low-probability-high-impact

When circumstances are favourable, animals build up layers of fat. This insures them against any serious disruptions in the local food chain. Firms keep "excess" cash and ready-to-draw credit lines in order to protect themselves against future liquidity shocks. None of these insurances come for free. Building and carrying around extra layers of fat is energy-consuming. Credit lines require upkeep fees and undeployed cash has an opportunity cost.

Question 1: Why do firms generally not insure themselves against low-probability-high-impact events?

That is because the cost of doing so is likely to be higher than the probability weighted gains. (Of course the calculations involved here are strictly subjective. Overestimations and unestimations are quite common.) An elderly CEO who has vivid memories of such an event may choose to follow conservative and full-proof strategies. A young and over-confident CEO may have different thoughts.

Most animals can not plan ahead. Hence calculating the probability weighted gains entailed by various insurance mechanisms is not even an option for them. Any preparation that occurs has to take place at a genetic level.

Question 2: Could an accumulation of random DNA mutations prepare a species for a low-probability-high-impact event?

There is no a YES/NO answer to this question. Evolution does not work in a forward looking way. In fact it does not work on a strictly backward looking way neither. There is no guarantee that a species will survive future conditions that resemble those it survived some time ago.

Why? Because a mutation that was historically beneficial can be undone by another mutation. Since current circumstances may be quite different from those that prevailed during the times when the first mutation was considered "beneficial", the group experiencing the second mutation will not necessarily be at a relatively disadvantageous position.

Question 3: Could small shocks prepare a species for a large shock of a similar kind?

Again, evolution works blindly. Occasional draughts will not prepare a species for desert-like conditions. That lucky mutation may simply never occur!

Adaptation may lead to the development of a physiological capacity to learn. But this does not imply that adaptation itself is "learning".

Think of intellect as just another trait that has not yet been eliminated by environmental dynamics.

Question 4: Mass extinctions happen every 26 million years. Will we be able to survive our first destructive wave?

May be. Today evolution unfolds in two dimensions: Cultural and genetic. Soon these two will start interacting with each other. This interaction may yield the key to our ultimate survival. But who knows? Cultural evolution and the resulting accumulation of scientific knowledge could as well catalyse our own destruction.

Also, it is very likely that the unfolding of the next mass extinction will catch us by surprise. Just as we are mesmerised and stupefied by the causes of each recession!

P.S. The use of "locality" in the first paragraph may be misleading. The word is not used in a geographical sense. Each species belongs to a connected component in the universal food network. The kind of disruptions I am referring to are those that occur within this component. Hence what is "local" can change as time progresses. For example, as geological events lead to the development of new continents and the break up of the already existing ones, connected components within the food network will inevitably be altered.

debt-to-equity swaps

"...A contribution to the capital of a company has no purpose for the contributing company unless the entity making the contribution is getting or has an interest in the company it is contributing to. The easy solution would be to transfer some shares in the company to the contributing companies or to issue shares in the company to the contributing companies when contributions are made. This way any contribution would bring value to the company making the contribution because the value of the company receiving the contribution and in which the contributor owns shares, would increase..."

It is amazing how lawyers can render even the simplest statement opaque and incomprehensible. The situation is as follows:

Company X holds the debt of company Y which is currently in a distress. Having secured the consent of company Y, Company X will now be swapping some of this debt into equity. The corporate lawyer Mr.W (who is quoted above) claims that a debt-to-equity swap will be rational from the point of view of Company X only if Company X already has partial equity stake in Company Y.

Here is my take on the issue:

Please correct me if I am wrong, but the argument is false for the following two reasons:

1) In a distressed situation, it can be rational from the point of view of a creditor with no equity stake to even unconditionally forgive a part of the debt. Myers’ classic paper “Determinants of Corporate Borrowing” (1977) explains this point in detail. Here is the heart of his argument: “Most firms are valued as going concerns and this value reflects an expectation of continued future investment by the firm. However, the investment is discretionary... The firm financed with risky debt will, in some states of nature, pass up valuable investment opportunities – opportunities which could make a positive net contribution to the market value of the firm... If creditors and shareholders find themselves in a position where the net present value of an investment project is positive, but less than the payment promised to creditors, then it is in both sides’ interest to renegotiate the debt contract.”

2) As pointed out above, in some distressed situations (such as today), conducting a debt-equity swap (or even forgiving debt) can enrich the creditors. However this does not necessarily mean that such a move will increase the expected income of the already existing shareholders. The resulting lower leverage will decrease the return on equity and an enlargement of the shareholder base will dilute the incumbent shareholders’ claims. That is why, in practice, one sometimes sees cases where an opportunity to increase the market value of a firm is by-passed due to the stiff opposition by incumbent shareholders.

Here is the response from Mr.W:

Many thanks for your message this afternoon. I had just proposed an alternative solution to Mr.Z, but it does not seem it would work in these circumstances either. Since everyone involved seem also aware of the possible repercussions of bankruptcy and findings of fraudulent conveyances by trustees in bankruptcy, I could take out the problematic assumption if shareholder resolutions of the two contributors are provided, and would then just direct everyone's attention to the bankruptcy exception which is already in the opinion.

... and the amazing message that Mr.Z sent to my uncle:

I have just drafted the shareholder resolutions and sent to Mr.W for his approval. I will then send it to you for signature. I note your nephew’s input. With the greatest of respect to his knowledge, he should keep the business of MBA discrete with the knowledge of the law. I will revert shortly with Mr.W’s comments on the draft resolution.

Perhaps corporate laws do not need to make any economic sense. I do not know... (Note that I do not have a MBA degree.)

P.S. If interested, you can read the linked VoxEU article which contains another example where forgiving debt can enrich both the creditor and the debtor.

puritanism explained

Why do some rich people admire and imitate Warren Buffett's puritanist approach to life? There is something pathologically wrong with accumulating a lot of money and not spending any of it. The only rational explanation I can think of is a reminiscent of the following argument that John Maynard Keynes made in “Economic Consequences of Peace”:

The new rich of the nineteenth century were not brought up to large expenditures, and preferred the power which investment gave them to the pleasures of immediate consumption. In fact, it was precisely the inequality of the distribution of wealth which made possible those vast accumulations of fixed wealth and of capital improvements which distinguished that age from all others. Herein lay, in fact, the main justification of the capitalist system. If the rich had spent their new wealth on their own enjoyments, the world would long ago have found such a régime intolerable. But like bees they saved and accumulated, not less to the advantage of the whole community because they themselves held narrower ends in prospect. The immense accumulations of fixed capital which, to the great benefit of mankind, were built up during the half century before the war, could never have come about in a society where wealth was divided equitably. The railways of the world, which that age built as a monument to posterity, were, not less than the pyramids of Egypt, the work of labour which was not free to consume in immediate enjoyment the full equivalent of its efforts. Thus this remarkable system depended for its growth on a double bluff or deception. On the one hand the labouring classes accepted from ignorance or powerlessness, or were compelled, persuaded, or cajoled by custom, convention, authority, and the well-established order of society into accepting, a situation in which they could call their own very little of the cake that they and nature and the capitalists were co-operating to produce. And on the other hand the capitalist classes were allowed to call the best part of the cake theirs and were theoretically free to consume it, on the tacit underlying condition that they consumed very little of it in practice. The duty of 'saving' became nine-tenths of virtue and the growth of the cake the object of true religion. There grew round the non-consumption of the cake all those instincts of puritanism which in other ages has withdrawn itself from the world and has neglected the arts of production as well as those of enjoyment. And so the cake increased; but to what end was not clearly contemplated. Individuals would be exhorted not so much to abstain as to defer, and to cultivate the pleasures of security and anticipation. Saving was for old age or for your children; but this was only in theory -- the virtue of the cake was that it was never to be consumed, neither by you nor by your children after you.

twisted logic of foreign aid

What happens if UK chooses to finance its aid by simply printing money? Will the money minted by Bank of England and handed over to an African country create any difference in the lives of British citizens?

Assuming that there is a reasonable cap on the size of the aid provided, foreign exchange markets will easily absorb the conversion of these newly minted pounds. In other words, the British pound will retain its value against other major currencies. Hence the total effect of the foreign aid will depend only on what is actually bought with the money.

A price ripple caused by the purchases could in principle drive up the prices of goods that British citizens are consuming. Since UK aid to Africa consists of poverty reduction schemes that focus on health and education, this inflationary effect will probably be negligable . (Note that it is tough to gauge where the money will flow after it is spent on health and education. In other words, the total effect on UK price levels may accumulate over time in unpredictable ways.)

Similar Examples:
When a Turkish farmer sells grain to local wholesale buyers in dollars, he does not cause a price ripple that is relevant for US economy. When a German Bank buys a derivative product from a French Bank in dollars, it does not activate the inflationary forces in US economy.

(If all the dollars circulating around the world somehow find their way back into the US real economy, then the net result will be a massive inflation. However this scenario is extremely unlikely since most of the circulation stays completely outside the US real economy.)

coercion leads to cleaner signals

Why would a surge in mergers and acquisitions (M&A) activity not necessarily signal an economic recovery?

- In every transaction, there is a buyer and a seller. Assuming that neither side is under any coercion, the expectations regarding the future value of the company in question should diverge. In other words, an increase in M&A activity may contain the same signals as a surge in initial public offerings (IPOs) does.

Companies are not apples. They are complicated entities. (Let's ignore the irrelevant fact that the biological complexity of an apple probably surpasses the organizational complexity of any company.) That is essentially why buying and selling companies is more sensitive to information asymmetries than trading apples. If sellers (e.g. previous owners or founders of the company) are more informed than the buyers, then there are grounds for being suspicious that the current rally in valuations is unjustified.

- A peak in the number of sales of distressed companies may signal a trough in the economy. Note that this type of M&A activity differs from the one mentioned above. Here the equity holders, who have the informational edge, usually get wiped out. The new owners of the company (e.g. Debt holders), who are less informed than the original equity holders, are forced into an untimely sale due to lack of coordination, liquidity needs etc. The presence of coercion renders the signals remitted by these transactions more trustworthy.

Those signals could be any of the following: Credit markets have thawed / Risk appetite has returned back to the equity markets / Separation of good from the bad is setting clean grounds for a new sustainable economic revival.

oil vs other commodities

Historically commodities have demonstrated a remarkable tendecy to move along with crude oil prices. What is the explanation for this baffling correlation?

1) Finding causal links between the factors that influence a certain commodity's price and the factors that determine oil price can be a mind-bending exercise. Often these factors are not clear. Even if they are clear, there are hundreds of direct and indirect ways in which they can interact.

For example, the main inputs for steel are electricity, coking coal and iron ore. The latter two represent a massive fraction of the sea-borne dry-bulk trade. Hence their prices are inevitably affected by changes in fuel prices which are in turn affected by changes in crude oil prices. More over, the majority of electricity in steel-producing countries is generated by thermal power plants. Therefore steel prices are also sensitive to changes in thermal coal prices. However it is rather hard to find any concrete links between (locally-mined) thermal coal prices and crude oil prices. (Note that there is very little substitution between the two commodities.)

2) The correlation may be a spurious one that emerges from regressing one non-stationary time series onto another. (See this paper for technical details.)

3) There may be a tenuous link through the expectations (e.g.signalling) channel. Crude oil prices keep track of the global economic growth prospects. Their recovery sends a bullish signal to every other market where the aggregate supply can not adjust as quickly as the aggregate demand.

4) The correlation may be due to a third causal factor that simultaneously influences prices of both oil products and other commodities. Instead of looking for causal arrows that point from oil to another commodity (or vice versa), we should perhaps be searching for a third factor that spits out arrows towards these two commodities. (For example, as people get wealthier, they buy more cars and thereby consume more gasoline. Gasoline is distilled from crude oil and cars are made of steel. Hence a speculative housing bubble that lifts the overall wealth can lead to greater demand for both iron ore and crude oil.)

5) Perhaps the correlation is simply a monetary phenomenon. Markets may be pricing everything in energy units and not in US Dollars. The correlation ensures that the relative price relationships between the commodities remain in tact.

contracts and benchmarks

If the price on your purchasing (or supply) contract will be floating according to a formula that depends on a "benchmark", you should pay special attention to the following points:

1) There are liquid futures markets for several commodities. Benchmarks that are based on such markets are by definition "forward-looking." This is ideally what you want. At the beginning of each quarter, the price on your contract will be reset by factoring in price expectations for the next quarter.

Unfortunately, there is not a deep (i.e. hard-to-manipulate) futures market for every single commodity. For example, in the ferro-chrome business, the quarterly price that is collectively declared by major South African producers is often taken as the "forward-looking" indicator.

If your contract involves such a benchmark, then make sure that your counter party can not collude with the major producers who set the benchmark. It is not difficult to imagine cases where the major producers get side payments from your counter party for declaring a price that is favorable for him.

Often the physical markets have an air of competitiveness about them, but the reality can be quite different. So be inquisitive and gather some intelligence on your counter party's relationships.

Note that if the major suppliers have made a substantial switch to the spot markets, their price declarations will not have any binding effects even for their own future transactions. Especially in extremely volatile price environments, do not be surprised if nobody takes the "benchmark" seriously.

2) Sometimes (especially in very non-transparent markets) there may be no "forward-looking" benchmarks available. In that case you will have to rely on "backward-looking" indexes. The most frequently-used indexes are the ones published by leading commercial journals.

The intelligence that these indexes rely on is often quite shaky. Prices of past-transcations are pulled straight from the voluntary questionnaires that are sent to major commodity firms. These firms have all sorts of reasons to supply false data. (In fact, after tying the price formula on your purchasing contract to the journal's index, even you will be tempted to transmit false information by deflating the prices achieved on your recent spot deals.)

Indexes are open to manipulation even if the journal manages to collect data that is reliable on average. So make sure that your counter party does not have any "sweet" connections at the journal's headquarters. Note that these connections do not have to be at the top-level. Low-ranking officers are usually more open to cooperation. (These guys are easier to impress and manipulate. They are less experienced. They have less to lose. They also have more need for side payments and other "goodies".)

3) Of course, the silliest thing to do is to base your contract on a benchmark that is "technically" very easy to manipulate. Resetting the price on your annual contract according to the December 31st closing price of a derivatives market is not a good idea. Your counter party may step in just before the market closes, place a massive order and push the price towards the direction that is favorable for him. He may lose some money on the derivative transactions, but these losses will be easily offset by the annual gains he will be making on the physical contract that he signed with you.

4) If the contract stipulates delivery of a tonnage that is quite substantial in comparison with the size of the total market, then the contract will inevitably affect the benchmark it is based on. (Assume that the prices are temporarily down for some unclear reason. If this movement takes place in a fashion that affects the benchmark, then your contract will reinforce it and stretch its lifetime.) There is one simple way of preventing this endogenous interaction from happening: Do not disclose the price formula to the public.

turkish mortgage market

Apparently, Turkish banks have already started to issue fixed-rate mortgages with maturities that extend to 15 years. Competition is forcing them to offer lower rates and longer maturities. But can any one of them actually manage the risks entailed by holding such long-term, Turkish lira-denominated instruments?

Probably not. The average maturity length of Turkish banks' liabilities has historically been very short. Even if the liquidity of secondary markets improves in near future, these mortgages will still stay in hands which can not properly manage the associated risks. In fact, there is no natural holder of these instruments because there are no Turkish counter parts for the large Western private pension funds and college endowment funds which are financed by long-term minded investors.

Moreover, the spectrum of maturities available in the government and corporate bond markets is not suitable for the management of such long duration risks. (In other words, banks can not use these markets to align their net duration exposures with the duration of their liabilities.)

I guess that these mortgages will be kindly handed to the Turkish government once an unanticipated spike in inflation forces banks to roll-over their liabilities at punishingly higher rates.

Governments have always been the ultimate risk managers.(Check out this book which is currently on my reading list.) Development of "sophisticated" mathematical risk management techniques will not change this fact.

types of efficiencies

Nature seems to be optimizing at several levels. For example,

1) Particles minimize energy consumption.
2) Organisms minimize calorific consumption.
3) Companies minimize costs.

But why?

3) Shareholders press for higher returns. Cutting costs increase competitiveness and chances of survival.
2) Managing net calorific intake increases the possibility of successful reproduction by increasing resistance to environmental shocks.
1) No idea. In biology and economics, efficiency emerges out of the system constraints. However, in physics, it is just part of the system constraints.

There may be selectionary evolutionary pressures at work in physics too.

The organisms that we see around are good at minimizing calorific costs. Why? Because if they were not, they would not have survived until now and therefore would not be observable by us. Particles we see around are good at minimizing energy costs. Why? Because if they were not, the resulting physics would not exhibit the properties that render our presence possible, and therefore would not be observable by us. (See: Anthropic Principle and Cosmological Natural Selection)

Note that the discovery of such "environmental" constraints for physics may be outside our experimental reach. Let's just keep this discourse quiet so that we will not raise Karl Popper from his grave with our non-falsifiable conjectures.

Wittgenstein would have also shuddered at the thought of physics taking place in some environment. Physics is by definition all encompassing. Regularities in physics are not by-product of anything else. They can only be self-induced. In particular, they can not arise due to a competition in a greater realm.

Although it is silly, let's imagine that there indeed is a "greater realm". Then you can iterate the same question: "Why are the rules of competition between different physics the way they are? Is this set of rules also a result of some competition?" To answer such questions, you will inevitably end up conjuring competitions inside competitions inside competitions... realms inside realms inside realms... Ad infinitum!

In short, our speculation does not even make logical sense. Hence it would have been crossed out by Wittgenstein before it even reaches Popper.

In fact, calling the behaviour of a particle "efficient" is misleading. A particle is not making calculations within the theoretical framework we subscribe to nature. It is just being a particle. That is all. What we are observing is not efficiency but simply regularity, and our theoretical framework makes this regularity look like efficiency.


Update (August 2010)

I have just discovered that the questions posed above have first been considered in the 18th century:

In 1748 Maupertuis showed that Newton's laws of motion could be derived by the application of a teleological principle. It is possible to define a mathematical quantity, the action, which involves the product of mass, velocity, and distance travelled by bodies. Maupertuis's Principle, which we now call the Principle of Least Action, was that

If there occurs some change in Nature, the amount of action necessary for this change must be as small as possible.

This elegant idea turns out to be equivalent to the Newtonian laws of motion (although it is more powerful in the sense that it can be used to derive the equations of motion in other areas of physics once the appropriate action is identified.) But, unlike the formulation of Newton, it is teleological. It says that, of all the paths that could be taken by a body moving from A to B, it actually takes that path for which the associated action is a minimum. This path is therefore determined by both the initial and the final states. Maupertuis attached great metaphysical significance to this result, regarding it as a "proof of existence of Him who governs the world". Formerly, arguments of the sort that we lived in the "best of all possible worlds" were open to the objection that we did not know any other worlds with which to draw such a comparison, but Maupertuis claimed that the other worlds were those in which motion occurred with non-minimal action. Our world was optimal in this well-defined sense, and moreover there existed a teleological aspect to the laws of Nature (in fact, some nineteenth-century commentators interpreted the existence of fossils as relics of the still-born worlds of non-minimal action.)

Barrow - Universe That Discovered Itself (Pages 88-89)

a coding theorem and genetics

Here is a nice result from an information theory book:

(A code is uniquely decipherable if every finite sequence of code characters corresponds to at most one message. If no code word is a prefix of another code word then the code is also called instantaneous. Although a uniquely decipherable code is not necessarily instantaneous, the existence of such a code implies the existence of an instantaneous one.)

Let's try to apply this theorem to genetics...

The genetic code alphabet consists of only four letter: A,C,G,U. Therefore we have D=4 in the above formula.

We need to assign a code word to each of 20 existing amino acids: Alanine, Arginine, Asparagine, Aspartic Acid, Cysteine, Glutamic Acid, Glutamine, Glycine, Histidine, Isoleucine, Leucine, Lysine, Methionine, Phenylalanine, Proline, Serine, Threonine, Tryptophan, Tyrosine, Valine. Therefore we have M=20 in the above formula.

In vertebrates the relative observed frequencies of the above amino acids are respectively 7.4, 4.2, 4.4, 5.9, 3.3, 5.8, 3.7, 7.4, 2.9, 3.8, 7.6, 7.2, 1.8, 4.0, 5.0, 8.1, 6.2, 1.3, 3.3 and 6.8 percent. (Note that these numbers sum up to 100.) In other words, 7.4 percent of the amino acids needed for the next typical protein synthesis will be Alanine. 4.2% of them will be Arginine, 4.4% will be Asparagine etc. This vector of percentages will be our probability variables "p_i". (e.g. x_2=Arginine and p_2=0,042)

Let's enforce the additional requirement that the length of each code-word is equal. In other words, for all "i" we set "n_i" equal to some "n". (There may be some structural justifications for this extra assumption. I will not make any speculations though since my knowledge of molecular biology is close to nil.)

After inserting the numbers into their appropriate places, the theorem reveals that the lower bound for the probability-weighted average of code-word lengths is 2.1. Since we set all "n_i" equal to "n", the probability-weighted average is simply "n". Note that code-word length "n" has to be an integer. Hence what noiseless coding theorem tells us is that the minimum value "n" can assume is 3.

Guess the actual word-length that occurs in genetics! It is 3. If there was a single more letter in the code alphabet, then "n" could be 2! (Due to the anti-parallel structure of DNA the alphabet size has to remain even. Therefore I should have probably written "If there were two more letters...".) However, with only four letters, the word-length can not theoretically be pushed below 3.

Given the size of the alphabet, nature is as efficient as it can theoretically get. It even opportunistically exploits the difference between 2.1 and 3 by assigning more than a single codon (namely a three letter code) to some of the amino acids. The number of code-representations belonging to each amino acid is repectively 4, 6, 2, 2, 2, 2, 2, 4, 2, 3, 6, 2, 1, 2, 4, 6, 4, 1, 2 and 4.

There are some suggestions that the genetic code has evolved in an error-minimizing fashion. When a single-nucleotide mutation transforms UUU into UUC, tRNA still codes for Phenylalanine. Hence, in some sense, greater number of representations entails less sensitivity to mutations and operational errors during the decoding process.

When you compare the number of representations against the observed frequency of occurrence, the following pattern emerges:

Note that if you exclude the outlier Arginine, then the correlation becomes 0.78. Here are two possible explanations of this high correlation:

1) Assuming that the observed frequency distribution is a reliable indicator of the relative importance of each amino acid, the high correlation ensures that the formation of important amino acids is less affected by mutations and decoding mistakes.

2) Amino acids whose production is more resistant to random shocks (e.g. mutations and decoding mistakes) will sooner or later overpopulate the weaker ones.

Notice the striking similarity with the following graph:

Here expected frequency depicts the relative frequency of amino acids that one would get by a random, serially independent juxtaposition of the available bases (A,C,G,U) in the DNA. For example, since Glutamine is coded by CAA and CAG, its expected frequency in the metabolism is W*[(C%*A%*A%)+(C%*A%*G%)] where X% is the frequency of base X in the DNA and W (larger than 1) is a factor that corrects the addition for the presence of stop codons in the DNA.

If you exclude the outlier Arginine, then correlation in the above graph becomes 0.89. In other words, the observed frequency is remarkably in line with what would have happened if the transcription mechanism lacked any structure and acted randomly on DNA.

Two cases come to my mind:

1) What happens if the number of codons coding amino acid X increases (decreases) and if none of A%,C%,G% and U% change? Each of the 64 (=4*4*4) mathematically possible codons are either assigned to an amino acid or to a "stop" signal. Therefore, as the number of codons that code X increases (decreases), the number of codons assigned to some other amino acids needs to decrease (increase). The expected frequency of X will increase (decrease) while that of others will decrease (increase).

2) What happens if A%,C%,G% or U% change due to mass mutation and the code remains the same? Then the whole expected frequency distribution will change accordingly.

If the second graph depicts a causal relationship, then in each of the two cases above, observed frequencies will soon align themselves with the new expected frequencies. What happens if this development endangers the stability and survival of the metabolism? Will any dynamic mechanisms kick in and undo part of the mass mutation or switch the code-words around so that the expected frequencies remain as before?

One final question: What is wrong with Arginine?