JEE coaching and high school learning

One reason I’m not as good at machine learning as I can possibly be is because I suck at linear algebra. I totally completely suck at it. Seven years of usage of R has meant that at least I no longer get spooked out by the very sight of vectors or matrices, and I understand the concept of matrix multiplication (an operator rotating a vector), but I just don’t get linear algebra.

For example, when I see terms such as “singular value decomposition” I almost faint. Multiple repeated attempts at learning the concept have utterly failed. Don’t even get me started on the more complicated stuff – and machine learning is full of them.

My inability to understand linear algebra runs deep, and it’s mainly due to a complete inability to imagine vectors and matrices and matrix operations. As far back as I remember, I have hated matrices and have tried to run away from it.

For a long time, I had placed the blame for this on IIT Madras, whose mathematics department in its infinite wisdom had decided to get its brilliant Graph Theory expert to teach us matrices. Thinking back, though, I remember going in to MA102 (Vectors, Matrices and Differential Equations) already spooked. The rot had set in even earlier – in school.

The problem with class 11 in my school (a fairly high-profile school which was full of studmax characters) was that most people harboured ambitions of going to IIT, and had consequently enrolled themselves in formal coaching “factories”. As a result, these worthies always came to maths, physics and chemistry classes “ahead” of people like me who didn’t go for such classes (I’d decided to chill for a year after a rather hectic class 10 when I’d been under immense pressure to get my school a “centum”).

Because a large majority of the class already knew what was to be taught, teachers had an incentive to slack. Also the fact that most students were studmax had meant that people preferred to mug on their own rather than display their ignorance in class. And so jai happened.

I remember the class when vectors and matrices were introduced (it was in class 11). While I don’t remember too many details, I do remember that a vocal majority already knew about “dot product” and “cross product”. It was similar a few days later when the vocal majority knew matrix multiplication.

And so these concepts were glossed over, and lacking a grounding in fundamentals, I somehow never “got” the concept.

In my year (2000), CBSE decided to change format for its maths examination – everyone had to attempt “Part A” (worth 70 marks) and then had a choice between “Part B” (vectors, matrices, etc.) and “Part C” (introductory statistics). Most science students were expected to opt for Part B (Part C had been introduced for the benefit of commerce students studying maths since they had little to gain from reading about vectors). For me and one other guy from my class, though, it was a rather obvious choice to do Part C.

I remember the invigilator (who was from another school) being positively surprised during my board exam when I mentioned that I was going to attempt Part C instead of Part B. He muttered something to the extent of “isn’t that for commerce students?” but to his credit permitted us to do the paper in whatever way we wanted (I fail to remember why I had to mention to him I was doing Part C – maybe I needed log tables to do that).

Seventeen odd years down the line, I continue to suck at linear algebra and be stud at statistics. And it is all down to the way the two subjects were introduced to me in school (JEE statistics wasn’t up to the same standard as Part C so the school teachers did a great job of teaching that).

The Quants

Since investment bank bashing seems to be in fashion nowadays, let me add my two naya paise to the fire. I exited a large investment bank in September 2011, after having worked for a little over two years there. I used to work as a quant, spending most of my time building pricing and execution models. I was a bit of an anomaly there, since I had an MBA degree. What was also unusual was that I had previously spent time as a salesperson in an investment bank . Most other people in the quant organization came from a heavily technical background, with the most popular degrees being PhDs in Physics and Maths, and had no experience or interest in the business side of things at the bank.

You might wonder what PhDs in Physics and Maths do at investment banks. I used to wonder the same before I joined. Yes, there are some tough mathematical puzzles to be solved in the course of devising pricing and execution algorithms (part of the work that us quants did), which probably kept them interested. However, the one activity for which these pure science PhDs were prized for, and which they spent most of their time doing, was C++ coding. Yeah, you read that right. These guys could write mean algorithms – I don’t know if even Computer Science graduates (and there were plenty of those) could write as clean (and quick) C++ code as these guys.

While most banks stress heavily on diversity, and makes considerable efforts (in the form of recruitment, affiliation groups, etc.)  to ensure a diverse workplace, it is not enough to prevent a large portion of quants coming from a similar kind of background. And when you put large numbers of Physics and Math PhDs together, it is inevitable that there is some degree of groupthink. You have the mavericks like me who like to model things differently, but if everyone else in your organization thinks one way, who do you go to in order to push your idea? You stop dropping your own ideas and start thinking like everyone else does. And you become yet another cog in the big quant wheel.

The biggest problem with hardcore Math people working on trading strategies is that they do not seek to solve a business problem through their work – they seek to solve a math problem, which they will strive to do as elegantly and correctly as it is possible. It doesn’t matter to the quants if the assumption of asset prices being lognormal is widely off the mark. In fact, they don’t care how the models behave. All they care about is about their formulae and results being correct – GIVEN the model of the market. I remember once spending a significant amount of time (maybe a couple of weeks) looking for bugs in my pricing logic because prices from two methods didn’t match up to the required precision of twelve decimal places (or was it fourteen? I’ve forgotten). And this after making the not-very-accurate assumption that asset prices are log normal. The proverb that says, “measure with a micrometer, mark with a chalk, cut with an axe”, is quite apt to describe the priorities of most quants.

Before I joined the firm, I used to wonder how bankers can be so stupid to make the kind of obvious silly errors (like assuming that housing prices cannot go down) that led to the global financial crisis of 2008. Two years at the firm, however, made me realize why these things happen. In fact, the bigger surprise, after the two years there, was about why such gross mistakes don’t occur more regularly. I think I’ve already talked about the culprits earlier in the post, but I should repeat myself.

First, a large number of guys building models come from similar backgrounds, so they think similarly. Because so many people think similarly, the rest train themselves to think similarly (or else get nudged out, by whatever means). So you have massive organizations full of massively talented brilliant minds which all think similarly! Who is to ask the uncomfortable questions? Next, who has time to ask the uncomfortable questions? Every one, from Partner downwards, has significant amount of “day to day work” to take care of every day. Bankers are driven hard (in that sense, and in that they are mostly brilliant, they do deserve the money they make), and everyone has a full plate (if you don’t it is an indication that you may not have a plate any more). There is little scope for strategic thinking. Again, remember that in an organization full of people who think similarly, people who have got promoted and made it to the top are likely to be those that think best along that particular axis. While it is the top management of the firm that is supposed to be responsible for the “big” strategic decisions, the kind of attention to details (which Math/Physics PhDs are rich in) that takes them to the top doesn’t leave them enough bandwidth for such thinking.

And so shit happens. Anyone who had the ability to think differently has either been “converted” to the conventional way of thinking, or is playing around with big bucks at some tiny hedge fund somewhere – because he found that it wasn’t possible to grow significantly in a place where most people think different to the way he thinks, and no one has the patience for his thinking.

This is the real failure in investment banking (markets) culture that has led to innumerable crises. The screwing over of clients and loss of “culture” in terms of ethics is a problem that has existed for a long time, and nothing new, contrary to what Greg Smith (formerly of Goldman Sachs) has written. The real failure of banking culture is this promotion of one-dimensional in-line-with-the-party thought, and the curbs against thinking and acting contrary to popular (in the firm) wisdom. It is this failure of culture that has led to the large negative shocks to the economy in the years gone by, and it is these shocks that have led common people to lose money rather than one off acts by banks where they don’t necessarily act in the interest of clients. And irrespective of how many Business Standards Committees and Risk Committees banks constitute, it is unlikely that this risk is going to go away any time soon. And I can’t think of a regulatory cure against this.