The striking thing was no one defended existing programs, but there were a variety of strong opinions about how to improve them. I rewrote the chapter after seeing the range of ideas. Now that the book has gone to press, I’ve inclined to the view that the most important improvements apply to all quantitative finance degrees, not just risk management ones.

The improvements I suggest here are all for the benefit of students, as opposed to program administrators or employers. Most administrators I know think the same way and are passionately committed to student welfare. It takes great energy and patience to put an academic program together and people do it mainly for love, not money. Still, you can’t ignore the fact that these programs are very profitable and allow academic departments to expand. Some of the flaws stem from these factors. Programs can charge based on the salary differential between applicants and graduates, which encourages accepting desperate people and getting them into the highest salary jobs available rather than the ones that offer the best career prospects.
As programs get older the long-term success of graduates becomes more important. But at the moment, most programs are too young to evaluate this. Another potential flaw is offering courses existing faculty want to teach instead of designing the best courses for student development.

The interests of employers can also differ from that of students. Wall Street has always chewed up talent. It hires lots of bright young people at higher salaries than other industries offer. It then works them hard and treats them badly in most respects other than cash payment. During its periodic downswings, it lets most of them go. When the good times resume, Wall Street prefers to hire cheap, up-to-date newcomers than to rehire former employees. To paraphrase Thomas Hobbes, many Wall Street quant careers are solitary, rich, nasty, brutish, and short. There may be some students who enter a quantitative finance degree program with the intention of earning a million dollars in a few years on Wall Street before getting on with their lives. But I assume most are looking to enter satisfying long-term careers and to advance the state of the profession.

1. Data
A common stereotype of inexperienced quants is that they are model-driven. They have a model they either wrote or got from a paper or textbook. They wander around asking for data to put into it. “What interest rate should I use?” “Where do I get the price?” Useful work is data-driven instead. You figure out what you know and, if it’s not enough, you find out more. You explore your data gently, letting it speak to you, not forcing it into a predefined analysis. Only when you have the right data and you understand that data, do you start building a model to process it. And just as important, you make sure your model produces useful data to feed into other firm processes.

Data flows in financial institutions and markets are complex and filled with noise. There are important subtleties to the individual items. A price might be a bid or an ask or a mid, it might be actionable or indicative or nonsense, it might be a trade or it might be a model output. It has a time and a size and a currency attached. It may be most relevant as a spread to something else. And prices are probably the simplest pieces of data that a quant will encounter. Mistakes from pure modeling are rarer and less serious than mistakes from models built on flimsy data foundations and mistakes because model outputs are not firm foundations for decisions and monitoring. And profitable quant advances are more commonly from better data or better understanding of data or better communication of data, than from improved models.

I like to see a quant with pre-degree experience in real, objective data. Ideally in finance in control, audit, operations or IT (but real IT with completed projects that satisfied users, not as a cog in a gigantic boondoggle); but also possibly in scientific research (again, real research) or another practical field. Fortunately, most good schools have accounting and computer science professors who keep up-to-date with the profession and have extensive practical experience. There are plenty of practitioners who can give guest lectures on financial data flows. These teachers can build on what students learned on the job before entering the program, but I’m skeptical that they can do much for someone who never tried on his own, or in a class dominated by such neophytes. Moreover, quantitative degree programs seldom put enough emphasis on these essential data skills.

These lessons can be reinforced by giving homework problems and exams on realistic data systems. Don’t give a student a few numbers and ask her to calibrate a zero-coupon treasury curve, give her a Bloomberg terminal or a Wall Street Journal. Then when students have hand calculations down, ask them to write useful procedures to do the calculation, using realistic systems for inputs and outputs, and insisting on rigorous IT standards.

2. Responsibility
An interview question I ask quants is, “Have you ever done a computation on which an important decision depended, and you have hard objective evidence that your answer was correct?” If you don’t make decisions based on computations, you’re no quant, however good your math skills. If you don’t test your results, rigorously and regularly, you will never be a successful quant. Ditto if you’re always wrong. Nevertheless, the majority of candidates with quantitative finance degrees flounder at the question. It baffles me why they think I can afford to let them find out if they are good quants on my time, with real money at stake.

A common bad answer I get describes a project in which the candidate made a computation, relying on someone else for the data and a third party to evaluate the result. The candidate’s role was limited to doing a calculation and delivering the result. The candidate may not admit this at first, but it becomes obvious when they cannot give any reason they had for believing the data were correct or that the decision was a good one—it’s only “someone told me” or worse, “everyone agreed”. If there was a bad decision, it was someone else’s fault, either a data error or a misinterpretation of the computation. The candidate is never responsible.

This person is a major danger in a financial institution, and probably anywhere else outside a classroom. They not only induce lots of errors, they poison the work atmosphere. Quantitative finance degree programs should have significant coursework where students are graded on results with real future data: do portfolios perform within parameters, do trading rules make money, do hedges hedge? No excuses for “irrational markets,” or “unexpected events,” or “you didn’t tell us to check that,” or “I got the answer right but the sign wrong.” Of course that introduces some luck into the grading (but it eliminates subjectivity which is a good trade in my book, at least for some of the coursework). I think any loss in fairness is offset preparing students for interviews, not to mention jobs. And if this discourages some students from getting the degree, it saves both them and the financial system a lot of trouble.

3. Rigor
My first two suggestions fall in the category of making instruction more like the job. This one goes in the opposite direction. Under the pressure of supporting a business, you seldom have time to go back to first principles. It’s handier to know how to guesstimate a one-touch price in your head than to remember the proof of Ito’s lemma or ponder the true meaning of randomness and information. But in the long run, principles matter more than techniques. Quants whose practical knowledge is firmly grounded have a compass that prevents them from getting completely off-track, and will be able to add to the profession. Quants who are quick at applying equations without thinking too hard about what anything means are much less valuable. These degree programs are not vocational training to show students how to do entry-level jobs, they are supposed to be producing professionals who will advance the state of the art.

When I look at the faculty and coursework for most programs, I do not see enough diversity beyond finance, physics, engineering and applied mathematics. None of these are rigorous fields. Some practitioners understand and can teach rigor, but it’s not a requirement; getting the answer right is what matters most. I would like to see more rigorous theory built into the curricula. That could come from pure mathematicians, philosophers, probability or statistical theorists, historians or theoretical economists. I would also like to see more original sources. Students should be familiar with the development of probability, economics and finance, not as summarized by modern thinkers but as described by the people who invented the fields.

One reason for all of this is I believe that training brains is more important than imparting facts. Breadth and depth of instruction will lead to better-trained brains than narrow drilling on solving textbook problems. But another reason is paradoxical. Because the financial world changes so dramatically, it is imperative to have training that goes to historical and philosophical basics. The speed of change is not the point. Physics also changes fast, but physicists do not need a deep appreciation of Isaac Newton. The change in physics is additive. In finance, by contrast, yesterday’s truth often turns out to be today’s trap. People who update their knowledge incrementally, with no grounding, eventually end up knowing nothing. That is one reason Wall Street quant careers are often short.

4. Betting
However much math you know, finance comes down to making bets. Successful betting requires skills that can be taught. Now not all quants will end up in portfolio management or trading jobs that require constant betting. But most will work in support of such betting. For this you don’t have to be good at betting, but it sure helps if you understand it. And, of course, skill in betting elicits respect in many financial circles and abject incompetence at betting elicits scorn.

If it were up to me, poker, advantage gambling and sports betting would be required courses and students would have to demonstrate consistent profitability at each one. With real money and significant stakes. I understand, however, that is unlikely to happen. Some daring programs might go so far as to encourage student organizations to nurture these skills. That helps, but I have another idea that might allow betting into the formal curriculum without causing apoplexy among conservative administrators and alumni.

Iowa Electronic Markets runs small-money betting markets on various current events.

It is academically respectable. I would have entering students take a one quarter course in strategies for beating this market. I would let them bet with play money, using the mid of bid and ask prices. This is a huge advantage, if you actually bet you have to take the unfavorable side of the price, or offer your own price and be subject to adverse selection. It is not difficult to win consistently if you can buy and sell at mid. But it takes training to identify good opportunities and, most crucially, size bets successfully.

A student would be required to double a play $1,000 during the quarter to pass the course. Students who failed would get a fresh$1,000 the next quarter to try again. This would continue until the student either succeeded or completed the last quarter. The penalty for failing at all attempts would be to write an analysis of the mistakes.

5. Perpetual education
When I started on Wall Street in the early 1980s, there weren’t many quants and there weren’t many computers. We communicated on dial-up bulletin boards. We had used DARPANet in school so we were familiar with digital information exchange, but the only available private technology required one individual to set up his computer and modem to answer telephone calls and allow uploads and downloads. This was the communications infrastructure that nurtured all the quant advances of the 1980s, until UseNet and Compuserve came on the scene.

As time passed, quants got more dispersed and were less likely to meet other quants, especially quants in other areas of finance. Firms became more careful about letting information leak out. An unfortunate result is many quants embark on idiosyncratic, firm-specific and market-specific, learning curves. Articles and seminars are nowhere near detailed enough to be much help. The problem is most acute for quants in smaller firms, outside the main financial centers and without support for professional development.

For similar reasons, no quantitative finance faculty can keep up with all areas of finance. Bringing in practitioners for seminars can help, as can guest lectures and adjunct faculty but by far the best resource for a program is former students learning on the job. Some programs are pretty good at developing a loyal body of graduates, some only seem to hear from former students who want placement assistance. But I don’t know of any that couldn’t improve their two-way communication so current students have access to the state of the art in all areas of finance, and graduates can remain balanced and up-to-date in their skills.

I am not a program administrator, and I have no doubt there are naiveties and errors in my suggestions. They are not offered in the spirit of criticism, but as sincere agitation for better quantitative finance degree programs. Despite claims that there is a glut of financial quants, the truth is that the need for properly-trained, talented people is huge and growing. The best quantitative finance degree programs can help fill this need, if they are run in the right spirit and, most important, run for the benefit of the students.

Illustrations by Eric Kim

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#### JesseLevermore

Absolutely stellar post, actually one of the best I have read on the site.

#### dstefan

##### Baruch MFE Director
I concur, excellent read on what financial engineering curricula need.

#### John G

" Ditto if you’re always wrong. "  Sorry, having someone who is always wrong is as good or better then having someone who is always right. Always right also goes hand in hand with  bad attitude problems and blow up risk taking personality disorder.
" If you don’t make decisions based on computations, you’re no quant, however good your math skills."  That is the same as saying a person who acts as your lifeline gateway to the computer, understanding how calculations really work is not a quant if they don't make decisions. Most of the time you do not want them making any decisions. They get too powerful then and don't need your dumb unskilled trader butt to go off on their own, taking the stuff that you paid them to write with them! I settled that power security principle a long time ago.

#### Aaron Brown

I meant "rigorous" in the sense of deep questioning of assumptions and insistence on logical consistency. There are rigorous physicists, but most of physics—and all of engineering and applied mathematics—is about getting the answer right. Pure mathematics and philosophy are more rigorous fields.

The reason rigor is more important in finance than engineering is that finance is competitive. If my theory of aerodynamics allows me to build good airplanes, it doesn’t matter much if it’s built on fuzzy or incorrect assumptions. At worst, some new design or circumstance will reveal the error. That will impose some cost, but the state of knowledge will improve.

Contrast that with a derivative pricing model or structured finance product that seems to work for a while. If there is any flaw, someone will exploit it for profit. The result can be a blow up that causes large economic damage and destroys the professional niche that might have learned from the error.

There aren’t a lot of people with credentials and past successes insisting on bad airplane designs, and it’s easy to tell if an airplane will not fly. There are a lot of people with credentials and apparent successes insisting on poor financial models that allow them to book profits while doing no work, or perhaps get paid for dispensing bad advice. There are many more of these people than genuine quants, and it takes insistence on rigor to identify them. If you judge by credentials or paper success, you will be fatally misled.

We trust airplanes because people have been building and flying them for a long time and the frequency of disasters is acceptable. We trust financial models only when we validate them rigorously every day versus independent market prices. We make precise objective predictions daily or more frequently and we check constantly that the predictions are correct. We challenge the assumptions. We expend effort to learn who is losing the money we’re making, and to monitor that they’re continuing to act the same way. We have independent back-up models. We know our models change the markets in ways that will eventually destroy them. We do not make excuses when the market deviates from our predictions; we immediately fix our models, shutting down businesses if necessary or prudent.

There are quants who do not understand the necessity for this discipline. They trust financial models because people have been building and using them for a long time and the frequency of disasters is acceptable. Also everyone says they work and someone must be checking them. This attitude leads to disaster. Unfortunately it’s an attitude easily picked up in courses where getting the right answer is valued over independent rigorous thinking (even worse is a course where getting the answer that agrees with the professor or text is valued over getting the right answer, and both are valued over rigor).

#### Yang_Pop

##### Tina.Yang
excellent and thoughtful article!
I take these principles in such a way that divide them into two groups:
A. Principle of data, responsibility, and betting;
B. Principle of rigor and perpetual education;

Principles in group A are more about improving the practical skills for a quant. They are the characteristics that distinguish a student in the program with a real quant in the financial market, and can help students act in their professional "quant" roles more readily.
Principle in group B, in my opinion, are good professional characteristics of a qualified quant. However, these characteristics needs more than training in the FE program, experience, personal perspective and altitude are also involved.
Principles in group A can be achieved by editing the curriculum of a program better than those in group B, I guess.
Besides, I think sometimes betting(or judging and making decision) is at least as important as calculating and modeling, since even the orbit of planets can be calculated and predicted while the craziness of public can not. Betting is not just betting, I guess, quants bet based on information, their intuitional judgement and sensibility about the economic circumstances, the market and industry. For example, some analysts can escape from the 2008 financial crisis, just because they "sense" it, and try to look into it, and believe it at last. And the development of such sensitivity would take no less time than the mathematical and engineering training.
However, as "people better focus on only one thing then on quite a few".
I was thinking that there would be some frictions, and if someone want to do a good job in all these aspects, he might fail to be distinguished in none of them.
So, should the quants have a slightly division of their responsibility and capasity?

#### Daniel Duffy

##### C++ author, trainer

what's the landscape in 2022?

@Aaron Brown

#### Ken Abbott

##### Managing Director
Wow. I only saw this today. I couldn't agree more. Ten years later, it couldn't be more relevant. I always give homework assignments based upon things I've actually had to do. Doing a Gaussian Copula in a vacuum is useless; you need to see how it's used. The same goes for hedge parameters and risk estimates and pricing algorithms. I like to give Bloomberg screen shots as a starting point. I also make my students learn S&P Capital IQ, Factset, and Refinitiv.

#### Andy Nguyen

@Ken Abbott Would love to read your outlook for the skills applicable to our audience. Would be nice to be in the form of an article. The landscape definitely has changed a lot since your last did so.

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