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.

Ramayana and Weight Training

There are several interpretations of the Ramayana. As AK Ramanujan compiled, there are more than “three hundred ramayanas“. In some versions, Ravana is Sita’s father. In others, he is her brother. Yet others have been written from Sita’s point of view. And some from Hanumantha’s. And some from Ravanas.

In fact, the Ramayana (contrary to the sanitised Ramanand Sagar version we were fed by Doordarshan) is a fascinating enough epic that there can be millions of interpretations of the story. So let me add mine.

In my opinion, the Ramayana is a shining example of the virtues of Strength Training, especially barbell training. I’ll illustrate this with two key episodes from the epic.

The first is Sita’s swayamvara, where Rama beats off all competition to be able to marry Sita. The test is rather simple. There is a rather heavy bow that the suitors should lift and then string. My interpretation is that most other suitors who had come to the swayamvara were “convenational gymmers” who spent hours every week honing their biceps and triceps and ignoring training their large muscles.

Basically, like most “gym rats” you see at most conventional gyms, these suitors focussed on the lifts that made them look good rather than those that gave them real strength. Rama, on the other hand, practiced simple barbell lifts, and was especially adept at the deadlift. So after all the shower-offs had failed, Rama walked up and deadlifted the bow (the weight was such that no other lift was possible) and strung it. And married Sita.

The other episode comes much later in the epic, when the scene of action has shifted to Sri Lanka. Angada, the monkey prince, has gone to Ravana’s court in the form of an advance party to negotiate Sita’s release before Rama declared war on Lanka. Ravana insulted him, and so Angada refused to budge until he had had an audience. Various members of Ravana’s court tried to physically dislodge him (as Angada had challenged them to do so), but Angada remained firm, with his feet firmly planted in the ground.

Clearly, Angada did squats, and members of Ravana’s army who fooled themselves into strength by solely concentrating on the arms didn’t realise that someone (who squatted) could have such heavy and firm feet. And so they failed to dislodge him.

Now to find episodes from the epic that show the virtues of the press and the bench press.

Thirty to twenty nine

I turned twenty nine today. Yesterday to be precise; I see the clock has just ticked past midnight. And I’m sensing that my “project thirty”, where I had decided to not take up a full time job until I turn thirty and do “all the things I ever wanted to do”, is already in trouble.

Sensing that over the last two months of joblessness I hadn’t been spending my time usefully (Parkinson’s law and all that), I decided to sit down today and make a list of all those things that I’ve ever wanted to do and haven’t been able to, which I want to do before I’m thirty. It took me a couple of hours maybe, maybe a little less than that. At the end of it, I had a grand two page bullet-pointed word document to show for my efforts. To be honest, it looked rather skinny.

I started a (time) budgeting and planning exercise, and figured out how much time I would need to do all that. Apart from a few big holidays I’ve planned, I realized that the rest of the activities can actually be worked around a “normal” work schedule, as long as I don’t take up a job that will eat away all my time. Yes, the list of “things I always wanted to do” include entrepreneurship and freelancing, but again, bereft of concrete ideas I’ve started getting doubts if this is the right time to do that. Things are quite unclear right now.

I’m more open to taking up a full time job now than I was a week or so back. I need to not make the mistake again of taking up something that I’m not suited for, or something that won’t inspire me, or something that wouldn’t allow me to do the other things that I’ve wanted to do. Again, I personally don’t mind a “portfolio life” also, where I have a couple of part time gigs rather than a full time job. Ideally, something that would allow me the time and mind space to do my side projects on the side, while also generating some revenue.

I know I want to live in Bangalore. I know that I don’t want to take up an offshored job again (a mistake I’ve done twice in the past; not something I would want to repeat, ever). I have a reasonable idea about the kind of work I want to do, though I’m quite flexible about it. I want to do something that I feel for and be proud of doing – something more than just a “CMP”. And again, something that gives me the time and space to do my own things also. And yes, I know it’s going to be hard to find something to fit these constraints (Bangalore and non-offshored reduces the sample space quite a bit, I know). And I’ll continue my Project Thirty while I seek to find something on these lines, I guess.

Or maybe I’m giving up too early. Or maybe not, that I’m just being pragmatic. Maybe I’m bowing to pressures, both internal and external. Maybe I’m just taking a rational decision. Nevertheless,

I shall not take up a job that I won’t be proud doing.

I shall not take up an offshored job.

I shall not give up on the agenda of project thirty, which is quite exhaustive. It remains a priority.

I want to have a fulfilling life, and not feel like I’m wasting time.

I’m going to keep my mind sane, and try not to succumb to pressures.

P Polie Exclusion Principle

The basic concept is that for any given person, no two romantic partners fulfil the same kind of needs.

Let us take all the possible ways in which a romantic partner (since we are talking about multiple partners for the same person, usuallly happening at different points of time in the person’s life, I don’t want to use the term “long-term gene propagating partner”) can help you out. The kind of needs that she can fulfil. Make a list of them, and represent them as a vector.

And to this, add a vector of binaries. Let us call it the “need vector”. You might have guessed that an element of this vector is 1 if the partner fulfils this particular need and 0 otherwise. So for each of your romantic partners (spanning across space and time), construct such a vector. Yeah of course some of these needs are more important than others so you might think you might want to give weights, but that is not the purpose of this exercise.

The Pauli Exclusion Principle in quantum mechanics states that no two electrons can have the same four quantum numbers. Similarly the P Polie Exclusion Principle in romantic relationships states that no two of your romantic partners have the same need vector. That the needs vector of any two of your romantic partners have a hamming distance of at least 1.

This principle has certain important consequences. Given that any two of your romantic partners are separated by a Hamming distance of at least 1 and using the Neha Natalya-xkcd argument, the number of romantic partners you can possibly have in your lifetime is bounded from above by 2^n, where n is the length of your need vector. So contrary to intuition, this shows that promiscuous people actually have a larger set of needs from romantic partners than committed people.

Pricing My Best Friend’s Wedding

Any of you remember this movie called “My Best Friend’s Wedding”? If you don’t, here is a brief description of the plot. Julia Roberts and Dermot Mulroney (had to look up imdb to remember his name) have this agreement that if they are both single as of her 28th birthday, they will get married to each other. As it happens, 3 weeks before that, the hero announces that he’s found a woomaan and is going to get married to her, much to the dismay of the heroine, who now puts fight to somehow spoil this new relationship.

I was thinking of this kind of arrangement as a financial product. Actually, the movie has what I call as the “European version”. More complicated is the “American version” which I describe here. Basically I give you the OPTION to marry me on any day before my 28th birthday (6th Dec 2010). That would be simple enough to “price” (or “value”, to put it in layman’s terms) – it is a standard American option. However, let me add this twist into it. I also reserve the right to withdraw this option on any day before expiry or exercise.

So basically some day before my 28th birthday I can wake up and cancel this option that I’ve given you. Now the challenge is to price this. One thing that is obvious is that the value of this is now less than the value of the pure American option. But pricing it is a challenge (though, thinking about it carefully, it shouldn’t be too hard to solve. I think we can use option-on-option fundaes in order to price it, but still it’s nontrvial).

The European option, of course (as it is done in My Best Friend’s Wedding) easier to price. Basically, there are two events that need to happen on the day of expiry for the option (ok technically it isn’t an option since if these two events happen, then the parties are forced to execute the contract) and so it can be easily modeled using a two-factor model. The American, as we discussed, is tougher (though I’m sure that if I were to present this problem to my colleagues, they’d solve it in a jiffy).

So the reason I’m writing this is that I’m planning to enter this kind of a deal with someone. And I’m wondering if it’s better to enter into a European deal or into an American. Remember that if it is the “American” deal, I’ll be giving away the option (to marry me before either my 28th birthday or I withdraw the option) for free. Considering this, under what conditions should I try to sign the European contract, and under what conditions should I give away the American?

Also, how does the pricing of the American option change if I’m allowed to give it away to more than one person (with the understanding that as soon as one person exercises the option, I withdraw the option from all the other people I’ve given it to). And typically, will I be able to get more benefit in total by giving away this American option to a number of people than if I give it away to one person (assuming I’m indiffernet between all these people with respect to marriage).

Ok it’s late in the night and it’ s my third post in the last 1 hour, so it might be a bit muddled up. Also, you might find it a bit too technical (remember that I’m a quant). Nevertheless, I hope I’ve been able to communicate what I wanted to communicate. And am looking forward to your advice on this.