mahalle berberi

- Adamin uzerinde niye beyaz onluk var? Cunku beyaz hijyen demek. Doktorlar da beyaz giyer. Iyi de benim ilkokul hocama da beyaz onluk giydiriyorlardi...

- Devasa aynanin yaninda asililar: Beykoz Futbol Takimi'nin armasi, berberlik locasi uyelik levhasi, Arapca bir kac dua, sararmis bir Ataturk resmi. Biz Ataturk'u de takim tutar gibi sevip, sayiyoruz. Kacimiz nutugunu okumusuzdur ki zaten? Batili, buyuklerine fikirlerinden dolayi saygi duyuyor. Biz ise baska sebeplerden oturu... (Bir resmi guzel yapan cercevesi olabilir mi?)

- Berberin makasi yanagima gotururken yaptigi estetik dansi hic bir zaman unutmayacagim. Bir dirsek hareketiyle beyaz onlugunu sivarken makasi havada guzel bir S cizmisti... Bana bir kez daha "gereksizlik" ile "estetik" kavramlari arasindaki o derin bagi farkettirmisti. Gereklilik hep "duz" cizgiler dogurur. Ornek: A ile B noktalari arasindaki en kisa cizgi duz cizgidir.

trivialities

Radio: "Every season has an end..."

A Mathematician: What a deep insight, isn't it? Of course not! What the hell was I expecting from a piece of pop lyrics anyway... How come a song with such silly lyrics be considered beautiful?

Another Mathematician: You seem to forget that all of mathematics is a large body of tautologies. Proofs may be long, convoluted, tricky or hard. But at the end of the day they are nothing but demonstrations of the fact that some statements are tautologies.

So why be surprised when common people celebrate life's trivialities? We mathematicians too celebrate trivialities!

For some reason tautologies are beautiful. For some reason they have the power to unify people and resonate across barriers.

In some sense, trivialities are the only thing we can hold onto. All of our beliefs will sooner or later be challenged, improved upon or even discarded. But trivialities will stay... They will perpetuate because they simply "are".

There in lies a profound, bottomless source of religious fervour and aesthetic appreciation.

içselleştirmek vs anlamak

"Artık onu daha iyi anlıyorum" lafı bir uydurmadır. Karşınızdaki kişiyi daha iyi anladığınızı zannetmeniz aranızda geçen aktivitelerin sayısının, uzunluğunun ve yoğunluğunun artışından ileri gelmektedir. Bu bir nevi o insana daha alıştığınız anlamına gelir.

İnsanoğlunun en zayıf yönü içselleştirdiği şeyleri daha iyi anladığını zannetmesidir.

Bu gözlem daha da genellenir ise, çoğu bilim diye sıfatlandırılmış akademik alanların aslında sadece "yeni alışılagelinenler" listeleri oldukları açıkça görülecektir. Daha iyi tanımak derivasyon yapabilmeyi gerektirir.

içi boş zenginlikler

Günümüzde çok fazla kelimenin içi boşaltılmıştır. Sanmayın ki bu kelimeler doğduklarında içleri doluydu.

Örneğin "aşk" kelimesini ele alalım. Açıklanmak istenen fenomen son derece karmaşık. Dolayısıyla bu isimlendirme baştan hatalı. Bu hata edebiyatçılar aracılığıyla hemen üretken bir etkene dönüşüverir. İyi edebiyatçı, basit isimlendirmeler sonucu ulaştığımız temelleri sağlam kelimeler arasında çeşitli bağlar kurarak bu içi boş kelimeleri bir nebze doldurabilir.

Sonuç: Aşk kelimesinin edebi açıdan zenginliği içinin tamamen boş olmasından kaynaklanır.

cahil fikirler

Cahillerin beyan ettikleri fikirlerin kaynağını (hangi kişiden veya kitaptan geldiğini) anlamak kolaydır. Neden?

• Okuduklarını ve duyduklarını içselleştirmeyi, sonra da kendilerine has bir biçimde sunmasını beceremezler.
• Farklı bakış açılarıyla karşılaşmadıkları için yarattıkları fikir harmanı zengin bir harman değildir ve dolayısıyla bu harmanın kaynaklarını deşifre etmek için çok da kitap karıştırmak gerekmez.

Eğitimli adamın fikirlerinin kaynağını kestirmek ise zordur. Bu yüzden kendine has bir havası vardır. Fakat bu demek değildir ki fikirleri cahilinkine oranla daha özgündür. Genelde var olan tek ekstra şey kafa karışıklığıdır.

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.