Little Bets

Here is an interesting question: “How do we organize the underlying trading platform so as to achieve the following desired dynamics: a large number of little bets guided by robust models built upon imperfect data leading to many small but early and sure wins?” Notice that we are not interested in “one big win from one big bet”, nor are we concerned with perfect data that may be expensive to collect or maintain. The focus here is on building robust models that are useful for trading.

Failing quickly to learn fast: Using thought experiments (or Gedankenexperiment) driven by pre-mortems to speculate about potential antecedents for a designated consequent to counter intrinsic human biases and blind spots, as soft launches are a lot cheaper when they are simply imagined! But what about operating via Fingerspitzengefühl, or “finger-tip feeling”, based upon phenomenological awareness and tacit knowledge?

Failing forward is a well-known empirical approach of learning from mistakes and failures in order to find the way forward. It is not so much that one intentionally try to fail, but rather that one knows important discoveries will be made by being willing to be imperfect, especially at the initial stages of exploring new ideas or markets. Rough prototyping is often the method of choice for embracing the learning potential of failure, while affordable small bets are used to uncover unpredictable opportunities. The fast pace of change in a constantly evolving market highlights the value of the little bets approach, where moment-to-moment, creative opportunity-seeking can have no substitute. Working from the ground up and learning from the environment, the trading platform crafts new tactics to address the opportunities as they are discovered.

This is a whole new way of looking at the problem: one of experimentation and discovery, a creative approach to trading. Pre-conceived templates or strategies are obsolete. Two fundamental advantages of the little bets approach, according to Professor Saras Sarasvathy, are that: (i) it puts the focus on what we can afford to lose rather than make assumptions about how much we can expect to gain, and (ii) it facilitates the development of capabilities as trading opportunities are sought and discovered. In short, affordable loss and capabilities development are the bedrock foundation of the little bets approach to trading.

The Dragonfly Telephoto Array, a robotic imaging system optimized for the detection of extended ultra-low surface brightness structure. The ten Canon 400mm lenses are mounted on a common framework and are co-aligned to image simultaneously the same position on the sky, enabling removal of unwanted scattered light to reveal extremely faint galaxy structure that eludes even the largest, most advanced telescopes today. The Dragonfly "compound eye" is 10 times more sensitive and 1,000 times cheaper than the best large telescopes, and has already made a big new discovery about the structure of the universe. (Image Credit: University of Toronto/Yale University).

Dr. Carol Dweck, a professor of social psychology at Stanford University, initially developed the fixed versus growth mind-set distinction by studying how schoolchildren reacted to failure and challenges. To her surprise, she found that some students relished difficulty and challenge. Dozens of studies later, Dweck’s findings suggest that people exhibiting fixed mind-sets tend to gravitate to activities that confirm their abilities, whereas those with growth mind-sets tend to seek activities that expand their abilities. People with fixed mind-sets want to appear capable, even if that means not learning in the process. People with a growth orientation, on the other hand, are willing to take more risks since challenging experiences represent chances to grow.

We wonder if the "electronic brain" of a trading platform can be programmatically imbued with an inherent growth mind-set, anthropomorphically speaking, so as to more easily capture new opportunities for growth through experimentation, exploration and improvisation? After all, the market environment already specifies the underlying design constraints. Depending upon the time of day or the specifics of the trading calendar, one can learn a little from a lot of venues, or learn a lot from just a few venues. From this perspective, robust models that exert computational efforts probing the market for answers via little bets (i.e., which provide the foundational capabilities development and affordable loss protection) are beginning to look like a winning combination deserving of further investigation.

Perhaps the most important question that we can ask is this: What is the purpose of a trading platform? Is it to supply data and facts and to run models and strategies? Or is it to support experimentation and effortful problem-solving, facilitate growth of new trading opportunities, and nurture a capacity for continuous learning from the market? It seems that little bets could be potentially interesting as a central organizing principle for a novel trading platform that can learn and adapt quickly.

It’s a numbers game after all: How one can realize the statistical information advantage of many small wins from little bets over one big bet, and do so without incurring the infrastructure overhead of traditional high-frequency trading?

“The side that learns and adapts the fastest often prevails.”

— David Petraeus (2010)

References:

1. Sims, Peter (2011). Little Bets: How breakthrough ideas emerge from small discoveries. Free Press.
2. Maddock, Mike (2012, October 10). If You Have To Fail — And You Do — Fail Forward. Forbes. Retrieved from: http://www.forbes.com/sites/mikemaddock/2012/10/10/if-you-have-to-fail-and-you-do-fail-forward/#6a66f0e97a9a
3. Sarasvathy, Saras (2005). What Makes Entrepreneurs Entrepreneurial? Retrieved from: http://www.effectuation.org/sites/default/files/documents/what-makes-entrepreneurs-entrepreneurial-sarasvathy.pdf
4. Dyson, Freeman (2016). Doing More with Less. Edge. Retrieved from: https://www.edge.org/response-detail/26738
5. Carden, Michael J. (2010, May 7). Petraeus Describes Changes in Army Structure, Doctrine. DoD News. Retrieved from: http://archive.defense.gov/news/newsarticle.aspx?id=59063

Datasets Over Algorithms

“Content without method leads to fantasy; method without content to empty sophistry.”

— Johann Wolfgang von Goethe (“Maxims and Reflections”, 1892)

“Perhaps the most important news of our day is that datasets — not algorithms — might be the key limiting factor to development of human-level artificial intelligence,” according to Alexander Wissner-Gross in a written response to the question posed by Edge: “What do you consider the most interesting recent scientific news?”

At the dawn of the dield of artificial intelligence, two of its founders famously predicted that solving the problem of machine vision would only take a summer. We now know that they were off by half a century. Wissner-Gross began to ponder the question of: “What took the AI revolution so long?” By reviewing the timing of the most publicized AI advances over the past 30 years, he found evidence that suggests a provocative explanation: perhaps many major AI breakthroughs have actually been constrained by the availability of high-quality training datasets, and not by algorithmic advances. Here we summarize the key AI milestones:

The average elapsed time between key algorithm proposals and corresponding advances was about 18 years, whereas the average elapsed time between key dataset availabilities and corresponding advances was less than 3 years, or about 6 times faster.

If true, this hypothesis have foundational implications for future progress in AI. For example, prioritizing the cultivation of high-quality training datasets might allow an order-of-magnitude speedup in AI breakthroughs over purely algorithmic advances. After all, focusing on dataset rather than algorithm is a potentially simpler approach. “Although new algorithms receive much of the public credit for ending the last AI winter,” concluded Alexander Wissner-Gross, “the real news might be that prioritizing the cultivation of new datasets and research communities around them could be essential to extending the present AI summer.”

We wonder if algorithmic trading systems might similarly benefit from the cultivation of new datasets and research communities around them. What might that look like? How do we learn to work with imperfect data? What are the risks of trusting the data too much?

References:

1. Wissner-Gross, Alexander (2016). Datasets Over Algorithms. Edge. Retrieved from: https://www.edge.org/response-detail/26587
2. Klein, Gary (2016). Blinded by Data. Edge. Retrieved from: https://www.edge.org/response-detail/26692

Trading Places

David Swenson, who is chief investment officer at Yale University in charge of managing and investing its endowment assets, explained security selection as a tool of the investment professional: “One of the really important facts about security selection is that if you play for free, it’s a zero sum game. Because if you’re overweight on Ford and underweight on GM, there has to be some other investor, or group of investors, that are underweight on Ford or overweight on GM, because this is all relative to the market. And so, if you are overweight on Ford and underweight on GM, and somebody else is underweight on Ford and overweight on GM, but at the end of the day the amount by which the winner wins equal the amount by which the loser loses. And so it’s a zero sum game. But of course, if you take into account the fact that it costs money to play the game, it turns into a negative sum game.”

Professor Robert Shiller explained Fisher’s Theory of Interest by way of an example (i.e., Crusoe A and Crusoe B on an island): “You can see that both A and B have achieved higher utility than they did when they didn’t trade. So this is the function of a lending market. A who wants to consume a lot this period, the production point is here, and B lends this amount of consumption to A, so that A can consume a lot, A can consume this much. B, since he’s lent it to A, consumes only this much this period. But you see they are both better off. They’ve both achieved a higher indifference, a higher utility.”

So the question here is: What really happens when you “trade” with another?

• (a) Are you better off if and only if your counter-party is worse off (as in the stock trading example with Ford and GM)?
• (b) Are you both better off (as in the island economy with Crusoe A and B)?
• (c) None of the above (John Locke said “words” like “trading” get us all confused)?

Is “trading” in the “financial market” fundamentally different from trading in David Ricardo's “goods and services” market? Does Ricardo assume perfect information about the market, known to all participants? Does the concept of time even play a role in Ricardo’s model?

Is this how we trade fundamentally related yet relatively mispriced assets? All based upon differences in one’s preferences, circumstances, and predictions about the future?

Philip Maymin offered a parable that illuminates interesting aspects of financial trading. It goes as follows: A non-Jew once approached the two leading rabbis two thousand years ago. He asked the first to teach him the whole Torah while standing on one foot: in other words, quickly. The first rabbi chased him away with a stick.

The non-Jew asked the second rabbi, named Hillel. Hillel answered, and his response encoded what has come to be known as the golden rule: “What is hateful to you, do not do unto others. This is the whole Torah; the rest is commentary. No go and study.”

According to Maymin, there are three important aspects here. First, the real Golden Rule of Hillel is not what you might usually think. He does not say to treat others as you would like them to treat you. Instead, he says to refrain from treating others as you would not like them to treat you. It is the difference between a command to do good and a command to abstain from evil. It is impossible to fulfill the duty to do good; one can always do more, and the goodness itself subjectively depends on others. But it is possible to fulfill the duty to abstain from evil: one can simply not hurt others, and the harm, if done, is more objectively noticeable.

Second, Hillel’s wisdom frames all ethical knowledge and teachings around this simple principle. In this way, when details begin to confuse, as they always tend to do, one can retreat to the big picture to see how it all fits in.

Third, Hillel points out that the Golden Rule is not the end of knowledge but rather the beginning. The important thing is not what you know, but what you have yet to find out.

If Hillel were a trader today, and a non-trader were to ask him to teach him all there is about financial hacking while standing on one foot, one would imagine Hillel might answer something like this: “Accumulate risks that are hateful to others; dispose of risks that are hateful to you. That is the whole of financial hacking; the rest is commentary. No go and trade.”

References:

1. Maymin, Philip Z. (2012). Financial Hacking: Evaluate risks, price derivatives, structure trades, and build your intuition quickly and easily. World Scientific.
2. Sharpe, William F. (1993). Nuclear Financial Economics. Research Paper 1275, Stanford University. Retrieved from: http://web.stanford.edu/~wfsharpe/art/RP1275.pdf
3. Bouchaud, Jean-Philippe and Farmer, J. Doyne and Lillo, Fabrizio (2008, September 11). How Markets Slowly Digest Changes in Supply and Demand. Available at SSRN: http://ssrn.com/abstract=1266681 or http://dx.doi.org/10.2139/ssrn.1266681

Theories and Models

“There is nothing so terrible as activity without insight.”

— Johann Wolfgang von Goethe (“Maxims and Reflections”, 1892)

The world is impossible to grasp in its entirety. The human mind can focus on only a small part of its vast confusion. Models project detailed and complex world onto a smaller subspace, where regularities appear and then, in that smaller subspace, allow us to extrapolate and interpolate from the observed to the unknown. At some point, of course, the extrapolation will break down. But this strategy of reduction works very well in the physical sciences. Models in finance, by extension, use the same strategy in the hope that some of its magic would rub off nicely.

The aim of finance, like that of physics, is to find not only the relationships between the abstractions themselves, e.g., markets, money, assets, securities, but also the relationships between the realities they represent. In both physics and finance the first major struggle is to gain some intuition about how to proceed; the second struggle is to transform that intuition into something more formulaic, a set of rules anyone can follow, rules that no longer require the original insight itself. One person’s breakthrough thus becomes everybody’s possession.

The Efficient Market Hypothesis imagines price movements to be a diffusion process, i.e., a random walk. One of its origins is in the description of the drift of pollen particles through a liquid as they collide with its molecules. Einstein used the diffusion model to successfully predict the square root of the average distance the pollen particles move through the liquid as a function of temperature and time, thus lending credence to the existence of hypothetical molecules and atoms too small to be seen.

For particles of pollen, the model is also a theory, and pretty close to a true one. For stock prices, however, it is only a model. It is how we choose to imagine the the way changes in stock prices occur, not what actually happens. Models are simplifications, and simplification can be dangerous. It is naïve to imagine that the risk of every stock in the market can be condensed into just one quantity, its volatility σ. Risk has too many aspects to be accurately captured by that one number. In short, the Efficient Market Model’s price movements are too constrained and elegant to reflect the market accurately. After all, the movements of stock prices are more like the movements of humans than of molecules.

Model parameters that are implied from market prices are often easier to have an intuition about than are the market prices themselves, especially if the model is itself intuitive. For example, being told that an option has a particular price means nearly nothing, but being told that an option has a particular implied volatility gives a sense of meaning to it, something that can be pondered, something on which an opinion could be formed and a trade proposed. This is the power of model parameters. The idea is not that the model is correct, or that the assumptions can never be violated, but simply that the model is useful in explaining the risks. The parameters help the intuition.

We need models to explain what we see and to predict what will occur. We use models for envisioning the future and influencing it. The world of people is unpredictable and begs for divination as well. At every moment we face choices with uncertain outcomes. Each decision, even one made on the spur of the moment involves some imagined model for how the future may evolve and how our choices will affect it. We are always weighing the odds, estimating the relative importance of causality and chance. As time passes, possibilities narrow. Because our lifetime is finite, time, choice, risk, and reward are of the essence. Unless one can live in the perpetual present, one needs theories and models to exert some control. Theories and models are thus a kind of magic that bridges the visible and invisible worlds.

Models are analogies; they always describe one thing relative to something else. Models need a defense or an explanation. Theories, in contrast, are the real thing. The need confirmation rather than explanation. A theory describes an essence. The abstractions of mathematics are often more suitable than words for formulating theories. A successful theory can become a fact, i.e., by describing the object of its focus so accurately that the theory becomes virtually indistinguishable from the object itself. The creator of a theory is attempting to discover the invisible principles that hide behind the appearances. The role of theory is to make evident what is hidden. Unlike models, a theory doesn’t simplify. It observes the world and tries to describe the principles by which the world operates.

It takes hard work to master a model. But models splinter when you look at them closely. Theories are irreducible, the foundations on which new metaphors can be built. But a theory doesn’t have to be complete or unmodifiable. There are theories that are not exactly right, but they are not models. Theories are the thing itself; when you look closely, there isn’t anything more to see. The surface and the object, the outside and the inside, are one.

The similarity of physics and finance thus lies more in their syntax than their semantics. For example, financial modelers use a process similar to renormalization in physics to force their less than perfect, less than real models to fit the world they observe. They call this process calibration, the tuning of parameters in a model until it agrees with the observable prices of liquid securities whose values we know. But calibration in finance works much less well than renormalization in physics: in physics the normal and abnormal are governed by the same laws, whereas in markets the normal is normal only while people behave conventionally. In crises the behavior of people changes and normal models fail. While quantum electrodynamics is a genuine theory of all reality, financial models are only mediocre metaphors for a part of it. Financial models, because of their incompleteness, inevitably mask risk. When you use a model you are trying to shoehorn the real world into a container too small for it to fit perfectly.

In human affairs, history matters, and people are altered by every experience. But it’s not only the past that leaves its trace on humans. In physics, effects propagate only forward through time, and the future cannot affect the present. In the social sciences the imagined future can affect the present, and thereby the actual future, too. Despite this, the Efficient Market Model assumes that all uncertainties about the future are quantifiable. It claims that at any instant current prices reflect all current and past information, and that the best estimate of value is the current price. That’s why it is a model of a possible world rather than a theory about the one we live in.

In finance, a useful guiding principle is the Law of One Price: If you want to know the value of one financial security, your best bet is to use the known price of another security that’s as similar to it as possible. When we compare it with almost everything else in economics, the wonderful thing about this law of valuation by analogy is that it dispenses with utility functions, the undiscoverable hidden variables whose ghostly presence permeates economic theory. The Law of One Price, however, is not a consistent law of nature. It is a general reflection on the practices of fickle human beings, who, when they have enough time, resources, and information, would rather buy the cheaper of two similar securities and sell the richer, thereby bringing their prices into equilibrium. The law usually holds in the long run, in well-oiled markets with enough savvy participants. In crises, however, duress forces people to behave in what looks like irrational ways, and even in normal time there are persistent shorter- or longer-term exceptions to the law.

To use the Law of One Price that underpins financial modeling, one simply shows that a target security and its replicating portfolio have identical future payoffs under all circumstances. Most of the mathematical complexity of modeling in finance involves the description of the range of future behavior that composes all circumstances. One can easily invent more complicated models of risky stock prices that incorporate violent moves and ferocious outbursts of risk. But in using such models one gives up simplicity for a still imperfect but more complex model that doesn’t necessarily do better.

As with earthquakes, it may be wiser to ensure that one owns a portfolio that will not suffer too badly under disastrous scenarios than it is to try to estimate the probability of destruction. When models in physics fail, they fail precisely, and often expose a paradox that opens a door. When models in the social sciences fail, they fail bluntly, with no hint as to what went wrong and no clue as to what to do next. Financial models are always metaphors.

How finance is fundamentally different from  physics.

Financial modeling is not the physics of markets. Physics models begin with the current state of the world and evolve it into the future. Financial models begin with the current perception about the future and use them to move back into the present to estimate current values. And it is humans doing the perceiving. In other words, financial models don’t forecast; they simply transform one’s forecasts of the future into present value. The point of a model in finance is not the same as the point of a model in physics. In physics one wants to predict or control the future. In finance one wants to determine present value and goes about it by forming opinions about the future, about the interest rates or defaults or volatilities or housing prices that will come to pass. One uses a model to turn those opinions about the future into an estimate of the appropriate price to pay today for a security that will be exposed to that imagined future.

Overall, models are useful in finance and here are some of their major benefits: (i) models facilitate interpolation; (ii) models transform intuition into a dollar value; (iii) models are used to rank securities by value. However, to confuse a model with a theory is to believe that humans obey mathematical rules, and so to invite future disaster. Therefore, financial modelers must compromise. They must decide what small part of the financial world is of greatest current interest to them, describe its key features, and then mock up those features only. A successful financial model must have limited scope and must work with simple analogies. In the end you are trying to rank complex objects by projecting them onto a scale with only a few dimensions.

“A good model can advance fashion by ten years.”

— Yves Saint Laurent

References:

1. Derman, Emanuel (2011). Models. Behaving. Badly. Why Confusing Illusion with Reality can Lead to Disaster, on Wall Street and in Life. Free Press.
2. Derman, Emanuel (2013). The Young Person’s Guide to Pricing and Hedging. Retrieved from: http://www.emanuelderman.com/media/The_Young_Persons_Guide.pdf
3. Maymin, Philip Z. (2012). Financial Hacking: Evaluate risks, price derivatives, structure trades, and build your intuition quickly and easily. World Scientific.