Sunday, May 5, 2013

Benoît Mandelbrot's contribution to Finance

  Other mathematicians of probability like Kolmogorov may be more academic or progressive but Mandelbrot was unique he proved that mathematicians actually understand randomness, he is called by Nassim Nicholas Taleb as 'poet of randomness'. Before Nassim Taleb ,Black Swans were dealt by him in a philosophical and aesthetic way.Mandelbrot was initially a probability guy but later went into other fields of maths and made his name in other fields.In 1960s Mandelbrot presented his ideas on prices of commodity and stock prices and made a contribution on mathematics of randomness in economic theory.Mandelbrot also knew the pitfalls in Bachelier's model.Mandelbrot linked randomness to geometry and made randomness a more natural science.If stock markets were Gaussian then stock market crashed would have happen once in a Billion years. Mandelbrot's randomness methods make the statistics methods look useless. 



Benoît Mandelbrot , the late Sterling Professor of Mathematical Sciences at Yale University

The first formal model for security price changes was put forward by Bachelier (1900). His price difference process in essence sets out the mathematics of Brownian Motion before Einstein and Wiener rediscovered his results in 1905 and 1923 in the context of physical particles, and in particular generates a Normal (i.e. Gaussian) distribution where variance increases proportionally with time. A crucial assumption of Bachelier’s approach is that successive price changes are independent. His dissertation, which was awarded only a “mention honorable” rather than the “mention très honorable” that was essential for recognition in the academic world, remained unknown to the financial world until Osborne (1959), who made no reference to Bachelier’s work, rediscovered Brownian Motion as a plausible model for security price changes.

But in 1963 the famous mathematician Mandelbrot produced a paper pointing out that the tails of security price distributions are far fatter than those of normal distributions (what he called the “Noah effect” in reference to the deluge in biblical times) and recommending instead a class of independent and identically distributed “alpha-stable” Paretian distributions with infinite variance. Towards the end of the paper Mandelbrot observes that the independence assumption in his suggested model does not fully reflect reality in that “on closer inspection … large changes tend to be followed by large changes – of either sign – and small changes tend to be followed by small changes.” Mandelbrot later called this the “Joseph effect” in
reference to the biblical account of seven years of plentiful harvests in Egypt followed by seven years of famine. Such a sequence of events would have had an exceptionally low probability of taking place if harvest yields in successive years were independent. While considering how best to model this dependence effect, Mandelbrot came across the work of Hurst (1951, 1955) which dealt with a very strong dependence in natural events such as river flows (particularly in the case of the Nile) from one year to another and developed the Hurst exponent H as a robust statistical measure of dependence. Mandelbrot’s new model of
Fractional Brownian Motion, which is described in detail in Mandelbrot & van Ness (1968), is defined by an equation which incorporates the Hurst exponent H. Many financial economists, particularly Cootner (1964), were highly critical of Mandelbrot’s work, mainly because – if he was correct about normal distributions being seriously inconsistent with reality – most of their earlier statistical work, particularly in tests of the Capital Asset Pricing Model and the Efficient Market Hypothesis, would be invalid. Indeed, in his seminal review work on stockmarket efficiency, Fama (1970) describes how non-normal stable distributions of precisely the type advocated by Mandelbrot are more realistic than standard distributions .

“Economists have, however, been reluctant to accept these results, primarily because of the wealth of statistical techniques available for dealing with normal variables and the relative paucity of such techniques for non-normal stable variables.”

Partly because of estimation problems with alpha-stable Paretian distributions and the mathematical complexity of Fractional Brownian Motion, and partly because of the conclusion in Lo (1991) that standard distributions might give an adequate representation of reality, Mandelbrot’s two suggested new models failed to make a major impact on finance theory, and he essentially left the financial scene to pursue other interests such as fractal geometry. However, in his “Fractal Geometry of Nature”, Mandelbrot (1982) commented on what he regarded as the “suicidal” statistical methodologies that were standard in finance
theory: “Faced with a statistical test that rejects the Brownian hypothesis that price changes are Gaussian, the economist can try one modification after another until the test is fooled. A popular fix is censorship, hypocritically called ‘rejection of outliers’. One distinguishes the ordinary ‘small’ price changes from the large changes that defeat Alexander’s filters. The former are viewed as random and Gaussian, and treasures of ingenuity are devoted to them … The latter are handled separately, as ‘nonstochastic’.”

Shortly after the “Noah effect” manifested itself with extreme severity in the collapse of Long-Term Capital Management, Mandelbrot (1999) produced a brief article, the cover story of the February 1999 issue of “Scientific American”, in which he used nautical analogies to highlight the foolhardy nature of standard risk models that assumed independent normal distributions. He also pointed out that a more realistic depiction of market fluctuations, namely Fractional Brownian Motion in multifractal trading time, already existed.

Fractals are linked with power laws, Mandelbrot worked on it and applied it to randomness. Mandelbrot designed the mathematical object called "Mandelbrot set" and later worked on shapes and fractals of maths and also worked on Chaos Theory. These objects play an important role on aesthetics , music , architecture , poetry , gestures and tones are derived from fractals . Mandelbrot's book "Fractal Geometry of Nature" it made a fame in arts , visual arts and every artistic circle. He was later offered a position in Medicine , all artists used to call Mandelbrot "The Rock Star of Mathematics". Mandelbrot became famous because of the number of applications of mathematics in our society.



Mandelbrot used his fractal theory to explain the presence of extreme events in Wall Street.


In fact he was one of the pioneers in studying the variation of financial prices even before Bchelier's Brownian model became widely accepted in academia and Mandelbrot also knew the pitfalls in Bachelier's model.For this reason many call him as the "father of Quantitative Finance".Mandelbrot has been best known since the early 1960s as one of the pioneers in studying the variation of financial prices.He pointed out that two features of Bachelier's model are unacceptable(in 1960s when Bachelier's model got accepted by academia and financial world).These flaws were based on power-law distributions and so Mandelbrot scaled these both by fractal theory and thus correcting the errors and flaws.Since then scaling by use of fractal theory has become important in finance and as well as in Physics.In fact Nassim Nicholas Taleb's "Black Swan Theory" is inspired by work of Mandelbrot as Mandelbrot was much concerned about high-risk rare events(Black Swans).Nassim and Mandelbrot collaborated in  research tasks related to risk management.



Mandelbrot's contribution in finance fall into three main stages:

He was the first to stress the essential importance, even in a first approximation, of large variations that may occur as sudden price discontinuities. The Brownian model is unjustified in neglecting them. They are not “outliers” one can safely disregard or study separately. To the contrary, their distribution is much more important than that of the "background noise" constituted by the small changes of Brownian motion. He followed this critique in by showing in 1963 that the big discontinuities and the small "noise" fall on a single power-law distribution and represented them by a scenario based on Levy stable distributions. He and Taylor introduced in 1967 the new notion of intrinsic "trading time." In recent years, fractal trading time and his 1963 model have gained wide acceptance.

Secondly, Mandelbrot tackled the fact that the “background noise” of small price changes is of variable “volatility.” This feature was ordinarily viewed as a symptom of non-stationality that must be studied separately. To the contrary, Mandelbrot interpreted this variability as indicating that price changes are far from being statistically independent. In fact, for all practical purposes, their interdependence should be viewed as continuing to an infinitely long term. In particular, it is not limited to the short term that is studied by Markov processes and more recently ARCH and its variants. In fact, it too follows a power-law side of dependence. He followed this critique and illustrated long-dependence by introducing in 1965  a process called fractional Brownian motion which has become very widely used.

Thirdly, he introduced the new notion of multifractality that combines long power-law tails and long power-law dependence. Early on, his work was motivated by the context of turbulence, but he immediately observed and pointed out that in 1972 the same ideas also apply to finance. After a long hiatus while he was developing other aspects of fractal geometry, he returned to finance in the mid-1990s and developed the multifractal scenario theory in detail in his 1997 book "Fractals and Scaling in Finance". The concept of scaling invariance used by Mandelbrot started by being perceived as suspect, because at that time other fields did not use it. However the period after 1972 also saw the growth of a new subfield of statistical physics concerned with “criticality.” The concepts used in that field are similar to those Mandelbrot had been using in finance.


Sunday, February 24, 2013

The 2008 Financial Crisis.


The 2008 Financial Crisis.

This article is compiled from Rand Corporation articles, Wall Street Journal articles and my own research.


The crisis was faced in 2007-2008 and it occurred in U.S and with effects all over the world , still in 2013 we have not recovered. Since the Great depression of U.S the Government and Financial industry of U.S boomed consistently for about 40 years, till 1980s.In 1980s U.S had few big companies who controlled a lot of capital and in the term of Bill Clinton regulations were relieved to advantage of the big companies and investors so risking society's safety and benefits. Later in 1990s the Financial Services Authority in Washington relieved laws for big investment banks i.e UBS, Goldman Sachs and Lehman Brothers which is a criminal act in a legal terms.

Citi Bank was financing the Iran's weapon supply and also took part in sales of Mexico's Cocaine market for high profits. The rich investors started to invest in U.S because of lack of proper regulations and high interest rates. Government made laws lenient to attract investors from all over the world and thus increasing the systematic risk in U.S Financial market. Then came the era of hedge funds and derivatives, derivatives is the riskiest financial instrument. Hedging techniques and the models for derivatives were being practised in almost all major banks .The models were mathematical and complex, even the use of High Frequency Computing in trading floor was practised. Graduates with Phd in Mathematics , Physics or Computer Science were being hired to handle these complex derivatives. Many Noble Prize winners started their own Hedge Funds and attracted big investors to make profits, the models were so complex that only a few can grasp the understanding. Derivatives traders were using mathematical models to manage the derivatives and securities. These quants were playing with high risk/high return financial derivatives and were at that time confident of the models being used by them.

Nouriel Roubini, the first economist to warn against the crisis and is aginst the use of derivatives.

 The other big cause was the imprudent mortgage lending, as house prices boomed in later 1990s many people were unable to afford homes and so they required home loans and Government facilitated them by home loan scheme. Many banks started giving loans to these people and later investment banks came to give mortgage loans. These big banks preferred sub-prime loans for higher interest rates. Sub-prime loans increased 10 times from 1996-2006 , Lehman Brothers were biggest gainers from such mortgage loans. In fact  mortgage loans are a sort of derivative which is traded in financial system and it is prone to both systematic and default risk. Rating agencies started to give even the financially weaker companies a AAA credit rating so they can attract mortgage loans customers. So subprime loans were packed as AAA bonds. Credit rating agencies gave AAA ratings to numerous issues of subprime mortgage-backed securities .

The big companies and investment banks who controlled the most of world's money were involved in such derivatives and mortgage loans. Risk management was poorly handled by companies and firms separated analysis of market risk and credit risk This division did not work for complex structured products like derivatives. Complexity of financial instruments at the heart of crisis had two effects: 1. investors were unable to make independent judgements on merits of investments, 2.regulations were baffled.  Investors do not always make optimal choices as they suffer from bounded rationality and limited self-control and even regulators did not help them to manage complexity through better disclosure.

Quants ruled Wall Strret in 1990s and 2000s

The computer models used were bad , expectations of the performance of complex structured products linked to mortgages were based on only a few decades worth of data. In the case of subprime loans. As complex instruments like derivatives were new and so not much data was available as well for forecasting.Low interest rates and abundant capital forced investors to borrow funds to boost the return of their capital, excessive leverage magnified the impact of housing downturn. Excessive leverage leads to mispricing of risk and credit bubble. Even the regulation laws were relaxed for excessive leverage. New laws in 1990s and 2000s i.e. GLBA and the CFMA permitted financial institutions to engage in unregulated risky transactions on vast scale. Over the counter derivatives which are largely unregulated  began to get exercised extensively. CDOs ,an investment-grade security backed by a pool of bonds, loans and other assets. CDOs do not specialize in one type of debt but are often non-mortgage loans or bonds. CDOs are sort of derivatives used by banks for profits , they are actually derivative based loans. The last cause was use of Gaussian curve for risky and low probability instruments in financial industry i.e if you use Bell curve in top stocks,derivatives and genetic measures, extreme events if calculated by Bell curve may cause disaster. Head -tail on a coin is a random walk (left or right or win or loose) is a mediocre event so we use Gaussian curve.This idea was popularized by Nassim Nicholas Taleb who stated this as "Black Swan theory".He suggested that markets are non-linear , random and highly complex and chaotic and so the events with low probability and high impact i.e Black Swan events are not calculated by Gaussian curve.These events are outliers with massive impact and economic advisers were not aware of this and so were unable to forecast these events.

Hedge funds did not contribute to the crisis itself but they contributed to high systematic risk (though sysmematic risk is known as risk caused by randomness in financial parameters i.e interest rates, inflation but in generic term it is the possibility of failure of whole financial system i.e a Crisis or a Black Swan event) in financial system.Many top financial engineers attracted investors and spent millions of dollars for high return, but due to the volume of hedge funds in terms of dollar value these caused highest systematic risk  in financial system as compared to any other financial instrument. So, when system fails due to causes like mortgage lending , hedge funds increase the effect of the damage i.e. hedge fund act as a catalyst when crisis happens but do not itself contribute to crisis. Hedge funds make market parameters like interest rates and inflation go random due to their high return behavior, also weak regulatory laws for hedge funds made them even more riskier financial instrument. Hedge fund managers were greedy and traded in high risk/high return funds and thus making financial system more complex and more prone to crisis.John Paulson made billions in trading complex derivatives and mortgage loans.Many people blamed hedge funds for crisis but that is not true , they only increased the damage of crisis because of their systematic risk but never were the cause of crisis.

No regulator had comprehensive jurisdiction over all systemically important financial instructions, the Federal Reserve Bank had role of systematic risk regulator by default but lacked authority to oversee investment banks , hedge funds, nonbank derivative dealers. Even the rating agencies did the worst by giving good rating to risky securities and borrowers, AAA rated firms increased from few hundred to thousands in few years(early 2000s). All in all this crisis was the biggest the world has seen so far in terms of damage, many academics and economic advisors like Nouriel Roubini ,Peter Schiff, Raghuram Rajan , Nassim Nicholas Taleb, Kenneth Rogoff, George Soros,Robert J. Shiller and Andrew Lo warned against crisis and wrote extensively against the deregulation of Financial acts and excessive use of derivatives. At the same time there were advisors like Larry Summers and Frederic Mishkin favoured deregulation of financial system and favoured use of derivatives and risky financial instruments and even were advisors to such instruments and hedge funds for their own profits. 

Henry Paulson

 Henry Paulson the U.S Treasury Governor along with Ben Bernanke were unable to understand or predict this crisis and gave his precautions and new regulations after four month of crisis. Many CEOs of large companies including Lehman Brothers, Goldman Sachs  went away with billions of dollars inside their pocket after damaging the whole financial system, the U.S Government and the world. Many other Harvard economists and other top university economists made millions by consulting to firms and promoting the deregulation of the financial system. This also contributed to the corruption of economics studies in universities and business schools.

Larry Summers

Computational models need to be more precise and forecasting should be done by taking sufficient amount of data, and if data is not available i.e in case of derivatives then unreliable forecasting should not be made and even the financial instrument with high risk and low data should be banned from financial system.Black-Scholes equation has no flaw,though many went against it and it should be used within its underlying assumptions and limitations.Mathematical models do give accurate results and a bit of error is always involved and only more research can decrease it but the use of Gaussian curve in calculation of complex derivatives and other financial instruments should be banned and other relevant models and distributions should be used(this is a new research field for Probability Theory experts i.e to advance the work of Benoit Mandelbrot).Oliver Blanchard, the chief economist of IMF stated that the Crisis will last for a decade and argues that for supply-side reasons(after the Crisis), government spending should go towards financial infrastructure projects, not cash handouts.

Oliver Blanchard

Friday, December 14, 2012

Andrew Lo on Mathematical Models


If Adam Smith had a mind meld with Charles Darwin, Andrew Lo might result. A professor at MIT's Sloan School of Management, Lo is known for his multidisciplinary approach to finance, using everything from statistical analysis to neuroscience to better understand the markets. One of his most important ideas involves the "adaptive markets" theory.For a long time, many economists believed in the "rational markets" theory, which posited that all available information was reflected in a stock's price and investors were rational and so, therefore, were prices (yeah, right). Lo, 52, believes markets are less like rule-based physics and more like messy biological systems. Market participants aren't coldly rational creatures but squirmy, evolving species interacting with one another in a primordial sludge of money.

"Blaming quantitative analysis is akin to blaming E=MC2 for nuclear meltdowns," says MIT Sloan School of Management's Andrew W. Lo.

Instead of blaming quantitative analysis he says, a more productive line of inquiry might be to look deeper into the underlying causes of financial crisis, which ultimately leads to the conclusion that bubbles, crashes, and market dislocation are unavoidable consequences of hardwired human behavior coupled with free enterprise and modern capitalism. However, even though crises cannot be legislated away, there are many ways to reduce their disruptive effects. Lo will conclude his talk with a set of proposals for regulatory reform.

By tracking the data trails left by this Darwinian process, we might be able to get a better picture of how markets really work. The U.S. Treasury buys it; Lo helped set up the new Office of Financial Research, which aims to provide better data and insights about the industry. "Policymakers are always looking for the financial-system equivalent of the MRI," said Treasury Secretary Tim Geithner at the launch of the OFR last year. Digging in the financial dirt may be the way to get it.

Andrew Lo, a financial economist and a leading authority on Hedge Funds.Lo is also the director of the MIT Sloan School of Management’s Laboratory for Financial Engineering


In 2009 Andrew Lo delivered the I.E. Block Community Lecture.Andrew Lo, the Harris & Harris Group Professor in the Sloan School of Management at MIT, titled his lecture "Kill All the Quants? Models and Mania in the Current Financial Crisis."Lo, who is also director of the MIT Laboratory for Financial Engineering, began with a brief history of the crisis, the seeds of which were sown during the period of low interest rates in the late 1990s. The ensuing housing boom was sustained by a proliferation of adjustable-rate mortgages and subprime mortgages (a.k.a. "liar loans") extended to borrowers lacking the means to repay, as well as by the wholesale issuance of mortgage-backed securities (MBSs) by financial institutions, including the government-sponsored enterprises known as Fannie Mae and Freddie Mac. Such instruments could be leveraged investors could use them as collateral against which to borrow more money to make more such investments, which could then be reused in the same fashion, and so on. Their acceptability as collateral was due in large part to the AAA ratings slapped on them by well-established credit-rating agencies, such as S&P, Moody's, and Fitch, and to the availability of default insurance in the form of credit-default swaps. But the wealth so created could not survive the interest rate increases of 2004 and the consequent decline of housing prices from 2006 highs. Default rates increased, inflicting losses on investors, dealers, insurers, and mortgage originators, which led to further declines in home prices, and so on. The resulting "death spiral" continues.

When it came to assigning blame, Lo named the usual suspects. Homebuyers deserve a share for assuming loans they couldn't hope to repay, as do the real estate agencies and mortgage companies that rewarded their brokers for persuading such buyers to assume unserviceable loans. The investment banks that purchased their contracts, bundled them into MBSs, and persuaded the rating agencies to label them AAA-the better to sell them to the proverbial "widows and orphans" funds are surely at fault as well, as are the investors who failed to peer behind the ratings. Also blameworthy are the insurance companies that guaranteed payment; the rating agencies that gave apparently inflated ratings; the regulators (the SEC, the Fed) that looked the other way; the politicians and government-sponsored enterprises that promoted the "ownership society"; and the business media that (mostly) applauded the orgy of "wealth creation."

All this was familiar ground. Lo was really more interested in assessing the blame to be borne by risk managers and other quants. To that end, he had to explain how some of those quants had contrived to turn mortgages with unappealing risk/return ratios into MBSs that sold like hotcakes to investors of every description. That was an achievement worthy of Jimmy (The Greek) Snyder, who invented the point-spread wager as a way of enticing the betting public to gamble on football and basketball games in which---as is usually the case one of the teams is a clear favorite to win. The packagers reduced the risk in part by spreading it geographically: On the basis of evidence that epidemics of homebuyer defaults tend to be regional, they assembled mortgages from every time zone into MBSs that were or seemed to be inherently less risky than the individual mortgages. Mainly, however, they did it by separating the underlying mortgages into "tranches" with different risk/return characteristics.

Andrew Lo was included in the Times Magazine's "World's 100 Most Influential People" list.

Lo explained the mechanics of the tranche system with an extremely simple model. The ingredients were a pair of identical $1000 IOUs, to be redeemed on a certain date in the not too distant future, each with a 10% chance of default. The expected value of each individual asset, which he equated with its price, is 90% × $1000 + 10% × $0 = $900. Under the assumption that defaults are statistically independent events, a portfolio containing both assets should be worth 81% × $2000 + 18% × $1000 + 1% × $0 = $1800, because either, neither, or both borrowers might ultimately default.
But there are other ways to package the same pair of assets. Modern financial institutions, Lo said, are more likely to create two dissimilar asset-backed securities (ABSs), one outranking the other. In his example, purchasers of the "senior-tranche" ABS stand to collect $1000 unless both borrowers default, while "junior-tranche" purchasers collect $1000 only if both borrowers repay. The expected value of the senior-tranche ABS is thus 99% × $1000 + 1% × $0 = $990, that of the junior-tranche ABS 81% × $1000 + 1% × $0 = $810.

The senior-tranche ABS is thus a low-risk/low-return investment, suitable for purchase for the benefit of widows and orphans, while the junior-tranche ABS is a high-risk/high-return opportunity attractive to hedge funds and the like. The "high rollers" who invest in such funds understand the need to bear extraordinarily high risk in order to obtain extraordinarily high returns on their investments, and they actively seek out opportunities to do exactly that. But what happens if the defaults cease to be statistically independent? If the two become perfectly correlated, either paying or defaulting together, they will have the same expected value: 90% × $1000 + 10% × $0 = $900. The senior-tranche investors have then paid $990 for an asset worth $900, while the investors in junior-tranche (and riskier) ABSs find themselves in possession of assets worth $900 for which they paid only $810!
Simple though his model was, Lo confirmed during the question-and-answer session that the illustrated effect is entirely real: Hedge funds that invested heavily in the high-risk tranches have (on balance) been hurt less than more risk-averse investors. That may seem unfair, but it is not inconsistent with the history of financial crises. Fortune smiles on those who buy low! Despite the large number of hedge funds shut down during the crisis, Lo said at the reception following his talk, he expects that new ones will form in coming months, taking advantage of the many high-risk/high-return opportunities so reliably spawned by disorderly markets.

Lo found no fault with the bundling of loans to create a more attractive line of financial products. He expressed concern, rather, with those in the industry and here he specifically included quants who were in a position to see, yet failed to see, the danger with which the industry was so obviously flirting. But he did not hasten to judge even then, on the ground that it isn't always easy to see the obvious while striving to observe something else. He emphasized this point by showing a well-known video (which about a tenth of the audience had seen previously) in which two teams of three students each one dressed in white, the other in black strove to pass a pair of basketballs back and forth without fumbling. The audience was to count the number of times the white team passed the ball successfully from one member to another, as Lo called out random numbers to confuse the counters.
When the action ceased, Lo asked for the white team's total, and for anything else the audience had seen. Many laughed when a voice from the back of the room asked whether he meant "the guy in the gorilla suit." For a surprising number of those present, intent as they were on counting passes, had failed to see anything unexpected. When Lo reran the video, however, it was impossible to miss the person in a gorilla suit walking brazenly out into the middle of the action, pausing to beat his chest several times before exiting stage right. It was a memorable way to make the point that it's easy to see what you expect to see, and surprisingly difficult to see the unexpected. Because people in the finance industry hear no end of talk about the heroic quantities of wealth they are creating, and little if anything about the danger they pose to the economy as a whole, it is hardly surprising that the latter should be all but invisible to them.

Lo quoted with approval Charles Perrow, a systems-behavior expert who, after studying the tragedies at Chernobyl and Bhopal, as well as the near tragedy at Three Mile Island, formulated a theory of "normal accidents" in high-tech industries. The gist is that catastrophic failures are to be expected in such industries: Complex nonlinear systems (which are famously hard to predict) abound, and the various subsystems are so tightly coupled that a failure in one is likely to produce failure in others. And, because they cannot be prevented, they should be planned for! To this, Lo would add that human failure is the main cause of such breakdowns, and that the absence of negative feedback (of the sort that results in the identification and correction of mistakes) over an extended time is a virtual guarantee of human failure. Finally, he said, all of these observations apply directly to the finance industry, in which investors, managers, legislators, and regulators receive little constructive feedback.

It's not a tragedy when hedge funds lose money, Andrew Lo pointed out in Denver; it is a crisis when banks or retirement funds lose money. The key to avoiding future crises? More training in financial mathematics and engineering, not less.

Wondering whether the crisis could have been avoided, Lo described the probable fate of various operatives, had they known with certitude in 2005 that a crisis was on the way. A Wall Street CEO might have shut down one or two groups in the firm that were earning money hand over fist, as were similar groups at rival firms. But the CEO would probably have been fired for doing so, as the groups at rival firms would have continued for two more years to record "supernormal" profits and bonuses. A credit-risk officer might have hedged the firm's exposure with investments designed to underperform MBSs while the boom lasted, but to offset losses from them during the bust to follow. But that officer too would probably have been fired, for leaving two years worth of extraordinary profits on the table. Lowly portfolio managers might have purged their clients' accounts of MBSs, thereby reducing their rates of return. But some if not all of those clients would then have requested different account managers, or moved to different firms, probably costing the managers their jobs! In short, there was hardly a desk on Wall Street from which it would have been safe to act on the knowledge that the housing bubble was ready to burst, without knowing the precise date on which it would do so. In Lo's opinion, the psychology of greed makes periodic crises unavoidable. That being the case, the prudent course would seem to be to prepare for them.

Lo closed with a 14-point program of preparations worth making in anticipation of the next crisis.  His suggestion that banks and brokerages that seem too big to fail be broken up into smaller units needs no explanation. Nor do two suggestions pertaining to education that finance, economics, and risk management be taught in high school, and that a new discipline of "risk accounting" be created. Finally, his call for a small "derivatives tax" to fund university programs in financial engineering is straightforward.

Monday, November 26, 2012

Randomness in Markets and Life



Complied from works of Nassim Nicholas Taleb.



Randomness is everywhere from social science , life events or financial markets. Fat tails or wild events are probably the ones with massive impact.  Nature has designed us to fool ourselves easily , we are incompetent to understand randomness and that we are unable to know "what we do not know" . The lack of understanding of  "what we do not know"  is what makes us more prone to random events. We see hard working people on top but there is a group of people with high intellect on top so we cannot suggest which trait leads to success. Risk takers are able to capture profits and at the same time they are more prone to loss. 

Trick is to stay away from people who think they are thinkers but actually they are just mere entertainers. Journalists are somehow intellectual as they pin out the loop holes in society and are not part of herds. My principle hobby is to tease those who take themselves and their knowledge too seriously. Probability is something that fools us easily , it is not an engineering or science but it is knowledge of skepticism. It is the acceptance of ignorance and development of knowledge which we do not know.Skepticism is generally any questioning attitude towards knowledge, facts, or opinions/beliefs stated as facts and doubts regarding claims that are taken for granted elsewhere.
Hard work and discipline are part of success and not itself road to success as randomness and Black Swans can attack these and people may call you a looser or maybe someone who failed. But some state that chance plays no part in success , yet I see many not so hard working and not so intelligent people at top while few hard working geniuses failed. Risk takers are more prone to profits and failures and they usually are the confident geniuses. Black Swan can be good or bad, Google's success was a good Black Swan event while 9/11 was a bad Black Swan. Literary minds are more prone to randomness as many concepts lead to confusion and more thinking puts one to contradictions. Bad information is worse than no information as it makes us more prone to Black Swans. Small losses do not matter if profits are high, this is the code of a true risk taker but at the same time he should be educated enough to be able to estimate or catch the Black Swans as these may completely destroy him.

Never ask a guy if he is from Sparta , because if he is you will know by his habits and if he is not you are hurting him by asking him. In same way do not ask a trader how much profit he made or how mush loss he had to face it will make him sad. Accountants can never understand Randomness and Probability and even the financial movements are not to be calculated by accountants and they are book-keepers only.1990s saw the arrival of scientists in Wall Street, most of these were Phds and were mostly from Physics (Theoretical) along with Mathematics from Russia, France and China. Most of these came from Russia, Russian Physics-PHd quants were ruling the Wall Street. This was due to the reason that MBAs wanted more and in half the price firms were able to hire Russian Scientists trained under the most mathematical minds. In face Russian Physics departments were top at that time in Maths and Theoretical Physics. But the lack of knowledge in Probability is vital for me as it gives me profits but at the same time I need few to understand my theories on Randomness. More erudition in Probability and Science of Randomness will make my business go down but academically I might get more fame. Useful tools like Monte Carlo Simulation and Stochastic Models are known to many but real philosophy of randomness requires more than just models and machines. Perfection on randomness and probability requires the right information the calculation of biasness for which we need psychologists and other academics.


Learning from history is another way to forecast and understand current events. Children learn from their mistakes but I think adults suffer from same condition but though Machiavelli was smart enough to learn from history and infact wrote treatise from history and experiences, his experiences were those which he had to face due to rare randomness. Risk takers are those people who know enough through history , experiences that they are confident to put them in that random event.
Historical determinism is the word used to describe the study of history to forecast or understand randomness. Those who are good in predicting the past and good in predicting the future  so we read history to learn the mechanism of randomness. Civil servants or classical think tanks were those who were capable and meant to forecast human behaviours and social events. Journalists are ones who use Historical determination to understand the results of a random event. Wise perceive things about to happen and silence is far better.

Bell curve has 68% observation falling between standard deviation of 1 and -1 yet the intelligent brain accepts this accuracy. Experiences and statistics may have high randomness i. e I may have a bad experience with  a New Yorker but my friends may have opposite experience. Statistics can never be 100% true and those who fall in outliers or face the unexpected have their own approach as everyone prefers experience over statistics.

I like Philosophy of Karl Popper (all his ideas on epistemology, scientific methods and open society) and David Hume(especially his Epistemology and Problem of Induction) or to some extent I am obsessed with it. George Soros is the only "rich investor" who is intellectual and also a Professor type , the only money man with intellectual power. Soros learned and understood Popper and also went on to live a Popperian life. Soros spread the ideas of Popper in banking system and in society. Popper always had problems with Statisticians and especially statistical inference .He suggests that repeated events causes one to increase acceptance and hence the error of truth increases. One experiment is not enough  to get accurate result. The more data we have the more we are prone to traps.

In fact I came across Popper through Soros (Soros being my favourite investor)Popper is the man who is unworldly a man who was isolated, self focused , arrogant ,closed to outside world, independent and very bad listener and always firm on his beliefs though he helped people for good ideas and helped them to guide in their careers. Soros used more philosophy in banking than other banker, he was creative enough to apply every bit of Popper's philosophy in banking. Popper shared that Open Society is one where no permanent truth can exist and his idea was made to use by Friedrich Hayek .

What is the probability of winning New Jersey lottery twice...... 1/17 trillion. Randomness does not look random, we do know what events have high or low randomness but we are not able to catch it so in turn we are always fooled . Calculating randomness is hard for  every event (whether high or low randomness). High randomness though can either ruin you or make you billionaire but low randomness is not that massive in impact. Even when patients get the news of cancer etc their reaction is random towards it i. e some get sad and some even faint.
Brownian Random Walk used in finance has one condition that probability of success does not change with incremental step, same as Binomial model. Non-linearity and linearity is another effect that can cause drastic changes. If you try playing piano you may fail a lot of time and suddenly you start playing Chopin's sonatas .For such non-linear events we need not use Linear Statistical models as we will have large errors. Same is true for marginal benefit , the glass of water you drink after gym will have no effect and suddenly the 4th one satisfies you. 

Who exerted most influence in economics in past two centuries.... it was not Keynes, Milton Friedman , Samuelson or Marshall but they are two non-economists: Amos Tversky and Daniel Kahneman who made new ideas in Behavioural Finance/Economics. They worked on field of Heuristics and Rationality. 

The more out of the world you are i.e.  the more anarchist or rebel you are the more you are prone to randomness as you are not part of normal people and that you have less ability to predict social randomness. One great example is that of a man who is not into social media like me and so the recent music or most debated topic are not known to him and thus he faces trouble when he goes to a nightclub or even to a cafe for relaxation.  The more mathematics and Probability you know the more prone you are to randomness , this is because for events which are 2 dimensional or more are studied using sampling and other mathematical models and thus increasing error in results. Luckily the most events in a normal person's life are one dimensional. In same way if you are more emotional then it means you are less rational .Some people get angry when the car behind you gives you a loud horn when you do not act rapidly when light gets green , now 1 millisecond is not worth anything but for the back car it is something. Emotions also change your decisions accordingly , emotions might cause you to loose i. e some people leave their job if they are slightly taunted while more rational people or the less emotional think about the loss and stay calm and so are in control of their emotions and decisions in life.

But how do we know that we are going to face a rare and random event?This is the problem that needs to be perfected in order to avoid being fooled.

Sunday, November 25, 2012

Actuaries VS Quants


The following article is taken from August 2008 issue of The Actuary magazine.
    
Those working in the two fields of actuarial science and quantitative finance have not always been totally appreciative of each others’ skills. Actuaries have been dealing with randomness and risk in finance for centuries. Quants are the relative newcomers, with all their fancy stochastic mathematics. Rather annoyingly for actuaries, quants come along late in the game and thanks to one piece of insight in the early ‘70s completely change the face of the valuation of risk. The insight I refer to is the concept of dynamic hedging, first published by Black, Scholes and Merton in 1973. Before 1973 derivatives were being valued using the “actuarial method,” i.e. in a sense relying, as actuaries always have, on the Central Limit Theorem. Since 1973 and the publication of the famous papers, all that has been made redundant. Quants have ruled the financial roost. But this might just be the time for actuaries to fight back.   

I am putting the finishing touches to this article a few days after the first anniversary of the “day that quant died.” In early August 2007 a number of high-profile and previously successful quantitative hedge funds suffered large losses. People said that their models “just stopped working.” The year since has been occupied with a lot of soul searching by quants, how could this happen when they’ve got such incredible models?

In my view the main reason why quantitative finance is in a mess is because of complexity and obscurity. Quants are making their models increasingly complicated, in the belief that they are making improvements. This is not the case. More often than not each ‘improvement’ is a step backwards. If this were a proper hard science then there would be a reason for trying to perfect models. But finance is not a hard science, one in which you can conduct experiments for which the results are repeatable. Finance, thanks to it being underpinned by human beings and their wonderfully irrational behaviour, is forever changing. It is therefore much better to focus your attention on making the models robust and transparent rather than ever more intricate. As I mentioned in a recent wilmott.com blog, there is a maths sweet spot in quant finance. The models should not be too elementary so as to make it impossible to invent new structured products, but nor should they be so abstract as to be easily misunderstood by all except their inventor (and sometimes even by him), with the obvious and financially dangerous consequences. I teach on the Certificate in Quantitative Finance and in that our goal is to make quant finance practical, understandable and, above all, safe.
When banks sell a contract they do so assuming that it is going to make a profit. They use their complex models, with sophisticated numerical solutions, to come up with the perfect value. Having gone to all that effort for that contract they then throw it into the same pot as all the others and risk manage en masse. The funny thing is that they never know whether each individual contract has “washed its own face.” Sure they know whether the pot has made money, their bonus is tied to it. But each contract? It makes good sense to risk manage all contracts together but it doesn’t make sense to go to such obsessive detail in valuation when ultimately it’s the portfolio that makes money, especially when the basic models are so dodgy. The theory of quant finance and the practice diverge. Money is made by portfolios, not by individual contracts.
Imperial College London started the famous MSc Actuarial Finance , which gave birth to the new field of actuary concerned with investment banking.

Actuaries have a deep knowledge of  Derivatives, Risk Management/Financial Risk(actuaries are better in accessing risk than Quants),Equity and Portfolio Management

In other words, quants make money from the Central Limit Theorem, just like actuaries, it’s just that quants are loath to admit it! Ironic. It’s about time that actuaries got more involved in quantitative finance. They could bring some common sense back into this field. We need models which people can understand and a greater respect for risk. Actuaries and quants have complementary skill sets. What high finance needs now are precisely those skills that actuaries have, a deep understanding of statistics, an historical perspective, and a willingness to work with data.With Solvency II coming up in 2013 there will be sudden increase in the demand of actuaries.