Looking back at these writings of mine, I feel as though I may have been a bit unfair on us. I did try to blunt my accusations of avarice (and perhaps decadence) by pointing out that it was the general air of insatiable greed of the era that we live in that spawned the obscenities and the likes of Madoff. But I did concede the existence of a higher level of greed (or, more to the point, a more sated kind of greed) among us bankers and quantitative professionals. I am not recanting my words in this piece now, but I want to point out another aspect, a justification if not an absolution.

Why would I want to defend bonuses and other excesses when another wave of public hatred is washing over the global corporations, thanks to the potentially unstoppable oil spill? Well, I guess I am a sucker for lost causes, much like Rhett Butler, as our quant way of tranquil life with insane bonuses is all but gone with the wind now. Unlike Mr. Butler, however, I have to battle and debunk my own arguments presented here previously.

One of the arguments that I wanted to poke holes in was the fair compensation angle. It was argued in our circles that the fat paycheck was merely an adequate compensation for the long hours of hard work that people in our line of work put in. I quashed it, I think, by pointing out other thankless professions where people work harder and longer with no rewards to write home about. Hard work has no correlation with what one is entitled to. The second argument that I made fun of was the ubiquitous “talent” angle. At the height of the financial crisis, it was easy to laugh off the talent argument. Besides, there was little demand for the talent and a lot of supply, so that the basic principle of economics could apply, as our cover story shows in this issue.

Of all the arguments for large compensation packages, the most convincing one was the profit-sharing one. When the top talents take huge risks and generate profit, they need to be given a fair share of the loot. Otherwise, where is the incentive to generate even more profits? This argument lost a bit of its bite when the negative profits (by which I indeed mean losses) needed to be subsidized. This whole saga reminded me of something that Scott Adams once said of risk takers. He said that risk takers, by definition, often fail. So do morons. In practice, it is hard to tell them apart. Should the morons reap handsome rewards? That is the question.

Having said all this in my previous articles, now it is time to find some arguments in our defense. I left out one important argument in my previous columns because it did not support my general thesis — that the generous bonuses were not all that justifiable. Now that I have switched allegiance to the lost cause, allow me to present it as forcefully as I can. In order to see compensation packages and performance bonuses in a different light, we first look at any traditional brick-and-mortar company. Let’s consider a hardware manufacturer, for instance. Suppose this hardware shop of ours does extremely well one year. What does it do with the profit? Sure, the shareholders take a healthy bite out of it in terms of dividends. The employees get decent bonuses, hopefully. But what do we do to ensure continued profitability?

We could perhaps see employee bonuses as an investment in future profitability. But the real investment in this case is much more physical and tangible than that. We could invest in hardware manufacturing machinery and technology improving the productivity for years to come. We could even invest in research and development, if we subscribe to a longer temporal horizon.

Looking along these lines, we might ask ourselves what the corresponding investment would be for a financial institution. How exactly do we reinvest so that we can reap benefits in the future?

We can think of better buildings, computer and software technologies etc. But given the scale of the profits involved, and the cost and benefit of these incremental improvements, these investments don’t measure up. Somehow, the impact of these tiny investments is not as impressive in the performance of a financial institution compared to a brick-and-mortar company. The reason behind this phenomenon is that the “hardware” we are dealing with (in the case of a financial institution) is really human resources — people — you and me. So the only sensible reinvestment option is in people.

So we come to the next question — how do we invest in people? We could use any number of euphemistic epithets, but at the end of the day, it is the bottom line that counts. We invest in people by rewarding them. Monetarily. Money talks. We can dress it up by saying that we are rewarding performance, sharing profits, retaining talents etc. But ultimately, it all boils down to ensuring future productivity, much like our hardware shop buying a fancy new piece of equipment.

Now the last question has to be asked. Who is doing the investing? Who benefits when the productivity (whether current or future) goes up? The answer may seem too obvious at first glance — it is clearly the shareholders, the owners of the financial institution who will benefit. But nothing is black and white in the murky world of global finance. The shareholders are not merely a bunch of people holding a piece of paper attesting their ownership. There are institutional investors, who mostly work for other financial institutions. They are people who move large pots of money from pension funds and bank deposits and such. In other words, it is the common man’s nest egg, whether or not explicitly linked to equities, that buys and sells the shares of large public companies. And it is the common man who benefits from the productivity improvements brought about by investments such as technology purchases or bonus payouts. At least, that is the theory.

This distributed ownership, the hallmark of capitalism, raises some interesting questions, I think. When a large oil company drills an unstoppable hole in the seabed, we find it easy to direct our ire at its executives, looking at their swanky jets and other unconscionable luxuries they allow themselves. Aren’t we conveniently forgetting the fact that all of us own a piece of the company? When the elected government of a democratic nation declares war on another country and kills a million people (speaking hypothetically, of course), should the culpa be confined to the presidents and generals, or should it percolate down to the masses that directly or indirectly delegated and entrusted their collective power?

More to the point, when a bank doles out huge bonuses, isn’t it a reflection of what all of us demand in return for our little investments? Viewed in this light, is it wrong that the taxpayers ultimately had to pick up the tab when everything went south? I rest my case.

But, this dictum of denying bonus to the whole firm during bad times doesn’t work quite right either, for a variety of interesting reasons. First, let’s look at the case of the AIG EVP. AIG is a big firm, with business units that operate independently of each other, almost like distinct financial institutions. If I argued that AIG guys should get no bonus because the firm performed abysmally, one could point out that the financial markets as a whole did badly as well. Does it mean that no staff in any of the banks should make any bonus even if their particular bank did okay? And why stop there? The whole economy is doing badly. So, should we even out all performance incentives? Once we start going down that road, we end up on a slippery slope toward socialism. And we all know that that idea didn’t pan out so well.

Another point about the current bonus scheme is that it already conceals in it the same time segmentation that I ridiculed in my earlier post. True, the time segmentation is by the year, rather than by the month. If a trader or an executive does well in one year, he reaps the rewards as huge bonus. If he messes up the next year, sure, he doesn’t get any bonus, but he still has his basic salary till the time he is let go. It is like a free call option implied in all high-flying banking jobs.

Such free call options exist in all our time-segmented views of life. If you are a fraudulent, Ponzi-scheme billionaire, all you have to do is to escape detection till you die. The bane of capitalism is that fraud is a sin only when discovered, and until then, you enjoy a rich life. This time element paves the way for another slippery slope towards fraud and corruption. Again, it is something like a call option with unlimited upside and a downside that is somehow floored, both in duration and intensity.

There must be a happy equilibrium between these two slippery slopes — one toward dysfunctional socialism, and the other toward cannibalistic corruption. It looks to me like the whole financial system was precariously perched on a meta-stable equilibrium between these two. It just slipped on to one of the slopes last year, and we are all trying to rope it back on to the perching point. In my romantic fancy, I imagine a happier and more stable equilibrium existed thirty or forty years ago. Was it in the opposing economic ideals of the cold war? Or was it in the welfare state concepts of Europe, where governments firmly controlled the commanding heights of their economies? If so, can we expect China (or India, or Latin America) to bring about a much needed counterweight?

Sections

• Bonus Plans of Mice and Men
• Hard Work
• Talent and Intelligence
• Talent Retention
• Profit Sharing
• Slippery Slopes

Among all the arguments for hefty bonuses, the most convincing is the one on profit generation and sharing. Profit for the customers and stakeholders, if generated by a particular executive, should be shared with him. What is wrong with that?

The last argument for bonus incentives we will look at is this one in terms of profit (and therefore shareholder value) generation. Well, shareholder value in the current financial turmoil has taken such a beating that no sane bank executive would present it as an argument. What is left then is a rather narrow definition of profit. Here it gets tricky. The profits for most financial institutes were abysmal. The argument from the AIG executive is that he and his team had nothing to do with the loss making activities, and they should receive the promised bonus. They distance themselves from the debacle and carve out their tiny niche that didn’t contribute to it. Such segmentation, although it sounds like a logical stance, is not quite right. To see its fallacy, let’s try a time segmentation. Let’s say a trader did extremely well for a few months making huge profits, and messed up during the rest of the year ending up with an overall loss. Now, suppose he argues, “Well, I did well for January, March and August. Give me my 300% for those months.” Nobody is going to buy that argument. I think what applies to time should also apply to space (sorry, business units or asset classes, I mean). If the firm performs poorly, perhaps all bonuses should disappear.

As we will see in the last post of the series, this argument for and against hefty incentives is a tricky one with some surprising implications.

Sections

• Bonus Plans of Mice and Men
• Hard Work
• Talent and Intelligence
• Talent Retention
• Profit Sharing
• Slippery Slopes

Even after we discount hard work and inherent intelligence as the basis of generous compensation packages, we are not quite done yet.

The next argument in favour of hefty bonuses presents incentives as a means of retaining the afore-mentioned talent. Looking at the state of affairs of the financial markets, the general public may understandably quip, “What talent?” and wonder why anybody would want to retain it. That implied criticism notwithstanding, talent retention is a good argument.

As a friend of mine illustrated it with an example, suppose you have a great restaurant thanks mainly to a superlative chef. Everything is going honky dory. Then, out of the blue, an idiot cook of yours burns down the whole establishment. You, of course, sack the cook’s rear end, but would perhaps like to retain the chef on your payroll so that you have a chance of making it big again once the dust settles. True, you don’t have a restaurant to run, but you don’t want your competitor to get his hands on your ace chef. Good argument. My friend further conceded that once you took public funding, the equation changed. You probably no longer had any say over payables, because the money was not yours.

I think the equation changes for another reason as well. When all the restaurants in town are pretty much burned down, where is your precious chef going to go? Perhaps it doesn’t take huge bonuses to retain him now.

Sections

• Bonus Plans of Mice and Men
• Hard Work
• Talent and Intelligence
• Talent Retention
• Profit Sharing
• Slippery Slopes

In the last post, I argued that how hard we work has nothing much to do with how much reward we should reap. After all, there are taxi drivers who work longer and harder, and even more unfortunate souls in the slums of India and other poor countries.

But, I am threading on real thin ice when I compare, however obliquely, senior executives to cabbies and slum dogs. They are (the executives, that is) clearly a lot more talented, which brings me to the famous talent argument for bonuses. What is this talent thing? Is it intelligence and articulation? I once met a taxi driver in Bangalore who was fluent in more than a dozen languages as disparate as English and Arabic. I discovered his hidden talent by accident when he cracked up at something my father said to me — a private joke in our vernacular, which I have seldom found a non-native speaker attempt. I couldn’t help thinking then — given another place and another time, this cabbie would have been a professor in linguistics or something. Talent may be a necessary condition for success (and bonus), but it certainly is not a sufficient one. Even among slum dogs, we might find ample talent, if the Oscar-winning movie is anything to go by. Although, the protagonist in the movie does make his million dollar bonus, but it was only fiction.

In real life, however, lucky accidents of circumstances play a more critical role than talent in putting us on the right side of the income divide. To me, it seems silly to claim a right to the rewards based on any perception of talent or intelligence. Heck, intelligence itself, however we define it, is nothing but a happy genetic accident.

Sections

• Bonus Plans of Mice and Men
• Hard Work
• Talent and Intelligence
• Talent Retention
• Profit Sharing
• Slippery Slopes

One argument for big bonuses is that the executives work hard for it and earn it fair and square. It is true that some of these executives spend enormous amount of time (up to 10 to 14 hours a day, according the AIG executive under the spotlight here). But, do long hours and hard work automatically make us “those who deserve the best in life,” as Tracy Chapman puts it?

I have met taxi drivers in Singapore who ply the streets hour after owl-shift hour before they can break even. Apparently the rentals the cabbies have to pay are quite high, and they end up working consistently longer than most executives. Farther beyond our moral horizon, human slum dogs forage garbage dumps for scraps they can eat or sell. Back-breaking labour, I imagine. Long hours, terrible working conditions, and hard-hard work — but no bonus.

It looks to me as though hard work has very little correlation with what one is entitled to. We have to look elsewhere to find justifications to what we consider our due.

Sections

• Bonus Plans of Mice and Men
• Hard Work
• Talent and Intelligence
• Talent Retention
• Profit Sharing
• Slippery Slopes

This philosophical clarity inspires analyses (and columns, of course) that are at times self-serving and at times soul-searching. We now worry about the moral rectitude behind the insane bonus expectations of yesteryears, for instance. The case in point is Jake DeSantis, the AIG executive vice president who resigned rather publicly on the New York Times, and donated his relatively modest bonus of a million dollars to charity. The reasons behind the resignation are interesting, and fodder to this series of posts.

Before I go any further, let me state it outright. I am going to try to shred his arguments the best I can. I am sure I would have sung a totally different tune if they had given me a million dollar bonus. Or if anybody had the temerity to suggest that I part with my own bonus, paltry as it may seem in comparison. I will keep that possibility beyond the scope of this column, ignoring the moral inconsistency others might maliciously perceive therein. I will talk only about other people’s bonuses. After all, we are best in dealing with other people’s money. And it is always easier to risk and sacrifice something that doesn’t belong to us.

Sections

• Bonus Plans of Mice and Men
• Hard Work
• Talent and Intelligence
• Talent Retention
• Profit Sharing
• Slippery Slopes

Ominous as it looks now, this dark hour will pass, as all the ones before it. How can we avoid such dark crises in the future? We can start by examining the root causes, the structural and systemic reasons, behind the current debacle. What are they? In my series of posts this month, I went through what I thought were the lessons to learn from the financial crisis. Here is what I think will happen.

The notion of risk management is sure to change in the coming years. Risk managers will have to be compensated enough so that top talent doesn’t always drift away from it into risk taking roles. Credit risk paradigms will be reviewed. Are credit limits and ratings the right tools? Will Off Balance Sheet instruments stay off the balance sheet? How will we account for leveraging?

Regulatory frameworks will change. They will become more intrusive, but hopefully more transparent and honest as well.

Upper management compensation schemes may change, but probably not much. Despite what the techies at the bottom think, those who reach the top are smart. They will think of some innovative ways of keeping their perks. Don’t worry; there will always be something to look forward to, as you climb the corporate ladder.

Nietzsche may be right, what doesn’t kill us, may eventually make us stronger. Hoping that this unprecedented financial crisis doesn’t kill us, let’s try to learn as much from it as possible.

Sections

• Ambition vs. Greed
• Risky Business
• Hedging Dilemma
• Where Credit is Due
• Quant Culprits
• Free Market Hypocrisy
• House of Cards

If commodity markets were free, we would have no tariff restrictions, agricultural subsidies and other market skewing mechanisms at play. Heck, cocaine and heroine would be freely available. After all, there are willing buyers and sellers for those drugs. Indeed, drug lords would be respectable citizens belonging in country clubs rather than gun-totting cartels.

If labor markets were free, nobody would need a visa to go and work anywhere in the world. And, “equal pay for equal work” would be a true ideal across the globe, and nobody would whine about jobs being exported to third world countries.

Capital markets, at the receiving end of all the market turmoil of late, are highly regulated with capital adequacy and other Basel II requirements.

Derivatives markets, our neck of the woods, are a strange beast. It steps in and out of the capital markets as convenient and muddles up everything so that they will need us quants to explain it to them. We will get back to it in future columns.

So what exactly is free about the free market economy? It is free — as long as you deal in authorized commodities and products, operate within prescribed geographies, set aside as much capital as directed, and do not employ those you are not supposed to. By such creative redefinitions of terms like “free,” we can call even a high security prison free!

Don’t get me wrong. I wouldn’t advocate making all markets totally free. After all, opening the flood gates to the formidable Indian and Chinese talent can only adversely affect my salary levels. Nor am I suggesting that we deregulate everything and hope for the best. Far from it. All I am saying is that we need to be honest about what we mean by “free” in free markets, and understand and implement its meaning in a transparent way. I don’t know if it will help avoid a future financial meltdown, but it certainly can’t hurt.

Sections

• Ambition vs. Greed
• Risky Business
• Hedging Dilemma
• Where Credit is Due
• Quant Culprits
• Free Market Hypocrisy
• House of Cards

The failure was really in understanding how much credit and market risks were inter-related, given that they were independently managed using totally different paradigms. I think an overhauling is called for here, not merely in modeling and pricing credit risks, also in the paradigms and practices used in managing them.

Ultimately, we have to understand how the whole lifecycle of a trade is managed, and how various business units in a financial institution interact with each other bearing one common goal in mind. It is this fascination of mine with the “big picture” that inspired me to write The Principles of Quantitative Development, to be published by Wiley Finance in 2010.

Sections

• Ambition vs. Greed
• Risky Business
• Hedging Dilemma
• Where Credit is Due
• Quant Culprits
• Free Market Hypocrisy
• House of Cards

We manage credit risk in two ways — by demanding collateral or by credit limit allocation. In the consumer credit market, they correspond to secure lending (home mortgages, for instance) and unsecured loans (say, credit lines). The latter clearly involves more credit risk, which is why you pay obscene interests on outstanding balances.

In dealing with financial counterparties, we use the same two paradigms. Collateral credit management is generally safe because the collateral involved cannot be used for multiple credit exposures. But when we assign each counterparty a credit limit based on their credit ratings, we have a problem. While the credit rating of a bank or a financial institution may be accurate, it is almost impossible to know how much credit is loaded against that entity (because options and derivatives are “off balance sheet” instruments). This situation is akin to a bank’s inability to check how much you have drawn against your other credit lines, when it offers you an overdraft facility.

The end result is that even in good times, the leverage against the credit rating can be dangerously high without counterparties realizing it. The ensuing painful deleveraging takes place when a credit event (such as lowering of the credit rating) occurs.

Sections

• Ambition vs. Greed
• Risky Business
• Hedging Dilemma
• Where Credit is Due
• Quant Culprits
• Free Market Hypocrisy
• House of Cards

When the oil price hit $147 a barrel in July ’08, with all the pundits predicting sustained $200 levels, what would you have done if you were risk managing an airline’s exposure to fuel? You would have ran and paid an arm and a leg to hedge it. Hedging would essentially fix the price for your company around $150 level, no matter how the market moved. Now you sit back and relax, happy in the knowledge that you saved your firm potentially millions of dollars.

Then, to your horror, the oil price nosedives, and your firm is paying $100 more than it should for each barrel of oil. (Of course, airlines don’t buy WTI, but you know what I mean.) So, thanks to the risk managers’ honest work, airlines (and even countries) are now handing over huge sums of money to energy traders. Would you rather be a trader or a risk manager?

And, yes, the airfares will come down, but not before the risk managers take their due share of flak.

Sections

• Ambition vs. Greed
• Risky Business
• Hedging Dilemma
• Where Credit is Due
• Quant Culprits
• Free Market Hypocrisy
• House of Cards

Risk management should be our first line of defense — it is a preventive mechanism, while regulatory framework (which also needs beefing up) is a curative, reactive second line.

The first reason for the inadequacy of risk management is the lack of glamour the risk controllers in a financial institution suffer from, when compared to their risk taking counterparts. (Glamour is a euphemism for salary.) If a risk taker does his job well, he makes money. He is a profit centre. On the other hand, if a risk controller does his job well, he ensures that the losses are not disproportionate. But in order to limit the downside, the risk controller has to limit the upside as well.

In a culture based on performance incentives, and where performance is measured in terms of profit, we can see why the risk controller’s job is sadly under-appreciated and under-compensated.

This imbalance has grave implications. It is the conflict between the risk takers and risk managers that enforces the corporate risk appetite. If the gamblers are being encouraged directly or indirectly, it is an indication of where the risk appetite lies. The question then is, was the risk appetite a little too strong?

The consequences of the lack of equilibrium between the risk manager and the risk taker are also equally troubling. The smarter ones among the risk management group slowly migrate to “profit generating” (read trading or Front Office) roles, thereby exacerbating the imbalance.

The talent migration and the consequent lack of control are not confined merely within the walls of a financial institution. Even regulatory bodies could not compete with the likes of Lehman brothers when hunting for top talent. The net result was that when the inevitable meltdown finally began, we were left with inadequate risk management and regulatory defenses.

Sections

• Ambition vs. Greed
• Risky Business
• Hedging Dilemma
• Where Credit is Due
• Quant Culprits
• Free Market Hypocrisy
• House of Cards

Greed, or its euphemistic twin ambition, probably had some role to play in the pain and suffering of the current financial turmoil and the unfolding economic downturn. But, it is not just the greed of Wall Street. Let’s get real. Jon Steward may poke fun at the twenty something commodity trader earning his thirty million dollar bonus by pushing virtual nothingness around, but nobody complained when they were (or thought they were) making money. Greed is not confined to those who ran fifty billion dollar Ponzi schemes; it is also in those who put their (and other people’s) money in such schemes expecting a too-good-to-be-true rate of returns. They were also made of the sterner stuff.

Let’s be honest about it. We in the financial industry are in the business of making money, for others and for ourselves. We don’t get into this business for philanthropic or spiritual reasons. We get into it because we like the rewards. Because we know that “how to get rich quick” or “how to get even richer” is the easiest sell of all.

We hear a lot about how the CEOs and other fat cats made a lot of money while other normal folks suffered. It is true that the profits were “private” while the losses are public, which is probably why the bailout plan did not get much popular support. But with or without the public support, bailout plan or not, like it or not, the pain is going to be public.

Sure, the CEOs of financial institutions with their private jets and eye-popping bonuses were guilty of ambition, but the fat cats didn’t all work in a bank or a hedge fund. It is the legitimization of greed that fueled this debacle, and nobody is innocent of it.

Sections

• Ambition vs. Greed
• Risky Business
• Hedging Dilemma
• Where Credit is Due
• Quant Culprits
• Free Market Hypocrisy
• House of Cards

The financial meltdown is such a rich topic with reasons and ramifications so overarching that all self-respecting columnists will be remiss to let it slide. After all, a columnist who keeps his opinions to himself is a columnist only in his imagination. I too will share my views on causes and effects of this turmoil that is sure to affect our lives more directly than anybody else’s, but perhaps in a future column.

The chaos and uncertainty I want to talk about are of different kind — the physics kind. The terms chaos and uncertainty have a different and specific meanings in physics. How those meanings apply to the world of finance is what this column is about.

Symmetries and Patterns

Physicists are a strange bunch. They seek and find symmetries and patterns where none exists. I remember once when our brilliant professor, Lee Smolin, described to us how the Earth could be considered a living organism. Using insightful arguments and precisely modulated articulation, Lee made a compelling case that the Earth, in fact, satisfied all the conditions of being an organism. The point in Lee’s view was not so much whether or the Earth was literally alive, but that thinking of it as an organism was a viable intellectual pattern. Once we represent the Earth in that model, we can use the patterns pertaining to organism to draw further predictions or conclusions.

Expanding on this pattern, I recently published a column presenting the global warming as a bout of fever caused by a virus (us humans) on this host organism. Don’t we plunder the raw material of our planet with the same abandon with which a virus usurps the genetic material of its host? In addition to fever, typical viral symptoms include sores and blisters as well. Looking at the cities and other eye sores that have replaced pristine forests and other natural landscapes, it is not hard to imagine that we are indeed inflicting fetid atrocities to our host Earth. Can’t we think of our city sewers and the polluted air as the stinking, oozing ulcers on its body?

While these analogies may sound farfetched, we have imported equally distant ideas from physics to mathematical finance. Why would stock prices behave anything like a random walk, unless we want to take Bush’s words (that “Wall Street got drunk”) literally? But seriously, Brownian motion has been a wildly successful model that we borrowed from physics. Again, once we accept that the pattern is similar between molecules getting bumped around and the equity price movements, the formidable mathematical machinery and physical intuitions available in one phenomenon can be brought to bear on the other.

Looking at the chaotic financial landscape now, I wonder if physics has other insights to offer so that we can duck and dodge as needed in the future. Of the many principles from physics, chaos seems such a natural concept to apply to the current situation. Are there lessons to be learned from chaos and nonlinear dynamics that we can make use of? May be it is Heisenberg’s uncertainty principle that holds new insights.

Perhaps I chose these concepts as a linguistic or emotional response to the baffling problems confronting us now, but let’s look at them any way. It is not like the powers that be have anything better to offer, is it?

Chaos Everywhere

In physics, chaos is generally described as our inability to predict the outcome of experiments with arbitrarily close initial conditions. For instance, try balancing your pencil on its tip. Clearly, you won’t be able to, and the pencil will land on your desktop. Now, note this line along which it falls, and repeat the experiment. Regardless of how closely you match the initial conditions (of how you hold and balance the pencil), the outcome (the line along which it falls) is pretty much random. Although this randomness may look natural to us — after all, we have been trying to balance pencils on their tips ever since we were four, if my son’s endeavours are anything to go by — it is indeed strange that we cannot bring the initial conditions close enough to be confident of the outcome.

Even stranger is the fact that similar randomness shows up in systems that are not quite as physical as pencils or experiments. Take, for instance, the socio-economic phenomenon of globalization, which I can describe as follows, admittedly with an incredible amount of over-simplification. Long time ago, we used to barter agricultural and dairy products with our neighbours — say, a few eggs for a litre (or was it pint?) of milk. Our self-interest ensured a certain level of honesty. We didn’t want to get beaten up for adding white paint to milk, for instance. These days, thanks to globalization, people don’t see their customers. A company buys milk from a farmer, adds god knows what, makes powder and other assorted chemicals in automated factories and ships them to New Zealand and Peru. The absence of a human face in the supply chain and in the flow of money results in increasingly unscrupulous behaviour.

Increasing chaos can be seen in the form of violently fluctuating concentrations of wealth and fortunes, increasing amplitudes and frequency of boom and bust cycles, exponential explosion in technological innovation and adaptation cycles, and the accelerated pace of paradigm shifts across all aspects of our lives.

It is one thing to say that things are getting chaotic, quite another matter to exploit that insight and do anything useful with it. I won’t pretend that I can predict the future even if (rather, especially if) I could. However, let me show you a possible approach using chaos.

One of the classic examples of chaos is the transition from a regular, laminar flow of a fluid to a chaotic, turbulent flow. For instance, when you open a faucet slowly, if you do it carefully, you can have a pretty nice continuous column of water, thicker near the top and stretched thinner near the bottom. The stretching force is gravity, and the cohesive forces are surface tension and inter-molecular forces. As you open the faucet still further, ripples begin to appear on the surface of the column which, at higher rates of flow, rip apart the column into complete chaos.

In a laminar flow, macroscopic forces tend to smooth out microscopic irregularities. Like gravity and surface tension in our faucet example, we have analogues of macroscopic forces in finance. The stretching force is probably greed, and the cohesive ones are efficient markets.

There is a rich mathematical framework available to describe chaos. Using this framework, I suspect one can predict the incidence and intensity of financial turmoils, though not their nature and causes. However, I am not sure such a prediction is useful. Imagine if I wrote two years ago that in 2008, there would be a financial crisis resulting in about one trillion dollar of losses. Even if people believed me, would it have helped?

Usefulness is one thing, but physicists and mathematicians derive pleasure also from useless titbits of knowledge. What is interesting about the faucet-flow example is this: if you follow the progress two water molecules starting off their careers pretty close to each other, in the laminar case, you will find that they end up pretty much next to each other. But once the flow turns turbulent, there is not telling where the molecules will end up. Similarly, in finance, suppose two banks start off roughly from the same position — say Bear Stearns and Lehman. Under normal, laminar conditions, their stock prices would track similar patterns. But during a financial turbulence, they end up in totally different recycle bins of history, as we have seen.

If whole financial institutions are tossed around into uncertain paths during chaotic times, imagine where two roughly similar employees might end up. In other words, don’t feel bad if you get a pink slip. There are forces well beyond your control at play here.

Uncertainty Principle in Quantitative Finance

The Heisenberg uncertainty principle is perhaps the second most popular theme from physics that has captured the public imagination. (The first one, of course, is Einstein’s E = mc2.) It says something seemingly straightforward — you can measure two complementary properties of a system only to a certain precision. For instance, if you try to figure out where an electron is (measure its position, that is) more and more precisely, its speed becomes progressively more uncertain (or, the momentum measurement becomes imprecise).

Quantitative finance has a natural counterpart to the uncertainty principle — risks and rewards. When you try to minimize the risks, the rewards themselves go down. If you hedge out all risks, you get only risk-free returns. Since risk is the same as the uncertainty in rewards, the risk-reward relation is not quite the same as the uncertainty principle (which, as described in the box, deals with complementary variables), but it is close enough to draw some parallels.

To link the quantum uncertainty principle to quantitative finance, let’s look at its interpretation as observation altering results. Does modelling affect how much money we can make out of a product? This is a trick question. The answer might look obvious at first glance. Of course, if we can understand and model a product perfectly, we can price it right and expect to reap healthy rewards. So, sure, modelling affects the risk-reward equation.

But, a model is only as good as its assumptions. And the most basic assumption in any model is that the market is efficient and liquid. The validity of this assumption (or lack thereof) is precisely what precipitated the current financial crisis. If our modelling effort actually changes the underlying assumptions (usually in terms of liquidity or market efficiency), we have to pay close attention to the quant equivalent of the uncertainty principle.

Look at it this way — a pyramid scheme is a perfectly valid money making model, but based on one unfortunate assumption on the infinite number of idiots at the bottom of the pyramid. (Coming to think of it, the underlying assumption in the sub-prime crisis, though more sophisticated, may not have been that different.) Similar pyramid assumptions can be seen in social security schemes, as well. We know that pyramid assumptions are incorrect. But at what point do they become incorrect enough for us to change the model?

There is an even more insidious assumption in using models — that we are the only ones who use them. In order to make a killing in a market, we always have to know a bit more than the rest of them. Once everybody starts using the same model, I think the returns will plummet to risk-free levels. Why else do you think we keep inventing more and more complex exotics?

Summing up…

The current financial crisis has been blamed on many things. One favourite theory has been that it was brought about by the greed in Wall Street — the so-called privatization of profits and socialization of losses. Incentive schemes skewed in such a way as to encourage risk taking and limit risk management must take at least part of the blame. A more tempered view regards the turmoil as a result of a risk management failure or a regulatory failure.

This column presents my personal view that the turmoil is the inevitable consequence of the interplay between opposing forces in financial markets — risk and rewards, speculation and regulation, risk taking and risk management and so on. To the extent that the risk appetite of a financial institute is implemented through a conflict between such opposing forces, these crises cannot be avoided. Worse, the intensity and frequency of similar meltdowns are going to increase as the volume of transactions increases. This is the inescapable conclusion from non-linear dynamics. After all, such turbulence has always existed in the real economy in the form cyclical booms and busts. In free market economies, selfishness and the inherent conflicts between selfish interests provide the stretching and cohesive forces, setting the stage for chaotic turbulence.

Physics has always been a source of talent and ideas for quantitative finance, much like mathematics provides a rich toolkit to physics. In his book, Dreams of a Final Theory, Nobel Prize winning physicist Steven Weinberg marvels at the uncanny ability of mathematics to anticipate physics needs. Similarly, quants may marvel at the ability of physics to come up with phenomena and principles that can be directly applied to our field. To me, it looks like the repertoire of physics holds a few more gems that we can employ and exploit.

Box: Heisenberg’s Uncertainty Principle Where does this famous principle come from? It is considered a question beyond the realms of physics. Before we can ask the question, we have to examine what the principle really says. Here are a few possible interpretations: Position and momentum of a particle are intrinsically interconnected. As we measure the momentum more accurately, the particle kind of “spreads out,” as George Gamow’s character, Mr. Tompkins, puts it. In other words, it is just one of those things; the way the world works. When we measure the position, we disturb the momentum. Our measurement probes are “too fat,” as it were. As we increase the position accuracy (by shining light of shorter wavelengths, for instance), we disturb the momentum more and more (because shorter wavelength light has higher energy/momentum). Closely related to this interpretation is a view that the uncertainty principle is a perceptual limit. We can also think of the uncertainly principle as a cognitive limit if we consider that a future theory might surpass such limits. The first view is currently popular and is related to the so-called Copenhagen interpretation of quantum mechanics. Let’s ignore it for it is not too open to discussions. The second interpretation is generally understood as an experimental difficulty. But if the notion of the experimental setup is expanded to include the inevitable human observer, we arrive at the third view of perceptual limitation. In this view, it is actually possible to “derive” the uncertainty principle, based on how human perception works. Let’s assume that we are using a beam of light of wavelength to observe the particle. The precision in the position we can hope to achieve is of the order of . In other words, . In quantum mechanics, the momentum of each photon in the light beam is inversely proportional to the wavelength. At least one photon is reflected by the particle so that we can see it. So, by the classical conservation law, the momentum of the particle has to change by at least this amount() from what it was before the measurement. Thus, through perceptual arguments, we get something similar to the Heisenberg uncertainty principle We can make this argument more rigorous, and get an estimate of the value of the constant. The resolution of a microscope is given by the empirical formula , where is the numerical aperture, which has a maximum value of one. Thus, the best spatial resolution is . Each photon in the light beam has a momentum , which is the uncertainty in the particle momentum. So we get , approximately an order of magnitude bigger than the quantum mechanical limit. Through more rigorous statistical arguments, related to the spatial resolution and the expected momentum transferred, it may possible to derive the Heisenberg uncertainty principle through this line of reasoning. If we consider the philosophical view that our reality is a cognitive model of our perceptual stimuli (which is the only view that makes sense to me), my fourth interpretation of the uncertainty principle being a cognitive limitation also holds a bit of water.