I'm tired of seeing posts (especially in the trading forums) asking whether or not "I should study XYZ quantitative major" to have a shot in finance, and I'm guessing I'm not the only one. I feel like many college students need a reality check if they think that most of finance requires you to be quantitatively talented to break into the industry. I know I was totally guilty of this back in college too.
Finance Mathematics Needed
So I'm going to address this today (and hopefully once and for all) by listing out most of the fields of math you could potentially learn before graduating from college and in which industries (if any) you could use them.
Note: This list only contains topics that I have personally studied or applied/known others to apply. It would be unfair for me to comment on fields of math that I have not studied (I was not a math major), so if you know number theory, various types of analysis, graph theory, numerical methods, etc. and have used them in finance, feel free to chip in!
Will I Need Basic Arithmetic in Finance?
Come on, we should all hopefully have some knowledge of this. No matter what field of finance you're in, your job probably will require you to compute numbers. Luckily, Excel and your trusty TI-83 have your back for basic arithmetic.
Mental/"Fast" Arithmetic for Finance
However, sometimes Excel and calculators just don't cut it if you have to make quick decisions within seconds. This is most useful for options trading, whether pure prop or market making, for pricing (obviously) but also for mentally estimating your greeks. But it can also be useful in trading underlyings as well if you're asked to price a more complex products.
Math of Finance - Algebra
I haven't seen many uses for this, at least in the traditional way. I know that many financial models (both trading and banking) require you to solve for a variable, but with Excel doing all the work, it's hardly algebra.
Geometry and Trigonometry in Finance
Um...don't think so.
Trigonometry
Not unless you count modeling something that requires sines, cosines, etc. (potentially in quantitative trading).
Calculus for Financial Management
As far as I can tell, it's only useful when you're taking derivatives for a pricing/trading model in quantitative trading. Although it's definitely helpful to generally know how derivatives work and what they mean for a function.
Differential Equations
I haven't seen/heard it being used, but it's possible that it's used somewhere in quantitative trading (doubt it though).
Stochastic Calculus
Ah, the language of options pricing. If you're going to be a derivatives trader, you will probably still not touch this. But if you're a quant working on pricing models for derivatives, I imagine this would be useful.
Most Used Mathematical Course in Finance - Basic Statistics/Probability
I can't stress how important this is. As mentioned above, this industry is full of numbers, whether or not you work with them directly. That means that you can often make an argument/point by using statistics because people usually find it hard to disagree with numbers. Having a good understanding of basic statistics (mean, standard deviation, etc.), statistical significance, and expected value can take you a very long way in finance.
Advanced Statistics/Data Analysis
This is probably the most difficult subject here that's still at least moderately useful in finance. Advanced statistical methods of data analysis (regression, principal component analysis, etc.) can take an overly complex data set and turn it into a solid conclusion. Time series analysis (ARIMA, ARCH, etc.) is often used in quantitative trading as a way to analyze/predict price movements.
Stochastic Systems
Stochastic systems are used to model random behaviors, so it's naturally a good fit for quantitative price models for trading.
Linear Algebra
It's somewhat useful when used in conjunction with some of the more advanced statistical topics mentioned above. You'd be surprised what eigenvalues can mean in the real world.
Review of Math Needed for Finance
I hope the pattern is obvious by now. Unless you plan on doing very quantitative trading or quantitative research, it is not useful to have knowledge of most of these subjects. However, I have to differentiate knowledge and intelligence here. If you're intelligent/smart (or maybe "creative" is a better word), then you could probably apply your knowledge of these fields to just about anything. Ok, maybe not geometry. But then again, if you were that smart, you should probably be in academia or another industry that's trying to make this world a better place. Only the not-so-intelligent ones like me end up in finance, or so I hope.
Learn more about this topic with the below video.
Read More About Math on WSO
- How Much Math Is Enough Math?
- Better Major: Math, Econ, Or Applied Math?
- Math Major - Pure Math, Stats, Or Some Other Field
Looking to Break into the Hedge Fund World?
Want to land at an elite hedge fund use our HF Interview Prep Course which includes 814 questions across 165 hedge funds. The WSO Hedge Fund Interview Prep Course has everything you’ll ever need to land the most coveted jobs on the buyside.
Great post.
yeah great post peyo, thanks
I could not agree more with this topic.
Great post. +1
Two identical resumes except one dude majored in Business and the other dude majored in Electrical Engineering. Who do you think they're going to take?
I would take the ELE not because of his knowledge, but because it's probably harder to get good grades in his department, assuming the two had equal GPAs.
This is definitely true, plus the fact that the EE major has some good technical academic knowledge that is very applicable to not only the Tech sector of IB but any kind of company utilizing technology.
Considering that way too many resumes that we look at have people with Business/Finance/Econ majors, something of a different flavor goes a long way to breaking yourself out. For you high schoolers and college freshman out there, if you are not interested in STEM that is totally fine but look at a double major with Finance and something else. Or, maybe minor in finance or accounting. I see so many resumes for analysts with "BBA with a concentration in Finance." If I were to see "Art History with a minor in finance" plus some good extra-curics that show interest in the business world as well as other things it would really make you break out.
Depends on the position and how well the person interviews. If you're hiring a guy that you expect to ultimately develop business then I would be reluctant to even bring the electrical engineer in for an interview.
That stereotyping.
+1. For IBD, none of this stuff minus maybe high school mathematics. As full disclosure, I double-majored + minored in college in all pretty technical subjects, and the one takeaway I got was that it was not fully applicable and general overkill. If anything I would have done more CS work instead of more grad-levelish math.
For S&T, I'll defer to the experts for the trading roles; from what I see/know, most of the professional quants in derivatives pricing have PhDs in something very technical so a technical undergrad is naturally a prerequisite. I suppose you can help yourself out by taking a numerical PDEs class/learn how to set up efficient Monte Carlo simulations if you truly want to get into pricing nasty stuff. But if it's not a highly ridiculous product anything beyond what peyo212 said is unnecessary, and they have the PhDs if it is a ridiculous product.
For the buyside, unless you are working in a quant fund everything in excess of some basic econometrics, time series analysis, and probability is not very useful. Linear Algebra is naturally a prerequisite for the above. I'm pretty certain the fundamental guys truly DGAF, neither do the special situations guys, the macro guys care mildly depending on what style of macro (the qualitative guys don't care), whereas the quant guys and any of the non-event-driven arbitrage guys acre a lot more (statistical/convertible/volatility/fixed income because the argument and position sizing is inherently mathematical prima facie even though the reasons why it's risky arb/why it exists are more complicated and the Finance PhDs argue about it).
If you are working for a quant fund, econometrics/time series analysis, a few semesters of probability, optimization (get past linear programming!), and numerical methods form a really solid base of stuff to build on. You really don't need that much stochastic calculus, PDE stuff (sellside stuff) and ultra-advanced mathematics unless you have the luxury of not needing to explain your blackest of boxes to other people. You can get cute and branch off into machine learning. CS for everyday work and programming skills are much much more important; obnoxiously those two semesters of real analysis are not going to do you much good even though they were the hardest part of undergrad.
I have always liked the Buffett quote, "Beware of geeks bearing formulas."
Of course, for most of my life I (and I imagine most of the people on WSO) have been the geek with the formula. But I think you have to be very careful applying mathematics in econ/finance where the subjects of analysis are humans. As complex as physics/etc is, humans are much more complex and difficult to understand. And I think the use of mathematical models in these subjects, while not bad in and of itself, creates a false appearance of precision which can be dangerous when the results are taken literally.
I think that for the average person in Finance, you're better off brushing up on your computer skills and learning things about basic programming/script writing than you are learning more and more complex math. Go learn some python or C++ and work on VBA--start automating things, and most importantly, learn shortcuts that will help you build scalable models. Half the time that people are pulling all nighters is when something changes (and something always changes) in such a way that the original model you developed is now useless and must be rebuilt from scratch.
fundamental P&L/valuation models (ie IB/PE operation projections and valuations....) aren't sophisticated enough to really benefit from the VBA mastery you mentioned, are they?
I'll start with telling you that you should take everything I say with an oceanfull of salt.
Yeah, obviously advanced computer skills are more important in S&T than they are in IBD, but I do believe that IBD can be easier if you are able to quickly automate certain things. A lot of this is only useful at the analyst level of course; you might be building some models, but a lot of times the thinking will be done by the associates/assistant vp's of the world. Many times your job is to do due diligence and tons of data scrubbing. I wouldn't say that learning some basic programming is necessary, nor would I even say that it is always going to give you a leg up. Still, I think it is more applicable to the real world than just getting good at higher level math.
I think it's true that people over estimate the usefulness of math in finance. I can literally only imagine how anyone would make more than tangential use of number theory or galois groups in finance and I can't even really imagine a plausible situation where it would come up.
However, I have a good knowledge of quant stuff (math major) and I think that is useful for what I do on the buy side. The basic point, which I think you allude to, is that I can engage with PhDs without sounding like an idiot. That matters more than you might think sometimes.
Also, I think there is an "IQ test" aspect to majors as an undergrad and I am far more impressed by quantitative majors when interviewing than by humanities or social sciences. I think most people at my organization feel the same way.
Somebody posed the electrical engineers vs. business question above, if I'm your interviewer that isn't even close. EE every day unless there is an "intangible" gap.
Great post, bro
Thanks so much for this very informative post!
STEM degrees are just long IQ tests, thats all.
Was reading a post recently that Banks are hiring drama, history majors -no lie.
http://news.efinancialcareers.com/us-en/152746/do-you-really-need-to-st…
Included is a graph at Goldman Sachs recruiting -liberal arts graduates are its second biggest cohort of employees.. http://www.goldmansachs.com/careers/why-goldman-sachs/explore-goldman-s…
During Blankfein's address to interns, one of the intern noted that he was a history major, just like Lloyd. So I'm not surprised to see how Goldman hires many people with non-traditional degrees.
"Blankfein was a history major in college and he loves to read biographies. "
(You can watch the video and see where the intern says it somewhere near the middle) http://www.businessinsider.com/lloyd-blankfeins-advice-for-interns-2013-10
Nice post. I guess the best route to finance is a psychology major with an econ minor.
Do it uP.
Math major here. I agree You don't need a lot of math but IMO if you have no experience and can't get past calculus, I have serious doubts on your ability. C'mon, if kids in India are learning calculus at 11 surely 21 year old forced to take calc should still know it.
great post.
They are not a dime a dozen, but the ratio of those qualified to be IB analysts to spots available is extremely high.
Any 15-year-old is qualified to be an IB analyst. You can train an intelligent monkey to do the job. What's exceptional is highly motivated young people who have demonstrated a passion for FINANCE, not simply a "passion" to make money. My advice to you is to ask the question, "why?" Cut right through the BS and ask them why they are passionate about finance. If they can't answer that question then they are another overachieving, one dimensional robot who has probably never looked to the stars and wondered "why?"
For me, I became passionate about finance around the age of 21 when I realized that a strong grasp of world history, current events and finance could tell an amazing narrative about humanity, about where we've been, where we are and where we're going.
That's exactly my point. However, sometimes the one-dimensional robots that only want to talk about finance are one and the same with those looking only to make money. I want a candidate that can not only get his or her technicals, but also show that they are a normal person who can carry on a conversation about something other than a discounted cash flow analysis.
Hahahahaha - oh. You're serious. Very well then.
What math courses should I take? (Originally Posted: 05/09/2014)
Hi everyone! A confused undergraduate here with just one simple question to ask:
I'm currently majoring in Economics and Finance and have the option to either do a minor in mathematics which will encompass courses from calc, lin. algebra, complex analysis to hilbert spaces or I can just forgo the minor and take a bunch of stat courses. Now, though IB is my dream target at the moment, I really want to keep my options open to as many other paths as possible in the financial sector and was wondering whether I should go for a math minor (will it involve redundant courses in the context of finance?) or just take a bunch of stat courses (which sound far more relevant to me but I could be wrong)?
Thank you in advance! :)
As far as redundant courses: you could easily figure this out by checking your school's major requirements online. If you can ace the courses, the minor can't possibly hurt, especially for quantitative roles. Most business/finance major requirements don't go too far beyond the lower level math courses. ie; most schools don't require anything beyond calc and stat 1 or 2 unless your are an engineering/physics major. Obviously economics requires a certain degree of competency in stat.
Veritatis qui laboriosam officia dolores quis sint. Incidunt enim soluta dolorem ea. Earum odio architecto est maxime minima. Cum velit eum maxime officiis. Assumenda qui ipsum ex id doloremque dolorem quia. Et commodi esse natus odio illo autem.
See All Comments - 100% Free
WSO depends on everyone being able to pitch in when they know something. Unlock with your email and get bonus: 6 financial modeling lessons free ($199 value)
or Unlock with your social account...
Ea ut modi minima aut quia. Quia consequatur voluptatem quis ullam non. Earum et officia et vitae. Sint neque non doloribus sunt.
Hic error ut id esse dignissimos dolores a. Voluptatem vitae sed alias quo molestiae qui a earum.
Corrupti voluptas beatae eum reiciendis asperiores voluptatem. Veniam necessitatibus magni commodi harum. Eius blanditiis omnis aspernatur dolor inventore earum omnis.