## Conductors and CAPM

For a long time I used to wonder why orchestras have conductors. I possibly first noticed the presence of the conductor sometime in the 1990s when Zubin Mehta was in the news. And then I always wondered why this person, who didn’t play anything but stood there waving a stick, needed to exist. Couldn’t the orchestra coordinate itself like rockstars or practitioners of Indian music forms do?

And then i came across this video a year or two back.

And then the computer science training I’d gone through two decades back kicked in – the job of an orchestra conductor is to reduce an O(n^2) problem to an O(n) problem.

For a  group of musicians to make music, they need to coordinate with each other. Yes, they have the staff notation and all that, but still they need to know when to speed up or slow down, when to make what transitions, etc. They may have practiced together but the professional performance needs to be flawless. And so they need to constantly take cues from each other.

When you have $n$ musicians who need to coordinate, you have $\frac{n.(n-1)}{2}$ pairs of people who need to coordinate. When $n$ is small, this is trivial, and so you see that small ensembles or rock bands can easily coordinate. However, as $n$ gets large, $n^2$ grows well-at-a-faster-rate. And that is a problem, and a risk.

Enter the conductor. Rather than taking cues from one another, the musicians now simply need to take cues from this one person. And so there are now only $n$ pairs that need to coordinate – each musician in the band with the conductor. Or an $O(n^2)$ problem has become an $O(n)$ problem!

For whatever reason, while I was thinking about this yesterday, I got reminded of legendary finance professor R Vaidya‘s class on capital asset pricing model (CAPM), or as he put it “Sharpe single index model” (surprisingly all the links I find for this are from Indian test prep sites, so not linking).

We had just learnt portfolio theory, and how using the expected returns, variances and correlations between a set of securities we could construct an “efficient frontier” of securities that could give us the best risk-adjusted return. Seemed very mathematically elegant, except that in case you needed to construct a portfolio of $n$ stocks, you needed $n^2$ correlations. In other word, an $O(n^2)$ problem.

And then Vaidya introduced CAPM, which magically reduced the problem to an $O(n)$ problem. By suddenly introducing the concept of an index, all that mattered for each stock now was its beta – the coefficient of its returns proportional to the index returns. You didn’t need to care about how stocks reacted with each other any more – all you needed was the relationship with the index.

In a sense, if you think about it, the index in CAPM is like the conductor of an orchestra. If only all $O(n^2)$ problems could be reduced to $O(n)$ problems this elegantly!

## On reliably asking for help

Last evening while I was trying to teach the wife to ride a geared motorcycle, a middle-aged woman accosted us. She told us that she was a teacher from Hiriyur (Chitradurga district) and had lost all her money and needed help for her bus charge to go back to town. This sounded suspiciously similar to the couple from Nagpur with a similar story that I’ve encountered a few times, and so I told her off, rather rudely I must say.

She seemed to be taken aback, and hurled some curses on me as she walked away, and then my wife pointed out that there were some things about this woman’s story that made it sound genuine. So now I wonder (given that it is a finite possibility that I might be stuck in an unknown city without money) what one needs to do in order to reliably ask for monetary help – given that fraudsters abound (if I had been convinced that this woman wasn’t a fraud I would’ve helped her out, so let’s take that as a given).

Here are some points that I can quickly think of:

• Location – would you think someone who would come to you in a residential area (Jayanagar) where not too many people were walking around, and ask for help if they really wanted money? Wouldn’t they rather try at bus stops, or even get on to buses and try get the ticket off a conductor or a fellow-passenger? Or considering that this lady had to make an inter-city journey, wouldn’t it be more reliable for her to have somehow got to the bus stand and asked someone there?
• Persistence – after I’d told this woman off, she just kept hanging around, and refused to go after I told her in no uncertain terms that I’m not helping her out. Wouldn’t you expect people who are really in need to be more rational and try and look for other sources rather than hanging on to the one person she sees on the street?
• What you ask for – again ties back to the first point that it might be easier to convince people to buy you a ticket than give you money. Or if you were to walk up to a shop and ask to use their landline phone? (mobile doesn’t work, since that’s a well-known method of swindling mobiles; was once tried on me in Bombay)
• Abuses – when you are really in need, and someone doesn’t help you out, you don’t loudly abuse them when you go. You’d rather quietly slink away and try your luck elsewhere .

I must say that the woman was rather “respectably dressed”, and before she started abusing she spoke “good Kannada”. It’s just that I wasn’t convinced she wasn’t a fraud so didn’t give her any money.

In any case, what signals would you look for when someone were to come and ask you for monetary help? And what signals would you try to give out if you were to ask for monetary help?

## Wagah Border

Ok this post is approximately one month late. Truth is that I’d thought this up almost a month back – in fact more than a month back, as I got my ass roasted by the hot concrete galleries while waiting for the flag-down ceremony to begin at the Wagah Border. My mind had then gone back to the old IITM chant “start the f***ing show”, but given that I couldn’t actually utter those words, I’d thought up this blog post instead. I had constructed each and every sentence of how I was going to write this. It was a maze of thoughts. Unfortunately, I’d forgotten most of it until I’d gotten back to Delhi two days later – which was when I had access to the net.

I attempted to write this post back when I was in Delhi, but couldn’t get beyond a paragraph. What I had written would never measure up to what I’d constructed in my head on that day at the Wagah, and I kept scrapping it. But then, there’s a story to be told, so I think it’s time I tell the story, “in my own words”.

Ok so now that I’ve gotten beyond two paragraphs, the rest of this should flow, hopefully. It was a hot and crowded afternoon. There were three stalls, and one had been kept closed. People were piled into the other two stalls – one for ladies and one for men. It was as hot as a Punjabi summer afternoon could get. The concrete benches were all heated up, and there were the military men who were exhorting people to sit down and get their asses roasted.

And there was the master of ceremonies. One man in plain clothes with a mic. Periodically he’d surface and shout slogans, which the over-enthusiastic crowd would complete. He would drag young women out of their stands and make them run around the place with the National Flag, which they enthusiastically did. He would wave his hands as if his repressed dream was to be a band conductor, and people would tone up or tone down their cheers.

And the people! It was incredible. I had never known that the Indian mango man could be so enthusiastic. There seemed to be something special in the air as everyone shouted and cheered, and danced and swung, as the patriotic songs blared and the master of ceremonies waved his hands around. People seemed to be remembering their mis-spent youths and trying to re-live it in the name of patriotism. It was like going back to one of those wonderful inter-school cul-fests. The kind of enthu seen at the Wagah Border would put the Saarang Pro-shows to shame.

Sadly, it had no effect on me. I stood by myself, in one corner, bored, and observing the people. Maybe it was a good thing that I was bored, since I managed to get my thoughts in order – though I was to subsequently forget them. Music was blaring, people were shouting, but it didn’t seem to make any sense to me. We were there to witness a military parade, which I thought was a fairly solemn occasion. And here you had people who were “letting go” like nobody’s business. Maybe I’ve become too cynical. Maybe a certain libertarian-leaning group that I’m part of is having too much of an influence on me.

I was a reluctant visitor to the border. I didn’t want to go. The reason I was at Amritsar was to see the Golden Temple and thulp the food that I’d heard so much about. Wagah wasn’t part of my plans. My mother, however, had other ideas. For some reason, she had happened to really enjoy the border parade when she had visited there six years back along with my father. And she wanted me to “experience this experience”. While we were driving back, however, she admitted that the show wasn’t as spectacular as it was six years ago.

In the beginning of the post, I had mentioned ot you that I’d wanted to chant an IITM chant. Once the “show” started, another favourite IITM chant came to my head. “STOP the f***ing show”. It was drab and boring. Say what you want, but I somehow don’t find the idea of a bunch of armymen marching and performing drills exciting. And it can be consumed in small doses only. To their credit, the show at Wagah wasn’t too long – it lasted only for about half an hour or so.

However, given the conditions (crowd, weather, etc.) it didn’t turn out to be a pleasant experience. The idea of going to the border to watch the ceremonies was so not worth it. Only a couple of days earlier, I had read about the Hillsborough tragedy, and given the way the crowd was pushing and jostling and continued to pour in after the stands were full brought up thoughts of an encore. At one point, I even left  my prized spot in one of the stands in order to go to the relative safety of the ground outside the stands. I only went back in after they opened the third stand (which had been closed till half an hour before the show) and could find a relatively peaceful spot to stand there.

I don’t think I’ve documented all that I’d thought of when I stood there in that relatively peaceful spot in that third stand. I’ll probably make a separate post out of all that if I do manage to remember it sometime.