## Brahmastra

Sometimes we overdo “option value”. We do things that have a small possibility of a big upside, and big possibility of no or very minimal downside, in the belief that “nothing can go wrong in trying”.

My father used to term this “pulling a mountain with a string”, with the reasoning being that if you actually manage to pull, then you have moved a mountain. If not, all that you have lost is a string.

There is one kind of situation, however, where I think we might overindex on option value – these are what I call “one shot events” or “brahmastras”.

Going into a little bit of mythology, there is the story of the Brahmastra in the Mahabharata. Famously, Karna possesses it. It is an incredibly powerful weapon with the feature (or bug, rather) that it can be used only once. Karna would have set it aside to use on Arjuna, but the Pandavas decide to send Ghatotkacha to create havoc during the night fight when Karna is forced to use up his brahmastra on Ghatotkacha – meaning he didn’t have access to it in his battle with Arjuna, where he (Karna) ultimately got killed.

Because the Brahmastra could be used only once, Karna wanted to maximise the impact of the weapon. His initial plan was to use it on what he thought might be a decisive battle with Arjuna. The Pandavas’ counterplan was to force him to use it earlier.

Actually, thinking about it – the Brahmastra can be thought of as another kind of option. The problem here being one of optimal exercise. Actually, there is a very stud paper written by economist Avinash Dixit on this topic – regarding Elaine’s sponges.

Read the whole paper. It is surely worth it. To quickly summarise, Elaine has a limited number of “contraceptive sponges”, and wants to maximise her “utility” of using them. When a guy comes along, she needs to decide whether it is worth expending a sponge on him. Dixit derives a nice equation to determine a function for this.

Basically, Brahmastra occurs when you have only one sponge left, and you need to use it at an “optimal time”. There is another problem in economics  called the “secretary problem” (nothing to do with secretary birds) that deals with this.

Recently I’ve been thinking – these kind of Brahmastra / sponge / secretary problems are important to solve when you are thinking of talking to someone.

Let’s say you have what you think is a studmax application of GenAI and want to talk to VCs about it. If you go too early, the VC will only see a half-baked version of your idea, and even if you go to them later once you have fully formed it, the half-baked idea you had showed them will influence them enough to discount your later fully formed idea.

And if you go too late, the idea may not be that studmax any more, and the VC might dismiss it. So it’s a problem of “optimal exercise” (note that this is an issue only with American options, not European).

It is similar with asking someone out (or so I think – I’ve been out of this business for 14 years now). You approach them “too early” (before they know you), they will dismiss you then and then forever. You approach too late and the option would have expired.

In the world of finance, we focus too much on the PRICE of options and (based on my now limited knowledge) too little on optimal expiry of the said options. In the real world, the latter is also important.

## Party Games

A year and half back, my wife had gone to Gurgaon on work. One evening, she called and told me that she was “going to go for a party at the guest house”, which I duly conveyed to our daughter.

The next morning, our daughter woke up and asked me about her mother’s party. Having been appraised of the proceedings late in the night, I shared the summary. “That is all fine, Appa”, she want, “but WHAT WAS THERE at the party?”.

I was a bit puzzled by the question and said there was nothing. “Why does a party need to have anything?”, I replied, “in this case there was big people juice, which people drank and talked to each other”.

It was in the course of that conversation that I realised that most kids’ parties usually have “something”. Some have bouncy castles. Some take place in play areas. Some people organise magic shows. Others have art workshops. And so on. A lot of kids’ parties are “structured”, with “stuff to do”.

Coming to think of it, this is not true of kids’ parties alone. Even a lot of adult parties nowadays have “themes”. So people have “poker nights”, or “board game nights”, or “movie nights” for which they call other people and socialise and together perform what can sometimes be a perfectly satisfactory single player activity.

Poker nights, I can understand, since it is sport, and one that can be much better played offline. However, I can’t imagine calling a bunch of random friends for a “poker night” – if it’s a poker night, it ought to be a bunch of people who are also interested in poker.

That aside, why should you bother hosting a party for a bunch of friends, and then not give them the opportunity to talk to one another, and instead subject them to some “party game”? “What is even the point of having structured activities at a party?”, my wife wondered loudly one morning.

My theory is this – not everyone is interesting and capable of holding an intelligent conversation. However, everyone has the need to talk to other people and socialise.

So if you are not sure about the quality of conversations that the people you are inviting to a party are likely to contribute, you want to somehow ensure that the party is at least somewhat interesting to everyone that attends. And so, you get rid of the upside (of some fantastic conversation happening at the party), and instead limit the downside (of everyone there getting bored), and put some structured activity on the party.

In other words, you put a “collar” on the party.

I have written here about the concept of “alcohol buddies“:

My friend Hari The Kid has this concept of “alcohol buddies”. These are basically people who you can hang out with only if at least one of you is drunk (there are some extreme cases who are so difficult to hang out with that the only way to do it is for BOTH of you to be drunk). The idea is that if both of you are sober there is nothing really to talk about and you will easily get bored. But hey, these are your friends so you need to hang out with them, and the easiest way of doing so is to convert them into alcohol buddies.

Now, there are some people who you can’t hang out with in “ground state”, but when one or both of you is drunk you can have an interesting conversation. Those are alcohol buddies.

However, there is a (possibly small) set of people who are fundamentally so uninteresting that even if both of you are pissed drunk, it is impossible to have a conversation is interesting to both people. And if you are having a largish party with a diverse set of guests, it is likely that there are many such pairs of guests, who cannot talk to each other even when pissed drunk.

And that is where having a party game helps. It prevents people from having random conversations and instead corrals (notice that wordplay there) everyone into the party game collar. No upside, no downside, nobody needs to find that there are others at the party who are absolutely boring to them. They all go home happy.

So far, we have resisted this “themed party” concept, except maybe in the context of NED Talks. Even our daughter’s birthday parties, so far, have been at home (once in Lalbagh during the pandemic), with the only “planned activity” being eating cake and snacks, and kids randomly playing in her room.

Let’s see how far we can carry this on!

## Algo trading and ice cream

I refuse to share ice cream with my daughter, just like I used to refuse to share peanuts with my father. This refusal to share in both cases primarily has to do with the differential speed of consumption.

With my father and peanuts, it was a matter of ability – as someone who had grown up on a peanut farm (and thus he was a fan of Jimmy Carter), he was an expert at shelling peanuts. The Bangalore-born me was much less expert, and so before I knew it he would have finished the lot of it.

With my daughter and ice cream, it is a matter of willingness – she likes to finish it quickly, in big spoons. I like to savour it over a long time – at home,  I use a rather small spoon and eat it slowly. Nowadays I’ve been trying to cut down sugars and so when I eat them I try to get the maximum benefit out of them and thus eat slowly. However, even as a child I would eat my desserts slowly, trying to “extract maximum benefits”.

So last night we were having ice cream (individual small tubs of course). Daughter finished hers quickly and came to me, to see that my tub was still half full (and I was blogging as I was eating it).

“Appa, why do you like to turn your ice cream into milkshake?”, she asked.

“I don’t”, I said, “I just try to get the maximum value out of it, and thus I eat it slowly”.

“But then if you take too long to eat, then it turns into milkshake which is much less enjoyable than ice cream”, she countered. She had a valid point.

And then I realised this is exactly the problem I worked on during my stint as an investment banking quant in 2009-11. I was working on algo trading, specifically execution of large block deals.

The tradeoff there was that if you traded too quickly, you would end up moving the market and thus trading at an unfavourable price. On the other hand, if you traded too slowly, the natural volatility of the stock would mean that the market might move against you. And so you had to balance the two and trade.

I won’t go into the details on how we solved it (my erstwhile bank might not like it), but it suffices to say here that it is similar to eating ice cream.

If you eat too quickly, you run the risk of not getting sufficient “benefit” out of the ice cream at hand. If you eat too slowly, then there is the risk that the ice cream itself will melt and thus be less enjoyable for you.

I tried explaining this analogy to my daughter last night, but she didn’t get it. I guess she is too young to understand risk, volatility, market impact and the like.

And so I’m inflicting this on you!

## It’s not just about status

Rob Henderson writes that in general, relative to the value they add to their firms, senior employees are underpaid and junior employees are overpaid. This, he reasons, is because senior employees trade off money for status.

Quoting him in full:

Robert Frank suggests the reason for this is that workers would generally prefer to occupy higher-ranked positions in their work groups than lower-ranked ones. They’re forgoing more earnings to hold a higher-status position in their organization.

But this preference for a higher-status position can be satisfied within any given organization.

After all, 50 percent of the positions in any firm must always be in the bottom half.

So the only way some workers can enjoy the pleasure inherent in positions of high status is if others are willing to bear the dissatisfactions associated with low status.

The solution, then, is to pay the low-status workers a bit more than they are worth to get them to stay. The high-status workers, in contrast, accept lower pay for the benefit of their lofty positions.

I’m not sure I agree. Yes, I do agree that higher productivity employees are underpaid and lower productivity employees are overpaid. However, I don’t think status fully explains it. There are also issues of variance and correlation and liquidity (there – I’m talking like a real quant now).

One the variance front – the higher you are in the organisation and the higher your salary is, the more the variance of your contribution to the organisation. For example, if you are being paid $350,000 (the number Henderson hypothetically uses), the actual value you are bringing to your firm might have a mean of$500,000 and a standard deviation of $200,000 (pulling all these numbers out of thin air, while making some sense checks that broadly risk pricing holds). On the other hand, if you are being paid$35,000, then it is far more likely that the average value you bring to the firm is $40,000 with a standard deviation of$5,000 (again numbers entirely pulled out of thin air). Notice the drastic difference in the coefficient of variation in the two cases.

Putting it another way, the more productive you are, the harder it is for any organisation to put a precise value on your contribution. Henderson might say “you are worth 500K while you earn 350K” but the former is an average number. It is because of the high variance in your “worth” that you are paid far lower than what you are worth on average.

And why does this variance exist? It’s due to correlation.

More so at higher ranked positions (as an aside – my weird career path means that I’ve NEVER been in middle management) the value you can add to a company is tightly coupled with your interactions with your colleagues and peers. As a junior employee your role can be defined well enough that your contributions are stable irrespective of how you work with the others. At senior levels though a very large part of the value you can add is tied to how you work with others and leverage their work in your contributions.

So one way a company can get you to contribute more is to have a good set of peers you like working with, which increases your average contribution to the firm. Rather paradoxically, because you like your peers (assuming peer liking in senior management is two way), the company can get away with paying you a little less than your average worth and you will continue to stick on. If you don’t like working with your colleagues, there is the double whammy that you will add less to the company and you need to be paid more to stick on. And so if you look at people who are actually successful in their jobs at a senior level, they will all appear to be underpaid relative to their peers.

And finally there is liquidity (can I ever theorise about something without bringing this up?). The more senior you go, the less liquid is the market for your job. The number of potential jobs that you want to do, and which might want you, is very very low. And as I’ve explained in the first chapter of my book, when a market is illiquid, the bid-ask spread can be rather high. This means that even holding the value of your contribution to a company constant, there can be a large variation in what you are actually paid. And that is a gain why, on average, senior employees are underpaid.

So yes, there is an element of status. But there are also considerations of variance, correlation and bid-ask. And selection bias (senior employees who are overpaid relative to the value they add don’t last very long in their jobs). And this is why, on average, you can afford to underpay senior employees.

## Christian Rudder and Corporate Ratings

One of the studdest book chapters I’ve read is from Christian Rudder’s Dataclysm. Rudder is a cofounder of OkCupid, now part of the match.com portfolio of matchmakers. In this book, he has taken insights from OkCupid’s own data to draw insights about human life and behaviour.

It is a typical non-fiction book, with a studmax first chapter, and which gets progressively weaker. And it is the first chapter (which I’ve written about before) that I’m going to talk about here. There is a nice write-up and extract in Maria Popova’s website (which used to be called BrainPickings) here.

Quoting Maria Popova:

What Rudder and his team found was that not all averages are created equal in terms of actual romantic opportunities — greater variance means greater opportunity. Based on the data on heterosexual females, women who were rated average overall but arrived there via polarizing rankings — lots of 1’s, lots of 5’s — got exponentially more messages (“the precursor to outcomes like in-depth conversations, the exchange of contact information, and eventually in-person meetings”) than women whom most men rated a 3.

In one-hit markets like love (you only need to love and be loved by one person to be “successful” in this), high volatility is an asset. It is like option pricing if you think about it – higher volatility means greater chance of being in the money, and that is all you care about here. How deep out of the money you are just doesn’t matter.

I was thinking about this in some random context this morning when I was also thinking of the corporate appraisal process. Now, the difference between dating and appraisals is that on OKCupid you might get several ratings on a 5-point scale, but in your office you only get one rating each year on a 5-point scale. However, if you are a manager, and especially if you are managing a large team, you will GIVE out lots of ratings each year.

And so I was wondering – what does the variance of ratings you give out tell about you as a manager? Assume that HR doesn’t impose any “grading on curve” thing, what does it say if you are a manager who gave out an average rating of 3, with standard deviation 0.5, versus a manager who gave an average of 3, with all employees receiving 1s and 5s.

From a corporate perspective, would you rather want a team full of 3s, or a team with a few 5s and a few 1s (who, it is likely, will leave)? Once again, if you think about it, it depends on your Vega (returns to volatility). In some sense, it depends on whether you are running a stud or a fighter team.

If you are running a fighter team, where there is no real “spectacular performance” but you need your people to grind it out, not make mistakes, pay attention to detail and do their jobs, you want a team full of3s. The 5s in this team don’t contribute that much more than a 3. And 1s can seriously hurt your performance.

On the other hand, if you’re running a stud team, you will want high variance. Because by the sheer nature of work, in a stud team, the 5s will add significantly more value than the 1s might cause damage. When you are running a stud team, a team full of 3s doesn’t work – you are running far below potential in that case.

Assuming that your team has delivered, then maybe the distribution of ratings across the team is a function of whether it does more stud or fighter work? Or am I force fitting my pet theory a bit too much here?

## 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!

## IPOs and right to match

Long time readers of the blog might know that I’m not a big fan of the IPO pop. I’ve traditionally belonged to the party (led by Bill Gurley) that says that a big IPO pop is akin to “leaving money on the table” for the company.

And so as my party has grown, the IPO process itself has also changed. Way back in 2004, Google allocated shares using a simple Dutch auction. Facebook pushed its bankers hard enough on the IPO price that the IPO “pop” in that case was negative. Spotify and Slack and a few other companies went public in a direct listing. Nowadays you have SPACs. It’s all very interesting stuff for anyone interested in market design.

Over the last few years, though, Matt Levine has been trying hard (and sort of succeeding), in getting to move me to the side that says IPO pops are okay. His first compelling argument was the demand-supply (and market depth) one – in an IPO there is a large offload of shares, and so an IPO buyer can expect to get a discount on the shares. Another is that since the IPO is the first time the stock will be traded, buyers in the IPO are taking risk, and need to be compensated for it in the form of a lower price. Fair enough again.

Matt has outdone himself in his latest newsletter on the topic, where he talks about the IPOs of Roblox and Coupang. About Roblox, he wrote:

I mean, I’ll tell you the answer[1]: Roblox sold stock to venture capitalists at $45, and then it traded up in public markets to$70. In a traditional initial public offering, a company sells stock to mutual funds at $45, and then it trades up in public markets to$70. Venture capitalists are not happy when mutual funds get underpriced stock: It dilutes existing shareholders and “leaves money on the table.” Venture capitalists are of course perfectly happy when venture capitalists get underpriced stock; that’s the business they are in.

This served the purpose of moving me more to his side.

This blogpost, however, is about the Coupang IPO.

All normal enough. But here’s the unusual thing about Coupang. Apparently, of the hundreds of investors who put in orders to buy shares in the IPO—many of whom did roadshow meetings and put in work to understand the company and come up with a price—fewer than 100 were allocated any shares, with most of those shares going to about 25 accounts handpicked by Coupang. Coupang apparently kept tight control over the allocation, choosing its investors itself rather than deferring to its underwriters (led by Goldman Sachs Group Inc.). Now those favored investors—investors favored by Coupang, not investors favored by Goldman—will benefit from the IPO pop. Everyone else, who put in the work and decided they wanted to own Coupang, will have to buy in the aftermarket, from those initial investors, and pay up to do so.

Obviously Coupang has left money on the table, but who cares? Coupang underpriced its IPO, but the beneficiaries of the underpricing are the existing investors that it wanted to benefit.

Basically Coupang announced an IPO at a $27-30 price range. It did a roadshow to gauge investor demand. Demand was strong. And then the price range was upped to$31-34. Demand was strong once again. And then, instead of letting its banker Goldman Sachs price the IPO at 34, and allocate the shares to who Goldman thought would make the best investors, Coupang went to its existing investors and told them “we have a bunch of investors willing to buy our stock at $34. What do you think?” And the existing investors, finding validation, said “Oh, in that case we can pay$35 for it”. In IPL auction parlance, Coupang’s existing investors basically had a “right to match option”. All the other potential investors were asked, and then the existing investors were “more equal” than the others.

The stock duly popped.

Now, right to match in an IPO might be an interesting structure, but I highly doubt that it will sustain. Basically banks won’t like it. Put yourself in Goldman’s shoes for a moment.

They have done all the hard work of pricing the IPO and taking it to potential clients and doing all the paperwork, and at the end of it, their buy side clients are a mostly pissed of bunch – they’ve again done all the hard work of deciding whether the IPO was worth it and then told that they were cut out of the deal.

The least Goldman’s buy side clients would have wanted is the right to match Coupang’s original investors’ offer ($35). Having done all the hard work, and then being forced to buy the stock (if at all) at the popped price of$49, they will be a totally miffed lot. And they would have conveyed their displeasure to Goldman.

One thing about IPOs is that the companies selling the stock play a one-time game, while the bankers (and IPO investors) play a repeated game, participating in IPOs regularly. And because of this, the incentive structure of IPOs is that bankers tend to favour buy side clients than sell side, and so the big pop. And so bankers will not regularly want to do things that will piss off the buy side, such as offering “right to match” to the selling company’s chosen investors.

So will we see more such IPOs?

My take is that inspired by Coupang, some more companies might insist on a right to match while selling their shares in an IPO. And this right to match will piss off the buy side, who will push back against the bankers and demand a right to match for themselves.

And what happens when both sides (company’s favourite investors and bank’s favourite investors) insist on a mutual right to match? We get an auction of course.

I don’t think anyone will have that much of a problem if IPO share allocation gets resolved by a Dutch auction, like Google did way back in 2004.

I’m catching up on old newsletters now – a combination of job and taking my email off what is now my daughter’s iPad means I have a considerable backlog – and I found this gem in Matt Levine’s newsletter from two weeks back  ($; Bloomberg). “it comes from monetizing volatility, that great yet under-appreciated resource.” He is talking about equity derivatives, and says that this is “not such a good explanation”. While it may not be such a good explanation when it comes to equity derivatives itself, I think it has tremendous potential outside of finance. I’m reminded of the first time I was working in the logistics industry (back in 2007). I had what I had thought was a stellar idea, which was basically based on monetising volatility, but given that I was in a company full of logistics and technology and operations research people, and no other derivatives people, I had a hard time convincing anyone of that idea. My way of “monetising volatility” was rather simple – charge people cancellation fees. In the part of the logistics industry I was working in back then, this was (surprisingly, to me) a particularly novel idea. So how does cancellation fees equate to monetising volatility? Again it’s due to “unbundling”. Let’s say you purchase a train ticket using advance reservation. You are basically buying two things – the OPTION to travel on that particular day using that particular train, sitting on that particular seat, and the cost of the travel itself. The genius of the airline industry following the deregulation in the US in the 1980s was that these two costs could be separated. The genius was that charging separately for the travel itself and the option to travel, you can offer the travel itself at a much lower price. Think of the cancellation charge as as the “option premium” for exercising the option to travel. And you can come up with options with different strike prices, and depending upon the strike price, the value of the option itself changes. Since it is the option to travel, it is like a call option, and so higher the strike price (the price you pay for the travel itself), the lower the price of the option. This way, you can come up with a repertoire of strike-option combinations – the more you’re willing to pay for cancellation (option premium), the lower the price of the travel itself will be. This is why, for example, the cheapest airline tickets are those that come with close to zero refund on cancellation (though I’ve argued that bringing refunds all the way to zero is not a good idea). Since there is uncertainty in whether you can travel at all (there are zillions of reasons why you might want to “cancel tickets”), this is basically about monetising this uncertainty or (in finance terms) “monetising volatility”. Rather than the old (regulated) world where cancellation fees were low and travel charges were high (option itself was not monetised), monetising the options (which is basically a price on volatility) meant that airlines could make more money, AND customers could travel cheaper. It’s like money was being created out of thin air. And that was because we monetised volatility. I had the same idea for another part of the business, but unfortunately we couldn’t monetise that. My idea was simple – if you charge cancellation fees, our demand will become more predictable (since people won’t chumma book), and this means we will be able to offer a discount. And offering a discount would mean more people would buy this more predictable demand, and in the immortal jargon of Silicon Valley, “a flywheel would be set in motion”. The idea didn’t fly. Maybe I was too junior. Maybe people were suspicious of my brief background in banking. Maybe most people around me had “too much domain knowledge”. So the idea of charging for cancellation in an industry that traditionally didn’t charge for cancellation didn’t fly at all. Anyway all of that is history. Now that I’m back in the industry, it remains to be seen if I can come up with such “brilliant” ideas again. ## How do bored investors invest? Earlier this year, the inimitable Matt Levine (currently on paternity leave) came up with the “boredom markets hypothesis” ($, Bloomberg).

If you like eating at restaurants or bowling or going to movies or going out dancing, now you can’t. If you like watching sports, there are no sports. If you like casinos, they are closed. You’re pretty much stuck inside with your phone. You can trade stocks for free on your phone. That might be fun? It isn’t that fun, compared to either (1) what you’d normally do for fun or (2) trading stocks not in the middle of a recessionary crisis, but those are not the available competition. The available competition is “Animal Crossing” and “Tiger King.” Is trading stocks on your phone more fun than playing “Animal Crossing” or watching “Tiger King”?

The idea was that with the coming of the pandemic, there was a stock market crash and that “normal forms of entertainment” were shut, so people took to trading stocks for fun. Discount brokers such as Robinhood or Zerodha allowed investors to trade in a cheap and easy way.

In any case, until August, a website called RobinTrack used to track the number of account holders on Robinhood who were invested in each stock (or ETF or Index). The service was shut down in August after Robinhood shut down access to the data that Robintrack was accessing.

In any case, the Robintrack archives exist, and just for fun, I decided to download all the data the other day and “do some data mining”. More specifically I thought I should explore the “boredom market hypothesis” using Robintrack data, and see what stocks investors were investing in, and how its price moved before and after they bought it.

Now, I’m pretty certain that someone else has done this exact analysis. In fact, in the brief period when I did consider doing a PhD (2002-4), the one part I didn’t like at all was “literature survey”. And since this blog post is not an academic exercise, I’m not going to attempt doing a literature survey here. Anyways.

First up, I thought I will look at what the “most popular stocks” are. By most popular, I mean the stocks held by most investors on Robinhood. I naively thought it might be something like Amazon or Facebook or Tesla. I even considered SPY (the S&P 500 ETF) or QQQ (the Nasdaq ETF). It was none of those.

The most popular stock on Robinhood turned out to be “ACB” (Aurora Cannabis). It was followed b y Ford and GE. Apple came in fourth place, followed by American Airlines (!!) and Microsoft. Again, note that we only have data on the number of Robinhood accounts owning each stock, and don’t know how many stocks they really owned.

In any case, I thought I should also look at how this number changed over time for the top 20 such stocks, and also look at how the stocks did at the same time. This graph is the result. Both the red and blue lines are scaled. Red lines show how many investors held the stock. Blue line shows the closing stock price on each day.

The patterns are rather interesting. For stocks like Tesla, for example, yoou find a very strong correlation between the stock price and number of investors on Robinhood holding it. In other words, the hypothesis that the run up in the Tesla stock price this year was a “retail rally” makes sense. We can possibly say the same thing about some of the other tech stocks such as Apple, Microsoft or even Amazon.

Not all stocks show this behaviour, though. Aurora Cannabis, for example, we find that the lower the stock price went, the more the investors who invested. And then the company announced quarterly results in May, and the stock rallied. And the Robinhood investors seem to have cashed out en masse! It seems bizarre. I’m sure if you look carefully at each graph in the above set of graphs, you can tell a nice interesting story.

Not satisfied with looking at which stocks most investors were invested in this year, I wanted to look at which the “true boredom” stocks are. For this purpose, I looked at the average number of people who held the stock in January and February, and the maximum number of of people who held the stock March onwards. The ratio of the latter to the former told me “by how many times the interest in a stock rose”. To avoid obscure names, I only considered stocks held by at least 1000 people (on average) in Jan-Feb.

Unsurprisingly, Hertz, which declared bankruptcy in the course of the pandemic, topped here. The number of people holding the stock increased by a factor of 150 during the lockdown.

And if you  go through the list you will see companies that have been significantly adversely affected by the pandemic – cruise companies (Royal Caribbean and Carnival), airlines (United, American, Delta), resorts and entertainment (MGM Resorts, Dave & Buster’s). And then in July, you see a sudden jump in interest in AstraZeneca after the company announced successful (initial rounds of) trials of its Covid vaccine being developed with Oxford University.

And apart from a few companies where retail interest has largely coincided with increasing share price, we see that retail investors are sort of contrarians – picking up bets in companies with falling stock prices. There is a pretty consistent pattern there.

Maybe “boredom investing” is all about optionality? When you are buying a stock at a very low price, you are essentially buying a “real option” (recall that fundamentally, equity is a call option on the assets of a company, with the strike price at the amount of debt the company has).

So when the stock price goes really low, retail investors think that there isn’t much to lose (after all a stock price is floored at zero), and that there is money to be made in case the company rallies. It’s as if they are discounting the money they are actually putting in, and any returns they get out of this is a bonus.

I think that is a fair way to think about investing when you are using it as a cure for boredom. Do you?

## Conductors and CAPM

Recently I watched this video that YouTube recommended to me about why orchestras have conductors.

The basic idea is that an orchestra  needs a whole lot of coordination, in terms of when to begin and end, when to slow down or speed up, when to move to the next line and so on. And in case there is no conductor, the members of the orchestra need to coordinate among themselves.

This is easy enough when there is a small number of members, so you don’t see bands (for example) needing conductors. However, notice that if the orchestra has to coordinate among themselves, coordination is an $O(n^2)$ problem. By appointing an external conductor whose only job is to conduct and not play, this $O(n^2)$ problem is reduced to an $O(n)$ problem.

When I saw this, this took me back to my Investments course in IIMB, where the professor one day introduced what he called the “Sharpe single index model“, which is sort of similar to the CAPM.

Just before learning the Sharpe Single Index Model, we had been learning about Markowitz’s portfolio theory. And then, as he introduced the Sharpe Single Index Model, Vaidya said something to the effect that “instead of knowing so many correlation terms” (which is an $O(n^2)$ problem), “we only need to know the correlation of each stock to the market index” (makes it an $O(n)$ problem).

As someone who has studied computer science formally, converting $O(n^2)$ problems to $O(n)$ problems is a massive fascination. It is interesting how I connected two such reductions from completely different fields.

In other words, conductors are the “market of the orchestra”.