Category Archives: Quantitative Finance

Quantitative Finance is my professional field. I write columns for a well-known periodical in the field called The Wilmott Magazine. Here are those columns and more.

Columns, Corporate Life, Humor, Philosophy, Quantitative Finance, The Wilmott Magazine

The Ultra Rich

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Let’s first take a look at how people make money. Loads of it. Apparently, it is one of the most frequently searched phrases in Google, and the results usually attempt to separate you from your cash rather than help you make more of it.

To be fair, this column won’t give you any get-rich-quick, sure-fire schemes or strategies. What it will tell you is why and how some people make money, and hopefully uncover some new insights. You may be able to put some of these insights to work and make yourself rich – if that’s where you think your happiness lies.

By now, it is clear to most people that they cannot become filthy rich by working for somebody else. In fact, that statement is not quite accurate. CEOs and top executives all work for the shareholders of the companies that employ them, but are filthy rich. At least, some of them are. But, in general, it is true that you cannot make serious money working in a company, statistically speaking.

Working for yourself – if you are very lucky and extremely talented – you may make a bundle. When we hear the word “rich,” the people that come to mind tend to be

  1. entrepreneurs/industrialists/software moguls – like Bill Gates, Richard Branson etc.,
  2. celebrities – actors, writers etc.,
  3. investment professionals – Warren Buffet, for instance, and
  4. fraudsters of the Madoff school.

There is a common thread that runs across all these categories of rich people, and the endeavors that make them their money. It is the notion of scalability. To understand it well, let’s look at why there is a limit to how much money you can make as a professional. Let’s say you are a very successful, highly-skilled professional – say a brain surgeon. You charge $10k a surgery, of which you perform one a day. So you make about $2.5 million a year. Serious money, no doubt. How do you scale it up though? By working twice as long and charging more, may be you can make $5 million or $10 million. But there is a limit you won’t be able to go beyond.

The limit comes about because the fundamental economic transaction involves selling your time. Although your time may be highly-skilled and expensive, you have only 24 hours of it in a day to sell. That is your limit.

Now take the example of, say, John Grisham. He spends his time researching and writing his best-selling books. In that sense, he sells his time as well. But the big difference is that he sells it to many people. And the number of people he sells his product to may have an exponential dependence on its quality and, therefore, the time he spends on it.

We can see a similar pattern in software products like Windows XP, performances by artists, sports events, movies and so on. One performance or accomplishment is sold countless times. With a slight stretch of imagination, we can say that entrepreneurs are also selling their time (that they spend setting up their businesses) multiple times (to customers, clients, passengers etc.) All these money-spinners work hard to develop some kind of exponential volume-dependence on the quality of their products or the time they spend on them. This is the only way to address the scalability issue that comes about due to the paucity of time.

Investment professionals (bankers) do it too. They develop new products and ideas that they can sell to the masses. In addition, they make use of a different aspect of money that we touched upon in an earlier column. You see, money has a transactional value. It plays the role of a medium facilitating economic exchanges. In financial transactions, however, money becomes the entity that is being transacted. Financial systems essentially move money from savings and transforms it into capital. Thus money takes on an investment value, in addition to its intrinsic transactional value. This investment value is the basis of interest.

Columns, Corporate Life, Humor, Philosophy, Quantitative Finance, The Wilmott Magazine

Philosophy of Money

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Money is a strange thing. It is quite unlike any other “thing” that we know. Its value manifests itself only in a social context where we have pre-agreed conventions as to what it should be. In this sense, money is not a thing at all, but a meta-thing, which is why you are happy when your boss gives you a letter stating that you got a fat bonus even though you never actually see the physical thing. Well, if it is not physical, it is metaphysical, and we can certainly talk about the philosophy of money.

The first indication of the meta-ness of money comes from the fact that it has a value only when we assign it a value. It doesn’t possess an intrinsic value that, for instance, water does. If you are thirsty, you find that water has enormous intrinsic value. Of course, if you have money, you can buy water (or Perrier, if you want to be sophisticated), and quench your thirst.

But we may find ourselves in situations where we may not be able to buy things with money. Stranded in a desert, for instance, dying of thirst, we may not be able to buy water despite our sky-high credit limits or the hundreds of dollars we may have in our wallet. One reason for this inability of ours is obvious – we may be alone. The basic transactional value of money evaporates when we have nobody to transact with.

The second dimension of the meta-ness of money is economical. It is illustrated in the well-worn supply-and-demand principle, assuming transactional liquidity (which is a term I just cooked up to sound erudite, I confess). I mean to say, even if we have willing sellers of water in the desert, they may see that we are dying for it and jack up the price – just because we are willing and able to pay. This apparent ripping off on the part of the devious vendors of water (perfectly legal, by the way) is possible only if the commodity in question is in plentiful supply. We need commodity liquidity, as it were.

It is when the liquidity dries up that the fun begins. The last drop of water in a desert has infinite intrinsic value. This effect may look similar to the afore-mentioned supply-and-demand phenomenon, but it really is different. The intrinsic value dominates everything else, much like the strong force over short distances in particle physics. And this domination is the flipside of the law of diminishing marginal utility in economics.

The thing that looks a bit bizarre about money is that it seems to run counter to the law of diminishing marginal utility. The more money you have, the more you want it. Now, why is that? It is especially strange given its lack of intrinsic value. Great financial minds could not figure it out, but came up with pithy and memorable statements like, “Greed, for lack of a better word, is good.” Although that particular genius was only fictional, he does epitomize much of the thinking in the modern corporate and financial world. Good or bad, let’s assume that greed is an essential part of human nature and look at what we can do with it. Note that I want to do something “with” it, not “about” it – an important distinction. I, intrepid columnist that I am, want to show you how to use other people’s greed to make more money.

Photo by 401(K) 2013

Books, Quantitative Finance

Principles of Quantitative Development

[This post is a review of my forthcoming book, “Principles of Quantitative Development,” to be published by John Wiley & Sons in Feb 2010. This review is written by Shayne Fletcher, Executive Director, Nomura, and author of “Financial Modelling in Python,” and is posted here with the reviewer’s permission.]

In “Principles of Quantitative Development”, Thulasidas has offered a contribution that is somewhat unique in the literature associated with the field of Quantitative Development. In that specialised, narrow domain, technical books abound. Most such titles are concerned with the intricacies of the application of specific programming language to the problems of financial engineering or, expositions of advanced mathematics as used in the pricing models of exotic financial derivative products. Thulasidas however has taken a very different tact. Focusing instead on what he terms “the big picture”, Thulasidas offers us his insights into the role of Quantitative Development in the broader context of a bank’s “trading platform”. Armed with such insights, he shows us how an understanding of the varied usages of the trading platform can and should be used to influence and shape its design.

In the opening chapters, the book is concerned with defining what is meant by the term “trading platform”. In doing so, Thulasidas necessarily reviews the “architecture” of a bank from the point of view of a Quantitative Developer. That is, he discusses the nature and interactions of the front, middle and back offices of a bank, the different roles that professionals in each of those areas satisfy and how each of their respective needs induce a different set of requirements on the trading platform. Moving on, he reviews the nature of trades, the so-called trade “life cycle” and how different views of a trade are required as a function of the life cycle and the business role of the user.

Having established a broad understanding of the requirements for a trading platform, Thulasidas turns his attention to translating those requirements into design decisions for trading platforms. Along the way he considers such aspects of design as choice of programming languages, issues relating to scalability and extensibility, security and auditing, representations for market and trade data and a trading platform’s macro architecture whilst all the way remaining focussed on ensuring that all business needs identified in the earlier chapters are given consideration and catered for.

Going from the general to the specific, Thulasidas in later chapters introduces a flexible derivatives pricing tool (the source code for which accompanies the book). This program in itself will no doubt serve as an excellent starting point for Quantitative Development teams charged with the production of an in-house trading platform. Perhaps of even greater benefit though is Thulasidas’s critique of the pricing tool, that is, in his explanation of how the supplied program fails to meet the requirements of a complete trading platform and how the program needs to be extended in order to be considered one. In this way, the line of thought of earlier chapters is reinforced and brought sharply into focus.

Throughout the book, Thulasidas manages to convey his ideas with remarkable eloquence and lucidity. Understanding is enhanced by numerous rich graphics outlining processes and their design (both in the software and work-flow sense). The reader’s attention and interest is never lost and a great deal of entertainment is to be found in the numerous side-bars, the “Big Pictures” (in effect an enjoyable mini-series of magazine style articles in their own right).

As Thulasidas himself notes, the subject matter of his book is broad. Accordingly, the potential readership of this title is equally broad. Notably, Quantitative Developers at the beginning of their careers stand most to gain from this book. The fact is though that even the most seasoned of banking professionals would profit from its reading. Quantitative Developers, Quantitative Analysts, Traders, Risk Managers, IT professionals and their Project Managers, individuals considering switching from academia or other industries to a career in banking… Readers from each and all of these groups will find Thulasidas’s work informative and thought provoking.

Quantitative Finance, Work and Life

How to Make Money

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After my musings on God and atheism, which some may have found useless, let’s look at a supremely practical problem — how to make money. Loads of it. Apparently, it is one of the most frequently searched phrases in Google, and the results usually attempt to separate you from your cash rather than help you make more of it.

To be fair, this post won’t give you any get-rich-quick, sure-fire schemes or strategies. What it will tell you is why and how some people make money, and hopefully uncover some new insights. You may be able to put some of these insights to work and make yourself rich — if that’s where you think your happiness lies.

By now, it is clear to most people that they cannot become filthy rich by working for somebody else. In fact, that statement is not quite true. CEOs and top executives all work for the shareholders of the companies that employ them, but are filthy rich. At least, some of them are. But, in general, it is true that you cannot make serious money working in a company, statistically speaking.

Working for yourself — if you are very lucky and extremely talented — you may make a bundle. When we hear the word “rich,” the people that come to mind tend to be (a) entrepreneurs/industrialists/software moguls — like Bill Gates, Richard Branson etc., (b) celebrities — actors, writers etc., (c) investment professionals — Warren Buffet, for instance, and (d) fraudsters of the Madoff school.

There is a common thread that runs across all these categories of rich people, and the endeavors that make them their money. It is the notion of scalability. To understand it well, let’s look at why there is a limit to how much money you can make as a professional. Let’s say you are a very successful, highly-skilled professional — say a brain surgeon. You charge $10k a surgery, and perform one a day. So you make about $2.5 million a year. Serious money, no doubt. How do you scale it up though? By working twice as long and charging more, may be you can make $5 million or $10 million. But there is a limit you won’t be able to go beyond.

The limit comes about because the fundamental economic transaction involves selling your time. Although your time may be highly-skilled and expensive, you have only 24 hours in a day to sell. That is your limit.

Now take the example of, say, John Grisham. He spends his time researching and writing his best-selling books. In that sense, he sells his time as well. But the big difference is that he sells it to many people.

We can see a similar pattern in software products like Windows XP, performances by artists, sports events, movies and so on. One performance or accomplishment is sold countless times. With a slight stretch of imagination, we can say that entrepreneurs are also selling their time (that they spend setting up their businesses) multiple times (to customers, clients, passengers etc.) This is the only way to address the scalability issue that comes about due to the paucity of time.

Investment professionals (bankers) do it too. They develop new products and ideas that they can sell to the masses. In addition, they make use of a different angle that we discussed in the Philosophy of Money. They focus on the investment value of money to make oodles of it. It not so much that they take your money as deposits, lend it out as loans, and earn the spread. Those simple times are gone for good. The banks make use of the fact that investors demand the highest possible return for the lowest possible risk. Any opportunity to push this risk-reward envelope is a profit potential. When they make money for you , they demand their compensation and you are happy to pay it.

Put it that way, investment sounds like a positive concept, which it is, in our current mode of thinking. We can easily make it a negative thing by portraying the demand for the investment value of money as greed. It then follows that all of us are greedy, and that it is our greed that fuels the insane compensation packages of top-level executives. Greed also fuels fraud – ponzi and pyramid schemes.

There is a thin blurry line between the schemes that thrive on other people’s greed and confidence jobs. If you can come up with a scheme that makes money for others, and stay legal (if not moral), then you will make money. You can see that even education, traditionally considered a higher pursuit, is indeed an investment against future earnings. Viewed in that light, you will understand the correlation between the tuition fees at various schools and the salaries their graduates command.

Columns, Corporate Life, Physics, Quantitative Finance, The Wilmott Magazine

Modeling the Models

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Mathematical finance is built on a couple of assumptions. The most fundamental of them is the one on market efficiency. It states that the market prices every asset fairly, and the prices contain all the information available in the market. In other words, you cannot glean any more information by doing any research or technical analysis, or indeed any modeling. If this assumption doesn’t pan out, then the quant edifice we build on top of it will crumble. Some may even say that it did crumble in 2008.

We know that this assumption is not quite right. If it was, there wouldn’t be any transient arbitrage opportunities. But even at a more fundamental level, the assumption has shaky justification. The reason that the market is efficient is that the practitioners take advantage of every little arbitrage opportunity. In other words, the markets are efficient because they are not so efficient at some transient level.

Mark Joshi, in his well-respected book, “The Concepts and Practice of Mathematical Finance,” points out that Warren Buffet made a bundle of money by refusing to accept the assumption of market efficiency. In fact, the weak form of market efficiency comes about because there are thousands of Buffet wannabes who keep their eyes glued to the ticker tapes, waiting for that elusive mispricing to show up.

Given that the quant careers, and literally trillions of dollars, are built on the strength of this assumption, we have to ask this fundamental question. Is it wise to trust this assumption? Are there limits to it?

Let’s take an analogy from physics. I have this glass of water on my desk now. Still water, in the absence of any turbulence, has a flat surface. We all know why – gravity and surface tension and all that. But we also know that the molecules in water are in random motion, in accordance with the same Brownian process that we readily adopted in our quant world. One possible random configuration is that half the molecules move, say, to the left, and the other half to the right (so that the net momentum is zero).

If that happens, the glass on my desk will break and it will make a terrible mess. But we haven’t heard of such spontaneous messes (from someone other than our kids, that is.)

The question then is, can we accept the assumption on the predictability of the surface of water although we know that the underlying motion is irregular and random? (I am trying to make a rather contrived analogy to the assumption on market efficiency despite the transient irregularities.) The answer is a definite yes. Of course, we take the flatness of liquid surfaces for granted in everything from the useless lift-pumps and siphons of our grade school physics books all the way to dams and hydro-electric projects.

So what am I quibbling about? Why do I harp on the possibility of uncertain foundations? I have two reasons. One is the question of scale. In our example of surface flatness vs. random motion, we looked at a very large collection, where, through the central limit theorem and statistical mechanics, we expect nothing but regular behavior. If I was studying, for instance, how an individual virus propagates through the blood stream, I shouldn’t make any assumptions on the regularity in the behavior of water molecules. This matter of scale applies to quantitative finance as well. Are we operating at the right scale to ignore the shakiness of the market efficiency assumption?

The second reason for mistrusting the pricing models is a far more insidious one. Let me see if I can present it rather dramatically using my example of the tumbler of water. Suppose we make a model for the flatness of the water surface, and the tiny ripples on it as perturbations or something. Then we proceed to use this model to extract tiny amounts of energy from the ripples.

The fact that we are using the model impacts the flatness or the nature of the ripples, affecting the underlying assumptions of the model. Now, imagine that a large number of people are using the same model to extract as much energy as they can from this glass of water. My hunch is that it will create large scale oscillations, perhaps generating configurations that do indeed break the glass and make a mess. Discounting the fact that this hunch has its root more in the financial mess that spontaneously materialized rather than any solid physics argument, we can still see that large fluctuations do indeed seem to increase the energy that can be extracted. Similarly, large fluctuations (and the black swans) may indeed be a side effect of modeling.

Columns, Corporate Life, Quantitative Finance, The Wilmott Magazine, Work and Life

Group Dynamics

When researchers and academicians move to quantitative finance, they have to grapple with some culture shock. Not only does the field of finance operate at a faster pace, it also puts great emphasis on team work. It cuts wide rather than deep. Quick results that have immediate and widespread impact are better than perfect and elegant solutions that may take time to forge. We want it done quick rather than right. Academicians are just the opposite. They want to take years to mull over deep problems, often single-handedly, and come up with solutions elegant and perfect.

Coupled with this perfectionism, there is a curious tendency among academic researchers toward creating a “wow” factor with their results, as opposed to finance professionals who are quite content with the “wow” factor in their bonuses. This subtle mismatch generates interesting manifestations. Academics who make the mid-career switch to finance tend to work either alone or in small groups, trying to perfect an impressive prototype. Banking professionals, on the other hand, try to leverage on each other (at times taking credit for other people’s work) and roll out potentially incomplete solutions as early as possible. The intellectual need for a “wow” may be a factor holding back at least some quant deliverables.

Columns, Coming Soon, Corporate Life, Quantitative Finance, The Wilmott Magazine

Philosophy of Money

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Underlying all financial activity are transactions involving money. The term “transactions” means something philosophically different in economics. It stands for exchanges of goods and services. Money, in economic transactions, has only a transactional value. It plays the role of a medium facilitating the exchanges. In financial transactions, however, money becomes the entity that is being transacted. Financial systems essentially move money from savings and transforms it into capital. Thus money takes on an investment value, in addition to its intrinsic transactional value. This investment value is the basis of interest.

Given that the investment value is also measured and returned in terms of money, we get the notion of compound interest and “putting money to work.” Those who have money demand returns based on the investment risk they are willing to assume. And the role of modern financial system becomes one of balancing this risk-reward equation.

We should keep in mind that this signification of money as investment entity is indeed a philosophical choice that we have made over the past few centuries. Other choices do exist — Islamic banking springs to mind, although its practice has be diluted by the more widely held view of money as possessing an investment value. It is fascinating to study the history and philosophy of money, but it is a topic that calls for a full-length book on its own right. Understanding money at its most fundamental level may in fact enhance our productivity — which is again measured in terms of the bottom line, consistent with the philosophy of money that enjoys currency.

Columns, Corporate Life, Quantitative Finance, The Wilmott Magazine

Slippery Slopes

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

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

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

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

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Columns, Corporate Life, Quantitative Finance, The Wilmott Magazine

Profit Sharing

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

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

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

Sections

Columns, Corporate Life, Quantitative Finance, The Wilmott Magazine

Talent Retention

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

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

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

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

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