I'm often asked by individuals in high-school or sixth-form (for those of us in the UK!), as well as those contemplating heading back to university, as to what the most appropriate degree course is to take in order to become a quant.

If I had to pick one course to cover all aspects of quant finance I would choose mathematics. However, when we dig deeper into the assumptions within the question, we find that a longer answer requires more thought.

I would say that the best overall course for becoming a quant is a degree in mathematics.

However, to answer the question properly requires understanding the current landscape for quantitative finance roles and what technical skills are necessary for each one.

The Current Quant Landscape

Broadly, I have categorised the four major quant roles available today. Each of these roles can be subdivided into varying levels of seniority, pay and responsibility, although I won't dwell on these details here. The roles are:

• Quant Analyst - A.k.a. "financial engineer". This is the traditional concept of the "quant", at least up until relatively recently. Such quants are employed to put a price on complex "exotic" derivatives contracts. This was extremely popular during the years leading uo to the financial crisis of 2007/2008. It also lead to the prevalance of the Masters in Financial Engineering (MFE) postgraduate course now offered by many universities. Skills required in this arena include stochastic calculus, stochastic time series modelling and programming in a statically-typed language such as C++, C# or Java. Another type of role that has cropped up in the last few years is the "model val" quant. These roles typically require checking other models for validity, as opposed to developing models directly.
• Quant Developer - The "quant dev" is a programmer at heart. The role is extremely varied and recruiters tend to "pad out" more traditional IT roles with the word "quant", when there is really very little quantitative work in such roles. The true quant developer will likely be in the more senior end of the "middle office" of an investment bank or even in the "front office" (i.e. close to the money!). On the buy side (asset management), quant devs will generally be building trading infrastructure, designing analytics/reporting engines or taking a prototype quantitative model and optimising it for execution speed. Generally quant devs will have a computer science background, but sometimes will have a more mathematical skillset with substantial programming experience. Quant devs write software in a wide variety of languages from C, C++, C#, Java through to Python, Julia, Go and Haskell.
• Quant Trader/Researcher - As I've written before, this is generally the most coveted role in the quant hierarchy. This is primarily because it involves pay that is (usually) directly linked to performance (which in this case means trading returns). In some firms it also provides the most flexibility, and possibly interest, due to its collegiate/research nature. The skills required to be a quant trader are essentially linked with the models used to generate returns. Almost certainly it will involve a strong statistical skillset, as well as time series modelling, signals analysis and, more recently, machine learning and Bayesian statistics. A PhD and/or post-doc experience, with a strong academic publishing record, are generally prerequisites for the top quant trading positions. Within the category of quant trader I will add "high frequency trader". This is an individual who excels at low-level systems engineering, network latency analysis or optimised hardware programming. Such individuals are often drawn from EEE backgrounds (see below).
• Quant Risk Manager - Since the financial crisis there has been a significant emphasis placed on trade-, portfolio- and firm-wide risk management. Many quants are now employed to measure and minimise risk in such institutions. Such risk assessment is not particularly straightforward, especially in firms that have multiple levels of risk exposure across counter-parties, obscure derivatives contracts and incorrect model usage. A background in advanced statistics is highly valued for roles in quantitative risk management. These skills can be obtained on a mathematics degree or even an interdisciplinary course such as MORSE. The latter involves a mixture of mathematics, operations research, statistics and economics and thus provides a good grounding in the quantitative and qualitative risks that financial firms are exposed to.

Each of these roles requires a vastly different set of technical skills. If you have your heart set on one of these roles in particular, it makes sense to choose a degree course that will optimise your chances for learning these skills.

Top Undergraduate Degree Course

There are four degree majors that I personally consider to be the most appropriate for landing a quant role. This is based on my own experience working in quantitative finance as well as discussions with a substantial number of quant recruiters currently working in industry.

This list is not the "final word" in quant recruitment, but I do want you to be aware that your chances are going to be substantially improved if you possess one of the following undergraduate degrees from a top school.

At the very least the following degrees will provide you with sufficient mathematical maturity to continue in a postgraduate course, such as a Masters in Financial Engineering or PhD.

Mathematics

Why do I consider mathematics to be the "best" degree programme for a quant? Simply put, many quant roles require a substantial grounding in mathematics and mathematical modelling. Unfortunately, if you wish to work in a quantitative role, then there is no getting around having to learn some hard mathematics!

A good mathematical degree, with strong options choices, will cover all of the areas needed by a practising quant. These include real analysis, probability theory, frequentist and Bayesian statistics, stochastic analysis, fourier analysis, linear algebra, numerical linear algebra, linear analysis, numerical analysis, ordinary and partial differential equations, optimisation, mathematical modelling and vector calculus.

Nearly all high-end mathematics degrees include some form of optional programming courses, some of which use more modern languages such as Python, MatLab and R.

In addition, the level of rigour promoted by a mathematics degree produces good candidates for further postgraduate research work. An additional benefit of learning "how to learn mathematics" is that it makes it somewhat easier to jump to other fields, as often the subject-specific mathematics can be the barrier to learning a new subject.

That being said, mathematics is not an easy course to take. It requires a substantial commitment to obtain grades that would impress a recruiter (and hiring firm!). Mathematics is not something that can easily be "sailed through". It requires deep thought and a substantial awareness of many disparate areas. However, it is an extremely rewarding degree to take and can "open your eyes" to some very interesting abstract concepts.

Mathematics is not an easy course to take. It requires a substantial commitment to obtain grades that would impress a hiring firm. However, it is probably the most suitable degree to choose to become a quant.

As I stated above, if I had to recommend one particular course, I would choose mathematics.

What quant roles lead naturally from a mathematics degree or appropriate postgraduate course? Predominantly a quant analyst (financial engineer) or quant researcher/trader. It is also possible to head into a quant risk analyst role, although it is likely some specific postgraduate training would be required.

Note also that it is possible to become a quant developer after doing a mathematics degree (that's what I did, after all!), although I had quite an extensive programming background that I carried out in addition to my degree.

Theoretical Physics

Physics is the study of how the universe works at the smallest and largest scales. Theoretical physics, in particular, is concerned with development of models that attempt to predict, and infer, behaviour of physical phenomena. Such skills are very similar to those of a quant researcher or financial engineer, who is constantly attempting to try and model complex stochastic phenomena.

There is a substantial overlap of material covered by a mathematics degree and a theoretical physics degree. However, the manner in which the material is presented is far more practical and does not provide as much rigour as that of a mathematics degree. Such rigour is generally unnecessary when modelling so if you are more interested in "how things work" then you might find physics more appropriate.

On a theoretical physics course you will learn about classical mechanics, including Lagrangian and Hamiltonian dynamics, electromagnetism, quantum mechanics, special and general relativity, cosmology, statistical physics, particle physics and perhaps more advanced courses such as quantum field theory and string theory.

Crucially, these modules will teach you about mathematical modelling via ordinary differential equations, vector calculus, partial differential equations, statistics, linear algebra, linear analysis and probably some programming (albeit lilkely in Fortran or C, although you may be lucky enough to use MatLab or Python).

Theoretical physics is almost perfect for quant research and you will see a lot of physicists becoming quant researchers.

Hence a theoretical physics degree will cover nearly everything you might need to learn in a mathematics degree, but with an emphasis on applications to physical phenomena and less of a concentration on theorems and proofs. For certain quant roles, this may even be more optimal.

What quant roles are most appropriate for a theoretical physicist? As with mathematics, the two most appropriate roles are a quant researcher/trader and perhaps a quant analyst. The former requires intuitive modelling skills. Theoretical physics is almost perfect for this and you will see a lot of physicists becoming quant researchers. The latter will evidently require some stochastic analysis experience, which for a physicist, will likely come at the postgraduate level, unless their course allowed optional mathematics modules to be taken.

Once again, risk analyst or quant dev roles are also appropriate assuming a strong statistics or programming background, possibly in addition to your degree modules. This is often carried out at postgraduate level.

Computer Science

There is a misconception in general society that computer science involves going to university to learn "coding". This is particular pervasive due to the immense rise of technology startup culture and web development. However, this notion is incorrect, and somewhat harmful.

Computer science is actually a subset of applied mathematics, dealing with the particular mathematical areas involved in computation. In addition a modern computer science degree involves a substantial amount of computer architecture design, computer hardware engineering, software engineering, compiler design, algorithmic design/complexity as well as database design.

There is a misconception in general society that computer science involves going to university to learn "coding". However, this notion is incorrect.

A lot of these skills are now seen as "outdated" by a technology startup culture that values rapid iteration and abstraction from the hardware. However, in quantitative finance, the above topics are precisely those that allow various quant shops to give them an edge in a highly competitive sector. Hence a computer science degree should NOT be considered an anachronism in todays job market.

A good junior quant developer, who has aspirations to lead their own team some day, will need to be extremely well versed in the above topics if they are to work in the more lucrative (and arguably more interesting) areas of quant finance.

Quantitative trading and pricing infrastructure involves some extremely interesting areas of computer science and engineering including high availability (redundancy), low-latency applications, large codebase design and refactoring, robust high-frequency systems, GPU processing farms and other high-performance computation (HPC) applications, real-time high-throughput responsive analytics engines as well as database cluster design and monitoring.

In addition, being a quant dev either via a consultancy structure or as a direct employee can be extremely lucrative, particularly after a career spent in a specialisation or niche.

As a side-benefit, because there is an under-supply of strong software developers, it is straightforward to jump back-and-forth between financial services and technology startup roles, particularly in finance/tech hubs such as New York or London. Hence there is strong job security in being a quantitative developer with a strong computer science background.

Electrical & Electronic Engineering

As with computer science there is a misconception that electrical and electronic engineering (EEE) students spend the majority of their time soldering electrical circuits and poring over component datasheets. While this is clearly part of the degree course, in actual fact top EEE courses are often quite theoretical and have a strong mathematical component associated with them.

Typical courses include embedded programming (in a language like C or Assembly), digital signal processing (which is highly valued in higher frequency trading), hardware optimisation design (including usage of tools such as FPGA) and robust/high availability system design. These are all skills useful in high-frequency trading or as quant developers programming low-latency high-availability architecture for trading applications.

Postgraduate "Triple E" students are great candidates for eventual roles in high-frequency trading firms.

"Triple E" students are great candidates for eventual roles in high-frequency trading firms. After an undergraduate degree in EEE, it is common for postgraduate students to specialse in specific embedded hardware implementations that provide substantial experience with low-latency optimisation and high-throughput. These skills are the natural domain of the high-frequency trader and as such EEE students are often in demand from these (rather secretive!) firms.

Other Appropriate Undergraduate Degree Course

While an undergraduate degree in mathematics, theoretical physics, computer science or EEE are most appropriate for quant roles, there are also other degrees that can lead to a top quant role, usually via a postgraduate route.

Mechanical/Aeronautical Engineering

Mechanical and Aeronautical Engineering are concerned primarily with the applications of Newtonian mechanics, particularly in the areas of statics, dynamics, fluid dynamics and control theory. All of these areas require a substantial knowledge of non-linear calculus and continuum mechanics. However, there is less of an emphasis on advanced statistical methods or time series analysis - at least during the undergraduate level.

I would advise that if you are interested in a strong quantitative finance role within a fund or bank to carry out some postgraduate research into an area which deepens your mathematical maturity, as well as programming ability. Being able to discuss an applied thesis with a heavy programming element will provide you with a strong advantage in an interview situation.

I would like to mention here that I carried out postgraduate research in aeronautical engineering, namely in compressible computational fluid dynamics. The ability to solve multi-dimensional PDEs and rapidly program new models was heavily in demand at the time, although the market for these skills has cooled somewhat since exotic derivatives have fallen out of favour when compared to their pre-crisis levels!

Economics

One might think that economics is a highly appropriate degree for becoming a quant, but it is actually not as suitable as the degrees listed above. This is because economics courses are not as mathematically rigourous as mathematics, physics or EEE and as such this presents a question mark for many recruiters and hiring firms.

That being said, an economics degree leads naturally into a PhD programme ("grad school") in econometrics or time series analysis. These skills are highly valued by hedge funds and asset management firms, so if you are currently taking an economics degree and have aspirations to become a quant, then you should try and take as many mathematically heavy courses as you can (including as much statistics as possible!) in order to get a place on a mathematically-rigourous grad school programme.

Economics degrees are particularly relevant for certain asset management firms, particularly those making large scale macroeconomics forecasts, e.g. "global macro" funds. While not as quant heavy as an options pricing or high-frequency trading fund, such roles are still highly prized.

Choosing a Particular University

I won't list my own opinions on the "best" Universities for becoming a quant, as that is an article in itself! However, I will provide some basic guidance on choosing a degree structure. There are substantial differences across locales when it comes to degree structure and I can't possibly hope to list every conceivable variation, but I will provide some broad pointers.

• Module Choices - Make sure that whatever degree course you pick provides a lot of choice in choosing your modules, at least in the later years (years 3 and 4). You will want to tailor your degree to include the topics that quants require for the job. My own undergraduate degree course was very well structured in this manner (and in fact was the principle reason I chose it) and it really helps when progressing to the next stage of your career, either in further study or in direct employment. Irrespective of module choices, you should be sitting in on as many lectures as you possibly can while at University, even if you don't ultimately take the exam in the module.
• Four-Year Masters - I would highly recommend (at least in the UK!) applying for a four-years masters programme, rather than a three-year bachelors course. Simply put, you will find it easier to apply for PhDs with an MSc/MPhys/MMath. You will also have a greater mathematical maturity since you will need to take harder prerequisite courses in your third year to prepare for the fourth. However, most importantly, you will not have to worry about applying for a separate MSc, potentially at another university, with all of the associated administrative and financial headache that this incurs. The drawback is the fact that you will need to finance an additional undergraduate year, but a quick back-of-the-envelope NPV calculation should convince you that the extra investment in yourself is worth it!
• Strong Financial Network - Many universities have particularly strong networks with investment banks and asset management firms. Often these are universities situated in or near major financial hub cities. London and New York are good examples of this. This will make it easier to apply for internships. In addition, it will save on administrative and financial headache if you are studying and working in the same city. In order to leverage these networks you should at the very least be joining your university's finance/investing club. However, you really should be attending seminars in the business/finance schools (even if not taking a degree in this field) and meet with professors for potential interdisciplinary undergraduate project collaboration.
• Strong Research Reputation - Universities lead from the top down. The quality of the teaching in harder modules will only ever be as good as the quality of the research being carried out. A strong research reputation will introduce you to more advanced project topics and thus greater likelihood to impress a potential employer. Make sure you are fully aware of the individual research groups/labs that exist in your department or faculty. In fact, it is worth being aware of -all- the research labs within your broader area of interest. For instance, mathematicians and physicists should keep aprised of the applied modelling groups in the maths, physics and finance departments, for potential project ideas and collaborations.
• MFE? - If you are attending a top school then they will almost certainly have a postgraduate MFE programme. There is nothing stopping you from asking the course organiser if you can sit in on the classes. At worst they can say no, at best you have just met another potential contact/collaborator for a project. Sitting on the courses will give you a greater idea of what topics interest you as well as prepare you for taking the course yourself if you decide to do so later. It will give you a "head start" over all of the other candidates. Naturally you will need to fit this in to your undergraduate time-table, but if time permits, you should consider it.

In my next article on universities I will provide my opinion on the best UK universities to apply for (and attend!) in order to secure a quant role.