cost of capital

Cost of capital for a company depends on many factors among which the following are essential:

- Managerial experience and competency
- Specific business risk
- Financial structure of the company
- Past cash flows, and their variability and consistency

However, for most financial institutions, the calculation of the cost of capital is quite complicated. For instance, a commercial bank is not pre-committed to a specific industry or business risk. The investor can discover the exact constituents of the asset risk profile only after the capital is deployed by the bank manager. (For instance, loans could all of a sudden be directed to the shipping industry.) Hence beliefs play a big role here. If the investor believes that the bank manager will deploy capital to high risk/high return sectors, then he will ask for a high interest rate. If bank manager believes that the cost of capital will be expensive, then he will be pre-disposed to employing the capital to a high risk/high return sector. In such a fashion, some Bayesian Nash equilibrium will sooner or later be reached.

Note that the following factors also complicate the cost of capital calculation for banks:

- Explicit government guarantees such as deposit guarantees
- Implicit government guarantees such as being regarded as too big to fail in a systemic crisis.
- Banks' exposure to each other can make it hard to pinpoint the business sectors that each bank is exposed to.

options everywhere

In the aftermath of one of the most severe economic crises ever recorded, the public perception of options and futures has changed significantly. These instruments are now viewed as dangerous financial tools that come with high leverage ratios.

This perception is based on a misunderstanding. Options and forwards contracts are not new financial innovations. They have been with us since the inception of the notion of a limited liability company: Equity has an option-like pay-off structure due to the limited liability clause.

Here is an even more mundane example: Every supply and purchase agreement is essentially a forward contract where two parties agree on a quantity, a price and a delivery date. (In case the buyer side does not post any collateral, the leverage ratio is effectively infinite!) Sometimes these agreements even contain embedded options. This turns them into instruments far more complicated than the financial agreements that are currently the subject of public fear. Here are two examples of such embedded options:

- A right to buy additional quantities over the base quantity at a price that is set equal to or below the contract price.

- A right to postpone the delivery to a future date upon the payment of a previously determined penalty fee.

on wondering off

The following interesting discussion took place long time ago between Trayan Trayanov and myself.

Trayan first quotes a Harvard News article: "People spend 46.9 percent of their waking hours thinking about something other than what they’re doing, and this mind wandering typically makes them unhappy, according to research by Harvard psychologists Matthew A. Killingsworth and Daniel T. Gilbert."

Trayan - The ability to think about what is not happening is a cognitive achievement that comes at an emotional cost.

Sanja - Interesting. I have to agree with the conclusion!

Me - First a quote from the article: “Many philosophical and religious traditions teach that happiness is to be found by living in the moment, and practitioners are trained to resist mind wandering and to ‘be here now,’ Killingsworth and Gilbert note in Science... This new research, the authors say, suggests that these traditions are right."

Wise people have been saying the same thing for I don't know how many millennia. Now that 250,000 iPhone data points have been collected we can finally believe their conclusions?! Every time I read articles such as this one, I feel cramps in my stomach. Are these people plain insane? How much money will they keep spending on proving the already well-known?

Besides, the Harvard psychologists should try to broaden their population sample a little bit. People who own iPhones are on average a lot more novelty seeking and status conscious than those who do not. That definitely introduces a bias to the research. Also 74% of the participants were American. So there is a huge cultural bias in the study as well. (Instead of saying "People spend 46.9 percent of their...", they should have said "Americans spend...")

Social scientists are often very lousy with their experiment designs. They can afford to do this because, faced with obvious or very credible conclusions, their audience do not feel tempted to address any methodological problems.

Sanja - Good point, we have known these things for a long time. I nonetheless think there are benefits to testing that "common sense" through research. The methodology, albeit flawed, attempts to establish the conclusion not as a belief, but a fact within a correlation. I find that a laudable attempt because to a certain extent, it helps take down the imagined boundary between ethics and beliefs on the one hand and scientifically measurable outcome or "reality" on the other. Who knows, maybe if they improved the methodology like you suggested, the results would support the conclusion that the "be in the moment" mantra is not necessarily the way to happiness...

Trayan - Hey Buddy,

All good points but I in turn get cramps in the stomach when people say something is obvious or well-known. I dislike absolutisms of all kind, epistemic especially. There are clearly religious traditions out there that do not endorse living for the moment. The whole cultural edifice of the West is predicated on the idea that you live for a distant future moment of bliss & grace. (But yes, this study is obviously not qualified to adjudicate among different religious traditions' implicit theories of happiness).

I also always marvel when somebody tells me that just because something has been said / around for millennia, it is credible. That's some strange sort of a natural-selection theory of common sense (If it survived so long, it must be solid).

While it's easy to pick holes in one's methodological design, it's significantly harder to come up with a solid design & execute it yourself. And yes, your points are valid, but I think what I endorse here is a different idea. a) That you can run rationally & empirically approach to questions of the mind. Looking around me and seeing how many people believe in stuff like NLP makes me think people need to be reminded of that on a daily basis. b) That people can be happier & more content if they rigorously think about the way they think. That's my agenda really.

Milen - But the Japanese say: Torewarenai sunao-na kokoro - A mind that does not stick is one that is good for change. Which implicates then that we are inline with the nature of things - change.

There's also another definition for happiness by Brian Tracey: The feeling of prgressive realization towards a desired goal. Which also hints that wondering and movement is what would make us feeling happy.

Happy is just a word and definitions are only personal on this level.

Trayan - I haven't done that much thinking on this topic but it seems to me that while definitions abound, the concept & the experience of happiness are universal. So is the pursuit of it. The experience of happiness should have a common biochemical basis. Certain thoughts disrupt the chemical balance. The association is probably learned rather than innate. That's why in one context thinking about things non-present brings bliss (religious doctrines), while in others it brings anxiety.

The paper's claims to the validity of religious traditions is retarded. But what matters is the fact the undisciplined mind tends to not so much wander as follow pathways that are unproductive (in terms of solving pressing & immediate problems) and often disrupt the biochemical balance we experience as happniess. (Also known as dysfunctional congitive loops.)

Me - Trayan, I agree. The key is to discipline the mind. Wandering off does not necessarily have to induce unhappiness. We owe a substantial chunk of our literature, arts and philosophy to minds who productively wondered off into different modes. And these minds enjoyed what they were doing.

I am not saying that social scientists are inept people. They just happen to be studying a very complicated phenomenon. They often can not control the variables that need to be controlled. Besides, we are in such an ignorance about these matters that we do not even know which variables need to be controlled.

You don't need to take the words of "absolutist" wise people without any examination. Ideas such as these are very easy to test on yourself. If the idea does not work on you, it does not matter whether it is a scientist or a pop singer who preaching the sermon.

Yes Trayan, there are many examples of stupid ideas that persisted for a very long time. (e.g. Slavery) Nevertheless there is a reason why certain ideas persist. Sayings of wise people are kept alive because people find them helpful and applicable. Persistence through time is not a scientific proof of the validity of these sayings. But it is a pseudo-proof, which in most cases can be made rigorous by a "scientific" questionnaire.

Yes, Sanja. I totally agree with you. There is a gain in substituting "beliefs" with "correlations". But the gain, in this case, is not that substantial. The explanations they provide for such correlations should not satisfy a scientific mind. In the best case, they end up replacing the original belief with seven other beliefs which are equally unfounded.

Trayan - Dude, much respect, but I just can't agree with you on pretty much anything!

I'd think the best minds of philosophy, the arts, etc are rather focused minds. In some cases - obsessive minds. Compulsive minds. Cultural production requires a rather sustained focus of attention. And in all cases - were they all happy people, biochemically speaking? Aren't they what we usually call troubled/broading minds?

Yes, it's a complicated phenomenon that psychologists study. So? That's the utility of science. Assumptions & procedures for producing certain knowledge are transparent. Yes, you will get some of the variables wrong, some of the time. But someone else will build on that. It's a cumulative enterprise. With known, demonstrable results. I can't say the same thing about received wisdom and divinated knowledge of the religious / mystical kind. Ignorance on a given topic is an opportunity, not a constraint. And why certain unverifiable ideas persist has less to do with their being helpful and applicable. Inertia, vested interests, all that... (Not that there isn't any interia or vested interests in science but on the whole I'd rather put my money on science than on "wisdom").

Dang, I can't believe I am advocating science to a math PhD!:)

Me - Well. The really creative moments happen during the wondering-off periods which often lead to spontaneous associations. Try creating something original yourself, you will see what I mean. (This is not a challenge or an insult.) You may also want to read about how the truly ground-breaking scientific insights were born. Yes, there is obsession involved, but brute obsession can only lead to tinkering. When it comes to deep insights, you need little bit of wandering-off.

I don't understand what you mean by "biochemically happy"? How can somebody paint for all their lives without actually enjoying the act of painting?

Clearly, psychology and sociology have been very cumulative. Is that why they still teach the perspectives of different schools of thought on each fundamental problem?

I am not anti-scientist. In fact, I am just trying to protect the image of science here. You have missed my entire point. May be it is my fault. I just put too much rhetoric in my sentences.

PS: I have the feeling that your conception of mathematics is wrong. Mathematics is a language. Science and mathematics has as much in common as Shakespeare and English has. (Yes, it is a very crude analogy, but I do not want to delve into the subtle, philosophical issues here. The point is clear.)

Trayan - I think what you and I mean by "wandering" are two different things. I think I explained it in a different post - The mind does not so much wander as keeps haunting certain dysfunctional paths. Loops. It would be a great thing to get into the subtleties of that distinction but let's do it some other time :)

Not sure if I get the analogy but I don't think mathematics is that antithetical to science. See http://en.wikipedia.org/wiki/Experimental_mathematics

On a certain level, they perform pretty much the same procedures: Classify phenomena, define & logically prove relationships between them. More importantly, the two share the fundamental understanding that things add up to a whole - knowledge developed in one branch of science must logically fit knowledge produced in another field. If it doesn't, one of two pieces gets revised. They can't exist in contradiction. If they do, work is being done to close the gap. Wouldn't you say it's the same in mathematics? The distinction between mathematics & science is much smaller relative to the gap between science & non-scientific knowledge. In non-science, contradiction is institutionalized. Schools of thought. Warring sects. Leaps of faith.

Anyway, hope you understand what I'm fundamentally driving at - these days people love to poke holes in scientific research. Everyone is a sceptic & a relativist. One's gotta drive a stake in the ground i think.

Me - Hmm. I do not understand why anyone would use the word "wandering" for describing the tendency to get locked into dysfunctional loops. The dictionary definition of wandering is "to move about without a definite destination". (A loop has a definite destination.) Anyway. As you say, part of our disagreement stems from a miscommunication.

"Experimental mathematics" is a fringe activity that most mathematicians are not even aware of. (Of course, mathematicians like to play around with examples from which they derive more general results, but that is not the tenet of experimental mathematics.)

Another fringe activity is "paraconsistent mathematics" which is more tolerant of contradictions: http://en.wikipedia.org/wiki/Paraconsistent_mathematics

How about the fact that (almost all) mathematicians endorse the existence of structures which they do not know how to construct explicitly: http://en.wikipedia.org/wiki/Nonconstructive_proof

That would never fly in science where production of concrete evidence is vitally important.

There are a lot of contradictory scientific theorems. How about general relativity and quantum physics? These two can "peacefully" co-exist because each works extremely well in explaining the type of phenomena that it was designed to explain. However when they criss-cross into each others' domains, they make contradictory predictions.

Yes, researchers are trying to close the gap and find a consistent framework that encompasses these two theories. But there is no reason why we should believe that they will be able to succeed.

No, it is not "the same in mathematics". Contradictions do not drive the innovation of new mathematics. Pragmatic and aesthetic concerns drive it. Paradoxes once in a while surface in mathematics. But this is extremely rare.

Look, I do not want those petty sceptics to hear about this, but it is usually very difficult to prove whether a certain set of theorems is consistent. We do not even know whether our usual set theory is consistent. (It is an implication of the Godel's incompleteness theorems.) Imagine that! The consistency of something as simple as set theory is based on faith. You have no hope of achieving any consistency in sociology. Just forget about it. (You can not even formulate your theorems in a language that lends itself to the construction of consistency proofs.)

It is quite hard to tell in social sciences whether two theorems are contradictory. The reason is that, most of the time, the domain that each theorem is supposed to explain is extremely ill-defined. Hence, there is a lot of space for interpretation, re-interpretation... (I can give you many examples from psychology and economics.)

Contradiction is not institutionalized in religion (which is a non-science.) Theologists are well-trained in logic. In fact, logic and religious scriptures are basically all that they have got!

Very few people explicitly endorse contradictions. (I wish I could underline the word "explicitly" here.) And there is a huge amount of space where you can manoeuvre your beliefs without immediately contradicting yourself. (Let's also underline the word "immediately" here, since we do not know whether there may be a contradiction that lies several hundred derivations ahead.) I hate to say this but a properly defended scepticism is very hard to defeat on philosophical grounds. For instance, philosophers and physicists know pretty well that causation is an ill-defined concept. There seems to be something mysterious about causation, something that distinguishes it from a mere correlation. But we just can not pinpoint precisely what that thing is! Yet, today, even sociologists are taught that correlation and causation are two wildly different animals.

Don't worry about dumb people poking holes at science and rationalism. Such individuals are walking contradictions. How can they not be, while they are enjoying all the benefits of modern science? (e.g. modern medicine, telecommunications etc.) Nevertheless I believe that we should be easy on such people. Why? Because it is a human condition to be in a contradiction. Human mind is a pragmatic "machine". It operates on thousands of contradictory beliefs that pass undetected solely because of the fact that these beliefs do not entail any practical problems for its daily activities.

Update (November 2011): It seems like the key is to strike a delicate balance between "being here now" and wondering off:

The last bit of mind wandering research worth highlighting also comes from the Schooler lab. He’s demonstrated that people who consistently engage in more mind-wandering — Schooler gives subjects a slow section of War and Peace, and then times how long it takes before they start thinking about something else — also score significantly higher on various measures of creativity. However, not all daydreams are equally effective at inspiring new ideas. In his experiments, Schooler distinguishes between two types of daydreaming. The first type occurs when people notice they are daydreaming only when prodded by the researcher. Although they’ve been told to press a button as soon as they realize their mind has started to wander, these people fail to press the button. The second type of daydreaming occurs when people catch themselves during the experiment – they notice they’re mind-wandering on their own. According to Schooler’s data, individuals who are unaware of their mind-wandering don’t exhibit increased creativity.

The point is that it’s not enough to simply daydream. Letting the mind drift off is the easy part. What’s much more difficult (and more important) is maintaining a touch of meta-awareness, so that if you happen to come up with a useful new idea while in the shower or sitting in traffic you’re able to take note; the breakthrough isn’t squandered.

Lehrer - The Importance of Mind-Wandering

pessimistic marriage metaphors

Plastic Band Metaphor

Marriage, by raising the cost of a defection, causes each side to be more committed to the relationship. This has the following undesirable consequence: The magnitude of what each side is willing to bear increases. If one thinks of a relationship as a plastic band, the marriage contract has the effect of augmenting the elasticity of this band. Severe fights and disagreements, which would under normal circumstances result in the resolution of the relationship, will now be tolerated by each side. In other words, because of its greater elasticity, the band can now be strained more before it breaks.


Dog Ownership Metaphor

A dog that you can safely unleash on a public space is a joy to have. You can let it roam free with the assurance that it will come back to you after a while. A dog owner, who keeps his dog always on leash, suffers from loyalty problems. He is afraid that the dog will disregard his commands, and inflict harm to others or simply run away. A marriage contract can be pictured as each side putting a leash on the other. The need to enter such a contract hints at the presence of something unhealthy about the underlying relationship.

some non-questions

- Do you believe in God?
- God is not a sufficiently well-defined term to merit an answer to this question

- Don't you think that the spontaneous emergence of life is extremely unlikely?
- In order to measure the probability of any event, you first need to gather some preliminary information. In this case, you need to know the number of planets that can potentially harbour life. We currently have very little information about planets within our observable universe. Of course, we do not have (and will never have) any information about what lies outside the observable universe. In other words, we do not know the size of the entire universe and therefore have no idea about the number of "candidate" planets. Without this important input, we can not estimate the size of the experiment whose one by-product was life on earth. And without this estimation, it is nonsensical to make a statement about the likelihood of spontaneous emergence of life.

types of instabilities

Misanthropes thrive on physical instabilities. Catastrophic events of all sorts are welcome. If there are no such events happening now, then the misanthropes will forecast one to happen sometime soon.

Intellectuals thrive on political instabilities. Popular uprisings, wars and massacres are all welcome. If such events no longer occurred, then intellectuals would switch careers and become historians.

Traders thrive on economic instabilities. Any event that introduces volatility into the markets is welcome. Even if there is no such event happening now, sooner or later the susceptibility of traders to herd behavior will create one spontaneously.

two notes on logic

- Logical consequence and logical consistency are inter-definable. An axiomatic theory T is consistent if there is no sentence P such that P and ¬P are both consequences of the axioms; P is a consequence of the axioms of a theory T if the axioms together with ¬P are inconsistent.

- While doing calculations, it may be helpful to keep in mind a picture of what is happening in the dual world. Here is how one can quickly recognize that logical equivalence is an associative binary operator. Note that p⇔q can be stated as (q⇒p)∧(p⇒q) which in turn can be stated as (¬q∨p)∧(¬p∨q). Hence the negation of p⇔q can be written as ¬((¬q∨p)∧(¬p∨q)) which in turn can be written as (¬¬q∧¬p)∨(¬¬p∧¬q). But the last statement is simply ¬pΔ¬q, namely the symmetric difference of ¬p and ¬q. So ¬(p⇔q) holds if and only if ¬pΔ¬q holds. In other words, ⇔ is dual to Δ. Since Δ plays the role of addition in the Boolean ring corresponding to the Boolean Algebra (∧,∨,¬,0,1) and since addition is associative, we can conclude that ⇔ is associative as well.

causality and determinism

The necessity of the causal bond which is commonly postulated, and which is taken over from the idea of fate, is, according to Hume, not capable of a clear-cut empirical interpretation. He therefore replaces necessity by repetition and permanence; that is, whenever the same circumstances recur, the same effect will follow the same cause. But even with this nothing is gained, as an event happens in its full concretion only once. It is thus necessary that certain demands of continuity be added, stipulating that causes differing sufficiently little from one another have effects also differing but little; that sufficiently remote bodies or events have a negligible effect, and so on. The phenomena must be brought under the heading of concepts; they must be united into classes determined by typical characteristics. Thus the causal judgement, "When I put my hand in the fire I burn myself," concerns a typical performance described by the words "to put one's hand in the fire," not an individual act in which the motion of the hand and that of the flames is determined in the minutest detail. The causal relation therefore does not exist between events but between types of events. First of all -and this point does not seem to have been sufficiently emphasized by Hume- generally valid relations must be isolated by decomposing the one existing world into simple, always recurring elements. The formula "dissecare naturam [to dissect nature]" was already set up by Bacon.

- Weyl's "The Open World" lecture as published in Mind and Nature

Indeterminism is engrained in the notion of causality since the latter requires the separation of all possible world states into equivalence classes.

- If an equivalence class A is always followed by an equivalence class B, then we say "A deterministically causes B".

- If A is followed by a set of equivalence classes that includes B, then we say "B is probabilistically caused by A".

Note that there is indeterminism involved in both cases. In the first case, we don't actually know which element of A is followed by which element of B. Perhaps every instance of a fixed a∈A is followed by a different b∈B, and our causal scheme is too crude to detect this situation.

Since we have no hope of understanding reality without dissecting it, we should shelve away all discussions about determinism for good.