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.

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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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Columns, Corporate Life, Environment, Humor, Quantitative Finance, Science, The Wilmott Magazine, Work and Life

Talent and Intelligence

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

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

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

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

Hard Work

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

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

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

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Columns, Corporate Life, Quantitative Finance, The Wilmott Magazine

Bonus Plans of Mice and Men

Our best-laid plans often go awry. We see it all the time at a personal level — accidents (both good and bad), deaths (both of loved ones and rich uncles), births, and lotteries all conspire to reshuffle our priorities and render our plans null and void. In fact, there is nothing like a solid misfortune to get us to put things in perspective. This opportunity may be the proverbial silver lining we are constantly advised to see. What is true at a personal level holds true also at a larger scale. The industry-wide financial meltdown has imparted a philosophical clarity to our profession — a clarity that we might have been too busy to notice, but for the dire straits we are in right now.

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

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

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Corporate Life, Quantitative Finance, Work and Life

How Much is Your Time Worth?

I recently got a crazy idea. Suppose I tell you, “I will give you a ten-million-dollar job for a month. But I will have to kill you in two months.” Of course, you will have to know that I am serious. Let’s say I am an eccentric billionaire. Will you take the ten million dollars?

I am certain that most people will not take this job offer. In fact, there is a movie with Johnny Depp and Marlon Brando (IMDb tells me that it is The Brave) where Depp’s character actually takes up such an offer. Twenty-five thousand, I believe, was the price that he agreed upon for the rest of his life. For some of us, the price may be higher, but it is possible that there is a price that we will agree upon.

To me, my price is infinite — I wouldn’t trade the rest of my life for any amount of money. What does it help me to have all the money in the world if I don’t have the time to spend it? But, this stance of mine is neither consistent with what I do, nor fully devoid of hypocrisy. Hardly anything in real life is. If we say we won’t trade time for money, then how come we happily sell our time to our employers? Is it just that we don’t appreciate what we are doing? Or that our time is limited?

I guess the trade off between time and money is not straight forward. It is not a linear scale. If we have no money, then our time is worth nothing. We are willing to sell it for almost nothing. The reason is clear — it takes money to keep body and soul together. Without a bare minimum of money, there indeed is no time left to sell. As we make a bit of money, a bit more than the bare minimum, we begin to value time more. But as we make more money, we realize that we can make even more by selling more time, because the time is worth more now! This implicit vicious circle may be what is driving this crazy rat race that we see all around us.

Selling time is an interesting concept. We clearly do sell our time to those who pay us. Employees sell time to their employers. Entrepreneurs sell their time to the customers, and in deploying their businesses. But there is a fundamental difference between these two modes of selling. While employees sell their time once, businessmen sell their time multiple times. So do authors and actors. They spend a certain amount of time doing whatever they do, but the products they create (book, business, movies, Windows XP, songs etc.) are sold over and over again. That is why they can make their millions and billions while those who work for somebody else find it is very difficult to get really rich.

Environment, Work and Life

Little Materialists

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The other evening, I had a call from a headhunter. As I hung up, my six-year-old son walked in. So I asked him jokingly whether I should take another job. He asked,

“Does it mean you will get to come home earlier?”

I was mighty pleased that he liked to have me around at home, but I said,

“No, little fellow, I may have to work much longer hours. I will make a lot more money though. Do you think I should take it?”

I was certain that he would say, no, forget money, spend time at home. After all, he is quite close to me, and tries to hang out with me as much as he can. But, faced with this choice, he was quiet for a while. So I pressed him,

“Well, what do you think?”

To my dismay, he asked,

“How late?”

I decided to play along and said,

“I would probably get home only after you go to bed.”

He still seemed to hesitate. I persisted,

“Well, what do you think?”

My six-year-old said,

“If you have more money, you can buy me more stuff!”

Crestfallen as I was at this patently materialistic line of thinking (not to say anything about the blow to my parental ego), I had to get philosophical at this point. Why would a modern child value “stuff” more than his time with his parent?

I thought back about my younger days to imagine how I would have responded. I would have probably felt the same way. But then, this comparison is not quite fair. We were a lot poorer then, and my dad bringing in more money (and “stuff”) would have been nice. But lack of money has never been a reason for my not getting my kids the much sought after stuff of theirs. I could get them anything they could possibly want and then some. It is just that I have been trying to get them off “stuff” with environmental arguments. You know, with the help of Wall-E, and my threats that they will end up living in a world full of garbage. Clearly, it did not work.

May be we are not doing it right. We cannot expect our kids to do as we say, and not as we do. What is the use of telling them to value “stuff” less when we cannot stop dreaming of bigger houses and fancier cars? Perhaps the message of Wall-E loses a bit of its authenticity when played on the seventh DVD player and watched on the second big screen TV.

It is our materialism that is reflected in our kids’ priorities.

Computers, Topical, WordPress

Blank Screen after Hibernate or Sleep?

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Okay, the short answer, increase your virtual memory to more than the size of your physical memory.

Long version now. Recently, I had this problem with my PC that it wouldn’t wake up from hibernation or sleep mode properly. The PC itself would be on and churning, but the screen would switch to power save mode, staying blank. The only thing to do at that point would be to restart the computer.

Like the good netizen that I am, I trawled the Internet for a solution. But didn’t find any. Some suggested upgrading the BIOS, replacing the graphics card and so on. Then I saw this mentioned in a Linux group, saying that the size of the swap file should be more than the physical memory, and decided to try it on my Windows XP machine. And it solved the problem!

So the solution to this issue of blank screen after waking up is to set the size of the virtual memory to something larger than the memory in your system. If you need more information, here is how, in step-by-step form. These instructions apply to a Windows XP machine.

  1. Right-click on “My Computer” and hit “Properties.”
  2. Take a look at the RAM size, and click on the “Advanced” tab.
  3. Click on the “Setting” button under the “Performance” group box.
  4. In the “Performance Options” window that comes up, select the “Advanced” tab.
  5. In the “Virtual Memory” group box near the bottom, click on the “Change” button.
  6. In the “Virtual Memory” window that pops up, set the “Custom Size” to something more than your RAM size (that you saw in step 2). You can set it on any hard disk partition that you have, but if you are going through all these instructions, chances are you have only “C:”. In my case, I chose to put it on “M:”.
Life and Death

Gurus of a Disturbing Kind

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Perhaps it has got something to do with my commie roots, but I am a skeptic, especially when it comes to the “godmen” of India. I cannot understand how they can inspire such blind belief. Where the believers see miracles, I see sleight of hand. When they hear pearls of wisdom, I can hear only gibberish. And when the new age masters claim to be in deep meditation, I cannot help but suspect that they are just dozing off.

Although my skepticism renders me susceptible to seeing the darker side of these modern day saints, I do have a counterbalancing respect for our heritage and culture, and the associated wisdom and knowledge. It is always with thrill of awe and pride that I listen to Swami Vivekananda’s century-old Chicago speeches, for instance.

The speeches of the modern yogis, on the other hand, fill me with bewilderment and amused confusion. And when I hear of their billion dollar stashes, bevies of Rolls-Royces, and claims of divinity, I balk. When I see the yogis and their entourage jet-setting in first class to exotic holiday destinations with the money extracted in the name of thinly disguised charities, I feel a bit outraged. Still, I am all for live-and-let-live. If there are willing suckers eager to part with their dough and sponsor their guru’s lifestyle, it is their lookout. After all, there are those who financed Madoffs and Stanfords of the greedy era we live in, where fraud is a sin only when discovered.

Now I wonder if it is time that the skeptics among us started speaking out. I feel that the spiritual frauds are of a particularly disturbing kind. Whether we see it that way or not, we are all trying to find a purpose and meaning to our existence on this planet through our various pursuits. We may find the elusive purpose in fame, glory, money, charity, philanthropy, knowledge, wisdom and in any of the hundreds of paths. All these pursuits have their associated perils of excess. If you get greedy, for instance, there is always a Madoff waiting in the wings to rip you off. If you become too charitable, there are other characters eager to separate you from your money, as my Singaporean readers will understand.

Of all these pursuits, spirituality is of a special kind; it is a shortcut. It gives you a direct path to a sense of belonging, and a higher purpose right away. Smelling blood in the carefully cultivated need for spirituality (whatever spirituality means), the yogis and maharishis of our time have started packaging and selling instant nirvana in neat three or five day courses that fit your schedule, while demanding vast sums of “not-for-profit” money. Even this duplicity would be fine by me. Who am I to sit in judgment of people throwing money at their inner needs, and gurus picking it up? But, of late, I am beginning to feel that I should try to spread a bit of rationality around.

I decided to come of out my passive mode for two reasons. One is that the gurus engage their victims in their subtle multi-level marketing schemes, ensnaring more victims. A pupil today is a teacher tomorrow, fueling an explosive growth of self-serving organizations. The second reason is that the gurus demand that the followers donate their time. I think the victims do not appreciate the enormity of this unfair demand. You see, you have only a limited time to live, to do whatever it is that you think will lead to fulfillment. Don’t spend it on wrong pursuits because there is always something that you are sacrificing in the process, be it your quality time with your loved ones, opportunity to learn or travel, or enjoy life or whatever. Time is a scarce resource, and you have to spend it wisely, or you will regret it more than anything else in life.

So don’t be blind. Don’t mistake group dynamics for salvation. Or charisma for integrity. Or obscurity for wisdom. If you do, the latter day gurus, masters of manipulation that they are, will take you for a ride. A long and unpleasant one.

Photo by jeffreyw cc

Quantitative Finance, The Wilmott Magazine

A New Kind of Binomial Tree

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We can port even more complicated problems from mathematics directly to a functional language. For an example closer to home, let us consider a binomial pricing model, illustrating that the ease and elegance with which Haskell handles factorial do indeed extend to real-life quantitative finance problems as well.

The binomial tree pricing model works by assuming that the price of an underlying asset can only move up or down by constant factors u and d during a small time interval \delta t. Stringing together many such time intervals, we make up the expiration time of the derivative instrument we are trying to price. The derivative defined as a function of the price of the underlying at any point in time.

Figure 1
Figure 1. Binomial tree pricing model. On the X axis, labeled i, we have the time steps. The Y axis represents the price of the underlying, labeled j. The only difference from the standard binomial tree is that we have let j be both positive and negative, which is mathematically natural, and hence simplifies the notation in a functional language.

We can visualize the binomial tree as shown in Fig. 1. At time t = 0, we have the asset price S(0) = S_0. At t = \delta t (with the maturity T = N\delta t). we have two possible asset values S_0 u and S_0 d = S_0 / u, where we have chosen d = 1/u. In general, at time i\delta t, at the asset price node level j, we have

S_{ij} = S_0 u^j

By choosing the sizes of the up and down price movements the same, we have created a recombinant binomial tree, which is why we have only 2i+1 price nodes at any time step i\delta t. In order to price the derivative, we have to assign risk-neutral probabilities to the up and down price movements. The risk-neutral probability for an upward movement of u is denoted by p. With these notations, we can write down the fair value of an American call option (of expiry T, underlying asset price S_0, strike price K, risk free interest rate r, asset price volatility \sigma and number of time steps in the binomial tree N) using the binomial tree pricing model as follows:

\textrm{OptionPrice}(T, S_0, K, r, \sigma, N) = f_{00}

where f_{ij} denotes the fair value of the option at any the node i in time and j in price (referring to Fig. 1).

f_{ij} = \left{\begin{array}{ll}\textrm{Max}(S_{ij} - K, 0) & \textrm{if } i = N \\textrm{Max}(S_{ij} - 0, e^{-\delta tr}\left(p f_{i+1, j+1} + (1-p) f_{i+1, j-1}\right)) & \textrm {otherwise}\end{array}\right

At maturity, i = N and i\delta t = T, where we exercise the option if it is in the money, which is what the first Max function denotes. The last term in the express above represents the risk neutral backward propagation of the option price from the time layer at (i+1)\delta t to i\delta t. At each node, if the option price is less than the intrinsic value, we exercise the option, which is the second Max function.

The common choice for the upward price movement depends on the volatility of the underlying asset. u = e^{\sigma\sqrt{\delta t}} and the downward movement is chosen to be the same d = 1/u to ensure that we have a recombinant tree. For risk neutrality, we have the probability defined as:

p = \frac{ e^{r\delta t} - d}{u - d}

For the purpose of illustrating how it translates to the functional programming language of Haskell, let us put all these equations together once more.

\textrm{OptionPrice}(T, S_0, K, r, \sigma, N) = f_{00}
where
&f_{ij} =& \left\{\begin{array}{ll}\textrm{Max}(S_{ij} - K, 0) & \textrm{if } i = N \\\textrm{Max}(S_{ij} - 0, e^{-\delta tr}\left(p f_{i+1\, j+1} + (1-p) f_{i+1\, j-1}\right)\quad \quad& \textrm{otherwise}\end{array}\right.
S_{ij} = S_0 u^j
u = e^{\sigma\sqrt{\delta t}}
d = 1/u
\delta t = T/N
p = \frac{ e^{r\delta t} - d}{u - d}

Now, let us look at the code in Haskell.

optionPrice t s0 k r sigma n = f 0 0
    where
      f i j =
          if i == n
          then max ((s i j) - k) 0
          else max ((s i j) - k)
                    (exp(-r*dt) * (p * f(i+1)(j+1) +
                    (1-p) * f(i+1)(j-1)))
      s i j = s0 * u**j
      u = exp(sigma * sqrt dt)
      d = 1 / u
      dt = t / n
      p = (exp(r*dt)-d) / (u-d)

As we can see, it is a near-verbatim rendition of the mathematical statements, nothing more. This code snippet actually runs as it is, and produces the result.

*Main> optionPrice 1 100 110 0.05 0.3 20
10.10369526959085

Looking at the remarkable similarity between the mathematical equations and the code in Haskell, we can understand why mathematicians love the idea of functional programming. This particular implementation of the binomial pricing model may not be the most computationally efficient, but it certainly is one of great elegance and brevity.

While a functional programming language may not be appropriate for a full-fledged implementation of a trading platform, many of its underlying principles, such as type abstractions and strict purity, may prove invaluable in programs we use in quantitative finance where heavy mathematics and number crunching are involved. The mathematical rigor enables us to employ complex functional manipulations at the program level. The religious adherence to the notion of statelessness in functional programming has another great benefit. It helps in parallel and grid enabling the computations with almost no extra work.

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