Category Archives: The Wilmott Magazine

My published (or soon to be published) column pieces in The Wilmott Magazine

Ambition vs. Greed

Growing up in a place like India, I was told early in life that ambition was a bad thing to have. It had a negative connotation closer to greed than drive in its meaning. I suspect this connotation was rather universal at some point in time. Why else would Mark Anthony harp on Brutus calling Caesar ambitious?

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

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

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

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

Chaos and Uncertainty

The last couple of months in finance industry can be summarized in two words — chaos and uncertainty. The aptness of this laconic description is all too evident. The sub-prime crisis where everybody lost, the dizzying commodity price movements, the pink slip syndrome, the spectacular bank busts and the gargantuan bail-outs all vouch for it.

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

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

Symmetries and Patterns

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

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

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

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

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

Chaos Everywhere

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

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

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

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

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

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

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

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

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

Uncertainty Principle in Quantitative Finance

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

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

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

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

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

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

Summing up…

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

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

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

Box: Heisenberg’s Uncertainty Principle

Where does this famous principle come from? It is considered a question beyond the realms of physics. Before we can ask the question, we have to examine what the principle really says. Here are a few possible interpretations:

• Position and momentum of a particle are intrinsically interconnected. As we measure the momentum more accurately, the particle kind of “spreads out,” as George Gamow’s character, Mr. Tompkins, puts it. In other words, it is just one of those things; the way the world works.
• When we measure the position, we disturb the momentum. Our measurement probes are “too fat,” as it were. As we increase the position accuracy (by shining light of shorter wavelengths, for instance), we disturb the momentum more and more (because shorter wavelength light has higher energy/momentum).
• Closely related to this interpretation is a view that the uncertainty principle is a perceptual limit.
• We can also think of the uncertainly principle as a cognitive limit if we consider that a future theory might surpass such limits.

The first view is currently popular and is related to the so-called Copenhagen interpretation of quantum mechanics. Let’s ignore it for it is not too open to discussions.

The second interpretation is generally understood as an experimental difficulty. But if the notion of the experimental setup is expanded to include the inevitable human observer, we arrive at the third view of perceptual limitation. In this view, it is actually possible to “derive” the uncertainty principle, based on how human perception works.

Let’s assume that we are using a beam of light of wavelength $lambda$ to observe the particle. The precision in the position we can hope to achieve is of the order of $lambda$. In other words, $Delta x approx lambda$. In quantum mechanics, the momentum of each photon in the light beam is inversely proportional to the wavelength. At least one photon is reflected by the particle so that we can see it. So, by the classical conservation law, the momentum of the particle has to change by at least this amount($approx constant/lambda$) from what it was before the measurement. Thus, through perceptual arguments, we get something similar to the Heisenberg uncertainty principle

$Delta x.Delta p approx constant$

We can make this argument more rigorous, and get an estimate of the value of the constant. The resolution of a microscope is given by the empirical formula $0.61lambda/NA$, where $NA$ is the numerical aperture, which has a maximum value of one. Thus, the best spatial resolution is $0.61lambda$. Each photon in the light beam has a momentum $2pihbar/lambda$, which is the uncertainty in the particle momentum. So we get $Delta x.Delta p approx 4hbar$, approximately an order of magnitude bigger than the quantum mechanical limit.

Through more rigorous statistical arguments, related to the spatial resolution and the expected momentum transferred, it may possible to derive the Heisenberg uncertainty principle through this line of reasoning.

If we consider the philosophical view that our reality is a cognitive model of our perceptual stimuli (which is the only view that makes sense to me), my fourth interpretation of the uncertainty principle being a cognitive limitation also holds a bit of water.

 About the Author The author is a scientist from the European Organization for Nuclear Research (CERN), who currently works as a senior quantitative professional at Standard Chartered in Singapore. More information about the author can be found at his blog: http//www.Thulasidas.com. The views expressed in this column are only his personal views, which have not been influenced by considerations of the firm’s business or client relationships.

Commodity Prices — Who’s Holding the Cards?

Economists have too many hands. On the one hand, they may declare something good. On the other hand, they may say, “Well, not so much.” Some of them may have even a third or fourth hand. My ex-boss, an economist himself, once remarked that he wished he could chop off some of these hands.

In the last couple of months, I plunged right into an ocean of economist hands as I sat down to do a minor research into this troubling phenomenon of skyrocketing food and commodity prices.

The first “hand” pointed out that the demand for food (and energy and commodities in general) has surged due to the increase in the population and changing consumption patterns in the emerging giants of Asia. The well-known demand and supply paradigm explains the price surge, it would seem. Is it as simple as that?

On the other hand, more and more food crops are being diverted into bio-fuel production. Is the bio-fuel demand the root cause? Bio-fuels are attractive because of the astronomical crude oil prices, which drive up the prices of everything. Is the recent OPEC windfall driving the price increases? What about the food subsidies in wealthy nations that skew the market in their favour?

Supply Side Difficulties

When explaining the food prices, one economic opinion puts the blame squarely on the supply side. It points an unwavering finger at the poor weather in food producing countries, and the panic measures imposed on the supply chain, such as export bans and smaller scale hoarding, that drive up the prices.

Looking at the bigger picture, let’s study oil as a proxy commodity and study its dynamics. Because of its effect on the rest of the economy, oil is indeed a good proxy.

In the case of oil, the dearth on the supply side is more structural, it is argued. The production capacity has stagnated over the last thirty years or so [1]. No infrastructural improvements have been made after the seventies. Indeed, new methodological improvements are expensive for all the easy methods have been fully exploited; all the low-hanging fruits have been picked, as it were.

The harder-to-reach “fruits” include deep sea explorations, crude oil from sand and, somewhat more tenuously, bio-fuels. The economic viability of these sources of oil depends on the oil price. Oil from sand, for instance, has an operating cost in the range of $20 to$25, as Shell’s CFO, Peter Voser is quoted as stating [2]. At $100 a barrel, oil from sand clearly becomes an economically viable source. Bio-fuels also are viable at high oil prices. The huge investments involved in exploiting these new sources and their unpredictable economic viability exert strong upward pressure on oil prices, purely from the supply side, regardless of the demand situation. Once you invest a huge amount banking on a sustained high oil price, and then find that the oil market has softened below your viability level, you have to write off the investment, forcing losses and consequent price hikes. With the high level of oil prices, investments are moving into infrastructure enhancements that will eventually ease the supply side crunch. But these fixes are slow in coming and are not going to ease the current dearth for about a decade. In other words, the high prices are here to stay. At least, so say the economists subscribing this supply side explanation of things. Demand Spike Although I personally find it hard to believe, people assure me that the exponential demand explosion in the emerging economies was completely unforeseen. My friend from a leading investment bank (who used to head their hybrids desk) told me that there was no way they could have anticipated this level of demand. I should probably shelve my scepticism and believe those in the know. One thing I do know from personal experience is that the dynamics of a demand crash is different in emerging economies for a variety of reasons. First of all, identical movements in fuel prices have different impact in the overall spending pattern depending on the proportion they represent in the purchasing power of an average consumer. A 30% increase in the pump price, for instance, might mean a 5% reduction in the purchasing power to a US consumer, while it might mean 20% reduction for an Indian customer. Besides, retail fuel prices in India are regulated and supported by government subsidies. Subsidies act as levies delaying the impact crude oil price movements. But when the crude oil prices rise beyond a certain point, the subsidies become untenable and the retail fuel prices surge upward, ushering in instant demand crash. I came across another view of the skyrocketing oil prices in terms of the Middle-Eastern and American politics. The view was that the Saudi oil capacity is going to increase by about 10% soon and the prices will drop dramatically in the first quarter of 2009. It was argued that the drop will come as boost to the new American president, and the whole show is timed and stage-managed with a clear political motivation. Speculation All these different opinions make my head spin. In my untrained view, I always suspected that the speculation in commodities market might be the primary factor driving the prices up. I felt vindicated in my suspicions when I read a recent US senate testimony where a well-known hedge fund manager, Michael Masters [3], shed light on the financial labyrinth of futures transactions and regulatory loopholes through which enormous profits were generated in commodity speculation. Since speculation is my preferred explanation for the energy and indeed other commodity price movements, I will go over some of the arguments in some detail. I hasten to state that the ideas express in this article are my own personal views (and perhaps those of Michael Masters [3] as well). They do not represent the market views of my employer, their affiliates, the Wilmott Magazine, or anybody else. Besides, some of these views are fairly half-baked and quite likely to be wrong, in which case I reserve the right to disown them and bequeath them to a friend of a friend. (Also, see the box on Biased Opinions). Masters points out that there is no real supply crunch. Unlike the Arab Oil Embargo time in 1973, there are no long lines at the gas pump. Food supplies are also healthy. So some new mechanism must be at work that drives up the commodity demand despite the price level. Masters blames the institutional investors (pension funds, sovereign wealth funds, university endowments etc.) for the unreasonable demand on commodity futures. Since futures prices are the benchmark for actual physical commodities, this hoarding of the futures contracts immediately reflects in the physical spot prices and in the real economy. And as the prices climb, the investors smell blood and invest more heavily, stoking a deadly vicious cycle. Masters points out that the speculative position in petroleum is roughly the same as the increase in demand from China, debunking the popular notion that it is the demand spike from the emerging giants of Asia that is driving the oil price. Similarly, bio-fuel is not the driver in food prices — the speculators have stockpiled enough corn futures to power the entire US ethanol industry for a year. Although quants are not terribly interested in the transient economic drivers of market dynamics or trading psychology, here is an interesting thought from Mike Master’s testimony. A typical commodity trader initiating a new trade is pretty much insensitive to the price of the underlying. He has, say, a billion dollars to “put to work,” and doesn’t care if the position he ends up holding has five million or ten million barrels of oil. He never intends to take delivery. This price-insensitivity amplifies his impact on the market, and the investor appetite for commodities increases as the prices go up. Most trading positions are directional views, not merely on the spot price, but on volatility. In a world of long and short Vega positions, we cannot expect to get a full picture of trading pressures exerted on oil prices by studying the single dimension of spot. Is there a correlation between the oil prices and its price volatility?  Figure 1. Scatter-plot of WTI Spot prices in Dollar and its volatility. Although the plot shows random clusters at low spot levels, at price >$75 (highlighted in the purple box), there appears to be a structure with significant correlation.

Figure 1 shows a scatter plot of the WTI spot price vs. the annualized volatility from publicly available WTI spot prices data [4]. Note than my definition of volatility may be different from yours [5]. At first glance, there appears to be little correlation between the spot price and volatility. Indeed the computed correlation over all the data is about -0.3.

However, the highlighted part of the figure tells a different story. As the spot price climbed over $75 per barrel, the volatility started showing a remarkable correlation (of 0.7) with it. Was the trading activity responsible for the concerted move on both prices and volatility? That is my theory, and Michael Masters may agree. Hidden Currency Theory Here is a dangerous thought — could it be that traders are pricing oil in a currency other than the once mighty dollar? This thought is dangerous because international armed conflicts may have arisen out of precisely such ideas. But an intrepid columnist is expected to have a high level of controversy affinity, so here goes… We keep hearing that the oil price is down on the back of a strong dollar. There is little doubt that the oil prices are highly correlated to the strength of the dollar in 2007 and 2008, as shown in Table 1. Let’s look at the oil prices in Euro, the challenging heavy-weight currency.  Figure 2. Time evolution of the WTI spot price in Dollar and Euro. The Euro price looks more stable. At first sight, Figure 2 does appear to show that the price is more stable when viewed in Euro, as expected. But does it mean that the traders are secretly pricing their positions in Euro, while quoting in Dollar? Or is it just the natural tandem movement of the Euro and WTI spots? If the hidden currency theory is to hold water, I would expect stability in the price levels when priced in that currency. But, more directly, I would naively expect less volatility when the price is expressed in the hidden currency.  Figure 3. WTI Volatilities measured in Dollar and Euro. They are nearly identical.  Figure 4. Scatter-plot of WTI volatilities in Dollar and Euro. The excess population above the dividing line of equal volatilities implies that the WTI spot is more volatile when measured in Euro. Figure 3 shows the WTI volatilities in Dollar and Euro. They look pretty much identical, which is why I replotted them as a scatter-plot of one against the other in Figure 4. If the Dollar volatility is higher, we will find more points below the red line, which we don’t. So it should mean that the hidden currency theory is probably wrong [6]. A good thing too, for nobody would be tempted to bomb me back to the stone ages now. Human Costs The real reasons behind the food and commodity price crisis are likely to be a combination of all these economic factors. But the crisis itself is a silent tsunami sweeping the world, as the UN World Food Program puts it. Increase in the food prices, though unpleasant, is not such a big deal for a large number of us. With our first world income, most of us spend about 20% of our salary on food. If it becomes 30% as a result of a 50% increase in the prices, we certainly won’t like it, but we won’t suffer that much. We may have to cut down on the taxi rides, or fine-dining, but it is not the end of our world. If we are in the top 10% income bracket (as the readers of this magazine tend to be), we may not even notice the increase. The impact of the high food prices on our lifestyle will be minimal — say, a business-class holiday instead of a first-class one. It is a different story near the bottom. If we earn less than$1000 a month, and we are forced to spend $750 instead of$500 on food, it may mean a choice between a bus ride and legging it. At that level, the increase in food prices does hurt us, and our choices become grim.

But there are people in this world who face a much harsher reality as the prices shoot up with no end in sight. Their choices are often as terrible as Sophie’s Choice. Which child goes to sleep hungry tonight? Medicine for the sick one or food for the rest?

We are all powerless against the juggernaut of market forces creating the food crisis. Although we cannot realistically change the course of this silent tsunami, let’s at least try not to exacerbate the situation through waste. Buy only what you will use, and use only what you need to. Even if we cannot help those who will invariably go hungry, let’s not insult them by throwing away what they will die yearning for. Hunger is a terrible thing. If you don’t believe me, try fasting for a day. Well, try it even if you do — for it may help someone somewhere.

Conclusions

Commodity speculation by institutional investors is one of the driving factors of this silent tsunami of rising food prices. Their trading strategies have been compared to virtual hoarding in the futures market, driving up real prices of physical commodities and profiting from it.

I don’t mean to portray institutional investors and commodity traders as criminal masterminds hiding behind their multiple monitors and hatching plots to swindle the world. The ones I have discussed with do agree on the need to curtail the potential abuse of the system by closing the regulatory loopholes and setting new accountability frameworks. However, we are still on the rising edge of this influx of institutional funds into this lucrative asset class. Perhaps the time is not ripe enough for robust regulations yet. Let us make a bit more money first!

Reference and Endnotes

[1] Jeffrey Currie et al. “The Revenge of the Old ‘Political’ Economy” Commodities (Goldman Sachs Commodities Research), March 14, 2008.
[2] Business Times, “Shell counts rising cost of squeezing oil from sand in Canada,” March 18, 2008. http://business.timesonline.co.uk/tol/business/article3572646.ece
[3] Testimony of Michael W. Masters (Managing Member / Portfolio Manager, Masters Capital Management, LLC) before the Committee on Homeland Security and Governmental Affairs. May 20, 2008. http://hsgac.senate.gov/public/_files/052008Masters.pdf
[4] Cushing, OK WTI Spot Price FOB (Dollars per Barrel) Data source: Energy Information Administration. http://tonto.eia.doe.gov/dnav/pet/hist/rwtcd.htm
[5] I define the WTI volatility on a particular day as the standard deviation of the spot price returns over 31 days around that day, annualized by the appropriate factor. Using standard notations, the volatility on a day t is defined as:
$sigma (t) = sqrt {frac{1}{{31}}sumlimits_{t - 15}^{t + 15} {left( {ln left[ {frac{{S(t)}}{{S(t - 1)}}} right] - mu } right)^2 frac{{252}}{{31}}} }$
[6] Given that the correlation between EUR/USD and WTI Spot is positive (in 2007 and 2008), the volatility, when measured in Euro, is expected to be smaller than the volatility in Dollar. The expected difference is tiny (about 0.3% absolute) because the EUR/USD volatility (defined as in [5]) is about 2%. The reason for the counter-intuitive finding in Figure 4 is probably in my definition of the volatility as in [5].
[7] Monwhea Jeng, “A selected history of expectation bias in physics,” American Journal of Physics, July 2006, Volume 74, Issue 7, pp. 578-583. http://arxiv.org/pdf/physics/0508199

 Box: Biased Opinions As an ex-experimental physicist, I am well aware of the effect of bias. Once you have a favoured view, you can never be free of bias. It is not that you actively misrepresent the data to push your view. But you tend to critically analyze the data points that do not match your view, and tend to be lenient on the ones that do. For instance, suppose I do an experiment to measure a quantity that Richard Feynman predicted to be, say, 1.37. I repeat the experiment three times and get values 1.34, 1.30 and 1.21. The right thing to do is to report a measurement of 1.29 with an error of 0.06. But, knowing the Feynman prediction (and, more importantly, knowing who Feynman is), I would take a hard look at the 1.21 trial. If I find anything wrong with it (which I will, because no experiment is perfect), I might repeat it and possibly get a number closer to 1.37. It is biases of this kind that physicists try very hard to avoid. See [7] for an interesting study on biases in physics. In this column, I do have a favoured view — that the main driver of the commodity price inflation is speculation. In order to avoid pushing my view and shaping my readers’ opinion, I state clearly that there is a potential of bias in this column. The view that I have chosen to favour has no special reason for being right. It is just one of the many “hands” popular among economists.
 About the Author The author is a scientist from the European Organization for Nuclear Research (CERN), who currently works as a senior quantitative developer at Standard Chartered in Singapore. The views expressed in this column are only his personal views, which have not been influenced by considerations of the firm’s business or client relationships. More information about the author can be found at his web site: http://www.Thulasidas.com.

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.

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.

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.

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 clichÃ© 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!

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?

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.

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).

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).

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

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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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. ClichÃ©s 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.

 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 $E$, Prove: $BD\perp A_1C$ Determine the angle between the two planes $A_1BD$ and $BC_1D$ Determine the angle formed by lines $AD$ and $BC_1$ which are in different planes.
 Diagnostic test set by an English university for first year students In diagram (not drawn to scale), angle $ABC$ is a right angle, $AB = 3m$ $BC = 4m$ What is the length $AC$? What is the area of triangle $ABC$ (above)? 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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