The purpose of reunions

So later today and tomorrow, the class of 2006 at IIMB is going to have a reunion. Reactions to this have been mostly mixed. Some people have been excited about it for months together. Some have been dismissive, loathing the idea of meeting some people they used to know. Most have gone along with the flow, quietly registering and promising to turn up.

As I’ve dealt with people showing all these reactions, I was thinking of why reunions make sense. I had even tweeted this last year:

As the reunion has come closer, though, my views have become more nuanced. Yes, I’ve kept in touch with all those batchmates I’ve wanted to keep in touch with. However, transaction costs (have I told you I’m writing a book on that topic? Just wrapped up third draft) mean that it’s not been possible to meet many of them.

It is not feasible, for example, to schedule a trip all the way to London because a handful of people you want to meet live there. Nor is it possible that even if you visit Mumbai, regularly, you are able to put “gencu” with everyone you have intended to put gencu with.

And so it remains, that you keep putting off meeting those people you want to meet until a time when transaction costs are low enough for you to be able to meet.

There are transaction costs that operate in other ways as well – a scheduled bilateral meeting is a commitment to exclusively talk to each other for at least close to an hour. And sometimes when you want to meet someone for the purpose of catching up, you aren’t sure if you can spend an hour with them without either of you getting bored. And so you put off that gencu.

The beauty of a scheduled reunion is that it takes into account both these costs. Firstly, by ensuring a large number of people congregate at one place at one time, it amortises (among all the counterparties you meet) the cost of having travelled to the meeting. Secondly, given that there are so many people around there, you don’t have an obligation to talk to anyone beyond the time when it’s pleasant for both of you (sadly, IIMB has outlawed alcohol on campus during the last decade so “i’ll go get a refill” trick of walking away won’t work).

The other great thing about a scheduled reunion (organised by the Alma Mater’s alumni office) is that it acts as what Thomas Schelling termed as “focal points“. Focal points are basically solutions to coordination games where each player plays in a natural or obvious way, expecting others to play the same way as well, so that they coordinate.

Now let’s say that the IIMB Class of 2006 decided to all meet sometime during the course of the year. Coordinating on a date would have been impossible, with any arbitrarily chosen date attracting too few people for network effects to take effect.

With the alumni office proposing a date and venue, it now becomes an “obvious solution” to everyone coming together and going through a process on that date (anchoring is also involved). People are willing to make the investment to meet on that date because they expect others to be there as well. So I’ve registered for this weekend’s event with the expectation that a large number of my batchmates would have done so as well, and each of them would have in turn registered for a similar reason.

Over the next couple of days I expect to spend a lot of time with people I’ve anyway been in touch with over the last 10 years. I might also spend a small amount of time with people I don’t really want to meet. But there is a large number of people I want to keep in touch with, but can’t due to transaction costs, and that is where I expect the reunion to add most value!

The problem with Slack, and why it’s inferior to DBabble

When two of the organisations I’m associated with introduced me to the chatting app Slack, it reminded me of the chatting app DBabble (known to us in IIMB as BRacket) that was popular back when I was in college.

There were two primary reasons because of which Slack reminded me of DBabble. The first was the presence of forums/groups. There was a “General” that everyone in the organisation was part of, and then were other groups that you could choose to join and be a conversation in. The second was that you could not only converse on the fora, but also send personal messages to each other – something DBabble also enabled.

There are several reasons why Slack is superior to DBabble. Most importantly, you can tag people in your messages on forums and they get notified, so that they can respond – this is a critical feature for using it for work purposes.

Secondly, Slack integrates well with other tools that people use for work – such as email and a lot of development tools, for example (which one of the organisations I’m associated with uses heavily, but I’ve never got into that loop). Slack also has a very nice search feature that allows you to pull up discussions based on keywords, etc.

What Slack sorely lacks, which makes me miss DBabble like crazy, however, is threaded conversations. The conversation structure in each channel in Slack is linear – which means you can effectively have only one thread of conversation at a time.

When you have a large number of people on the channel, however, people might initiate several different threads of conversation. As things are, however, a Darwinian process means that all but one of them get unceremoniously cut out, and we end up having only one conversation.

It is also a function of whether Slack is used for synchronous or asynchronous messaging (former implies everyone replies immediately, latter means conversations can take their own time and there’s no urgency to participate immediately, like email, for example). My understanding is that the way it’s built, it can be used in both ways. My attempts to use it as an asynchronous messenger, however, have failed because some of the conversations I’ve tried to initiate have gotten buried above other conversations others on the channel have tried to start.

The problem with Slack is that it assumes that each forum will have only one active conversation at a time. Instead, if (like DBabble) it allows us to have different conversation threads, things can become a lot more efficient.

One of the nice features of forums on DBabble was that everytime you went to the forum, it would show you all the active threads by showing them in bold. DBabble allowed infinite levels of threading, and only messages that were unread (irrespective of which branch of which thread they were in) would be in bold, meaning you could follow all threads of conversation (this also proved problematic for some as we developed an OCD to “unbold” – read every single message on every forum we were part of).

Imagine how powerful threaded conversations can be at the corporate level especially when you can tag people in them – so you go to a forum, and can see all open discussions and see where your attention has been called, and contribute. Threading also means that you can carry out several different personal (1-to-1) conversations at a time without losing track of any.

It’s interesting that after DBabble (which also died after a later edition gave the option of “chat mode” which did away with threaded conversations) there has been no decent chat app that has come up that allows threaded conversations. Apart from possible bandwidth issues (which can happen when each message is suffixed with the full thread below it), I don’t see any reason this can’t be implemented!

I want my BRacket (DBabble) back. But then, chat has powerful network effects and there’s no use of me wanting a particular technology if sufficient number of other people don’t!

Analysts, competition and Wall Street deaths

Yet another investment banking analyst has died. Sarvshreshth Gupta, a first year Analyst at Goldman Sachs’s San Francisco office reportedly killed himself after not being able to handle the workload. Reporting and commenting on this, Andrew Ross Sorkin writes:

Some banks, like Goldman, are also taking new steps, like introducing more efficient software and technology to help young analysts do their work more quickly. And investment banks say they are hiring more analysts to help balance the workload.

I simply fail to understand how these measures help balance the workload. I mean having more analysts is good in that the same work now gets split between a larger number of analysts. However, that there are more analysts doesn’t mean that the demand for Associates or Vice Presidents has actually gone up – that might go up only with deal flow.

In other words, what the above measure has done is to actually make the organisational structure “more pyramidal” (i.e. reduced the slope of the “pyramid’s walls”). So now you have a larger number of analysts competing for the same number of associate and VP positions. I don’t see how it makes things better at all!

On another note, I wonder if the number of deaths among Wall Street analysts has actually gone up, or if they have only started being reported more in recent times, after Wall Street got into trouble. Based on my limited understanding, I think it is the case of the former, and I attribute it to the lack of choice.

Back in 2004, I attended a talk by a Goldman Sachs MD (who worked in the Investment Banking Division, which does Mergers and Acquisitions, IPOs, etc.) in IIMB where he told me about the lifestyle in his division. That was the day I swore never to apply to that kind of a role. Given that the sales and trading side was doing rather well then, however, I had a choice to take up another equally lucrative, but less stressful-on-lifestyle career. That I chose not to (in 2006) is another matter.

The way I see it, following the crash of 2008, sales and trading have never recovered and don’t recruit as many as they used to. That takes care of one “competitor” of investment banking division. The other “competitor” is consulting, but they don’t pay just as well. In fact, with banking on the downswing, the supply of quality candidates to consulting firms has improved to the extent that they haven’t had to raise salaries as much. For example, starting salaries of IIM graduates at top-tier consulting firms in India have only grown at a CAGR of 6.5% since the time I graduated in 2006.

What this means is that few jobs can match the pay of investment banking, and that reduces the number of exit options. A few years back, anyone who found it too stressful had the option to move out to another job that was less demanding in terms of number of hours (though still stressful) without a cut in pay. This option has expired now, with the effect that people soldier on in investment banking jobs even if they’re not completely cut out for them.

And then some don’t make it. And so they go..

Another view from yet another other side

A few years back, after the first time I had interviewed people from campus, I had written a blog post about the experience. That post had ended up ruffling a few feathers, inviting angry comments from placement committees that it was my duty to make sure I read all the drivel they put out on their CVs and that the process I had followed was wrong.

Today I had an opportunity to be on the “other side” of another process I had gone through over a decade back – IIM admission interviews. This had nothing to do with my teaching position at IIMB; they had called for volunteers from among the alumni to help out with the admissions and I had put up my hand and thus went.

So there were two sessions, in each of which nine applicants were supposed to turn up. As it happened, only five and six respectively turned up, making our job easier. This is surprising since back in my days (2004) for most IIMs, most of the people who had applied would turn up for the interviews. The only IIM interview where I saw low attendance was Kozhikode (it was in Chennai, unlike others which were in Bangalore) where attendance was little over 50%.

The good news is that the group discussion (GD) has been done away with. It never really served much purpose anyway, and the IIMB Admissions Committee probably realised that. It is possible that GDs biased admission in favour of the more vocal and assertive, and I’m not sure if it was a great thing. Anyway, good riddance. The GD has now been replaced by a written test. Applicants are given a question they must comment on in writing. This is to test both their analytical reasoning skills and their written communication. I think that’s a great thing. We didn’t have to evaluate that though .

Coming to the interview itself, after the first few interviews I realised that there is a simple metric the professors use while judging a student. This is essentially a version of the O’Hare test used by investment bankers (banker bankers, not traders) to recruit. In the O’Hare test you evaluate if you’ll be able to get along with the applicant if you are stranded in a long layover with him/her. More generally, in a job interview you are testing if you’ll feel comfortable working with the applicant.

In a B-school admission interview, you evaluate if you want the student in your class. There are certain features that make for good students, and judgments of these vary from teacher to teacher of course. And decisions on whether to admit a particular student is made based primarily on whether the interviewing professor wants to see the student in class.

For example, if the student doesn’t display much energy, you’ll worry if she will participate enough in class. If the candidate is too loud and aggressive, you’ll fear that she may be a disruptive influence in class. If the candidate is stupid, then you know she’ll add no value to the class, and might hold back the class with her stupidity. If you think the candidate cannot work in groups, you’ll worry for her potential classmates who might have to team up with her for projects!

A similar list of examples can be produced for the other side. So essentially it boils down to this one thing – if you are going for an admission interview, you should be able to convince the interviewers that you will be an asset to the class that you’ll be sitting in, and that they should take you for that! Everything else is subordinate to this!

There are no other pertinent observations I can make without a breach of some kind, so I’ll stop here.

Programming assignments and blind men and the elephant

Evaluating a tough programming elephant is like the story of the blind men and the elephant. Let me explain.

The assignments that I’ve handed out as part of my Spreadsheet Modelling for Business Decision Problems course at IIMB involve fairly complex spreadsheet modelling (as the name of the course suggests). Thus, while it is a lot of effort on behalf of the student to do the assignment, it is also a lot of effort on my behalf if I’ve to go through the code line by line (these guys code using VBA macros), understand it and evaluate them.

Instead, I have come up with a set of “tests” – specific inputs that I give to the program (I’ve specified what the “front sheet” should look like so this is easy), and then see if the program gives out the desired outputs. Either way, I dig a little deeper and see if they’ve done it right, and based on that I grade the assignment.

If the assignments that they’ve turned in are elephants, it’s too much of an effort for me to open my eyes and actually see that they are elephants. Hence, I feel around, and check for a few different components to make sure they’ve submitted elephants. So for this assignment I might check if the trunk is like a snake, and if so, they’ve passed. For another assignment, I might check if the legs are like trees, and if they are, pass them. And so forth.

Now, this is evidently not perfect. For example, if you know that I’ll only check for the trunk to be like a snake, you’ll just submit a trunk that’s like a snake rather than submitting a full assignment! But if you don’t know what I’m going to check for, then it might be possible that you’ve only submitted a snake, I look for treetrunks and not finding them, give you a failing grade! There is a little bit of luck involved on both sides, but that’s how things work!

Extending this analogy to software testing, you can think of that too as an exercise of blind men learning about an elephant. The testers are the blind men of Indostan, trying to find out if the piece of code they’ve been given is an elephant. Each tester pokes around at a different part of the beast, trying to confirm if it fits what they’re looking for. And if the beast has a knife, a snake, a fan, a wall, a tree and a rope as part of it, it is declared as an elephant!

Speaking of software testing, I came across this brilliant video of a class in Hyderabad where software testing is being taught. Enjoy (HT: V Vinay).

How my IIMB Class explains the 2008 financial crisis

I have a policy of not enforcing attendance in my IIMB class. My view is that it’s better to have a small class of dedicated students rather than a large class of students who don’t want to be there. One of the upsides of this policy is that there has been no in-class sleeping. Almost. I caught one guy sleeping last week, in what was session 16 (out of 20). Considering that my classes are between 8 and 9:30 am on Mondays and Tuesdays, I like to take credit for it.

I also like to take credit for the fact that despite not enforcing attendance, attendance has been healthy. There have usually been between 40 and 50 students in each class (yes, I count, when I’ve bamboozled them with a question and the class has gone all quiet), skewed towards the latter number. Considering that there are 60 students registered for the course, this translates to a pretty healthy percentage. So perhaps I’ve been doing something right.

The interesting thing to note is that where there are about 45 people in each class, it’s never the same set of 45. I don’t think there’s a single student who’s attended all of my classes. However, people appear and disappear in a kind of random uncoordinated fashion, and the class attendance has remained in the forties, until last week that is. This had conditioned me into expecting a rather large class each time I climbed up that long flight of stairs to get into class.

While there were many causes of the 2008 financial crisis, one of the prime reasons shit hit the fan then was that CDOs (collateralised debt obligations) blew up. CDOs were an (at one point in time) innovative way of repackaging receivables (home loans or auto loans or credit card bills) so as to create a set of instruments of varying credit ratings.

To explain it in the simplest way, let’s say I’ve lent money to a 100 people and each owes me a rupee each month. So I expect to get a hundred rupees each month. Now I carve it up into tranches and let’s say I promise Alice the “first 60 rupees” I receive each month. In return she pays me a fee. Bob will get the “next 20 rupees”, again for a fee. Note that if fewer than 60 people pay me this month, Bob gets nothing. Let’s say Eve gets the next 10 rupees, so in case less than 80 people pay up, Eve gets nothing. So this is very risky, and Eve pays much less for her tranche than Bob pays for his which is in turn much less than what Alice pays for hers. The last 10 rupees is so risky that no one will buy it and so I hold it.

Let’s assume that about 85 to 90 people have been paying on their loans each month. Not the same people, but different, like in my class. Both Alice and Bob are getting paid in full each month, and the return is pretty impressive considering the high ratings of the instruments they hold (yes these tranches got rated, and the best tranche (Alice’s) would typically get AAA, or as good as government bonds). So Alice and Bob make a fortune. Until the shit hits the fan that is.

The factor that led to healthy attendance in my IIMB class and what kept Alice and Bob getting supernormal returns was the same – “correlation”. The basic assumption in CDO markets was that home loans were uncorrelated – my default had nothing to do with your default. So both of us defaulting together is unlikely. When between 10 and 15 people are defaulting each month, that 40 (or even 20) people will default together in a given month has very low probability. Which is what kept Alice and Bob happy. It was similar in my IIMB class – the reason I bunk is uncorrelated to the reason you bunk, so lack of correlation in bunking means there is a healthy attendance in my class each day.

The problem in both cases, as you might have guessed, is that correlations started moving from zero to one. On Sunday and Monday night this week, they had “club selections” on IIMB campus. Basically IIMB has this fraud concept called clubs (which do nothing), which recruiters value for reasons I don’t know, and so students take them seriously. And each year’s officebearers are appointed by the previous year’s officebearers, and thus you have interviews. And so these interviews went on till late on Monday morning. People were tired, and some decided to bunk due to that. Suddenly, there was correlation in bunking! And attendance plummeted. Yesterday there were 10 people in class. Today perhaps 12. Having got used to a class of 45, I got a bit psyched out! Not much damage was done, though.

The damage was much greater in the other case. In 2008, the Federal Reserve raised rates, thanks to which banks increased rates on home loans. The worst borrowers defaulted, because of which home prices fell, which is when shit truly hit the fan. The fall in home prices meant that many homes were now worth less than the debt outstanding on them, so it became rational for homeowners to default on their loans. This meant that defaults were now getting correlated! And so rather than 85 people paying in a month, maybe 45 people paid. Bob got wiped out. Alice lost heavily, too.

This was not all. Other people had bet on how much Alice would get paid. And when she didn’t get paid in full, these people lost a lot of money. And then they defaulted. And it set off a cascade. No one was willing to trade with anyone any more. Lehman brothers couldn’t even put a value on the so-called “toxic assets” they held. The whole system collapsed.

It is uncanny how two disparate events such as people bunking my class and the 2008 financial crisis are correlated. And there – correlation rears its ugly head once again!

 

The Peer Pressure of Finishing An Exam Early

Today is the final exam of my course at IIMB. It’s a two part exam – students have been given the problems today and they have to describe on paper how they are going to approach the problem. Tomorrow I’ll send them relevant data and then they need to build an Excel model and solve the problem.

The point of this blog post, however, is to do with the peer pressure of finishing an exam early. Today’s exam is taking place in two rooms, with the students having been divided equally between the rooms. I’m writing this two and a half hours into a four hour exam, and so far about a dozen students have handed in their papers. The interesting thing is that eleven of these are from one room, and one from the other.

This makes me wonder if there is some kind of “peer pressure” in terms of finishing an exam. When you hand in your paper early, you signal one of two things – either that you have really aced the exam or that you really have no clue. By looking at the people who have walked out so far and their academic reputations, it is possible for the remaining students to know whether the people who have left have aced the exam or given up.

So the question is if there is some kind of gamesmanship involved in finishing an exam early. Let’s say a stud walks out of a 4-hour exam in an hour. Does he walk out early in part to let his peers know that it was a bloody easy exam and that they should be doing better than they already are? And does this in part put pressure on the other studs to “preserve their reputations” in some manner by also finishing early? And does this imply that they might hurry up and not do a good enough job of the exam, leading to suboptimal performance and better grades (let’s assume a relative grading system) for the person who originally walked out?

Or do you think walkouts are independent? That two students walking out i close succession to each other were independent events that I’m reading into too much? I wish I had actually tabulated the timings at which papers had been handed in, and maybe perhaps correlated them with the actual performance in an exam (to analyse how early finishing affects performance). As it stands, though,I should work on the data available.

I’m writing this blog post siting in room 1 (posting later since Wi-Fi has been switched off here for purpose of the exam). After I started writing, one of the studs sitting in room 1 walked out. Almost in quick succession one other stud in this room followed him. This is the room where one guy had walked out really early, and he’s also one of the studs of the class.

This suggests that there is some kind of correlation. A sort of relationship. That one person walking out puts pressure on others to also walk out. And can result in some good “relative grading”!

I’ll end with an anecdote from my days as a student here, almost exactly 9 years back. It was an objective final exam, with multiple choice questions only. And in that series of exams it had been some sort of a competition as to who would walk out early.

So it was the last exam, and this one guy decided to “show off” by walking out within five minutes. Unfortunately one other guy had decided to turn up late for the exam. The institute rules state that nobody is allowed into an exam after at least one student has walked out. So the second guy was not allowed to take the exam.

As it turned out, he got a better grade than the guy who had walked out within five minutes!

Finance is boring, once again

So IIMB goes to placements this week. Two months back, though, in the first class I taught there, in an attempt to “understand the class”, I asked my students to tell me their “most preferred employer”. The intention was to tailor the course in a way that would be more suitable for their prospective careers.

Thinking back at that class, there is one thing that hits me – very few want to do finance (again that’s no indication of how many of them will end up in finance jobs this week). I initially thought it was a biased sample – there was a course of the same name offered to the same batch in an earlier term, and those that had taken the course then were not eligible to take the course now. Given the primacy of spreadsheets in finance, I thought students more inclined towards finance would have taken the course in the earlier offering. But then thinking about it (without data to back me), that so few want to do finance doesn’t surprise me at all.

When I tried putting myself in the shoes of my students and thought of what jobs I wanted to take, I realised that there weren’t any finance jobs that I could think of. With the derivatives world having undergone several downturns in the last decade, no one recruits for derivative sales and trading from IIMs any more (if my information sources are right – they could be wrong). And if you were to take out derivatives sales and trading, there is very little that excites about the other finance jobs that recruit MBAs.

There is investment banking (M&A, Equity/Debt Capital Markets) of course, but the job is insanely fighter, and while it is ultimately a finance job, finance forms a small portion of your day-to-day activities there (secondhand information again). Venture capital and private equity are again ostensibly finance but again there is very little finance you use in decision-making there – other “softer” stuff (such as evaluating “quality of founding team”, etc.) dominate.

Then there is commercial banking, which is finance only in name, for most jobs for which they recruit MBAs (data from a decade back) are in the realm of sales or business development. There is the odd treasury or risk management job, but those jobs are small in number compared to the others. And corporate finance jobs see excitement very rarely (when there is M&A or related activity). You have asset management and research roles, but they are again not the kind that you would call as “exciting”.

In short, finance has become boring, again. Most jobs on offer to fresh MBAs nowadays are for roles that are fairly routine and “boring” for the most part, and while finance still pays well, there are no adrenaline-pumping jobs on offer there as there used to be a decade ago. And from the macro point of view, that is a good thing.

Because finance is fundamentally a boring job, and is supposed to be a boring job. If finance had become “exciting”, it was because finance people were doing stuff that they were not supposed to be doing! Like taking highly levered bets for example, or concocting derivatives so complicated that nobody – not even most traders – would be able to understand it.

I had written recently that people have stopped considering coding “cool”, and that we should do something about it. A similar thing is happening to finance, where MBA students are not finding it “cool” any more (but people will take up the profession since it pays well). However, this is not a problem, and nothing needs to be done about it. This is how things ought to be. Finance is supposed to be boring!

Anyway, this might be biased opinion since if I could roll back nine years and were asked to pick a job, I couldn’t see myself working at ANY of the companies that had come to recruit from IIMB back when I graduated! So perhaps my hypothesis about finance jobs being boring now is a result of all typical post-MBA jobs being boring! Perhaps that explains why I’m doing what I’m doing now – a “job” so atypical it takes a lot of effort to explain to people what I’m doing.

Oh, and coming back to finance, I’m four weeks though with my Asset Pricing MOOC, and have been totally enjoying it so far!

Teaching at IIMB: Mid-term review

IIMB has a strange policy. They are not allowed to have classes tomorrow on account of it being a national holiday so they shifted tomorrow’s concept to today, indicating a complete lack of appreciation of the concept of the long weekend. Anyway, since I didn’t have any other plans for the day or the weekend I decided to not request for a slot change and went anyways. This was my eleventh class out of twenty.

I expected the attendance to be rather thin today, but the class surprised me with more than three-fourths of the registered students turning up (on par with most sessions so far). And despite the class being at 8 am in the morning, none of them slept (at least I didn’t notice anyone sleeping). That is again on par with the course so far – more than halfway though the course and I’m yet to catch a single person sleeping in class! Maybe I should take some credit for that.

The class before today’s was about ten days back (long gap due to mid-term exams), and that day I had a minor scare. I had formulated a case that involved solving the Newsboy Problem (now politically corrected to “Newsvendor model“) as a sub-step in the solution to the case. Having worked out the sketches of the case solution the previous night I went to sleep hoping to work out the full case before I went to class. And my brain froze.

So it was 6:30 on the morning of an 8am class and I wasn’t getting the head or tail of the newsboy problem despite having known it fairly well. Decided to have cereal at home rather than go to SN to give myself more time to read up and understand the model. And my brain refused to open up. Yet I made my way to class, hoping I could “wing it”.

I didn’t have to, for the class exceeded expectations and solved the case for me. One guy popped up with “newsvendor model”. Another guy said that we could consider a certain thing as a “spot price”, thus eliminating the need to make any assumptions on costs. Then we started working out the model on Excel (remember that this is a “spreadsheet modelling” course). And the time came to implement the newsvendor model. And my brain froze in anticipation. “How do we do this?”, I asked, trying to not give away my brain freeze.

“We calculate the critical ratio”, came the chorus (sometimes I dispense with the politeness and order of people raising their hands and speaking in order). “And what is that here?”, I asked. “B6/(B5+B6)” came back the chorus. And then when I asked them how to impute the ordering level based on this, the chorus had figured out the exact way in which we should use NormInv to determine this. The troubling bit of the newsvendor problem having been thus solved, I took control and went forward with the rest of the case. And my respect for the class went up significantly that day.

Later in the day I was relating the incident to the wife, who I might have mentioned is an MBA student at IESE Business School in Barcelona. “Oh my god, your class is so quant”, she exclaimed. This is a topic for another day but perhaps due to the nature of the admissions procedure, students at IIMs are definitely much much more quantitatively oriented than students at B-schools elsewhere. Yet, IIMs don’t seem to be doing much in terms of harnessing this quant potential which should be giving their students a global competitive advantage.

And coming back to my class, they’ll be sitting for placements starting the 9th of February. If my class is a representative sample (it is most likely not, since I’m teaching an elective and these people expressed interest in learning what I’m teaching, so there is a definite bias), this seems like a great batch at IIMB. So I encourage you to go and recruit!

 

Deranging groups

Ok so this is a mathematical problem. I plan to give three group assignments to my IIMB class. Let’s assume that there are 60 kids and for each assignment I want them to form groups of four members each. For the first assignment I’ve let them form the groups themselves.

For the second assignment, though, I want to create a “derangement” of these groups – in the sense that I want to form a different set of 15 groups of 4 members each such that no pair of students who are in the same group for assignment 1 will be in the same group for assignment 2. And I’m looking for an algorithm to thus “derange” my students. And whether it is possible at all to derange students thus.

My inclination is that this might have a solution in graph theory – in terms of graph colouring or something? Take the students from the first group and join every pair of students that are in the same group with an edge. Then colour the nodes of the graph. Pick nodes of the same colour (these are students that haven’t been in groups together) and randomly assign them to new groups. Repeat for all colours.

Question is how many colours we need to colour the graph. If it’s planar, we’ll need only 4 colours! And considering that the first assignment has 4 students per group, the maximum degree of a node is 3. If the maximum degree of an edge is 3, does that say anything about the planarity of the graph? If I derange the students once for assignment 2, can I do it again for assignment 3 (now each node has a degree of 6!) ? How do I think about this mathematically? Can you help?