Category Archives: Topical

Includes posts on physics, philosophy, sciences, quantitative finance, economics, environment etc.

Columns, Quantitative Finance, The Wilmott Magazine

Software Nightmares

To err is human, but to really foul things up, you need a computer. So states the remarkably insightful Murphy’s Law. And nowhere else does this ring truer than in our financial workplace. After all, it is the financial sector that drove the rapid progress in the computing industry — which is why the first computing giant had the word “business” in its name.

The financial industry keeps up with the developments in the computer industry for one simple reason. Stronger computers and smarter programs mean more money — a concept we readily grasp. As we use the latest and greatest in computer technology and pour money into it, we fuel further developments in the computing field. In other words, not only did we start the fire, we actively fan it as well. But it is not a bad fire; the positive feedback loop that we helped set up has served both the industries well.

This inter-dependency, healthy as it is, gives us nightmarish visions of perfect storms and dire consequences. Computers being the perfect tools for completely fouling things up, our troubling nightmares are more justified than we care to admit.

Models vs. Systems

Paraphrasing a deadly argument that some gun aficionados make, I will defend our addiction to information technology. Computers don’t foul things up; people do.

Mind you, I am not implying that we always mess it up when we deploy computers. But at times, we try to massage our existing processes into their computerised counterparts, creating multiple points of failure. The right approach, instead, is often to redesign the processes so that they can take advantage of the technology. But it is easier said than done. To see why, we have to look beyond systems and processes and focus on the human factors.

In a financial institution, we are in the business of making money. We fine-tune our reward structure in such a way that our core business (of making money, that is) runs as smoothly as possible. Smooth operation relies on strict adherence to processes and the underlying policies they implement. In this rigid structure, there is little room for visionary innovation.

This structural lack of incentive to innovate results in staff hurrying through a new system rollout or a process re-engineering. They have neither the luxury of time nor the freedom to slack off in the dreaded “business-as-usual” to do a thorough job of such “non-essential” things.

Besides, there is seldom any unused human resource to deploy in studying and improving processes so that they can better exploit technology. People who do it need to have multi-facetted capabilities (business and computing, for instance). Being costly, they are much more optimally deployed in the core business of making more money.

Think about it, when is the last time you (or someone you know) got hired to revamp a system and the associated processes? The closest you get is when someone is hired to duplicate a system that is already known to work better elsewhere.

The lack of incentive results in a dearth of thought and care invested in the optimal use of technology. Suboptimal systems (which do one thing well at the cost of everything else) abound in our workplace. In time, we will reach a point where we have to bite the bullet and redesign these systems. When redesigning a system, we have to think about all the processes involved. And we have to think about the system while designing or redesigning processes. This cyclic dependence is the theme of this article.

Systems do not figure in a quant’s immediate concern. What concerns us more is our strongest value-add, namely mathematical modelling. In order to come up with an optimal deployment strategy for models, however, we need to pay attention to operational issues like trade workflow.

I was talking to one of our top traders the other day, and he mentioned that a quant, no matter how smart, is useless unless his work can be deployed effectively and in a timely manner. A quant typically delivers his work as a C++ program. In a rapid deployment scenario, his program will have to plug directly into a system that will manage trade booking, risk measurements, operations and settlement. The need for rapid deployment makes it essential for the quants to understand the trade lifecycle and business operations.

Life of a Trade

Once a quant figures out how to price a new product, his work is basically done. After coaxing that stochastic integral into a pricing formula (failing which, a Crank-Nicholson or Monte Carlo), the quant writes up a program and moves on to the next challenge.

It is when the trading desk picks up the pricing spreadsheet and books the first trade into the system that the fun begins. Then the trade takes on a life of its own, sneaking through various departments and systems, showing different strokes to different folks. This adventurous biography of the trade is depicted in Figure 1 in its simplified form.

At the inception stage, a trade is conceptualized by the Front Office folks (sales, structuring, trading desk – shown in yellow ovals in the figure). They study the market need and potential, and assess the trade viability. Once they see and grab a market opportunity, a trade is born.

Fig. 1: Life of a Trade

Even with the best of quant models, a trade cannot be priced without market data, such as prices, volatilities, rates and correlations and so on. The validity of the market data is ensured by Product Control or Market Risk people. The data management group also needs to work closely with Information Technology (IT) to ensure live data feeds.

The trade first goes for a counterparty credit control (the pink bubbles). The credit controllers ask questions like: if we go ahead with the deal, how much will the counterparty end up owing us? Does the counterparty have enough credit left to engage in this deal? Since the credit exposure changes during the life cycle of the trade, this is a minor quant calculation on its own.

In principle, the Front Office can do the deal only after the credit control approves of it. Credit Risk folks use historical data, internal and external credit rating systems, and their own quantitative modelling team to come up with counterparty credit limits and maximum per trade and netted exposures.

Right after the trade is booked, it goes through some control checks by the Middle Office. These fine people verify the trade details, validate the initial pricing, apply some reasonable reserves against the insane profit claims of the Front Office, and come up with a simple yea or nay to the trade as it is booked. If they say yes, the trade is considered validated and active. If not, the trade goes back to the desk for modifications.

After these inception activities, trades go through their daily processing. In addition to the daily (or intra-day) hedge rebalancing in the Front Office, the Market Risk Management folks mark their books to market. They also take care of compliance reporting to regulatory bodies, as well as risk reporting to the upper management — a process that has far-reaching consequences.

The Risk Management folks, whose work is never done as Tracy Chapman would say, also perform scenario, stress-test and historical Value at Risk (VaR) computations. In stress-tests, they apply a drastic market movement of the kind that took place in the past (like the Asian currency crisis or 9/11) to the current market data and estimate the movement in the bank’s book. In historical VaR, they apply the market movements in the immediate past (typically last year) and figure out the 99 percentile (or some such pre-determined number) worst loss scenario. Such analysis is of enormous importance to the senior management and in regulatory and compliance reporting. In Figure 1, the activities of the Risk Management folks are depicted in blue bubbles.

In their attempts to rein in the ebullient traders, the Risk Management folks come across in their adversarial worst. But we have to remind ourselves that the trading and control processes are designed that way. It is the constant conflict between the risk takers (Front Office) and the risk controllers (Risk Management) that implements the risk appetite of the bank as decided by the upper management.

Another group that crunches the trade numbers every day from a slightly different perspective are the Product Control folks, shown in green in Figure 1. They worry about the daily profit and loss (P/L) movements both at trade and portfolio level. They also modulate the profit claims by the Front Office through a reserving mechanism and come up with the so called unrealized P/L.

This P/L, unrealized as it is, has a direct impact on the compensation and incentive structure of Front Office in the short run. Hence the perennial tussle over the reserve levels. In the long term, however, the trade gets settled and the P/L becomes realized and nobody argues over it. Once the trade is in the maturity phase, it is Finance that worries about statistics and cash flows. Their big picture view ends up in annual reports and stake holders meetings, and influences everything from our bonus to the CEO’s new Gulfstream.

Trades are not static entities. During the course of their life, they evolve. Their evolution is typically handled by Middle Office people (grey bubbles) who worry about trade modifications, fixings, knock-ins, knock-outs etc. The exact name given to this business unit (and indeed other units described above) depends on the financial institution we work in, but the trade flow is roughly the same.

The trade flow that I described so far should ring alarm bells in a quant heart. Where are the quants in this value chain? Well, they are hidden in a couple of places. Some of them find home in the Market Risk Management, validating pricing models. Some others may live in Credit Risk, estimating peak exposures, figuring out rating schemes and minimising capital charges.

Most important of all, they find their place before a trade is ever booked. Quants teach their home banks how to price products. A financial institution cannot warehouse the risk associated with a trade unless it knows how much the product in question is worth. It is in this crucial sense that model quants drive the business.

In a financial marketplace that is increasingly hungry for customized structures and solutions, the role of the quants has become almost unbearably vital. Along with the need for innovative models comes the imperative of robust platforms to launch them in a timely fashion to capture transient market opportunities.

In our better investment banks, such platforms are built in-house. This trend towards self-reliance is not hard to understand. If we use a generic trading platform from a vendor, it may work well for established (read vanilla) products. It may handle the established processes (read compliance, reporting, settlements, audit trails etc.) well. But what do we do when we need a hitherto unknown structure priced? We could ask the vendor to develop it. But then, they will take a long time to respond. And, when they finally do, they will sell it to all our competitors, or charge us an arm and a leg for exclusivity thereby eradicating any associated profit potential.

Once a vended solution is off the table, we are left with the more exciting option of developing in-house system. It is when we design an in-house system that we need to appreciate the big picture. We will need to understand the whole trade flow through the different business units and processes as well as the associated trade perspectives.

Trade Perspectives

The perspective that is most common these days is trade-centric. In this view, trades are the primary objects, which is why conventional trading systems keep track of them. Put bunch of trades together, you get a portfolio. Put a few portfolios together, you have a book. The whole Global Markets is merely a collection of books. This paradigm has worked well and is probably the best compromise between different possible views.

But the trade-centric perspective is only a compromise. The activities of the trading floor can be viewed from different angles. Each view has its role in the bigger scheme of things in the bank. Quants, for instance, are model-centric. They try to find commonality between various products in terms of the underlying mathematics. If they can reuse their models from one product to another, potentially across asset classes, they minimize the effort required of them. Remember how Merton views the whole world as options! I listened to him in amazement once when he explained the Asian currency crisis as originating from the risk profile of compound options — the bank guarantees to corporate clients being put options, government guarantees to banks being put options on put options.

Unlike quants who develop pricing models, quantitative developers tend to be product-centric. To them, it doesn’t matter too much even if two different products use very similar models. They may still have to write separate code for them depending on the infrastructure, market data, conventions etc.

Traders see their world from the asset class angle. Typically associated with a particular trading desks based on asset classes, their favourite view cuts across models and products. To traders, all products and models are merely tools to making profit.

IT folks view the trading world from a completely different perspective. Theirs is a system-centric view, where the same product using the same model appearing in two different systems is basically two different beasts. This view is not particularly appreciated by traders, quants or quant developers.

One view that all of us appreciate is the view of the senior management, which is narrowly focussed on the bottom line. The big bosses can prioritise things (whether products, asset classes or systems) in terms of the money they bring to the shareholders. Models and trades are typically not visible from their view — unless, of course, rogue traders lose a lot of money on a particular product or by using a particular model. Or, somewhat less likely, they make huge profits using the same tricks.

When the trade reaches the Market Risk folks, there is a subtle change in the perspective from a trade-level view to a portfolio or book level view. Though mathematically trivial (after all, the difference is only a matter of aggregation), this change has implications in the system design. Trading systems have to maintain a robust hierarchical portfolio structure so that various dicing and slicing as required in the later stages of the trade lifecycle can be handled with natural ease.

The busy folks in the Middle Office (who take care of trade validations and modifications) are obsessed with trade queues. They have a validation queue, market operation queue etc. Again, the management of queues using status flags is something we have to keep in mind while designing an in-house system.

When it comes to Finance and their notions of cost centres, the trade is pretty much out of the booking system. Still, they manage trading desks and asset classes cost centres. Any trading platform we design has to provide adequate hooks in the system to respond to their specific requirements as well.

Quants and the Big Picture

Most quants, especially at junior levels, despise the Big Picture. They think of it as a distraction from their real work of marrying stochastic calculus to C++. Changing that mindset to some degree is the hidden agenda behind this column.

As my trader friends will agree, the best model in the world is worthless unless it can be deployed. Deployment is the fast track to the big picture — no point denying it. Besides, in an increasingly interconnected world where a crazy Frenchman’s actions instantly affect our bonus, what is the use of denying the existence of the big picture in our nook of the woods? Instead, let’s take advantage of the big picture to empower ourselves. Let’s bite the bullet and sit through a “Big Picture 101.”

When we change our narrow, albeit effective, focus on the work at hand to an understanding of our role and value in the organization, we will see the potential points of failure of the systems and processes. We will be prepared with possible solutions to the nightmarish havoc that computerized processes can wreak. And we will sleep easier.

Creative, Environment, French, Philosophy

La logique

2 Comments

[The last of my French redactions to be blogged, this one wasn’t such a hit with the class. They expected a joke, but what they got was, well, this. It was written the day after I watched an air show on TV where the French were proudly showcasing their fighter technology.]

[In English first]

Science is based on logic. And logic is based on our experiences — what we learn during our life. But, because our experiences are incomplete, our logic can be wrong. And our science can lead us to our demise. When I watched the fighter planes on TV, I started thinking about the energy and effort we spend on trying to kill ourselves. It seems to me that our logic here had to be wrong.

A few months ago, I read a short story (by O.V. Vijayan, as a matter of fact) about a chicken who found itself in a cage. Everyday, by noon, the little window of the cage would open, a man’s hand would appear and give the chicken something to eat. It went on for 99 days. And the chicken concluded:

“Noon, hand, food — good!”

On the hundredth day, by noon, the hand appeared again. The chicken, all happy and full of gratitude, waited for something to eat. But this time, the hand caught it by the neck and strangled it. Because of realities beyond its experience, the chicken became dinner on that day. I hope we human beings can avoid such eventualities.

Les sciences sont basées sur la logique. Et la logique se base sur les expériences – ce que nous apprenons dans notre vie. Mais, comme nos expériences ne sont pas toujours completes, notre logique peut avoir tort. Et nos sciences peuvent nous diriger vers notre destruction. Lorsque je regardais les avions de combat à la télé, ils m’ont fait penser à l’énergie et aux efforts que nous gaspillons en essayant de nous tuer. Il me paraît que la
logique ici doit avoir tort.

J’ai lu une petite histoire d’une poule il y a quelques mois. Elle s’est trouvée dans une cage, un homme l’y avait mise. Chaque jour, vers midi, la petite fenêtre de la cage s’ouvrait, une main se montrait avec de quoi manger pour la poule. Ça s’est passé comme ça pendant quatre-vingt-dix-neuf jours. Et la poule a pensé:

“Aha, midi, main, manger – bien!”

Le centième jour est arrivé. Le midi, la main s’est montrée. La poule, toute heureuse et pleine de gratitude, attendait de quoi manger. Mais, cette fois, la main l’a prise par le cou et l’a étranglée. A cause des réalités au-delà de ses expériences, la poule est devenue le diner ce jour-là. J’espère que nous pourrons éviter les éventualités de cette sorte.

Books, Creative, Philosophy

1984

All great books have one thing in common. They present deep philosophical inquiries, often clad in superb story lines. Or is it just my proclivity to see philosophy where none exists?

In 1984, the immediate story is of a completely totalitarian regime. Inwardly, 1984 is also about ethics and politics. It doesn’t end there, but goes into nested philosophical inquiries about how everything is eventually connected to metaphysics. It naturally ends up in solipsism, not merely in the material, metaphysical sense, but also in a spiritual, socio-psychological sense where the only hope, the only desired outcome of life, becomes death.

I think I may be giving away too much of my impressions in the first paragraph. Let’s take it step by step. We all know that totalitarianism is bad. It is a bad political system, we believe. The badness of totalitarianism can present itself at different levels of our social existence.

At the lowest level, it can be a control over our physical movements, physical freedom, and restrictions on what you can or cannot do. Try voting against a certain African “president” and you get beaten up, for instance. Try leaving certain countries, you get shot.

At a higher level, totalitarianism can be about financial freedom. Think of those in the developed world who have to juggle three jobs just to put food on the table. At a progressively subtler level, totalitarianism is about control of information. Example: media conglomerates filtering and coloring all the news and information we receive.

At the highest level, totalitarianism is a fight for your mind, your soul, and your spiritual existence. 1984 presents a dystopia where totalitarianism is complete, irrevocable, and existing at all levels from physical to spiritual.

Another book of the same dystopian kind is The Handmaid’s Tale, where a feminist’s nightmare of a world is portrayed. Here, the focus is on religious extremism, and the social and sexual subjugation brought about by it. But the portrayal of the world gone hopelessly totalitarian is similar to 1984.

Also portraying a dark dystopia is V for Vendentta, with torture and terrorism thrown in. This work is probably inspired by 1984, I have to look it up.

It is the philosophical points in 1984 that make it the classic it is. The past, for instance, is a matter of convention. If everybody believes (or is forced to believe) that events took place in a certain way, then that is the past. History is written by the victors. Knowing that, how can you trust the greatness of the victors or the evil in the vanquished? Assume for a second that Hitler had actually won the Second World War. Do you think we would’ve still thought of him as evil? I think we would probably think of him as the father of the modern world or something. Of course, we would be having this conversation (if we were allowed to exist and have conversations at all) in German.

Even at a personal level, the past is not as immutable as it seems. Truth is relative. Lies repeated often enough become truth. All these points are describe well in 1984, first from Winston’s point of view and later, in the philosophically sophisticated discourses of O’Brien. In a world existing in our own brain, where the phenomenal reality as we see it is far from the physical one, morality does lose a bit of its glamor. Metaphysics can erode on ethics. Solipsism can annihilate it.

A review, especially one in a blog, doesn’t have to be conventional. So let me boldly outline my criticisms of 1984 as well. I believe that the greatest fear of a normal human being is the fear of death. After all, the purpose of life is merely to live a little longer. Everything that our biological faculties do stem from the desire to exist a little longer.

Based on this belief of mine, I find certain events in 1984 a bit incongruous. Why is it that Winston and Julia don’t fear death, but still fear the telescreens and gestapo-like police? Perhaps the fear of pain overrides the fear of death. What do I know, I have never been tortured.

But even the fear of pain can be understood in terms of the ultimate fear. Pain is a messenger of bodily harm, ergo of possible death. But fear of rats?! Perhaps irrational phobias, existing at a sub-cognitive, almost physical, layer may be stronger than everything else. But I cannot help feeling that there is something amiss, something contrived, in the incarceration and torture parts of 1984.

May be Orwell didn’t know how to portray spiritual persecution. Luckily, none of us knows. So such techniques as rats and betrayal were employed to bring about the hideousness of the process. This part of the book leaves me a bit dissatisfied. After all, our protagonists knew full well what they were getting into, and what the final outcome would be. If they knew their spirit would be broken, then why leave it out there to be broken?

Columns, Quantitative Finance, The Wilmott Magazine

Risks and Rewards

Everything in life comes at a cost — with a price tag seldom denominated in dollars and cents, and almost always hidden.

In our profession as quants and traders, we know we cannot accumulate if we don’t speculate (as P. G. Wodehouse puts it). So we accept and even welcome some of these price tags. We take certain risks, which we hope are calculated and understood, so that we can bring unto our employers what is theirs. These are good risks.

Bad risks are those we cannot understand and quantify, or measure and hedge against. They are bad because, even if we rake in some profits, we are never sure that they are commensurate with the downside we are throwing ourselves open to.
Market risk is a good risk. We know how to measure and model it, hedge against and reap rewards from it. We have smart people with bulging foreheads solving stochastic differential equations for us and simplifying the risk-reward equation.

Operational risk is a bad one. We can put as many software locks and control processes as we want around it. But we cannot prevent the rogue elements amongst us from sharing their passwords over a beer in some French brasserie. Worse, we have no idea what the rewards are when we expose ourselves to certain levels of operational risk. Heck, we don’t even know what the levels are because we have no means of quantifying it.

Incomplete appreciation of the risks involved in many situations is an almost philosophical factor that comes around to haunt us. It is not that we underestimate the risks; it is more like we are not aware of certain ramifications. The inconvenient warming of our home planet, for instance, is a consequence that the Wright brothers and Henry Ford simply could not have been aware of.

No such thing as a free lunch — the seemingly unlimited and practically free supply of nuclear energy has a not-so-hidden cost: the necessity to dispose of or securely store dangerous waste for, say, twenty thousand years. How do you store something for that long? After all, twenty thousand years ago, we were only barely human!

But the list of such boons and associated banes is endless. Think of the prosperity that a flattened world (using Thomas Friedman’s lingo) brought to emerging economies like India and China, which came at the expense of the cultural values that took thousands of years of careful nurturing.

A personal ramification of our high-powered corporate life is the alarming level of stress that we put ourselves through. Stress comes from market movements. As the sub-prime market tanked and heads started to roll, some of us had to worry about our heads. Fat bonuses of the first quarter usher in tax worries; lean bonuses indicate uncertain corporate future. Rogue traders burn billions and expose everybody to scrutiny and associated stresses. Even the lack of stress brings in some worries that the corporate world is perhaps passing us by!

When I first switched to the finance industry in late 2005, I happened to flip through an issue of the Bloomberg Market magazine. On of the first things struck me was that most of the advertisements seemed to be of expensive cars or alcohol. Is alcoholism the cost we readily dish out so that we can afford a gleaming dream machine?

Is stress a price worth paying for our corporate success? Are the risks worth their rewards?

Married to the Job — Till Death Do Us Part?

Stress is as much a part of our corporate careers as death is a fact of life. Still, it is best to keep the two (career and death) separate. This is the message that was lost on some hardworking young souls here in Singapore who literally worked themselves to death. So do a lot of Japanese, if we are to believe the media.

The reason for death in sedentary jobs is the insidious condition called deep vein thrombosis. This condition develops because of extended hours spent sitting, when a blood clot forms in the lower limbs. The clot then travels to the vital organs in the upper body, where it wreaks havoc including death.

The trick in avoiding such an untimely demise, of course, is not to sit for long. But that is easier said than done, when job pressure mounts, and deadlines loom.

Here is where you have to get your priorities straight. What do you value more? Quality of life or corporate success? The implication in this choice is that you can’t have both, as illustrated in the joke in investment banking that goes like: “If you can’t come in on Saturday, don’t bother coming in on Sunday!”

You can, however, make a compromise. It is possible to let go a little bit of career aspirations and improve the quality of life tremendously. This balancing act is not so simple though; nothing in life is.

Undermining work-life balance are a few factors. One is the materialistic culture we live in. It is hard to fight that trend. Second is a misguided notion that you can “make it” first, then sit back and enjoy life. That point in time when you are free from worldly worries rarely materializes. Thirdly, you may have a career-oriented partner. Even when you are ready to take a balanced approach, your partner may not be, thereby diminishing the value of putting it in practice.

These are factors you have to constantly battle against. And you can win the battle, with logic, discipline and determination. However, there is a fourth, much more sinister, factor, which is the myth that a successful career is an all-or-nothing proposition, as implied in the preceding investment banking joke. It is a myth (perhaps knowingly propagated by the bosses) that hangs over our corporate heads like the sword of Damocles.

Because of this myth, people end up working late, trying to make an impression. But an impression is made, not by the quantity of work, but by its quality. Turn in quality, impactful work, and you will be rewarded, regardless of how long it takes to accomplish it. Long hours, in my view, make the possibility of quality work remote.

Such melancholy long hours are best left to workaholics; they keep working because they cannot help it. It is not so much a career aspiration, but a force of habit coupled with a fear of social life.

To strike a work-life balance in today’s dog eat dog world, you may have to sacrifice a few upper rungs of the proverbial corporate ladder. Raging against the corporate machine with no regard to the consequences ultimately boils down to one simple realization — that making a living amounts to nothing if your life is lost in the process.

Spousal Indifference — Do We Give a Damn?

After a long day at work, you want to rest your exhausted mind; may be you want to gloat a bit about your little victories, or whine a bit about your little setbacks of the day. The ideal victim for this mental catharsis is your spouse. But the spouse, in today’s double income families, is also suffering from a tired mind at the end of the day.

The conversation between two tired minds usually lacks an essential ingredient — the listener. And a conversation without a listener is not much of a conversation at all. It is merely two monologues that will end up generating one more setback to whine about — spousal indifference.

Indifference is no small matter to scoff at. It is the opposite of love, if we are to believe Elie Weisel. So we do have to guard against indifference if we want to have a shot at happiness, for a loveless life is seldom a happy one.

“Where got time?” ask we Singaporeans, too busy to form a complete sentence. Ah… time! At the heart of all our worldly worries. We only have 24 hours of it in a day before tomorrow comes charging in, obliterating all our noble intensions of the day. And another cycle begins, another inexorable revolution of the big wheel, and the rat race goes on.

The trouble with the rat race is that, at the end of it, even if you win, you are still a rat!

How do we break this vicious cycle? We can start by listening rather than talking. Listening is not as easy as it sounds. We usually listen with a whole bunch of mental filters turned on, constantly judging and processing everything we hear. We label the incoming statements as important, useful, trivial, pathetic, etc. And we store them away with appropriate weights in our tired brain, ignoring one crucial fact — that the speaker’s labels may be, and often are, completely different.

Due to this potential mislabeling, what may be the most important victory or heartache of the day for your spouse or partner may accidentally get dragged and dropped into your mind’s recycle bin. Avoid this unintentional cruelty; turn off your filters and listen with your heart. As Wesley Snipes advises Woody Herrelson in White Men Can’t Jump, listen to her (or him, as the case may be.)

It pays to practice such an unbiased and unconditional listening style. It harmonizes your priorities with those your spouse and pulls you away from the abyss of spousal apathy. But it takes years of practice to develop the proper listening technique, and continued patience and deliberate effort to apply it.

“Where got time?” we may ask. Well, let’s make time, or make the best of what little time we got. Otherwise, when days add up to months and years, we may look back and wonder: Where is the life that we lost in living?

Stress and a Sense of Proportion

How can we manage stress, given that it is unavoidable in our corporate existence? Common tactics against stress include exercise, yoga, meditation, breathing techniques, reprioritizing family etc. To add to this list, I have my own secret weapons to battle stress that I would like to share with you. These weapons may be too potent; so use them with care.

One of my secret tactics is to develop a sense of proportion, harmless as it may sound. Proportion can be in terms of numbers. Let’s start with the number of individuals, for instance. Every morning, when we come to work, we see thousands of faces floating by, almost all going to their respective jobs. Take a moment to look at them — each with their own personal thoughts and cares, worries and stresses.

To each of them, the only real stress is their own. Once we know that, why would we hold our own stress any more important than anybody else’s? The appreciation of the sheer number of personal stresses all around us, if we stop to think about it, will put our worries in perspective.

Proportion in terms of our size also is something to ponder over. We occupy a tiny fraction of a large building that is our workplace. (Statistically speaking, the reader of this column is not likely to occupy a large corner office!) The building occupies a tiny fraction of the space that is our beloved city. All cities are so tiny that a dot on the world map is usually an overstatement of their size.

Our world, the earth, is a mere speck of dust a few miles from a fireball, if we think of the sun as a fireball of any conceivable size. The sun and its solar system are so tiny that if you were to put the picture of our galaxy as the wallpaper on your PC, they would be sharing a pixel with a few thousand local stars! And our galaxy — don’t get me started on that! We have countless billions of them. Our existence (with all our worries and stresses) is almost incomprehensibly small.

The insignificance of our existence is not limited to space; it extends to time as well. Time is tricky when it comes to a sense of proportion. Let’s think of the universe as 45 years old. How long do you think our existence is in that scale? Eight seconds if we are very lucky!

We are created out of star dust, last for a mere cosmological instant, and then turn back into star dust. DNA machines during this time, we run unknown genetic algorithms, which we mistake for our aspirations and achievements, or stresses and frustrations. Relax! Don’t worry, be happy!

Sure, you may get reprimanded if that report doesn’t go out tomorrow. Or, your trader may bite your head off if that pricing model is delayed again. Or, your colleague may send out that backstabbing email (and Bcc your boss) if you displease them. But, don’t you get it, in this mind-numbingly humongous universe, it doesn’t matter an iota. In the big scheme of things, your stress is not even static noise!

Arguments for maintaining a level of stress all hinge on an ill-conceived notion that stress aids productivity. It does not. The key to productivity is an attitude of joy at work. When you stop worrying about reprimands and backstabs and accolades, and start enjoying what you do, productivity just happens. I know it sounds a bit idealistic, but my most productive pieces of work happened that way. Enjoying what I do is an ideal I will shoot for any day.

Stress and Metaphysics

Realizing that our existence is a mere blink of an eye in time, and less than a speck of dust in space is a powerful way of cutting our stress to size. My favorite weapon, however, is even more potent. I ask myself a basic question — what are space and time to begin with?

These may sound like silly metaphysical musings that have no relevance to real life. But they have been the subject matter of many lifelong quests over the ages. If we, humanity as a whole, cannot stop pondering over such things, it is probably because they form the basis of our existence. Besides, our stress takes place in space and time.

Philosophical grand-standing aside, let’s get to the meat of the problem: What is space? Space seems to be closely associated with our sense of sight. It also forms the basis of our reality — everything happens in space and time. For this reason, “What are space and time?” is a question that cannot be reduced to simpler elements in our reality.

We can, however, approach the issue by posing a similar question “What is sound?” Sound is an experience associated with hearing, clearly. But what is it? The answer is hinted at in the age-old conundrum of a falling tree in a deserted forest. Does it make sound? A popular topic of conservation in cocktail parties, this question is also a serious contemplative inquiry for a Zen monk.

The knee-jerk response to the question is, yes, the tree does make sound. It’s just that there is nobody to hear it. But hear what exactly?

Sure, the falling tree creates air pressure waves. But, the waves are not sound. These waves create an electrical signal in the ear, if an ear is present. Electrical signals are electrical signals, not sound. These signals, when transported to the brain, induce neuronal firing, which is still not sound. It is a fallacy to think of sound as anything physical, anything real. Sound is an experience or a cognitive representation associated with the input signals (which are the pressure waves, we think. But are they?)

We can draw similar analogies between other sensations and the corresponding signals — taste and smell to chemical composition, for instance. What about sight? What is the “sensation” or the cognitive representation associated with sight? It is what we think of as space.

Of course, we think of space as real, as the basis of our reality. It takes more than this short column to shake our belief in it. That’s why I wrote my book — The Unreal Universe.

To me, the unreal nature of what we consider reality is more than a constant contemplation. It is a source of a Zen-like immunity against stress and other worldly worries.

Yes, stress is the cost exacted by the corporate chain of command. It is a cost most of us happily pay, for the rewards are abundantly clear. But we have to be aware of the risks associated with the rewards — both in accepting them and in declining them.

Articles and Essays, Philosophy, Physics

Perception, Physics and the Role of Light in Philosophy

Reality, as we sense it, is not quite real. The stars we see in the night sky, for instance, are not really there. They may have moved or even died by the time we get to see them. This unreality is due to the time it takes for light from the distant stars and galaxies to reach us. We know of this delay.

Even the sun that we know so well is already eight minutes old by the time we see it. This fact does not seem to present particularly grave epistemological problems – if we want to know what is going on at the sun now, all we have to do is to wait for eight minutes. We only have to ‘correct’ for the distortions in our perception due to the finite speed of light before we can trust what we see. The same phenomenon in seeing has a lesser-known manifestation in the way we perceive moving objects. Some heavenly bodies appear as though they are moving several times the speed of light, whereas their ‘real’ speed must be a lot less than that.

What is surprising (and seldom highlighted) is that when it comes to sensing motion, we cannot back-calculate in the same kind of way as we can to correct for the delay in observation of the sun. If we see a celestial body moving at an improbably high speed, we cannot calculate how fast or even in what direction it is ‘really’ moving without first having to make certain further assumptions.

Einstein chose to resolve the problem by treating perception as distorted and inventing new fundamental properties in the arena of physics – in the description of space and time. One core idea of the Special Theory of Relativity is that the human notion of an orderly sequence of events in time needs to be abandoned. In fact, since it takes time for light from an event at a distant place to reach us, and for us to become aware of it, the concept of ‘now’ no longer makes any sense, for example, when we speak of a sunspot appearing on the surface of the sun just at the moment that the astronomer was trying to photograph it. Simultaneity is relative.

Einstein instead redefined simultaneity by using the instants in time we detect the event. Detection, as he defined it, involves a round-trip travel of light similar to radar detection. We send out a signal travelling at the speed of light, and wait for the reflection. If the reflected pulse from two events reaches us at the same instant, then they are simultaneous. But another way of looking at it is simply to call two events ‘simultaneous’ if the light from them reaches us at the same instant. In other words, we can use the light generated by the objects under observation rather than sending signals to them and looking at the reflection.

This difference may sound like a hair-splitting technicality, but it does make an enormous difference to the predictions we can make. Einstein’s choice results in a mathematical picture that has many desirable properties, including that of making further theoretical development more elegant. But then, Einstein believed, as a matter of faith it would seem, that the rules governing the universe must be ‘elegant.’ However, the other approach has an advantage when it comes to describing objects in motion. Because, of course, we don’t use radar to see the stars in motion; we merely sense the light (or other radiation) coming from them. Yet using this kind of sensory paradigm, rather than ‘radar-like detection,’ to describe the universe results in an uglier mathematical picture. Einstein would not approve!

The mathematical difference spawns different philosophical stances, which in turn percolate to the understanding of our physical picture of reality. As an illustration, suppose we observe, through a radio telescope, two objects in the sky, with roughly the same shape, size and properties. The only thing we know for sure is that the radio waves from these two different points in the sky reach us at the same instant in time. We can only guess when the waves started their journeys.

If we assume (as we routinely do) that the waves started the journey roughly at the same instant in time, we end up with a picture of two ‘real’ symmetric lobes more or less the way see them. But there is another, different possibility and that is that the waves originated from the same object (which is in motion) at two different instants in time, reaching the telescope at the same instant. This possibility would additionally explain some spectral and temporal properties of such symmetric radio sources. So which of these two pictures should we take as real? Two symmetric objects as we see them or one object moving in such a way as to give us that impression? Does it really matter which one is ‘real’? Does ‘real’ mean anything in this context?

Special Relativity gives an unambiguous answer to this question. The mathematics rules out the possibility of a single object moving in such a fashion as to mimic two objects. Essentially, what we see is what is out there. Yet, if we define events by what we perceive, the only philosophical stance that makes sense is the one that disconnects the sensed reality from the causes lying behind what is being sensed.

This disconnect is not uncommon in philosophical schools of thought. Phenomenalism, for instance, holds the view that space and time are not objective realities. They are merely the medium of our perception. All the phenomena that happen in space and time are merely bundles of our perception. In other words, space and time are cognitive constructs arising from perception. Thus, all the physical properties that we ascribe to space and time can only apply to the phenomenal reality (the reality of ‘things-in-the-world’ as we sense it. The underlying reality (which holds the physical causes of our perception), by contrast, remains beyond our cognitive reach.

Yet there is a chasm between the views of philosophy and modern physics. Not for nothing did the Nobel Prize winning physicist, Steven Weinberg, wonder, in his book Dreams of a Final Theory, why the contribution from philosophy to physics had been so surprisingly small. Perhaps it is because physics has yet to come to terms with the fact that when it comes to seeing the universe, there is no such thing as an optical illusion – which is probably what Goethe meant when he said, ‘Optical illusion is optical truth.’

The distinction (or lack thereof) between optical illusion and truth is one of the oldest debates in philosophy. After all, it is about the distinction between knowledge and reality. Knowledge is considered our view about something that, in reality, is ‘actually the case.’ In other words, knowledge is a reflection, or a mental image of something external, as shown in the figure below.

ExternalToBrain

In this picture, the black arrow represents the process of creating knowledge, which includes perception, cognitive activities, and the exercise of pure reason. This is the picture that physics has come to accept. While acknowledging that our perception may be imperfect, physics assumes that we can get closer and closer to the external reality through increasingly finer experimentation, and, more importantly, through better theorization. The Special and General Theories of Relativity are examples of brilliant applications of this view of reality where simple physical principles are relentlessly pursued using formidable machine of pure reason to their logically inevitable conclusions.

But there is another, alternative view of knowledge and reality that has been around for a long time. This is the view that regards perceived reality as an internal cognitive representation of our sensory inputs, as illustrated below.

AbsolutelToBrain

In this view, knowledge and perceived reality are both internal cognitive constructs, although we have come to think of them as separate. What is external is not the reality as we perceive it, but an unknowable entity giving rise to the physical causes behind sensory inputs. In the illustration, the first arrow represents the process of sensing, and the second arrow represents the cognitive and logical reasoning steps. In order to apply this view of reality and knowledge, we have to guess the nature of the absolute reality, unknowable as it is. One possible candidate for the absolute reality is Newtonian mechanics, which gives a reasonable prediction for our perceived reality.

To summarize, when we try to handle the distortions due to perception, we have two options, or two possible philosophical stances. One is to accept the distortions as part of our space and time, as Special Relativity does. The other option is to assume that there is a ‘higher’ reality distinct from our sensed reality, whose properties we can only conjecture. In other words, one option is to live with the distortion, while the other is to propose educated guesses for the higher reality. Neither of these choices is particularly attractive. But the guessing path is similar to the view accepted in phenomenalism. It also leads naturally to how reality is viewed in cognitive neuroscience, which studies the biological mechanisms behind cognition.

The twist to this story of light and reality is that we seem to have known all this for a long time. The role of light in creating our reality or universe is at the heart of Western religious thinking. A universe devoid of light is not simply a world where you have switched off the lights. It is indeed a universe devoid of itself, a universe that doesn’t exist. It is in this context that we have to understand the wisdom behind the statement that ‘the earth was without form, and void’ until God caused light to be, by saying ‘Let there be light.’

The Koran also says, ‘Allah is the light of the heavens and the earth,’ which is mirrored in one of the ancient Hindu writings: ‘Lead me from darkness to light, lead me from the unreal to the real.’ The role of light in taking us from the unreal void (the nothingness) to a reality was indeed understood for a long, long time. Is it possible that the ancient saints and prophets knew things that we are only now beginning to uncover with all our supposed advances in knowledge?

There are parallels between the noumenal-phenomenal distinction of Kant and the phenomenalists later, and the Brahman-Maya distinction in Advaita. Wisdom on the nature of reality from the repertoire of spirituality is reinvented in modern neuroscience, which treats reality as a cognitive representation created by the brain. The brain uses the sensory inputs, memory, consciousness, and even language as ingredients in concocting our sense of reality. This view of reality, however, is something physics is still unable to come to terms with. But to the extent that its arena (space and time) is a part of reality, physics is not immune to philosophy.

In fact, as we push the boundaries of our knowledge further and further, we are discovering hitherto unsuspected and often surprising interconnections between different branches of human efforts. Yet, how can the diverse domains of our knowledge be independent of each other if all knowledge is subjective? If knowledge is merely the cognitive representation of our experiences? But then, it is the modern fallacy to think that knowledge is our internal representation of an external reality, and therefore distinct from it. Instead, recognising and making use of the interconnections among the different domains of human endeavour may be the essential prerequisite for the next stage in developing our collective wisdom.

Box: Einstein’s TrainOne of Einstein’s famous thought experiments illustrates the need to rethink what we mean by simultaneous events. It describes a high-speed train rushing along a straight track past a small station as a man stands on the station platform watching it speed by. To his amazement, as the train passes him, two lightening bolts strike the track next to either end of the train! (Conveniently, for later investigators, they leave burn marks both on the train and on the ground.)

To the man, it seems that the two lightening bolts strike at exactly the same moment. Later, the marks on the ground by the train track reveal that the spots where the lightening struck were exactly equidistant from him. Since then the lightening bolts travelled the same distance towards him, and since they appeared to the man to happen at exactly the same moment, he has no reason not to conclude that the lightening bolts struck at exactly the same moment. They were simultaneous.

However, suppose a little later, the man meets a lady passenger who happened to be sitting in the buffet car, exactly at the centre of the train, and looking out of the window at the time the lightening bolts struck. This passenger tells him that she saw the first lightening bolt hit the ground near the engine at the front of the train slightly ahead of when the second one hit the ground next to the luggage car at the rear of the train.

The effect has nothing to do with the distance the light had to travel, as both the woman and the man were equidistant between the two points that the lightening hit. Yet they observed the sequence of events quite differently.

This disagreement of the timing of the events is inevitable, Einstein says, as the woman is in effect moving towards the point where the flash of lightening hit near the engine -and away from the point where the flash of lightening hit next to the luggage car. In the tiny amount of time it takes for the light rays to reach the lady, because the train moves, the distance the first flash must travel to her shrinks, and the distance the second flash must travel grows.

This fact may not be noticed in the case of trains and aeroplanes, but when it comes to cosmological distances, simultaneity really doesn’t make any sense. For instance, the explosion of two distant supernovae, seen as simultaneous from our vantage point on the earth, will appear to occur in different time combinations from other perspectives.

In Relativity: The Special and General Theory (1920), Einstein put it this way:

‘Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.’

Columns, Quantitative Finance, The Wilmott Magazine

Quant Talent Management

The trouble with quants is that it is hard to keep them anchored to their moorings. Their talent is in high demand for a variety of reasons. The primary reason is the increasing sophistication of the banking clients, who demand increasingly more structured products with specific hedging and speculative motives. Servicing their demand calls for a small army of quants supporting the trading desks and systems.

Since structured products are a major profit engine on the trading floor of most banks, this demand represents a strong pull factor for quants from competing institutions. There is nothing much most financial institutions can do about this pull factor, except to pull them back in with offers they can’t refuse.

But we can try to eliminate the push factors that are hard to identify. These push factors are often hidden in the culture, ethics and the way things get done in institutions. They are, therefore, specific to the geographical location and the social settings where the banks operate.

Performance Appraisal — Who Needs It?

Performance appraisal is a tool for talent retention, if used wisely. But, if misused, it can become a push factor. Are there alternatives that will aid in retaining and promoting talent?

As it stands now, we go through this ordeal of performance appraisal at least once every year. Our career progression, bonus and salary depend on it. So we spend sleepless nights agonizing over it.

In addition to the appraisal, we also get our “key performance indicators” or KPIs for next year. These are the commandments we have to live by for the rest of the year. The whole experience of it is so unpleasant that we say to ourselves that life as an employee sucks.

The bosses fare hardly better though. They have to worry about their own appraisals by bigger bosses. On top of that, they have to craft the KPI commandments for us as well — a job pretty darned difficult to delegate. In all likelihood, they say to themselves that their life as a boss sucks!

Given that nobody is thrilled about the performance appraisal exercise, why do we do it? Who needs it?

The objective behind performance appraisal is noble. It strives to reward good performance and punish poor shows — the old carrot and stick management paradigm. This objective is easily met in a small organization without the need for a formal appraisal process. Small business owners know who to keep and who to sack. But in a big corporate body with thousands of employees, how do you design a fair and consistent compensation scheme?

The solution, of course, is to pay a small fortune to consultants who design appraisal forms and define a uniform process — too uniform, perhaps. Such verbose forms and inflexible processes come with inherent problems. One problem is that the focus shifts from the original objective (carrot and stick) to fairness and consistency (one-size-fits-all). Mind you, most bosses know who to reward and who to admonish. But the HR department wants the bosses to follow a uniform process, thereby increasing everybody’s workload.

Another, more insidious problem with this consultancy driven approach is that it is necessarily geared towards mediocrity. When you design an appraisal process to cater to everybody, the best you can hope to achieve is to improve the average performance level by a bit. Following such a process, the CERN scientist who invented the World Wide Web would have fared badly, for he did not concentrate on his KPIs and wasted all his time thinking about file transfers!

CERN is a place that consistently produces Nobel laureates. How does it do it? Certainly not by following processes that are designed to make incremental improvements at the average level. The trick is to be a center for excellence which attracts geniuses.

Of course, it is not fair to compare an average bank with CERN. But we have to realize that the verbose forms, which focus on averages and promote mediocrity, are a poor tool for innovation management, especially when we are trying to retain and encourage excellence in quant talent.

A viable alternative to standardized and regimented appraisal processes is to align employee objectives with those of the institutions and leave performance and reward management to bosses. With some luck, this approach may retain fringe geniuses and promote innovation. At the very least, it will alleviate some employee anxiety and sleepless nights.

To Know or Not To Know

One peculiar push factor in the Asian context is the lack of respect for technical knowledge. Technical knowledge is not always a good thing in the modern Asian workplace. Unless you are careful, others will take advantage of your expertise and dump their responsibilities on you. You may not mind it as long as they respect your expertise. But, they often hog the credit for your work and present their ability to evade work as people management skills.

People management is better rewarded than technical expertise. This differentiation between experts and middle-level managers in terms of rewards is a local Asian phenomenon. Here, those who present the work seem to get the credit for it, regardless of who actually performs it. We live in a place and time where articulation is often mistaken for accomplishments.

In the West, technical knowledge is more readily recognized than smooth presentations. You don’t have to look beyond Bill Gates to appreciate the heights to which technical expertise can take you in the West. Of course, Gates is more than an expert; he is a leader of great vision as well.

Leaders are different from people managers. Leaders provide inspiration and direction. They are sorely needed in all organizations, big and small.

Unlike people mangers, quants and technical experts are smart cookies. They can easily see that if they want to be people managers, they can get started with a tie and a good haircut. If the pickings are rich, why wouldn’t they?

This Asian differentiation between quants and managers, therefore, makes for a strong push factor for some quants who find it worthwhile to hide their technical skills, get that haircut, grab that tie, and become a people manager. Of course, it comes down to your personal choice between fulfilment and satisfaction originating from technical authority on the one hand, and convenience and promotions arising from people skills on the other.

I wonder whether we have already made our choices, even in our personal lives. We find fathers who cannot get the hang of changing diapers household chores. Is it likely that men cannot figure out washing machines and microwaves although they can operate complicated machinery at work? We also find ladies who cannot balance their accounts and estimate their spending. Is it really a mathematical impairment, or a matter of convenience? At times, the lack of knowledge is as potent a weapon as its abundance.

How Much is Talent Worth?

Banks deal in money. Our profession in finance teaches us that we can put a dollar value to everything in life. Talent retention is no different. After taking care of as much of the push factors as we can, the next question is fairly simple: How much does it take to retain talent?

My city-state of Singapore suffers from a special disadvantage when it comes to talent management. We need foreign talent. It is nothing to feel bad about. It is a statistical fact of life. For every top Singaporean in any field — be it finance, science, medicine, sports or whatever — we will find about 500 professionals of equal calibre in China and India. Not because we are 500 times less talented, just that they have 500 times more people.

Coupled with overwhelming statistical supremacy, certain countries have special superiority in their chosen or accidental specializations. We expect to find more hardware experts in China, more software gurus in India, more badminton players in Indonesia, more entrepreneurial spirit and managerial expertise in the west.

We need such experts, so we hire them. But how much should we pay them? That’s where economics comes in — demand and supply. We offer attractive expatriate packages that the talents would bite.

I was on an expatriate package when I came to Singapore as a foreign talent. It was a fairly generous package, but cleverly worded so that if I became a “local” talent, I would lose out quite a bit. I did become local a few years later, and my compensation diminished as a consequence. My talent did not change, just the label from “foreign” to “local.”

This experience made me think a bit about the value of talent and the value of labels. The local quant talents, too, are beginning to take note of the asymmetric compensation structure associated with labels. This asymmetry and the consequent erosion of loyalty introduce another push factor for the local quant talents, as if one was needed.

The solution to this problem is not a stricter enforcement of the confidentiality of salaries, but a more transparent compensation scheme free of anomalies that can be misconstrued as unfair practices. Otherwise, we may see an increasing number of Asian nationals using Singapore-based banks as a stepping stone to greener pastures. Worse, we may see (as indeed we do, these days) locals seeking level playing fields elsewhere.

We need to hire the much needed talent whatever it costs; but let’s not mistake labels for talent.

Handling Goodbyes

Losing talent is an inevitable part of managing it. What do you do when your key quant hands in the dreaded letter? It is your worst nightmare as a manager! Once the dust settles and the panic subsides, you should ask yourself, what next?

Because of all the pull and push factors discussed so far, quant staff retention is a challenge. New job offers are becoming increasingly more irresistible. At some stage, someone you work closely with — be it your staff, your boss or a fellow team member — is going to say goodbye. Handling resignations with tact and grace is no longer merely a desirable quality, but an essential corporate skill today.

We do have some general strategies to deal with resignations. The first step is to assess the motivation behind the career choice. Is it money? If so, a counter offer is usually successful. Counter offers (both making them and taking them) are considered ineffective and in poor taste. At least, executive search firms insist that they are. But then, they would say that, wouldn’t they?

If the motivation behind the resignation is the nature of the current or future job and its challenges, a lateral movement or reassignment (possibly combined with a counter offer) can be effective. If everything fails, then it is time to bid goodbye — amicably.

It is vitally important to maintain this amicability — a fact often lost on bosses and HR departments. Understandably so because, by the time the counter offer negotiations fail, there is enough bitterness on both sides to sour the relationship. Brush those wounded feelings aside and smile through your pain, for your paths may cross again. You may rehire the same person. Or, you may end up working with him/her on the other side. Salvage whatever little you can for the sake of positive networking.

The level of amicability depends on corporate culture. Some organizations are so cordial with deserting employees that they almost encourage desertion. Others treat the traitors as the army used to — with the help of a firing squad.

Both these extremes come with their associated perils. If you are too cordial, your employees may treat your organization as a stepping stone, concentrating on acquiring only transferable skills. On the other extreme, if you develop a reputation for severe exit barriers in an attempt to discourage potential traitors, you may also find it hard to recruit top talent.

The right approach lies somewhere in between, like most good things in life. It is a cultural choice that an organization has to make. But regardless of where the balance is found, resignation is here to stay, and people will change jobs. Change, as the much overused cliché puts it, is the only constant.

Summing Up…

In a global market that demands ever more customization and structuring, there is an unbearable amount of pull factor for good quants. Quant talent management (acquisition and retention) is almost as challenging as developing quant skills yourself.

While powerless against the pull factor, banks and financial institutions should look into eliminating hidden push factors. Develop respect and appreciation for hard-to-replace talents. Invent innovative performance measurement metrics. Introduce fair and transparent compensation schemes.

When it all fails and the talent you so long to retain leaves, handle it with tact and grace. At some point in the future, you may have to hire them. Or worse, you may want to get hired by them!

Columns, Quantitative Finance, The Wilmott Magazine

Benford and Your Taxes

Nothing is certain but death and taxes, they say. On the death front, we are making some inroads with all our medical marvels, at least in postponing it if not actually avoiding it. But when it comes to taxes, we have no defense other than a bit of creativity in our tax returns.

Let’s say Uncle Sam thinks you owe him $75k. In your honest opinion, the fair figure is about the $50k mark. So you comb through your tax deductible receipts. After countless hours of hard work, fyou bring the number down to, say, $65k. As a quant, you can estimate the probability of an IRS audit. And you can put a number (an expectation value in dollars) to the pain and suffering that can result from it.

Let’s suppose that you calculate the risk of a tax audit to be about 1% and decide that it is worth the risk to get creative in you deduction claims to the tune of $15k. You send in the tax return and sit tight, smug in the knowledge that the odds of your getting audited are fairly slim. You are in for a big surprise. You will get well and truly fooled by randomness, and IRS will almost certainly want to take a closer look at your tax return.

The calculated creativity in tax returns seldom pays off. Your calculations of expected pain and suffering are never consistent with the frequency with which IRS audits you. The probability of an audit is, in fact, much higher if you try to inflate your tax deductions. You can blame Benford for this skew in probability stacked against your favor.

Skepticism

Benford presented something very counter-intuitive in his article [1] in 1938. He asked the question: What is the distribution of the first digits in any numeric, real-life data? At first glance, the answer seems obvious. All digits should have the same probability. Why would there be a preference to any one digit in random data?

figure1
Figure 1. The frequency of occurrence of the first digits in the notional amounts of financial transactions. The purple curve is the predicted distribution. Note that the slight excesses at 1 and 5 above the purple curve are expected because people tend to choose nationals like 1/5/10/50/100 million. The excess at 8 is also expected because it is considered a lucky number in Asia.

Benford showed that the first digit in a “naturally occurring” number is much more likely to be 1 rather than any other digit. In fact, each digit has a specific probability of being in the first position. The digit 1 has the highest probability; the digit 2 is about 40% less likely to be in the first position and so on. The digit 9 has the lowest probability of all; it is about 6 times less likely to be in the first position.

When I first heard of this first digit phenomenon from a well-informed colleague, I thought it was weird. I would have naively expected to see roughly same frequency of occurrence for all digits from 1 to 9. So I collected large amount of financial data, about 65000 numbers (as many as Excel would permit), and looked at the first digit. I found Benford to be absolutely right, as shown in Figure 1.

The probability of the first digit is pretty far from uniform, as Figure 1 shows. The distribution is, in fact, logarithmic. The probability of any digit d is given by log(1 + 1 / d), which is the purple curve in Figure 1.

This skewed distribution is not an anomaly in the data that I happened to look at. It is the rule in any “naturally occurring” data. It is the Benford’s law. Benford collected a large number of naturally occurring data (including population, areas of rivers, physical constants, numbers from newspaper reports and so on) and showed that this empirical law is respected.

Simulation

As a quantitative developer, I tend to simulate things on a computer with the hope that I may be able to see patterns that will help me understand the problem. The first question to be settled in the simulation is to figure out what the probability distribution of a vague quantity like “naturally occurring numbers” would be. Once I have the distribution, I can generate numbers and look at the first digits to see their frequency of occurrence.

To a mathematician or a quant, there is nothing more natural that natural logarithm. So the first candidate distribution for naturally occurring numbers is something like RV exp(RV), where RV is a uniformly distributed random variable (between zero and ten). The rationale behind this choice is an assumption that the number of digits in naturally occurring numbers is uniformly distributed between zero and an upper limit.

Indeed, you can choose other, fancier distributions for naturally occurring numbers. I tried a couple of other candidate distributions using two uniformly distributed (between zero and ten) random variables RV1 and RV2: RV1 exp(RV2) and exp(RV1+RV2). All these distributions turn out to be good guesses for naturally occurring numbers, as illustrated in Figure 2.

figure2
Figure 2. The distribution of the first digits in the simulation of “naturally occurring” numbers, compared to the prediction.

The first digits of the numbers that I generated follow Benford’s law to an uncanny degree of accuracy. Why does this happen? One good thing about computer simulation is that you can dig deeper and look at intermediate results. For instance, in our first simulation with the distribution: RV exp(RV), we can ask the question: What are the values of RV for which we get a certain first digit? The answer is shown in Figure 3a. Note that the ranges in RV that give the first digit 1 are much larger than those that give 9. About six times larger, in fact, as expected. Notice how pattern repeats itself as the simulated natural numbers “roll over” from the first digit of 9 to 1 (as an odometer tripping).

figure3a
Figure 3a. The ranges in a uniformly distributed (between 0 and 10) random variable RV that result in different first digits in RV exp(RV). Note that the first digit of 1 occurs much more frequently than the rest, as expected.

A similar trend can be seen in our fancier simulation with two random variables. The regions in their joint distributions that give rise to various first digits in RV1 exp(RV2) are shown in Figure 3b. Notice the large swathes of deep blue (corresponding to the first digit of 1) and compare their area to the red swathes (for the first digit 9).

figure3b
Figure 3b. The regions in the joint distribution of two uniformly distributed (between 0 and 10) random variables RV1 and RV2 that result in different first digits in RV1 exp(RV2).

This exercise gives me the insight I was hoping to glean from the simulation. The reason for the preponderance of smaller digits in the first position is that the distribution of naturally occurring numbers is usually a tapering one; there is usually an upper limit to the numbers, and as you get closer to the upper limit, the probably density becomes smaller and smaller. As you pass the first digit of 9 and then roll over to 1, suddenly its range becomes much bigger.

While this explanation is satisfying, the surprising fact is that it doesn’t matter how the probability of natural distributions tapers off. It is almost like the central limit theorem. Of course, this little simulation is no rigorous proof. If you are looking for a rigorous proof, you can find it in Hill’s work [3].

Fraud Detection

Although our tax evasion troubles can be attributed to Benford, the first digit phenomenon was originally described in an article by Simon Newcomb [2] in the American Journal of Mathematics in 1881. It was rediscovered by Frank Benford in 1938, to whom all the glory (or the blame, depending on which side of the fence you find yourself) went. In fact, the real culprit behind our tax woes may have been Theodore Hill. He brought the obscure law to the limelight in a series of articles in the 1990s. He even presented a statistical proof [3] for the phenomenon.

In addition to causing our personal tax troubles, Benford’s law can play a crucial role in many other fraud and irregularity checks [4]. For instance, the first digit distribution in the accounting entries of a company may reveal bouts of creativity. Employee reimbursement claims, check amounts, salary figures, grocery prices — everything is subject to Benford’s law. It can even be used to detect market manipulations because the first digits of stock prices, for instance, are supposed to follow the Benford distribution. If they don’t, we have to be wary.

Moral

figure4
Figure 4. The joint distribution of the first and second digits in a simulation, showing correlation effects.

The moral of the story is simple: Don’t get creative in your tax returns. You will get caught. You might think that you can use this Benford distribution to generate a more realistic tax deduction pattern. But this job is harder than it sounds. Although I didn’t mention it, there is a correlation between the digits. The probability of the second digit being 2, for instance, depends on what the first digit is. Look at Figure 4, which shows the correlation structure in one of my simulations.

Besides, the IRS system is likely to be far more sophisticated. For instance, they could be using an advanced data mining or pattern recognition systems such as neural networks or support vector machines. Remember that IRS has labeled data (tax returns of those who unsuccessfully tried to cheat, and those of good citizens) and they can easily train classifier programs to catch budding tax evaders. If they are not using these sophisticated pattern recognition algorithms yet, trust me, they will, after seeing this article. When it comes to taxes, randomness will always fool you because it is stacked against you.

But seriously, Benford’s law is a tool that we have to be aware of. It may come to our aid in unexpected ways when we find ourselves doubting the authenticity of all kinds of numeric data. A check based on the law is easy to implement and hard to circumvent. It is simple and fairly universal. So, let’s not try to beat Benford; let’s join him instead.

References
[1] Benford, F. “The Law of Anomalous Numbers.” Proc. Amer. Phil. Soc. 78, 551-572, 1938.
[2] Newcomb, S. “Note on the Frequency of the Use of Digits in Natural Numbers.” Amer. J. Math. 4, 39-40, 1881.
[3] Hill, T. P. “A Statistical Derivation of the Significant-Digit Law.” Stat. Sci. 10, 354-363, 1996.
[4] Nigrini, M. “I’ve Got Your Number.” J. Accountancy 187, pp. 79-83, May 1999. http://www.aicpa.org/pubs/jofa/may1999/nigrini.htm.

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Debates, Physics, SFN - Science Forums

Tsunami

The Asian Tsunami two and a half years ago unleashed tremendous amount energy on the coastal regions around the Indian ocean. What do you think would’ve have happened to this energy if there had been no water to carry it away from the earthquake? I mean, if the earthquake (of the same kind and magnitude) had taken place on land instead of the sea-bed as it did, presumably this energy would’ve been present. How would it have manifested? As a more violent earthquake? Or a longer one?

I picture the earthquake (in cross-section) as a cantilever spring being held down and then released. The spring then transfers the energy to the tsunami in the form of potential energy, as an increase in the water level. As the tsunami radiates out, it is only the potential energy that is transferred; the water doesn’t move laterally, only vertically. As it hits the coast, the potential energy is transferred into the kinetic energy of the waves hitting the coast (water moving laterally then).

Given the magnitude of the energy transferred from the epicenter, I am speculating what would’ve happened if there was no mechanism for the transfer. Any thoughts?

Columns, Quantitative Finance, The Wilmott Magazine

Quant Life in Singapore

Singapore is a tiny city-state. Despite its diminutive size, Singapore has considerable financial muscle. It has been rated the fourth most active foreign exchange trading hub, and a major wealth management center in Asia, with funds amounting to almost half a trillion dollars, according to the Monitory Authority of Singapore. This mighty financial clout has its origins in a particularly pro-business atmosphere, world class (well, better than world class, in fact) infrastructure, and the highly skilled, cosmopolitan workforce–all of which Singapore is rightfully proud of.

Among the highly skilled workforce are scattered a hundred or so typically timid and self-effacing souls with bulging foreheads and dreamy eyes behind thick glasses. They are the Singaporean quants, and this short article is their story.

Quants command enormous respect for their intellectual prowess and mathematical knowledge. With flattering epithets like “rocket scientists” or simply “the brain,” quants silently go about their jobs of validating pricing models, writing C++ programs and developing complicated spreadsheet solutions.

But knowledge is a tricky thing to have in Asia. If you are known for your expertise, it can backfire on you at times. Unless you are careful, others will take advantage of your expertise and dump their responsibilities on you. You may not mind it as long as they respect your expertise. But, they often hog the credit for your work and present their ability to evade work as people management skills. And people managers (who may not actually know much) do get better compensated. This paradox is a fact of quant life in Singapore. The admiration that quants enjoy does not always translate to riches here.

This disparity in compensation may be okay. Quants are not terribly interested in money for one logical reason–in order to make a lot of it, you have to work long hours. And if you work long hours, when do you get to spend the money? What does it profit a man to amass all the wealth in the world if he doesn’t have the time to spend it?

Besides, quants seem to play by a different set of rules. They are typically perfectionist by nature. At least, I am, when it comes to certain aspects of work. I remember once when I was writing my PhD thesis, I started the day at around nine in the morning and worked all the way past midnight with no break. No breakfast, lunch or dinner. I wasn’t doing ground-breaking research on that particular day, just trying to get a set of numbers (branching ratios, as they were called) and their associated errors consistent. Looking back at it now, I can see that one day of starvation was too steep a price to pay for the consistency.

Similar bouts of perfectionism might grip some of us from time to time, forcing us to invest inordinate amounts of work for incremental improvements, and propelling us to higher levels of glory. The frustrating thing from the quants’ perspective is when the glory gets hogged by a middle-level people manager. It does happen, time and again. The quants are then left with little more than their flattering epithets.

I’m not painting all people managers with the same unkindly stroke; not all of them have been seduced by the dark side of the force. But I know some of them who actively hone their ignorance as a weapon. They plead ignorance to pass their work on to other unsuspecting worker bees, including quants.

The best thing a quant can hope for is a fair compensation for his hard work. Money may not be important in and of itself, but what it says about you and your station in the corporate pecking order may be of interest. Empty epithets are cheap, but it when it comes to showing real appreciation, hard cash is what matters, especially in our line of work.

Besides, corporate appreciation breeds confidence and a sense of self-worth. I feel that confidence is lacking among Singaporean quants. Some of them are really among the cleverest people I have met. And I have traveled far and wide and met some very clever people indeed. (Once I was in a CERN elevator with two Nobel laureates, as I will never tire of mentioning.)

This lack of confidence, and not lack of expertise or intelligence, is the root cause behind the dearth of quality work coming out of Singapore. We seem to keep ourselves happy with fairly mundane and routine tasks of implementing models developed by superior intelligences and validating the results.

Why not take a chance and dare to be wrong? I do it all the time. For instance, I think that there is something wrong with a Basel II recipe and I am going to write an article about it. I have published a physics article in a well-respected physics journal implying, among other things, that Einstein himself may have been slightly off the mark! See for yourself at http://TheUnrealUniverse.com.

Asian quants are the ones closest to the Asian market. For structures and products specifically tailored to this market, how come we don’t develop our own pricing models? Why do we wait for the Mertons and Hulls of the world?

In our defense, may be some of the confident ones that do develop pricing models may move out of Asia. The CDO guru David Li is a case in point. But, on the whole, the intellectual contribution to modern quantitative finance looks disproportionately lopsided in favor of the West. This may change in the near future, when the brain banks in India and China open up and smell blood in this niche field of ours.

Another quality that is missing among us Singaporean parishioners is an appreciation of the big picture. Clichés like the “Big Picture” and the “Value Chain” have been overused by the afore-mentioned middle-level people managers on techies (a category of dubious distinction into which we quants also fall, to our constant chagrin) to devastating effect. Such phrases have rained terror on techies and quants and relegated them to demoralizing assignments with challenges far below their intellectual potential.

May be it is a sign of my underestimating the power of the dark side, but I feel that the big picture is something we have to pay attention to. Quants in Singapore seem to do what they are asked to do. They do it well, but they do it without questioning. We should be more aware of the implications of our work. If we recommend Monte Carlo as the pricing model for a certain option, will the risk oversight manager be in a pickle because his VaR report takes too long to run? If we suggest capping methods to renormalize divergent sensitivities of certain products due to discontinuities in their payoff functions, how will we affect the regulatory capital charges? Will our financial institute stay compliant? Quants may not be expected to know all these interconnected issues. But an awareness of such connections may add value (gasp, another managerial phrase!) to our office in the organization.

For all these reasons, we in Singapore end up importing talent. This practice opens up another can of polemic worms. Are they compensated a bit too fairly? Do we get blinded by their impressive labels, while losing sight of their real level of talent? How does the generous compensation scheme for the foreign talents affect the local talents?

But these issues may be transitory. The Indians and Chinese are waking up, not just in terms of their economies, but also by unleashing their tremendous talent pool in an increasingly globalizing labor market. They (or should I say we?) will force a rethinking of what we mean when we say talent. The trickle of talent we see now is only the tip of the iceberg. Here is an illustration of what is in store, from a BBC report citing the Royal Society of Chemistry.

China Test
National test set by Chinese education authorities for pre-entry students As shown in the figure, in square prism ABCD-A_1B_1C_1D_1,AB=AD=2, DC=2\sqrt(3), A1=\sqrt(3), AD\perp DC, AC\perp BD, and foot of perpendicular is E,

  1. Prove: BD\perp A_1C
  2. Determine the angle between the two planes A_1BD and BC_1D
  3. Determine the angle formed by lines AD and BC_1 which are in different planes.
UK Test
Diagnostic test set by an English university for first year students In diagram (not drawn to scale), angle ABC is a right angle, AB = 3m BC = 4m

  1. What is the length AC?
  2. What is the area of triangle ABC (above)?
  3. What is the tan of the angle ABC (above) as a fraction?

The end result of such demanding pre-selection criteria is beginning to show in the quality of the research papers coming out of the selected ones, both in China and India. This talent show is not limited to fundamental research; applied fields, including our niche of quantitative finance, are also getting a fair dose of this oriental medicine.

Singapore will only benefit from this regional infusion of talent. Our young nation has an equally young (professionally, that is) quant team. We will have to improve our skills and knowledge. And we will need to be more vocal and assertive before the world notices us and acknowledges us. We will get there. After all, we are from Singapore–an Asian tiger used to beating the odds.

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Debates, Physics, SFN - Science Forums

Universe – Size and Age

1 Comment

I posted this question that was bothering me when I read that they found a galaxy at about 13 billion light years away. My understanding of that statement is: At distance of 13 billion light years, there was a galaxy 13 billion years ago, so that we can see the light from it now. Wouldn’t that mean that the universe is at least 26 billion years old? It must have taken the galaxy about 13 billion years to reach where it appears to be, and the light from it must take another 13 billion years to reach us.

In answering my question, Martin and Swansont (who I assume are academic phycisists) point out my misconceptions and essentially ask me to learn more. All shall be answered when I’m assimilated, it would appear! 🙂

This debate is published as a prelude to my post on the Big Bang theory, coming up in a day or two.

Mowgli 03-26-2007 10:14 PM
Universe – Size and Age
I was reading a post in http://www.space.com/ stating that they found a galaxy at about 13 billion light years away. I am trying to figure out what that statement means. To me, it means that 13 billion years ago, this galaxy was where we see it now. Isn’t that what 13b LY away means? If so, wouldn’t that mean that the universe has to be at least 26 billion years old? I mean, the whole universe started from one singular point; how could this galaxy be where it was 13 billion years ago unless it had at least 13 billion years to get there? (Ignoring the inflationary phase for the moment…) I have heard people explain that the space itself is expanding. What the heck does that mean? Isn’t it just a fancier way of saying that the speed of light was smaller some time ago?
swansont 03-27-2007 09:10 AM
Quote:
Originally Posted by Mowgli
(Post 329204)
I mean, the whole universe started from one singular point; how could this galaxy be where it was 13 billion years ago unless it had at least 13 billion years to get there? (Ignoring the inflationary phase for the moment…)

Ignoring all the rest, how would this mean the universe is 26 billion years old?

Quote:
Originally Posted by Mowgli
(Post 329204)
I have heard people explain that the space itself is expanding. What the heck does that mean? Isn’t it just a fancier way of saying that the speed of light was smaller some time ago?

The speed of light is an inherent part of atomic structure, in the fine structure constant (alpha). If c was changing, then the patterns of atomic spectra would have to change. There hasn’t been any confirmed data that shows that alpha has changed (there has been the occasional paper claiming it, but you need someone to repeat the measurements), and the rest is all consistent with no change.
Martin 03-27-2007 11:25 AM
To confirm or reinforce what swansont said, there are speculation and some fringe or nonstandard cosmologies that involve c changing over time (or alpha changing over time), but the changing constants thing just gets more and more ruled out.I’ve been watching for over 5 years and the more people look and study evidence the LESS likely it seems that there is any change. They rule it out more and more accurately with their data.So it is probably best to ignore the “varying speed of light” cosmologies until one is thoroughly familiar with standard mainstream cosmology.You have misconceptions Mowgli

  • General Relativity (the 1915 theory) trumps Special Rel (1905)
  • They don’t actually contradict if you understand them correctly, because SR has only a very limited local applicability, like to the spaceship passing by:-)
  • Wherever GR and SR SEEM to contradict, believe GR. It is the more comprehensive theory.
  • GR does not have a speed limit on the rate that very great distances can increase. the only speed limit is on LOCAL stuff (you can’t catch up with and pass a photon)
  • So we can and DO observe stuff that is receding from us faster than c. (It’s far away, SR does not apply.)
  • This was explained in a Sci Am article I think last year
  • Google the author’s name Charles Lineweaver and Tamara Davis.
  • We know about plenty of stuff that is presently more than 14 billion LY away.
  • You need to learn some cosmology so you wont be confused by these things.
  • Also a “singularity” does not mean a single point. that is a popular mistake because the words SOUND the same.
  • A singularity can occur over an entire region, even an infinite region.

Also the “big bang” model doesn’t look like an explosion of matter whizzing away from some point. It shouldn’t be imagined like that. The best article explaining common mistakes people have is this Lineweaver and Davis thing in Sci Am. I think it was Jan or Feb 2005 but I could be a year off. Google it. Get it from your local library or find it online. Best advice I can give.
Mowgli 03-28-2007 01:30 AM
To swansont on why I thought 13 b LY implied an age of 26 b years:When you say that there is a galaxy at 13 b LY away, I understand it to mean that 13 billion years ago my time, the galaxy was at the point where I see it now (which is 13 b LY away from me). Knowing that everything started from the same point, it must have taken the galaxy at least 13 b years to get where it was 13 b years ago. So 13+13. I’m sure I must be wrong.To Martin: You are right, I need to learn quite a bit more about cosmology. But a couple of things you mentioned surprise me — how do we observe stuff that is receding from as FTL? I mean, wouldn’t the relativistic Doppler shift formula give imaginary 1+z? And the stuff beyond 14 b LY away – are they “outside” the universe?I will certainly look up and read the authors you mentioned. Thanks.
swansont 03-28-2007 03:13 AM
Quote:
Originally Posted by Mowgli
(Post 329393)
To swansont on why I thought 13 b LY implied an age of 26 b years:When you say that there is a galaxy at 13 b LY away, I understand it to mean that 13 billion years ago my time, the galaxy was at the point where I see it now (which is 13 b LY away from me). Knowing that everything started from the same point, it must have taken the galaxy at least 13 b years to get where it was 13 b years ago. So 13+13. I’m sure I must be wrong.

That would depend on how you do your calibration. Looking only at a Doppler shift and ignoring all the other factors, if you know that speed correlates with distance, you get a certain redshift and you would probably calibrate that to mean 13b LY if that was the actual distance. That light would be 13b years old.

But as Martin has pointed out, space is expanding; the cosmological redshift is different from the Doppler shift. Because the intervening space has expanded, AFAIK the light that gets to us from a galaxy 13b LY away is not as old, because it was closer when the light was emitted. I would think that all of this is taken into account in the measurements, so that when a distance is given to the galaxy, it’s the actual distance.
Martin 03-28-2007 08:54 AM
Quote:
Originally Posted by Mowgli
(Post 329393)
I will certainly look up and read the authors you mentioned.

This post has 5 or 6 links to that Sci Am article by Lineweaver and Davis

http://scienceforums.net/forum/showt…965#post142965

It is post #65 on the Astronomy links sticky thread

It turns out the article was in the March 2005 issue.

I think it’s comparatively easy to read—well written. So it should help.

When you’ve read the Sci Am article, ask more questions—your questions might be fun to try and answer:-)