ponzi schemes

Bernard Madoff ran a huge Ponzi scheme. As the former head of NASDAQ he had exceptional credentials and connections. Therefore he did not have any trouble in developing a loyal customer base that included some of the most sophisticated institutional investors and wealthy individuals.

The annual returns of his fund was suspiciously stable. Nevertheless this consistency did not trigger any scepticisms. The returns did not draw the inquisitive spotlights, because they were not that outrageously high when compared to the performances of other top hedge funds. While typical Ponzi schemes are based on a contagious hysteria, his was built upon a calculated, slow-expanding exclusivity.

The fraud was detected only after a large number of clients attempted to draw their money at the same time. However, even if the financial crisis had not occurred, Madoff would sooner or later be caught. At some point, the incoming fresh capital would not be sufficient to cover the promised dividends to the already existing clients.

Question: Are all Ponzi schemes doomed to collapse?

Consider a simple scheme with the following properties:

1. Investors are promised an annual return of 10%.
2. Dividends are paid out at the beginning of each year.
3. Clients are allowed to enter or exit the fund only at the beginning of each year.
4. Net annual inflow of capital diminishes at a constant rate "R" where "R" is a real number between 0 and 1. (e.g. If this year's net inflow is 100, then the next year's will be R*100.)
5. Dividends for year "n" are paid entirely out of the net inflow for year "n".
6. The portion of net inflow that remains after dividend payments is confiscated and spent in a "non-recoverable" fashion.

This scheme collapses when the net annual inflow for year "n" becomes insufficient to cover the dividends for year "n".

Assume that net inflow for year zero is 100. Let's consider what happens at the beginning of year "n":

Due to property 4, the net inflow is 100*(R^n). The accumulation of net inflows from the previous periods is 100*[1+R+R^(2)+...+R^(n-1)]=100*[(1-R^n)/(1-R)]. The dividends are paid out on this accumulated amount. Hence, for the survival of the scheme, the net inflow needs to be greater than (10%)*100*[(1-R^n)/(1-R)]. This is true only for the (R,n) pairs that fall outside the black region:

No matter what R is, the fraud will be exposed within 10 years. If R=80%, then the fund collapses on its fifth year. If R=100%, then it survives till the beginning of year 10.

Question: What if R is greater than 100%? (i.e. What if the net inflow is perpetually increasing?)

If R assumes a value between 100% and 110%, then the Ponzi scheme will still collapse. However, in this region, there is no upper limit on the year of collapse. In fact, as R gets arbitrarily closer to 110%, downfall of the fund gets postponed to infinity.

Once R transgresses 110%, the scheme becomes collapse-proof.

Question: What if the investors are promised an annual return of D where D is a real number between 0 and 1? Can the results above be generalized beyond Property 1?

Yes, they can be.

When R=100%, the year of collapse is found by solving for "n" in the following equation: 100*(R^n)=D*100*[1+R+R^(2)+...+R^(n-1)]. So n=(1/D).

Hence, no matter what value R assumes between 0 and 1, the fraud will be exposed in (1/D) years.

In order to figure out when the scheme becomes collapse-proof, we need to solve the following problem:

Here we used the fact that 1+R+R^(2)+...+R^(n-1)=[(R^n)-1]/(R-1).

By a single application of the L'Hopital's Rule, it is easily seen that the limit of [(R^n)*(R-1)]/[(R^n)-1] as "n" goes to infinity is (R-1). Therefore, the solution to our minimization problem needs to be larger than (1+D).

But (1+D) obviously satisfies the inequality in the curly brackets for all "n". Hence, by the previous remark, it has to be the solution itself. (i.e. If R transgresses (1+D), the scheme becomes collapse-proof.)

If R assumes a value between 1 and (1+D), then the scheme still collapses. However, in this region, there is no strict upper bound on the year of collapse.

Here is a graphical summary:

As D gets smaller, the collapse-proof region expands, and the average survival duration for schemes that face strictly decreasing net inflow becomes greater.

P.S. The net inflow for year zero was completely inconsequential for our analysis. Assuming a value other than 100 would have made no difference.

P.S. Guess what is the biggest Ponzi Scheme on earth?

Read this for a detailed explanation.

perils of the sea

Here is a quote from Article IV of the Hague-Visby Rules (a multilateral agreement governing the carriage of goods by sea):

Neither the carrier nor the ship shall be responsible for loss or damage arising or resulting from:

(a) Act, neglect, or default of the master, mariner, pilot, or the servants of the carrier in the navigation or in the management of the ship.
(b) Fire, unless caused by the actual fault or privity of the carrier.
(c) Perils, dangers and accidents of the sea or other navigable waters.
(d) Act of God.
(e) Act of war.
(f) Act of public enemies.
(g) Arrest or restraint of princes, rulers or people, or seizure under legal process.
(h) Quarantine restrictions.
(i) Act or omission of the shipper or owner of the goods, his agent or representative.
(j) Strikes or lockouts or stoppage or restraint of labour from whatever cause, whether partial or general.
(k) Riots and civil commotions.
(l) Saving or attempting to save life or property at sea.
(m) Wastage in bulk of weight or any other loss or damage arising from inherent defect, quality or vice of the goods.
(n) Insufficiency of packing.
(o) Insufficiency or inadequacy of marks.
(p) Latent defects not discoverable by due diligence.
(q) Any other cause arising without the actual fault or privity of the carrier, or without the fault or neglect of the agents or servants of the carrier, but the burden of proof shall be on the person claiming the benefit of this exception to show that neither the actual fault or privity of the carrier nor the fault or neglect of the agents or servants of the carrier contributed to the loss or damage.

Does anything sound strikingly imprecise?

Phrases like "perils of the sea" help the contracting parties to circumvent the problem of listing down the infinite number of undesirable contingincies that may arise during a sea voyage. Although science has progressed substantially since the days when mighty Neptune used to rule the Mediterranian, we still can not forecast atmospheric events with any satisfactory precision. In other words there is still ample room for "acts of God".

I do not know which God is being referred to here, but I am pretty sure that his beard is not as tumultuous as Neptune's was.

asymmetry of debt

Nassim Nicholas Taleb:

"Debt and leverage cause fragility; they leave less room for errors as the economic system loses its ability to withstand extreme variations in the prices of securities and goods. Equity, by contrast, is robust: the collapse of the technology bubble in 2000 did not have significant consequences because internet companies, while able to raise large amounts of equity, had no access to credit markets. ... A loan hides volatility as it does not vary outside of default, while an equity investment has volatility but its risks are visible. Yet both have similar risks. Thus debt is the province of both the overconfident borrower who underestimates large deviations, and of the investor who wants to be deluded by hiding risks. ...Instead of sending hate mail to near-insolvent homeowners, banks should reach out to borrowers and offer lower interest payments in exchange for equity. Instead of debt becoming “binary” – in default or not – it could take smoothly-varying prices and banks would not need to wait for foreclosures to take action. Banks would turn from “hopers”, hiding risks from themselves, into agents more engaged in economic activity. Hidden risks become visible; hopers become doers."

Willem Buiter:

"The zero-sum redistribution characteristic of derivatives contracts in a frictionless world becomes a negative-sum redistribution when default and insolvency is involved. There is a fundamental asymmetry in the market game between winners and losers: there is no such thing as super-solvency for winners. But there is such a thing as insolvency for losers, if the losses are large enough."

Debt is more senior than equity. In other words cash first flows to creditors before it trickles down to shareholders.

Another important difference between the two instruments is highlighted by Taleb and Buiter: While equity absorbs both positive and negative income shocks in a continuous way, debt responds in a more discrete and asymmetric fashion.

A shock greater than a certain magnitude will trigger default. The indebted company may be saved from an outright liquidation via a successful restructuring, but the wounds inflicted by the direct and indirect costs of going through a bankruptcy process will stay with it. And what started out as a temporary problem, which could have been easily corrected by a contraction of the equity pillow, will acquire a long-lasting dimension.

detained for 16hrs

I got detained at the Gatwick Airport, placed on the next flight back to Istanbul and forced to spend 16 hours in a detainment room. The experience was quite uncomfortable. Nevertheless I can not claim that I was not treated well. We had access to TV, free coffee and sandwiches. I was even allowed to bring a pen and take some notes! Here are some of the observations I jotted down while trying to beat the overwhelming boredom:

Basic needs of human beings have changed. A Canadian girl almost cried for not having access to her iPod.

They are not afraid of you. They are afraid of you acting against yourself. Hence the reason why the toilet locks were removed. Of course, this does not explain why the flush was not working!

What is the lowliest/cheapest food in the 21st century? It is the ultimate combo of plastic bagged potato chips and tuna sandwiches.

Fake politeness is instantly recognizable. This is especially true if you are kept inside a room that is designed to be resistant against unpredictable bursts of aggression. The guards were polite in a way that asked to be reciprocated. A perfectly fine expectation... Unfortunately I could not simply reciprocate kindness when the other side assumed right from the beginning that I have unlimited potential for crude violence. (e.g. The TV was put inside some sort of a bullet proof glass.)

Who was actually being detained? Us or them? These were the questions that recurrently popped up in my mind whenever I gazed at the window that the guards used to keep an eye on us. Our guards had sadly pathetic jobs. Their office was a lot more cramped than the room that we were being hold in. They did not have access to unlimited amounts of TV time nor unlimited number of sandwiches. The extremely cheap coffee provided by the nearby beverage dispenser helped them stay awake through the quite and eventless night during which they stared at computer screens and security monitors for endless hours. Yes, they were freer than us. But what kind of freedom was theirs? Being able to leave the office for five minutes or surf on-line are not essential traits of what I consider as freedom.

Private phone conversation? Forget it. Being allowed to use cellphones without built-in cameras was not any good news for the detainees who were under emotional stress and were in dire need of engaging in a private conversation with their close relatives. The room was small and we could not help but eavesdrop each others' conversations.

Bookphiles prefer formal complaint letters. That is why the "complaint box" was placed on top of the little library in the detainment room. I was tempted to make a written reminder for the broken flush. Then I realized that the box was probably put up for more serious inquires. The West African lady nearby me chose the more efficient method of simply shouting out her complaints and demanding her legal rights.

Blankets from space age. At night we were delivered glittery, silver coloured blankets. Folded, they could literally fit into one's pocket. Unfolded, they looked like large sheets of wrinkled aluminium folio. It was literally impossible to not wake anybody up while shifting your body position under these hygienic-but-noisy blankets. Of course the guards could not care less. They were only burdened with the task of providing a hygienic accommodation. Comfort did not matter at all. Detainees covered themselves with metal blankets, lied on metal benches, and dreamed about being on a metal spaceship.

Developed vs. Developing World People I thought we were treated pretty well. (Guards kept asking us whether we desired any coffee or tea. Imagine that happening in Turkey!) A French lady thought otherwise. She said she was shocked by the "incredibly inhumane" treatment. Rather than sitting still and waiting for the decision, she wanted to be immediately deported back to France: "I am never ever going to come to UK again!" Sorry but UK could not care less.

Are women more talkative than guys? Yes! A Canadian girl talked on the phone for literally five hours! I understand that she felt lonely and stressed out. But can five hours of continuous gibberish be really that relieving?

Good Cop/Bad Cop trick is still being employed in these circles. Come on guys! How can you expect this trick to still work? Everyone is acquainted with it about from crappy films and soap operas.

Would you like a statistical profile of those who end up in the detainment room? Just have a look at the different languages that the detainee information booklet has been translated into: Arabic, Farsi, Turkish, Hindi, Mandarin, Punjab, Pushto, Urdu. There was also a French translation aimed at potential readers coming from the "colonial", French-speaking African countries.

BBC. We had no access to the remote controller. Hence we could not watch anything but the BBC channel. In fact, we were not even allowed to turn off the TV. We were literally forced to listen to BBC Teletex while trying to sleep amidst the ambient noise created by our space-age blankets which slowly wrinkled into 11 dimensions.

Choice of pictures. There were various pictures of the natural world on our walls: Elephants tramping towards us, hawks flying over us... The message: "You are temporarily trapped inside these four walls. Try to enjoy the cheap metal and plastic furnitures. Stay calm and be reasonable. A lively world is waiting outside for you!" Unfortunately the contrast between the illusionary odour emitted by the poster lilies and the disgusting smell of our left-over sandwiches was just too sharp to loosen ourselves and let our imaginations be taken over.

Writing out your thoughts can reduce mental strain. I had always thought that this cliche was baseless. Well... Now I can confirm that it really works. It may work for you too! So get yourself a notebook and a pen!

In UK, everything is privatized. I am not going to pass judgement on this. UK Border Agency apparently outsourced its detainee treatment business to a private company! Our guards were employed by Group 4 Securicor.

"So you would like to convince me?" Interrogators are extremely sceptical of anything that comes out of your mouth. That is why they focus on your body moves. Only after they are convinced that you are speaking the truth will they start to really listen to you. Most of these guys are communication experts. So be careful with those feet!

No Visitors. This was quite inconvenient. My sister ended up waiting at the airport for hours. I was not given any information about how long the process would take. I had no idea about the likelihood of being deported neither. So I could not tell her to simply go back home.

Life is full of irony. While detained, I watched a BBC film in which a lawless gang of African-Americans heroically fought against the social order and the policemen who tried to protect it.

"Can somebody please turn off these bright lights?" Nope. They have to be kept on. Yes, even at night. If you have spent any time in UK, you have probably figured out that the highest authorities present on the street and in the buildings are security cameras. These cameras watch everybody including gangsters, burglars, pimps, maniacs, normal citizens and policemen. Their presence in the room protect each detainee against the illegal offences that could be committed by guards and other detainees. Lights have to be kept on because otherwise the cameras will not work.

Eyes vs Cameras. I had always had the feeling that security cameras were intrusive. While detained, I realized that being under the constant surveillance of a real pair of eyes was a lot more intrusive.

Aquarium. For some reason, the security cameras gave me the feeling that we were kept inside an aquarium. The fact that fresh air was periodically pumped into our room through a noisy and old air conditioning system reinforced that sensation.

option auctions

Although slowed down, the privatization program is still ongoing in Turkey. One of the last auctioned assets was a closed-down raki factory that is located right on Bosporus. The point of interest was not the factory itself but the precious 54,870 square meters land that the factory had been built on. (Since none of the buildings are historical, the prospective investor is free to demolish everything and to use the land as he wishes.)

The winner of the auction was an obscure company with a bizarre and very long name: As Asya Gayrimenkul Pazarlama İnşaat Taahhüt Otomotiv Oto Kiralama Turizm Kamuoyu Araştırmaları Reklam Hizmetleri ve Matbaacılık Dayanıklı Tüketim Mamülleri Gıda Maddeleri İthalat İhracat Sanayi ve Ticaret Ltd. Şti.

Their bid was 303,100,000 TL. The result was shocking. After 40 rounds of fierce bidding, the prices had climbed to such high levels that even the government was caught by surprise.

A couple of weeks later the winning company made it to the headlines. Everyone was wondering who these obscure millionaires were. The fact that their company had only 50,000 TL of registered capital rendered the situation even more mysterious.

I was surprised, not by the result of the auction, but by the reaction of the newspapers. These guys were no millionaires. The government had lowered the entry barrier to such ridiculous levels that anybody who was willing to risk 50,000 TL (i.e. the collateral amount) could join the auction and bid for the small-but-realizable prospect of making millions of dollars. The goal was to attract more participants and to stimulate greater momentum and competition. Secretly the government hoped that the amateur investors would push up the prices and that the asset would nevertheless end up in the hands of a professional investor who will be able to close the deal by paying the promised amount.

However, in an almost paradoxical fashion, the design of the auction discouraged the serious investors who anticipated right from the beginning that the presence of obscure investors would lead to an irrational bidding war.

Claim: The behaviour of the winning company was aggressive but not irrational.

A privatization auction does not immediately result in a completed sale. There is a deadline for paying the promised amount. (The deadline is usually a year away from the auction date.) If the winner changes his mind, then he is forced to hand the entire collateral to the government. In other words, the auctioned object is not the asset itself. It is the strike price of the American call option to buy the asset before the deadline. This price is Y minus W where W is the value of the collateral and Y is the bid. (The collateral counts towards the purchasing price.) Since W is fixed from the beginning, the participants are essentially bidding for the strike price of the option. (Note that they are not bidding for the price of the option!)

Now let's look at how the bidding behaviour changes as the required collateral amount decreases.

Since the price of an American call option is close to that of an European one with exactly the same qualities, we can safely employ the classical Black-Scholes formula during the rest of our analysis. This is not an uncontroversial move. There may be monetary gains from an early payment to the government. (e.g. In numerous privatizations, early payment has been encouraged by a provision of discounts.) Nevertheless, the assumption that the early exercise of our American call option is non-optimal is harmless. The conclusion of our argument will be analytically independent from it.

If the value of the asset is greater than Y-W at the deadline date, then the option will be exercised. If it is not, then the option will expire and W will go wasted.

The Black-Scholes option price at time "t" is:

where

and where "S" is the value of the asset at time "t", "K" is the strike price of the option, "r" is the continuously-compounded annualized risk-free interest rate, "σ" is the volatility of the value of the asset, and N(x) is the standard normal cumulative distribution function:

In our case, we have K=Y-W, T=1 and t=0. (i.e. Deadline is a year away from the auction date.)

Without losing generality let's fix "σ" at 20% and "r" at 5%. And for convenience let's express both "Y" (the bid) and "W" (the collateral) as percentages of "S" (the value of the asset at t=0): Y=m*S and W=n*S where both "m" and "n" are strictly positive real numbers.

Note that the value of S at t=0 is universally observable and everyone agrees on it. You may ask: "Wait... Revealing the true value of S at t=0 was the whole purpose of the auction!" Nope. The auction is concerned with the value of S at t=1, not at t=0.

Moreover let's assume that auction participants and government share the same ideas about the dynamics that drive the evolution of "S" and "r". (In particular, they can agree on the values assigned to "σ" and "r".) This is indeed a strong assumption... (In economics, granted that its conclusions are instinctively realistic, the contents of a model do not matter much!)

During the auction, the bidders will never violate the following inequality:

This is simply because the auction participants are trying to make a profit. "W" is set by the government and it will be the cost of the option no matter what the winning bid is. (Here we implicitly take for granted that the interest earned on the collateral goes into the account of the government even if the winner ends up purchasing the asset before the deadline.) Hence participants will bid in a way that renders the value of the option greater than "W".

Since "S" is positive, dividing both sides by "S" preserves the inequality:

The term "ln(S/K)" in "d" is now "ln(1/(m-n))". Hence "S" has completely disappeared from the inequality. Since the government fixes "n" before beginning of the auction, the only unknown variable left here is "m".

Due to the competitive spirit reinforced by numerous rounds of bidding, the participants will be pressured to increase their bids (i.e. their "m") until the inequality above turns into an equality. In other words, once the government fixes "n", the above equation spits out a unique "m" that depicts the bidding behaviour of participants:

Independent variable "n" is located on the x-axis and dependent variable "m" is located on the y-axis.

Note that the relationship between the two variables is non-linear. As the government decreases the amount of collateral required as a percentage of the value of the auctioned asset, the bidding becomes more aggressive. The sensitivity of this interaction becomes greater at the lower ends of "n".

During the privatization of the raki factory, "n" was set incredibly low. Today the value of a square meter land on the Bosporus is about $2,000. Hence S at t=0 is roughly equal to 164,610,000 TL (=54,870*2,000*1.5). In other words, the government had set "n" equal to 0.02% (=30,000/164,610,000).

With the above assumptions for "σ" and "r", the corresponding "m" for 0.02% is 235%! In other words, the winning bid is 386,833,500 TL (=2.35*164,610,000). If the winning company has friends in the government, it may be able to extend the deadline to two years. (This has happened before!) In that case, "T" becomes 2 and the corresponding "m" increases to 360%!

Conclusion: The bidding behaviour was not irrational.

P.S. In retrospect we already know that "m" was 184% (=303,100,000 /164,610,000). Plugging 12% into "r" as a more realistic risk-free rate for the Turkish market, we can calculate the "expected σ": 12.5%

P.S. The owners of the winning company do not have fat offshore bank accounts. They need to find a real investor to whom they can pass the option before the deadline, or with whom they can finance the exercise of the option at the deadline. I am pretty sure that they are desperately flying around the world at the moment. Since they are virtually unknown in the investment community, it will be tough for them to find an interested foreign partner.

climate models as opinions

Gavin Schmidt, a climatologist at NASA's Goddard Institute for Space Studies, writes on computational climate models:

In some respects they all act in very similar ways — for instance, when you put in more carbon dioxide, which is a green house gas, it increases the opacity of the atmosphere and it warms up the surface. That is a universal feature of these models and it is universal because it is based on very, very fundamental physics that you don't actually need a climate model to work out. But when it comes to aspects which are slightly more relevant – I mean, nobody lives in the global mean atmosphere, nobody has the global mean temperature as an important part of their expectations – things change. When it comes to something like rainfall in the American Southwest or rainfall in the Sahel or the monsoon system in India, it turns out that those different assumptions that we made in building those models (the slightly different decisions about what was important and what wasn't important) have a very important effect on the sensitivity of very complex elements of the climate.

Some models suggest very strongly that the American Southwest will dry in a warming world; some models suggest that the Sahel will dry in a warming world. But other models suggest the exact opposite. Now, let's just imagine that the models have an equal pedigree in terms of the scientists who have worked on them and in terms of the papers that have been published — it's not quite true but it's a good working assumption. With these two models, you have two estimates — one says it's going to get wetter and one says it's going to get drier. What do you do? Is there anything that you can say at all? That is a really difficult question.

There are a couple of other issues that come up. It turns out that if you take the average of these 20 models, that average is a better model than any one of the 20 models. It has a better prediction of the seasonal cycle of rainfall; it has a better prediction of surface air temperatures; it has a better prediction of cloudiness. That is a little bit odd because these aren't random. You can't rely on the central limit theorem to demonstrate that that must be the case, because these aren't random samples. They are not 20 random samples of the space of all possible climate models. They have been tuned and they have been calibrated and they have been worked on for many years — everybody is trying to get the right answer.

Let us assume that there exists a "true" deterministic computational model in the space of all possible climate models. This true model may be computationally very demanding and therefore outside the reach of current technology. Nevertheless researchers will continue to tweak their models and try to develop "better" ones.

I put the word "better" in quotation marks because it is practically impossible to develop a metric that will measure how close a certain model is to the true one. Why? Firstly, we can not observe the true model directly. Secondly, the success of a model's predictions may be due to sheer luck and therefore does not necessarily tell us how close the model is to the true one.(This is similar to the idea that there is always going to be some ignorant traders who constantly get the direction of the stock market right.) Thirdly, since climate models have long time horizons and their forecasts can not be thoroughly checked against new data within a practically viable period of time.

Schmidt states that the average model tends to perform better than each individual model does. Ignoring the above mentioned complications, we can interpret this as follows: The average model is closer to the true one.

The possibility that the average expert opinion may be superior than individual opinions was recognized quite early by the Rand Institute. During 1950s the so-called Delphi Method was developed to assess the effects of technology on future warfare. Here is a short description from Wikipedia:

"The Delphi method is a systematic, interactive forecasting method which relies on a panel of independent experts. The carefully selected experts answer questionnaires in two or more rounds. After each round, a facilitator provides an anonymous summary of the experts’ forecasts from the previous round as well as the reasons they provided for their judgments. Thus, experts are encouraged to revise their earlier answers in light of the replies of other members of their panel. It is believed that during this process the range of the answers will decrease and the group will converge towards the "correct" answer. Finally, the process is stopped after a pre-defined stop criterion (e.g. number of rounds, achievement of consensus, stability of results) and the mean or median scores of the final rounds determine the results."

The process sounds remarkably similar to the dynamics that govern scientific progress. Academicians read each other's articles, which get filtered through peer-review processes, and revise their own models in the light of the new information. They also interact in seminars and conferences where they exchange unpublished ideas.

But there are important differences as well. For instance, the anonymity assumption does not hold in academia. Researchers never hide their identities. This has two important consequences. 1)Ideas of academicians with greater credentials may have more influence on others. 2)Unconventional and non-mainstream ideas may never be uttered due to concerns about reputation. Moreover, the average opinion often has very little scientific value. Especially in hard sciences, the most successful approximations to truth are not the anonymous ones. (These fields are replete with results that are called by the names of their originators.)

On the other hand, academic fields with extremely complex subject matters (e.g. climatology and economics) often admit co-existence of different points of view about the same phenomenon. When the truth is complex, no single approach is likely to yield the ultimate explanation. In such cases, the average expert opinion may have some scientific value.

It is well-known that the average public opinion can outperform individual predictions including those done by experts. For example, prediction markets are exceptionally good at forecasting election outcomes and Oscar nominations.

(When it comes to making predictions in politics and economics, the experts perform no better than the average citizen does. Does this mean that we should stop wasting public resources on the production of such "experts"?)

How can you ever expect a large group of uninformed agents, which are occasionally swayed by herd mentality, to generate ideas that can beat even the "best" experts'? Well... The secret lies in two buzz words: diversity and independence. When individuals are anonymously comtemplating on their own and are not worried about the consequences of their ideas, the resulting spectrum tends to be greater than what would appear in a non-anonymous environment that is open to instant interactions. In the prediction markets, the ugly face of group dynamics does not kick in because people are not allowed to influence each other. That way, reputation and imitation are prevented from distorting the average estimate.

We have the two prerequisites for the well-functioning of the climate prediction market:

1) Independence. Each climate-modelling team develops its ideas partly in secrecy. This increases the statistical independence of their efforts. Teams do not operate anonymously. However this lack of anonymity should not be a big obstacle. Reputational concerns are not that great in climatology. The phenomenon in question is so complex and the time horizon of the predictions is so long that no "sane" model can ever be outright refuted.

2) Diversity. Climatologists are probably making use of all the tools at their disposal. Hence the spectrum of technologically available models are explored fully.

Note that I have used the words "model" and "idea" interchangably. This was done on purpose. Both models and ideas spit out a bunch of predictions against which their validities are tested. Assume that the source of the predictions is hidden inside a black box and you only get to see the predictions. Can you infer which predictions are generated by computational models? You can make a guess but you can never be sure. It is sort of like John Searle's Chinese Room:

"Searle's thought experiment begins with this hypothetical premise: suppose that artificial intelligence research has succeeded in constructing a computer that behaves as if it understands Chinese. It takes Chinese characters as input and, by following the instructions of a computer program, produces other Chinese characters, which it presents as output. Suppose, says Searle, that this computer performs its task so convincingly that it comfortably passes the Turing test: it convinces a human Chinese speaker that the program is itself a human Chinese speaker. To all of the questions that the human asks, it makes appropriate responses, such that any Chinese speaker would be convinced that he or she is talking to another Chinese-speaking human being."

Can you conclude that the artificial intelligence understands Chinese?

What about a bunch of random guesses which happen to overlap with the predictions of a sophisticated climate model? Do those guesses have any value at all? Is there more to a model than just an input-output scheme? Does the internal mechanism of the scheme matter? Faced with some of the most complicated systems in the universe, do "sophisticated" macroeconomics and climate models really have any substantial difference from mere guesses?

(For those who are interested, here is a paper that compares the pros and cons of the Delphi Method and the prediction markets.)

The wisdom of crowds and the success of collective intelligence have created a lot of headaches for auction participants. Regardless of what is being auctioned (e.g. a company, an oil well, a ton of tuna fish), it turns out that the average bid usually corresponds the correct value. Of course the winner is not the average bidder. Hence he is cursed from the beginning. The fact that he has won means that he has overpaid by bidding more than the average estimate.

Here is a short description of the Winner's Curse from Wikipedia:

"In a common value auction, the auctioned item is of roughly equal value to all bidders, but the bidders don't know the item's market value when they bid. Each player independently estimates the value of the item before bidding. The winner of an auction is, of course, the bidder who submits the highest bid. Since the auctioned item is worth roughly the same to all bidders, they are distinguished only by their respective estimates. The winner, then, is the bidder making the highest estimate. If we assume that the average bid is accurate, then the highest bidder overestimates the item's value. Thus, the auction's winner is likely to overpay."

Can we apply this idea to climatology? Some models receive more policy and public attention than others. Media, for example, usually focuses on the impact value of the news reported. Hence it is naturally biased towards picking and publishing papers that make attention-grabbing and exciting predictions. We can imagine this whole process as an auction. The research teams submit their models as bids. Models with unexciting predictions are considered as not news-worthy. (Even academic journals seem to be biased against such papers.) The winner of this auction is going to be the model that predicts the most dire scenario. What will be the Winner's Curse? It will be the reputational cost that will be incurred in the long run for creating a model that was far off the truth. Of course the verification process will take a very long time. By the end of it, all academicians involved in the production of the winning model will probably be dead. Hence, when discounted to today, the cost of reputational loss is not that much. Consequently, the participants in this auction will care very little about the winner's curse. (i.e. There will not be any shifts in the bidding behavior.)

What is considered by the media as attention-grabbing seems to be changing. Climate models predicting dire scenarios have become so commonplace that important newspapers are now providing space to sceptical views of these models.

P.S. The validity of a proposition rests partly on the nature of the methodology used. How about the validity of the methodology itself? The usefulness of the Delphi Method can not reached by an application of the Delphi Method...

stability and confidence

A period of stability boosts self-confidence which in turn marks the beginning of the period of instability. The phenomenon is universal. In most cases, the confidence stems from the belief that one is in absolute control of what is being managed.

Here are three very different examples:

Giving up smoking:

"In one study, Nordgren looked at a group of people trying to quit smoking and found that it was those who rated their willpower particularly highly who were most likely to end up smoking again within a few months. The reason, Nordgren argues, is that they were more cavalier about exposing themselves to situations where they might be tempted to smoke."

Business cycles:

"When times are good, investors take on risk; the longer times stay good, the more risk they take on, until they've taken on too much. Eventually, they reach a point where the cash generated by their assets no longer is sufficient to pay off the mountains of debt they took on to acquire them. Losses on such speculative assets prompt lenders to call in their loans. "This is likely to lead to a collapse of asset values," Mr. Minsky wrote. When investors are forced to sell even their less-speculative positions to make good on their loans, markets spiral lower and create a severe demand for cash. At that point, the Minsky moment has arrived. The housing market is a case in point, says Investment Technology Group Inc. economist Robert Barbera, who first met Mr. Minsky in the late 1980s. When home buyers were expected to have a down payment of 10% or 20% to qualify for a mortgage, and to provide income documentation that showed they'd be able to make payments, there was minimal risk. But as home prices rose, and speculators entered the market, lenders relaxed their guard and began offering loans with no money down and little or no documentation. Once home prices stalled and, in many of the more-speculative markets, fell, there was a big problem."

Mountain climbing:

In Laurence Gonzales’s riveting book Deep Survival, he gives a sobering account of four mountain climbers who successfully scaled the 11,249-foot peak of Mount Hood in Oregon — considered a “beginner’s” mountain — only to fall disastrously during their descent... The climber in the top position — a veteran of much more challenging climbs — felt that belaying (the laborious process of anchoring a climber’s rope to the mountainside to arrest a fall) was an unnecessary precaution in this case, so when he lost his footing and fell, he yanked his three tethered colleagues, and five climbers below them, off the side of the snow-covered mountain. Three men died in this unfortunate incident, and the question posed by Gonzales is what leads some individuals to such tragic ends, while others faced with the same circumstances survive? The answer, which forms the major thesis of Deep Survival, may also be the ultimate explanation for the current financial crisis: "The climbers on Mount Hood were set up for disaster not by their inexperience, but by their experience. It was the quality of their thinking, the idea that they knew, coupled with hidden characteristics of the system they had so often used. The system … was capable of displaying one type of behavior for a long time and then suddenly changing its behavior completely."

the inflation monster

From a recent Economist article (02/07/2009) that depicts the increasing volatility in long-term inflation expectations:

As volatility has subsided in equities, it has popped up elsewhere. Interest-rate swaps allow investors and borrowers to switch from a fixed rate to a floating, or variable, rate and vice versa. You can buy an option to take part in a swap, a contract dubbed a “swaption”. The implied volatility of these contracts has shot up in recent months, indicating that investors are uncertain about long-term interest rates. With good reason: ten-year Treasury bond yields have veered between just over 2% and almost 4% since December. Although many countries are experiencing mild deflation, investors fret. David Woo of Barclays Capital says investors worry about the inflationary impact of fiscal deficits and quantitative easing. “Every European client asks in each meeting about inflation,” says Jan Loeys of JPMorgan. They are clearly acting to protect themselves.

Here we have the funny situation of clients protecting themselves against themselves.

Inflation can occur due to a variety of reasons. As the circulation speed and volume of money increases without a corresponding increase in the production of goods, prices of goods will naturally up. In other words, money will become less valuable. This is the classical explanation of inflation. The post-modern explanations are less intuitive. Nevertheless the underlying psychological mechanism behind them is pretty straight forward: Fear is contagious and collective worry can turn into a self-fulfilling prophecy. In other words, inflation expectations are as important as the inflation itself. For example, if each "European client" sells fixed-rate government bonds and takes measures to protect itself against a possible severe inflation, then the market indicators will adjust accordingly. These expectations may in turn spread into the non-financial markets as investment funds flock into commodity futures in the hope of hedging themselves against inflation. Once the oil prices take off, the inflation monster will be unleashed. (Note that there are numerous pathways through which expectations can influence the outcome. This example represents only one of them.)

Question 1: Why would spot oil prices increase when investment funds flock into the oil futures markets? Is the oil price not determined by the physical supply and demand conditions?

Oil futures are used by investors for a variety of purposes. They are usually conceived as a good hedge against inflation and against fluctuations in the value of US dollar. They are also bought by managers who would like to diversify their portfolios by adding in an exposure to commodities.

The resulting demand is not related to physical oil demand at all. Instead of correcting the order-flow-driven price hikes in the futures markets, the physical traders may simply succumb to the expectations indicated by these hikes.

There can not be any arbitrage opportunities between the spot and future prices.(Otherwise the law of one price is broken.) This is essentially the only constraint on the evolution of the two prices. Which price drives the other is not pre-determined. For example, spot market may instantenously absorb all indications given by the futures market. In that case, spot prices will move along with the future prices towards an arbitrage-free equilibrium without any occurrence of physical arbitrage. The alignment can also happen in a more balanced fashion. For example, the movement in the futures market may be transmitted to the spot market via physical arbitrages. In that case, spot and future prices will both move towards each other.

Last year's commodity bubble was probably fuelled by alignments of the first kind. On the other hand, it is pretty certain that last week's $3 surge in Brent Oil future prices was entirely due to the long positions taken by a single rogue trader. (I wonder how spot prices would have responded if the rogue transactions had gone unnoticed in the midst of a large inflow of momentum trades and the rogue trader had never been caught.)

Question 2: If the nature of inflation is so twisted, why do central banks bother with inflation targeting policies? How can they ever make credible commitments to maintain price stability if the monetary policy tools at their disposal are only partly capable of taming the inflation monster?

The magic word here is "credible".

Military commanders galvanize their soldiers and win wars that they would otherwise not be able to win. Religious leaders make their followers believe in things that are not empirically verifiable. Hypnotists can literally paralyse the limbs of their subjects. This mysterious art of influence is hard to master. However, once mastered, it can be very very powerful.

Ben Bernanke explains why central banks need to make use of this art for the successful execution of monetary policies:

In the 1960s, many economists were greatly interested in adapting sophisticated mathematical techniques developed by engineers for controlling missiles and rockets to the problem of controlling the economy. At the time, this adaptation of so-called stochastic optimal control methods to economic policymaking seemed natural; for like a ballistic missile, an economy may be viewed as a complicated dynamic system that must be kept on course, despite continuous buffeting by unpredictable forces.

Unfortunately, macroeconomic policy turned out not to be rocket science! The problem lay in a crucial difference between a missile and an economy--which is that, unlike the people who make up an economy, the components of a missile do not try to understand and anticipate the forces being applied to them. Hence, although a given propulsive force always has the same, predictable effect on a ballistic missile, a given policy action--say, a 25-basis-point cut in the federal funds rate--can have very different effects on the economy, depending (for example) on what the private sector infers from that action about likely future policy actions, about the information that may have induced the policymaker to act, about the policymaker's objectives in taking the action, and so on. Thus, taking the "right" policy action--in this case, changing the federal funds rate by the right amount at the right time--is a necessary but not sufficient condition for getting the desired economic response. Most inflation-targeting central banks have found that effective communication policies are a useful way, in effect, to make the private sector a partner in the policymaking process. To the extent that it can explain its general approach, clarify its plans and objectives, and provide its assessment of the likely evolution of the economy, the central bank should be able to reduce uncertainty, focus and stabilize private-sector expectations, and--with intelligence, luck, and persistence--develop public support for its approach to policymaking.

Of course, as has often been pointed out, actions speak louder than words; and declarations by the central bank will have modest and diminishing value if they are not clear, coherent, and--most important--credible, in the sense of being consistently backed up by action. But agreeing that words must be consistently backed by actions is not the same as saying that words have no value. In the extreme, I suppose a central bank could run a "Marcel Marceau" monetary policy, allowing its actions to convey all its intended meaning. But common sense suggests that the best option is to combine actions with words--to take clear, purposeful, and appropriately timed policy actions that are supported by coherent explanation and helpful guidance about the future.

The central bank will try to impress the crowd by occasionally whipping the inflation monster. The hope is that everyone will be convinced that the bank can control the monster even in case things get really out of hand. And the irony, of course, is that the crowd has greater power over this monster than the bank does.

The monster partly dwells in the mind of the crowd and its lifeblood is the aggregate fear. The central bank puts on a show that is sort of like fireworks. People forget their miserable conditions when they see colourful sparkles lightening up the sky. Similarly, people forget their own fears, when they see a villain suffering. Here the villain is the whipped monster and the illusion is that the monster is not audience.

Finally I would like to quote Emanuel Derman's blog post titled "Do Keynesians Laugh When They Tickle Themselves?" (12/02/2009). It is a variation on the same theme that is touched upon by Bernanke. It is also the most original comment I have read on the "stimulation debate":

When the government throws money at the populace, and keeps describing it as a Hail Mary pass they regret they have to make, it must vitiate the effect of the stimulus itself. The first time Keynesianism was used, it was a surprise move to a nation that wasn't an expert on economic theory; the second time around, everyone knows what is supposed to happen, and that can't be good. In human affairs, history matters. Penicillin works even if they tell you they're going to give it to you, maybe even better. But people's minds are different from people's bodies. Is a stimulus so stimulating when they keep telling you they are going to stimulate you? Can you get excited when everyone around you is watching to see how excited you get?

P.S. Targeting price stability is not equivalent to popping asset and commodity bubbles as they arise. Firstly, central banks are often incapable of distinguishing bubbles from price movements that are driven by fundamentals. Secondly, bubbles may be occurring outside the set of goods that are included in the formula which is used for price level calculation.

highly connected nodes

Here is an excerpt from "The Origin of Wealth" (Eric D. Beinhocker):

Jain and Krishna created a simulation of an evolving ecosystem of computer creatures. The researchers found that if they randomly removed a "species" from their simulated ecosystem, typically not much happened. Yet, once in a while, removing a random species would set off a cascade of events leading to a mass extinction. Certain species are very densely connected to other species in the web of food relationships and niche competition. Biologists call these keystone species. For example, one might imagine a species of amoeba that was a source of food for various insects and filter-feeding worms, which in turn were food for a variety of birds and mammals, which in turn also had an impact on various plant species, and so on. A sudden drop in the amoeba population at the bottom of this food chain could radiate widely throughout the ecosystem.

The production of cars and personal computers feed an extremely large network of businesses. Hence these consumer goods can be regarded as "keystone species" in the economy. For example, a drop in the aggregate demand for cars will lead to a cascade of negative effects down the extremely complicated supply chain. There will also be secondary effects as the affected firms cut back on investment and personnel.

As the percentage share of keystone consumer products increases in the GDP, economy becomes more sensitive to aggregate demand shocks. The experience (or the fear) of economic distress causes people to cut back on all unnecessary expenditure. The first victims are usually durable goods such as cars and PCs. (By definition, durable goods are things that can be repaired and used for extended periods of time.) When these densely connected industries start to suffer, the economic crisis spreads and deepens very quickly. Conversely, when these industries pick up, their contribution to economic growth is unintuitionally positive.

Consumption patterns will change as civilization advances and new technologies are developed. However our basic needs (e.g. food, shelter, health) will stay the same, and economic contractions (and expansions) will continue to be amplified by the densities introduced into the economy's network topology by the complex-but-non-essential goods.

on modern tragedy

I might almost say that there is no modern tragedy. Take Ibsen: his modern tragedies (even including Ghosts) are really melancholy comedies; the tragedy of their heroes lies in the fact that they are pathetic creatures who inevitably put themselves in the wrong, and so are essentially ridiculous. Your classical hero broke himself against the divine order of things, which is tragic; your modern hero breaks himself against the human order of things, which is slightly comic, but mainly sad. Shakespeare's heroes always die; that saves them from unwilling absurdity. Modern heroes usually live on, which is both laughable and pathetic. If Othello had not stabbed himself, but had been found guilty of manslaughter with extenuating circumstances and spent his old age as a retired general on half-pay, he would have been a modern hero; that is to say, a melancholy semi-hero. That is why anyone who wants to write a real tragedy must end his play with a wholesale massacre. It is not that death is in itself tragic and sublime, but that after that your hero can do nothing to disfigure his heroism. 

Karel Capek - Intimate Things

A tragic hero should be myopic. In fact he should not even be cognizant of the blurry distances. He should continue climbing and never know or worry about the peak height.

A tragic hero should be spirited and goal-oriented. His joys should be woven out of mountain peaks, not out of mountain pathways. Climbers who climb for the sake of climbing are just challenging themselves. Those who climb for the peak are challenging the Gods.

Most important of all, a tragic hero is someone who is unaware of the tragic aspects of his situation.. An eerie silence should not lead to self-contemplation of the kind that can lead to the realization of the "big picture".

Melancholy is not tragedy. It generates way too much ash for that purpose! A tragic hero should burn without realizing the heat. In particular, the heat should not leave any physical trails.