Math/Finance
CA · Member since 2011 · 762 posts · 182 votes
What's the connection?
I was at a graduation recently where the commencement speaker announced future plans for each of the Math graduates as they received their diplomas. As I expected, many were headed to either a job or graduate study in Math, Computer Science, Engineering, Actuary, etc. But, surprisingly to me, a (significant) number of them were going on to finance and investment banking. I didn't think there was a connection. Sure, finance and investment banking have some math, but isn't that something a business major gets as part of their routine education, why do they even need a Math major?
What am I missing?
"Investment banking" is today's buzzword for "make lots of money"...
Plus, the big math companies aren't hiring like they used to... :)
Okay, that puts things into perspective...and if that's your experience and background, I would agree with you...
While, in general, I would consider a typical comp sci or engineering major to have VASTLY more hands-on software experience when they graduate, the exception I would make is in the embedded and real-time embedded space (which is likely what you were doing based on what you say above).
Being able to design real-time and just-in-time systems -- and in general, working at the kernel level -- is something that VERY FEW graduates have any hands-on experience with when they come out of school. And, I'd even go so far as to say that the experience that comp sci grads have detracts from their ability to design RT systems, as they're so accustomed to having the processor/kernel delegate cycles that they can't even get their heads around the concept of those types of designs.
In fact, the first interview question I'd ask any potential college hire is, "What does 'real time' mean?" And the most common answer from comp sci majors: "It means that the system is really, really fast!" :-)
Engineering majors tends to be better versed in hardware/software interfaces, but not much. These days, ask a typical EE major how an interrupt works at the register level or talk about how to debug race conditions, and they have no idea what you're talking about. So, from an embedded standpoint, they aren't much better than comp sci majors.
Math, physics and other "hard-science" majors tend to have no more experience in these things than the CS and Engineering grads, but they tend to be a lot less indoctrinated into higher-level software development and tend to be a lot more inquisitive about how things work at the hardware level. This makes them a lot more trainable.
Not to mention -- and this is completely stereotypical, but true in my experience -- math and physics types tend to be smarter and more creative. When you're developing software without layers of abstraction (i.e. no GUIs and no virtual machines), this is a big benefit. So, when it comes to this type of development, I would agree that math and physics types -- especially those who have taken some hardware design courses -- tend to be just as qualified as most CS and Engineering majors.
Anyway, sorry for the rambling post that is likely not interesting to anyone, but the whole subject of CS and Engineering students not learning this stuff is a pet peeve of mine. And, coincidentally enough, that tech company that I mentioned earlier that I'm working on is focused on developing educational electronics toys, kits and tools for kids -- specifically teaching hardware and software interfaces...so, not only is it a pet peeve, it's something I'm trying to fix...
---------------------------------------------------------------------------------------------------
David,
Let me try to elaborate more on this subject. Forgive me if you think this is too technical.
The background math involved in modern finance here is mathematical analysis, which is a major branch of pure math that has little to do with C-coding. Computer skills, on the other hand, are typically required in applied math. Those who ascribe the recent surge on hiring mathematicians by financial industry to computer skills are at least 10 years behind the curve. Mathematical analysis was not a routine education for business major (not even for a PhD in business) until recent years.
To make a connection, for example, understanding of stochastic PDEs (used in math finance) requires a background of modern probability theory, which is in turn built on measure theory. Measure theory is also the foundation of math analysis.
By the way, measure theory is slightly above most math BAs in the US, but at least, a math BA is closer to it than any other majors.
Any openings for a math guy with a ton of programming experience?
Any openings for a math guy with a ton of programming experience?
Maybe in a couple months!
Do you do any board design or have any Raspberry Pi experience? Most of the stuff we're working on is pretty low level at this point...
Feel free to shoot me a PM...
Boy, you are really starting to bring back memories with all this talk about majors and technology. When I graduated there was no comp sci (I'm still not totally convinced computer science is a science, I'm sure that will offend some folks but everybody is entitled to an opinion). I have an ee degree. I remember taking my first programming class, it was fortran, it took me two weeks of listening to the lecture (and not understanding the homework) before I realized the guy was talking about computer programming, no kidding, it was a total wtf class for the first half of the quarter. When I got my first job I landed in department that was converting an analog autopilot for a commercial airliner to digital. All the control laws had to be converted from analog equations to digital equations to be implemented in sw, i loved working on that and did sw for the next several decades. I and a couple others were the only ones that could spell software, I felt like a king. Since there was no such thing as computer sci, who do you think they hired to do the job, yup, engineers, mathematicians and physicists...those guys can figure out anything and can think from the ground up. Comp Sci majors are really good an module testing, sorting, searching, hash codes, compiler design, TCP, fields, records, etc, everything in the software space, very little understanding of the hardware that surrounds the software. I think we are in total agreement as to the lack of preparation comp sci majors have when they have to become aware of the surrounding hardware. During my sw career I have programmed in machine language (the department was too cheap to buy an assembler), assembly, C, Java, PLI, Pascal, Simula, Lisp, and others. The only one that really threw me for a loop was Lisp, being that you can't write a line of code that is not recursive it tends to be mind bending, for me anyway.
Back in the day you had to write your own kernel, VxWorks ( the kernel that put the mars lander on mars) simply wasn't around, so one was forced to understand OS/Kernel concepts (interrupts, timers, interrupt vectors, timing overruns, I/O, drivers, etc). Nowadays, I have completely forgotten that stuff and simply tell the kernel guy what time slot my sw HAS to run in to meet the real time requirements, he can worry about time frame overruns and overall throughput. The lower level workings of the kernel are simply an abstraction (a term comp sci seems to like) these days. Speed and memory are practically free these days ... we used to spend days or weeks trying to figure out how to make code run faster or in less space. Real time to me means the sw has to run fast enough ... fast enough so the software can get done with a DFT on the radar angle tracking error data before the next frame, so the software can dampen the aileron motion before the wing reaches resonance and breaks off, so the software can advance the auto throttles before the airliner slams into the SF runway threshold. It's something you have to live through before you can truly appreciate and understand it. Races ... you really have to squeeze your brain to see the possible data races that can occur when you have two or more redundant computers running the same code at the same time. I was told the space shuttle has five computers that all calculate the same thing and vote, the majority rules and gets to command the shuttle flight, all in real time...try to imagine the possible races in that scenario.
Programming was fun in the early days. You could be creative and do your own thing. That whole wild west culture slowly evaporated as the field of computer science came alive. Nowadays, there is so much process and procedures involved in sw development that it's no fun anymore (design reviews, code walkthroughs, scolded for using recursion, SEI level 1,2,3,4,5). Yes, I understand why the change occurred, I just don't like that it did occur. I'm glad to be out of that arena and would be perfectly happy if I never saw a line of code again. The industry has become so over regulated (so to speak) that it just isn't fun anymore. REI is my new creative outlet:)
---------------------------------------------------------------------------------------------------
David,
Let me try to elaborate more on this subject. Forgive me if you think this is too technical.
The background math involved in modern finance here is mathematical analysis, which is a major branch of pure math that has little to do with C-coding. Computer skills, on the other hand, are typically required in applied math. Those who ascribe the recent surge on hiring mathematicians by financial industry to computer skills are at least 10 years behind the curve. Mathematical analysis was not a routine education for business major (not even for a PhD in business) until recent years.
To make a connection, for example, understanding of stochastic PDEs (used in math finance) requires a background of modern probability theory, which is in turn built on measure theory. Measure theory is also the foundation of math analysis.
By the way, measure theory is slightly above most math BAs in the US, but at least, a math BA is closer to it than any other majors.
Xing,
Thanks for your response. Hmmmm, my take away from your post is that math in finance mostly involves probability and statistics, is that fairly accurate? If so, I'm going to advise this new math grad to stay away from finance since he tends to not like probability and statistics, he tends to favor numerical analysis and computer science more.
Also what I'm getting from your post is that math in finance pretty much requires a PhD since the basic analytical tools required involve concepts beyond most math BA's, is that fairly accurate?
David,
Yes, if he does not like probability and statistics, there is practically no background advantage for him to get involved in finance.
Since you mentioned statistics, I'd like to make a few more comments.
From my point of view, statistics is more important than any other materials in math finance education for equity trading and management. Unfortunately, it is only a very small part in their curricula. Academics are often too fascinated by their Nobel results, which are often too theoretical and the basic hypotheses are too strong to be practical. An introductory level of statistics without modern probability theory can already be quite useful, and can be learnt quickly by math majored undergraduates.
It is true that it eventually requires a PhD to understand thorouly those modern concepts in math finance. Many math BAs look for jobs in investment banks to work for a couple of years and then go back to school, possible a business school to obtain a higher degree.
Yes, if he does not like probability and statistics, there is practically no background advantage for him to get involved in finance.
Since you mentioned statistics, I'd like to make a few more comments.
From my point of view, statistics is more important than any other materials in math finance education for equity trading and management. Unfortunately, it is only a very small part in their curricula. Academics are often too fascinated by their Nobel results, which are often too theoretical and the basic hypotheses are too strong to be practical. An introductory level of statistics without modern probability theory can already be quite useful, and can be learnt quickly by math majored undergraduates.
It is true that it eventually requires a PhD to understand thorouly those modern concepts in math finance. Many math BAs look for jobs in investment banks to work for a couple of years and then go back to school, possible a business school to obtain a higher degree.
Your comments on statistics start to clear up something that has bothered me for a while now. The school this math grad went to offers a degree in statistics, it's not an area of concentration withing math but its own major. Wow, I always thought statistics was at best a concentration within a math degree. I'm guessing it's coming out of the closet because of finance.
Xing is most correct, LOL
I would recommend finance David, it's a more marketable professional path I believe than any business avenue. I'm aware that programmers and comp sci is also a very marketable skill, I have no idea on the engineering front.
Finance is about solving the unknown by probability, I wouldn't say that one would be doomed to statistical analysis day in and day out, there are hundreds of avenues to take but the key to is understanding the theory behind the analysis. I'd hate being in actuarial sciences, but I understand basically how and what managerial data implicates an outcome or influences a solution. The upper pay scales are not crunching numbers but are dealing in the applications of modeling or in product development and markets. Most all CEOs of the fortune 500 have finance backgrounds.
The real math geeks I've known were more intelligent in some aspects as J/ Scott mentioned, but many lack common sense. Creativity must be tempered by common sense and set parameters in reality.
But then again, I've been in a similar spot as you with giving guidance, I'd rather inform as much as I could but not go to far in saying what one should do or not do. In 5 or 10 years if they are really unhappy and have racked up debt guess who gets the blame for taking them down that road?! He may dislike working in statistical probability models but need to find out if that is all he might do, if it's a period they go through to advance or if they have other avenues that only require an understanding of the analysis. His goal should be happiness and great monetary compensation in the future. Let him decide his future with a bit of guidance instead of directing. IMO
I got my degree in stats and am an ASA (associate actuary). My day-to-day work is very technical. I'd consider it a mix of tech and business (too much business for Comp Sci folks and too much programming for MBAs). I've noticed a LOT of analytics roles/departments popping up in the health care industry and all of them are looking for math (stats/actuary/etc.) with computer skills. The big languages they want are SAS, SQL and VBA.
If this person enjoys the technical type roles and not probability/statistics, then an analytics type role may fit what they're looking for. Steer them away from the actuarial exams though, if they don't like probability then getting through all of the exams probably won't happen!
David I don't think statistics and probability are becoming more popular due to explicitly stating their sexuality having previously been in the closet. I do think computational/quantitative finance and has something to do with it, but two other factors would probably be more pertinent in their increased application.
First the golden age of objective "straight" math seems to have passed (at least for now), we can all think of great mathematical achievements, not many of which have come in the last 40 years.
secondly, this is also is due to big data and ubiquitous data availability. This is a new phenomena which the application of probability computations and statistics can take advantage of. By applying not only the science of normal math but the art of proper application we can tease trends and patters out of huge, seemingly random, data sets which uncover curious and often profitable information. In the past the amount of data and computer power to do this simply wasn't available.
One adverse affect of this big data is that formerly "objective" facts rarely exist anymore in practice. If I have a political argument with anyone we can both bring up statistical studies, ad nauseum, which militate our points and contradict each others arguments. We can effectively torture the facts out of statistics, and when it comes to politics or making ourselves correct many have a disincentive to be truthful if they can hide behind suspect statistics.
@Bill Gulley I hear you. I'm not trying to direct, only advise. Just out of college one needs to start pruning the tree of opportunities (to use the words of the commencement speaker), whether you want to or not you make choices thereby eliminating other choices. He is at a cross roads. Technical path or finance path, that is the choice I see at this point. Yes, you can switch but because of company snobbery it's hard to switch fields after you have a few years experience in one field. I agree, it's probably too early to eliminate options...it's a bit of a dilemma.
@Steve B. I can't tell from you post if you were offended by the word closet or not. I always thought it was a general term that meant hiding something. I'm going to assume it did offend you and not use it again. Sometimes I wish there was a list of words I wasn't allowed to use. Anyway, I completely understand your comment "We can effectively torture the facts out of statistics" ... sounds like job security to me.
@Michael Seeker Thanks for the input. Actuary has pretty much always been off the table. Like others, I'm hearing from your comments that business/acutary/finance is about statistics.
David, You didn't offend me, that would be virtually impossible as I don't believe in political correctness nor do I get morally indignant if someone disagrees with me. What you witnessed was my failed attempt at humor.
Also I misquoted the quote you quoted me on. The proper expression is "torturing statistics to confess your desired "truth". It may have been Nate Silver who said that but I thought it was particularily clever when I read it somewhere.
Coming also from an Engineering, Math and Real Estate background, let's just say Real Estate does not require math that advanced. Most people should be able to handle to math side of this business as long as s/he has a decent grasp of arithmetic.
Sometimes in the academia, people may over-complicate things. I recalled in one of my graduate courses in Corporate Finance the professor started using Laplace's Transform to calculate the Net Present Values of the Cashflows (if you don't know what that is, that's the point... essentially some mathematical technique).
The reality is that using a basic calculator (or computer spreadsheet) you can approximate to the degree of accuracy that you need for all practical purposes.
Again, most of the times, we just use arithmetic. Question to all: Does anyone else use anything beyond?
Again, most of the times, we just use arithmetic. Question to all: Does anyone else use anything beyond?
I like IRR and NPV calculations, for which a spreadsheet (or at least a calculator) is required...
But, other than that, arithmetic is pretty sufficient...
Again, most of the times, we just use arithmetic. Question to all: Does anyone else use anything beyond?
I like IRR and NPV calculations, for which a spreadsheet (or at least a calculator) is required...
But, other than that, arithmetic is pretty sufficient...
And for landlords, PMT functions in a spreadsheet. (calculate amortized payments).
Thanks for resuscitating this old thread, I forgot about all this jappery.
I wouldn't even know how you can do arithmetic using Laplace's Transform's that is something I would like to see...if only once.
I am currently getting excited about using the NumPy and PANDAS libraries in python on Zillows free data sets. I'm still getting up to speed with using this technology so i'm not an expert yet but it shows some promise.
I am currently getting excited about using the NumPy and PANDAS libraries in python on Zillows free data sets. I'm still getting up to speed with using this technology so i'm not an expert yet but it shows some promise.
You'll probably find that for statistical modeling and graphing, Python is pretty bad. Numpy has some of the basics (arrays and simple math/stats calculations) and PANDAS is a little bit better with the graphing stuff.
But, if you're starting from scratch and really want to do statistical analysis and graphing, I'd recommend using a language like R.
Of course, if you want to do general programming, and stats is just one piece of what you want to do, Python is a great place to start...
Thanks for resuscitating this old thread, I forgot about all this jappery.
I wouldn't even know how you can do arithmetic using Laplace's Transform's that is something I would like to see...if only once.
I am currently getting excited about using the NumPy and PANDAS libraries in python on Zillows free data sets. I'm still getting up to speed with using this technology so i'm not an expert yet but it shows some promise.
@Steve B., just for you. This is one of the more readable examples found online.
Example First 5 pages.
Let's focus more on "real" real estate topics =)
How do you plan on using in ZIllow data? What fields do you use?
On Zillow, I had some success in building a query tool on Excel (with Macros). While it does not get all the attributes on the website, I was able to query certain fields which I find useful (Last Sold Date, Last Sold Price, Bedroom / Bathroom count, URL etc.). For example, sometimes I find out houses that have already been sold (ie. no longer interested) that are not even reflected in our "go-to" MLS.
More than happy to share my spreadsheet if you are interested.
Some of the high end financing jobs have some pretty crazy math. Yes, they teach this in biz school, but I think finance companies see math majors as a pretty logical fit so they look to hire them as well.
Thanks for resuscitating this old thread, I forgot about all this jappery.
I wouldn't even know how you can do arithmetic using Laplace's Transform's that is something I would like to see...if only once.
I am currently getting excited about using the NumPy and PANDAS libraries in python on Zillows free data sets. I'm still getting up to speed with using this technology so i'm not an expert yet but it shows some promise.
@Steve B., just for you. This is one of the more readable examples found online.
Example First 5 pages.
Let's focus more on "real" real estate topics =)
After looking at the paper you referenced, I wouldn't dismiss it so fast. While the math is daunting, the results are not. For example, to calculate Present Value most of us would run to a spreadsheet, not necessary given the Laplace results, PV is simply K/r (K=single cash flow payment, r=rate). There is however the underlying assumption that the cash flow is perpetual, which of course it never is. Based on a little spreadsheet analysis I just did, perpetuity is somewhere around 50 years, that is, the point where the approximation starts to approach actual. Hopefully I read it right, it's been a long time since I worked with this kind of math.
We use the rule of 72 all the time without caring what math was used to arrive at that approximation.
Thanks for resuscitating this old thread, I forgot about all this jappery.
I wouldn't even know how you can do arithmetic using Laplace's Transform's that is something I would like to see...if only once.
I am currently getting excited about using the NumPy and PANDAS libraries in python on Zillows free data sets. I'm still getting up to speed with using this technology so i'm not an expert yet but it shows some promise.
@Steve B., just for you. This is one of the more readable examples found online.
Example First 5 pages.
Let's focus more on "real" real estate topics =)
After looking at the paper you referenced, I wouldn't dismiss it so fast. While the math is daunting, the results are not. For example, to calculate Present Value most of us would run to a spreadsheet, not necessary given the Laplace results, PV is simply K/r (K=single cash flow payment, r=rate). There is however the underlying assumption that the cash flow is perpetual, which of course it never is. Based on a little spreadsheet analysis I just did, perpetuity is somewhere around 50 years, that is, the point where the approximation starts to approach actual. Hopefully I read it right, it's been a long time since I worked with this kind of math.
We use the rule of 72 all the time without caring what math was used to arrive at that approximation.
Yes, mathematically speaking, it does converge. (not going into about the continuous discounting vs discrete discounting...)
In actuality, the paper really means nothing for us though. Having a grasp of the uncertainty of the various parameters (e.g. discount rate, rent increase rate, ability to collect rent etc.) FAR outweighs the whatever results that the fancy formula comes out.
Simple approximation (like the Rule of 72), coupled with an awareness of the moving parts, is 100x better than being perfectly accurate of unrealistic assumptions.
Just my $0.02.
"In actuality, the paper really means nothing for us though. Having a grasp of the uncertainty of the various parameters (e.g. discount rate, rent increase rate, ability to collect rent etc.) FAR outweighs the whatever results that the fancy formula comes out."
I totally agree. This of course could be said about virtually every single formula discussed on this website. If one doesn't have a grasp on uncertainties even the "exact" formula won't help.
@Account Closed I would tend to agree with @Che Chiu Wong while the results mathematically may not be trivial, the realistic implications are nominal at best and misleading at worst. While it is definitely an admirable efforts by some serious quants or math nerds to apply some abstruse and erudite methods to a usually pedestrian computation, I think it is largely meaningless. As Che indicates, the big picture issues are going to make anything past the second decimal point largely meaningless. This is like saying our presidential poll is methodologically accurate within .023% while they end off being incorrect by 20%. It's not that the math is flawed it's the underlying assumptions, and unknown unknowable's, that obviate any actual value to this level of mathematical precision. This is reminiscent to the same arguments I have on this forum with spreadsheet obsessives which have every possible expense listed, including the expected bi-annual rate of increase in their garbage bill. After your top ten expenses and costs, most of these calculations add absolutely no accuracy to your realistic result but provide false confidence that you satisfied some kind of due diligence.
@Che Chiu Wong I think I wasn't specific enough in my previous post. You may be talking about making a pivot table or referring to making python "requests "to send POST data then maybe using PyQuery to pull data from the returned HTML - I.E. screen scrapping. These are also good methods. However I was referring to using "Zillow data" in .XLS format, which is freely downloadable, and performing various manipulations of that data using those tools mentioned, to extract some insightful info.