kinetic energy, not supply & demand

Eighteen years later the answer from many observation posts along the byways of public discourse appears to be: yes, they most certainly do, and so do their fellow travelers, business and financial markets experts.  After all, we just barely survived the most devastating economic event of our times, deeper and more far-reaching than any downturn since the Great Depression, and all the high priests of the field can do is shake their heads and say “wow, I sure didn’t see that coming.”  Distrust of fancy math is rampant in all walks of business life.  That presents a real problem for enterprise decision-makers at a time when they need smart quantitative tools – yes, fancy math and all – more than ever.  Markets are more complex than at any time in human history.  Giant waves of transactional data inundate marketing managers with new information every day.  Managers need science to help them gain valuable insights into the markets for their products and services – but how do they know that the growing number and variety of scientific marketing tools out there aren’t infected with the nasty symptoms of physics envy?

It’s a good question, and one that any decision-maker should ask before embarking on a quantitative marketing solution.  Here are three important questions the manager should ask of any solution being offered:

(a) Is the solution inextricably wedded to a single model of how the world works? This was one of the really fatal flaws in the thinking and modeling practices of economists and financiers in the lead-up to 2008, a flaw most poignantly confessed to by the highest of the high priests of rational economics, Alan Greenspan, in his post-crash testimony to Congress.  Models are supposed to simplify the real world, but not to the point of completely misinterpreting and distorting the behaviors and practices that actually prevail in the world.  Robust quantitative models need to be flexible, adaptable and agnostic in regard to any one single theory that, like rational economics, can become more of a rigid ideology than an objective attempt to explain how the world works.

(b) Is the solution measuring the right thing? Here is where even marketing models with no ideological baggage and with the best of intentions can fall into a trap.  For the past thirty-odd years marketers have tried to define their demand environments through approaches like customer segmentation – identifying demographic segments and then marketing and pricing to the perceived “average” customer in that segment.  A similar approach is segmentation by geography, otherwise known as the “country strategy”.  “How can we optimize our profits in country X?” goes a common problem definition.  But what if the model’s independent variables are (as is often the case) limited to country and product line – answering the question above with a formulation like “sell more turbo widgets in Country X to optimize profits” when in fact the most important influencing variable is actually something else, say a macroeconomic variable like growth in per-capita GDP?  In a world where products proliferate and sales cycles become ever shorter there are numerous variables that influence demand (and hence profitability), and decision-makers need to know these variables at a very granular level – ideally at the level of each potential interaction of customer and product.

(c) Are the right tools being used to measure the right thing? A third pitfall on the road to scientific marketing excellence is the danger of using the wrong tools from the toolkit.  There is a propensity among technology vendors to say things like “our algorithm is better than our competitors’ algorithms”.  In truth there is no one right algorithm because there is no one-size-fits-all solution to anything as complex as markets where product-customer combinations number in the tens of billions.  In this environment there is no such thing as an “average” customer and there is no one single scientific formulation that will solve the problem of making decisions that optimize firmwide performance goals like profitability or market share.  Solutions need to be customized to reflect the unique and constantly evolving contours of each enterprise’s market for its goods and services.

There may be no one perfect, fail-proof screen to detect and avoid the lurking ill effects of physics envy in the market for quantitative business solutions.  But answering a few simple questions like the ones suggested here may go a long way to helping decision-makers avoid the dangers of mathematics for its own sake – and appreciate the value of what mathematical methods can do when applied in the right way for the right reasons.

Looking at the human mind this way, as a machine constantly evaluating possible outcomes based on prior knowledge and assigning probability weights to those outcomes, gave rise to the notion of the “Bayesian brain,” a term popularized in 1983 by Geoffrey Hinton of the University of Toronto and Terry Sejnowski of Johns Hopkins University.  This notion has subsequently received a good amount of validation by neuroscientists as they continue to make advances in understanding how the brain really works.  Neuroscientists Alexandre Pouget and David Knill of the University of Rochester in 2004 referred to a “growing body of evidence that human perceptual computations are ‘Bayes optimal’ (“The Bayesian brain: the role of uncertainty in neural coding and computation,” Trends in Neurosciences, vol 27 issue 12, December 2004, pp 712-719).  That’s a fancy way of saying that we make estimations based on likelihood – for example we routinely make estimations about things like the distance from us of an object, or the speed at which it is traveling, based on our prior knowledge of the shape, clarity and movement patterns of such objects and the likelihood that the present reality fits into that a priori knowledge.

So far, so good.  But there is an Achilles heel to our hierarchical mental gymnastics.  Briefly, we may be great at the kind of proposition-within-proposition reasoning that our sales rep exhibited in getting to the essence of the competitive threat posed by the wholesaler’s move to town.  But we humans are generally pretty lame when it comes to computation.  Our intuitive reasoning skills fail at the task of instantaneously calculating that 34 x 57 X 71 = 137,598.  One way that we get around this failing is through heuristics – basically, shortcuts that we use in conditions of uncertainty to help us get from information to evaluation and decision.  Take the example above of evaluating the distance a particular object might be from us.  Now, there is a physics formula we could apply to measuring distance, height, momentum (if moving) and so forth to give us the precise answer as to how far away that bicyclist in the yellow jersey is from us.  But our brains lack the ability to do spontaneous physics equations.  Even if we precisely knew one or more of the variables it would be hard to do an on-the-spot computation.  So we need something else – a proxy, a heuristic.  That something might be clarity.  Can we see the bicyclist clearly?  Can we make out the details of his black helmet with red stripes, and the ‘Elf Aquitaine’ logo on the yellow jersey?  That can give us enough information to call upon our “cyclist in a yellow jersey” neuronal connections and infer a likelihood that he is, say, 50 yards away.

The problem with heuristics is that they are subject to error: not occasional lapses in judgment but systematic, predictable biases.  For example if we use clarity as a heuristic we may overestimate the distance of that cyclist from us if there is poor visibility.  Understanding the role of heuristic errors in human judgment and decision making was one of the main contributions of Amos Tversky and Daniel Kahneman to our understanding of behavioral factors in human decision-making (“Judgment Under Uncertainty: Heuristics and Biases,” Science New Series vol 185 no. 4157 Sep 1974 pp 1124-1131).  Tversky and Kahneman documented specific heuristic errors such as representativeness (drawing broad or sweeping conclusions from a limited data set), availability (assigning the likelihood of an event based on the easiest example that comes to mind, whether or not appropriate, and anchoring (relying heavily on one piece of information when making a decision even if it is irrelevant).

Since heuristic errors are part and parcel of human judgment and decision-making under uncertainty, we have to take this reality into account when we attempt to integrate quantitative modeling methods and qualitative human judgment.  What are the best mathematical tools and frameworks to integrate these two domains?  One area in which we at Sentrana are spending considerable time is that of Bayesian hierarchical modeling. The Bayesian approach is particularly useful in marketing situations such as modeling differences in the needs and wants of customers using both generalized and conditional assumptions involving multiple variables. Bayesian frameworks provide a natural way to pool disparate sources of information. A Bayesian model requires the formulation of prior distributions and the estimation of a likelihood function, which can add complexity to the model-building process.  However we expect future insights and innovations in this area, alongside the development of more robust computation capabilities to bring more firepower to bear on this difficult but potentially valuable quantitative approach.

It’s hard enough for enterprises to locate those rare possessors of this sales magic and retain their services, but harder still to deal with the fact that in today’s choice-rich, multifaceted demand environments even those talents alone are not sufficient to achieve sales excellence.  We live in a world, after all, where there are purportedly more SKUs (stock-keeping units) on the planet than there are species of living organisms (see for example Eric Beinhocker’s excellent book “The Origin of Wealth”).  A sales representative working for a company with over 100,000 SKUs, which is the norm for large companies in fast-moving goods industries, has to deal with a dimension to the art of the deal that unfortunately has little to do with charm, wits or good grooming: he or she has to figure out on a daily basis which subset of five or six products, out of that universe of tens of thousands, to offer to customers at whatever combination of price points might stand the greatest probability of winning the business.  The computational dimensions of that notion are staggering – quite simply, they are beyond the realm of the feasible when contemplated by the unaided human brain.

Enter technology and the computational powers of quantitative methods.  That which overwhelms the human mind amounts to a few split microseconds of run time for robust data management platforms.  Revenue optimization models can sift through billions of customer-product combinations to recommend pricing configurations with relatively high probabilities of success.  Perhaps these quantitative models could replace those hard-to-find sales skills – after all, if these models can really crunch all that data and recommend prices with the highest likelihood of success, then anyone holding a BlackBerry can access the information and make the sale, right?  Not so fast.  The world may have changed a great deal from 1964, when Mayer and Greenberg produced their article, but intuition is still intuition, and it is no less a necessary ingredient for sales success today than in years past.  For all that computers can achieve, intuition and empathy are simply not things they do.

But is it possible to teach intuition?  At first blush that would seem to be a stretch.  In the minds of many the concept of quantitative methods is intertwined with that of an opaque, algorithm-powered monolith that spits out Delphic recommendations based on historical data crunched through a process unknowable and unviewable by mere mortals – what is commonly (though not always accurately) referred to as a “black box.”  The problem is that in dynamic environments like consumer goods demand markets, decision makers have to negotiate offers based on a kaleidoscope of real-time inputs that require intuitive judgment.  For example, say that you are a distributor in the food services industry and you see a news item that a national wholesaler has opened a discount distribution center in your sales territory.  How would a salesperson process and assign a value to this information?  As human beings, we are uniquely able to compose propositions out of discrete units of information and then embed those propositions within other propositions and so on, creating a hierarchical tree of a limitless number of propositions.

For example, upon reading the headline “National Wholesaler Opens Discount Distribution Center” a sales rep might begin to formulate a succession of hierarchical propositions in rapid sequence:

• wholesaler opens discount distribution center
• wholesaler who is our competitor opens discount distribution center
• wholesaler who is our competitor opens discount distribution center right down the street from our biggest client
• wholesaler who is our competitor and offers everyday low prices opens discount distribution center right down the street from our biggest client
• wholesaler who is our competitor and offers everyday low prices opens discount distribution center right down the street from our biggest client who was a tough price negotiator in our last sale

Our empathetic, capable sales rep will immediately assign a value of high importance to this information and use it to gauge the tone, tenor and negotiating position of the upcoming sales call with this client.  What if the sales rep could also “inform” the quantitative revenue optimization system about this development and have it factored into the ensuing price recommendations ahead of the sales call?

In fact that is possible in today’s environment.  Market awareness models are able to take qualitative human insights, like our sales rep’s awareness of the real-time implications of the competitive threat, and translate them into quantitative factors the models can employ, in conjunction with all the other relevant variables, to produce improved decision support recommendations.  Of course this is not a brainlessly simple exercise: we still face the challenge of translating the sales rep’s instinctual thought process into a language the machine will understand and recognize.  Nonetheless, market awareness models are one of the leading areas of development in the application of quantitative methods to marketing and sales problems.  It all comes back to that basic question posed by Mayer and Greenberg more than 40 years ago: what makes a great salesperson, and how can we best capture and deploy those skills throughout our organization?

But let’s take a different look at this apparent tight coupling of mathematics and dire outcomes. Our recent correspondence with an author who has been widely published on the subject of Wall Street’s use of mathematical models recently offered to us an interesting opinion. His point was that the problem with the models was not so much their complexity, but rather that they were models in the first place. His argument was that you can’t ever perfectly hedge model risk.  Now, I agree with that observation: a model by definition selects some aspects of reality to represent and omits others, and the choice of what to include and what to omit is subject to human error, therefore fallible and not perfectly hedgable.  But I take issue with the idea that the fault lies in the existence of the models themselves.  Models can be misused – I think that much is clear. But the notion that models are all doomed to failure obscures a deeper truth about the goals of predictive modeling; namely that you can seek either to reduce the world or truly explain it. By trying to elegantly reduce the world to as few predictor variables as possible, you are more likely to be sowing the seeds of future failure, because complexity and actual drivers of outcomes are taken out of the equations to make them more solvable (or perhaps sellable, as in the case of the Gaussian copula function that was behind Wall Street’s demise, as we discussed in a previous posting “You Can’t Punt Away the Dimensionality Curse”). Predictive modelers don’t have to go down that road, however: they can also set out with the goal not of reducing an entire system to a single neat, tractable equation, but to quantify and explain all of the relationships that dictate outcomes to the absolute fullest extent possible. Tractability and computability are things to address later in the process, through technological means, but they should not dictate the fundamental mathematical approach at the outset.

As I see it, the problem with the financial market meltdown is not that David Li published an article in the Journal of Fixed Income Securities on the Gaussian copula function, or even that in his article Li, then an analyst with JPMorganChase, identified the price of credit default swap (CDS) contracts as a seemingly elegant proxy for the mortgage market – a proxy that greatly reduced the immense complexity of modeling values and risks in this market but, as it turned out, lost a great deal of critically important information along the way.  No – the real problem was with the incremental decisions practitioners made to adopt this model wholesale, to leverage it up to 50 or more times the worth of the underlying assets, and ultimately to heedlessly employ it as a path to untold riches.  In other words it was the people who used the model, not the model itself.  It was the rating agencies who, in conferring the AAA ratings without which the securities would have never been as widely distributed as they were, assumed that housing prices would never go down.  It was the investment bankers who successfully shouted down the warnings of their internal credit risk departments so that they could sell ever higher volumes of CDOs, with ever-higher levels of leverage, in order to maximize their year-end bonuses.

You can’t fully hedge model risk – that is true.  But you can mitigate model risk through the application of robust decision-making processes.  A model did not take down Wall Street. Models do not “screw up” – they do exactly what they are supposed to do once they have their inputs. The screw-ups occur solely in our application of models to inappropriate situations or to situations which we do not fully understand. The predictions may not reflect reality outcomes as precisely as we wish, but that possibility of error needs to be accounted for by the ultimate decision makers. The output of a model should be an input in any decision process, not the entire decision process. For that reason, the emerging generation of predictive technology solutions being employed by all varieties of business seeks to marry model holism (by including ALL of the relevant variables, rather than the most computationally feasible), computational firepower, and above all, ranges of probability-based recommendations, rather than a single output. It may sound heretical at the moment given the present economic calamity, but as the world gets ever more complex, models will become more valuable to decision makers, not less. Informed, prudent decision-making in regard to those models will not be a luxury, but an absolute necessity.

In trying to answer this postulation we must go back to examine the eternal challenge of good modeling: how to create a simplified representation of reality that in ignoring many real-world features still manages to convey an inherently robust facsimile of the real thing.  For example, one of those maps of New England you buy at Exxon gas stations can serve as a good model for getting you from Hartford, CT to Boston, MA even if it ignores most of the streets and alleyways and other real-world detail that exist along the route.  In their book “Complex Adaptive Systems: An Introduction to Computational Models of Social Life” John H. Miller and Scott E. Page observe that the “ability to ignore is a crucial component of scientific progress”, using the image of a parent’s being able to respond to the incessant “why” questions of a three year old child by saying “just because”.  The trick, as the authors point out, is knowing when (and perhaps more importantly when not) to say “just because”.

While I wholeheartedly agree with that assertion I don’t think that it quite gets us to an adequate level of comfort in applying foresight to the creation of good models.  In his fascinating book “The Origin of Wealth” Eric D. Beinhocker points out that economic modeling took what many consider to be a wrong turn back in the latter years of the 19th century when leading thinkers of the day like Leon Walras and William Stanley Jevons borrowed heavily from the referential context of physics to create models for explaining economic activity, including such notable concepts as a mathematically representable state of equilibrium that continue to serve as the conceptual foundations of modern economics textbooks.  As Beinhocker elaborates, the problem with these models was that some of their fundamental assumptions – like the perfect, robot-like rationality of human beings in making economic choices – didn’t seem to simplify reality as much as contradict reality.  Thus we find ourselves in the present ruminating over the precise, mathematically elegant language of physics and the complex, evolutionary language of biology and debating whether a choice of the wrong science by the founding fathers of economics back in the 19th century led to the failure of models to adequately explain much of what is going on in the economy today and in particular the string of boom-bust upheavals that have become part and parcel of the last 20-odd years of economic activity.

I still don’t think we are there yet in getting closure on the foresight question, but we may be getting closer.  To tie in the strands of thought presented by Miller & Page and Beinhocker, when we get to those basic defining assumptions, when we decide what the model is going to ignore and what it is going to retain, when we say “just because”, that is the point where we have the chance to either build a robust foundation that can withstand the slings and arrows of a continual barrage of economic X-factors or an elegant, commercially viable sandcastle that gets washed away with the next high tide.  If we are going to apply foresight, this is where we have to apply it.

Not that applying foresight is easy, of course, and that is why at Sentrana we are engaged in a continual process of building better models by going back to the basics, asking seemingly simple questions that have complex answers, and trying to ensure that we get it right when we get to that point where it is time to say “just because”.  In our world of Scientific Micromarket Management saying “just because” at the right time can, for example, open up the vista of a complex demand environment to reveal a unique configuration of product mix opportunities at optimal pricing points.  It’s good that we are seeing a heightened level of public discourse about these issues: models may seem to be abstract notions for abstemious minds, but they have real-world economic consequences.  Getting it right has never been more important.

The fault, dear investor, lies not in the head of AIG’s Financial Products Group or members of the Bear Stearns Investment Committee or any other anthropomorphic entity: rather it was a single mathematical formula that apparently felled the pillars of global finance.  That’s the gist of a recent article in the 3.17 edition of Wired magazine entitled “Recipe for Disaster: The Formula that Killed Wall Street” by Felix Salmon.  The formula, known as a Gaussian copula function (when is the last time that term became a fixture of the public discourse?), purported to solve the mother of all securitization problems: establishing default correlation factors between the many constituents of the pools of mortgages and other credit obligations whose cash flows served as the underpinning for the complex derivative securities known as collateralized debt obligations (CDOs).  Awareness of the potential in this arcane formula helped power the CDO market to some $4.7 trillion in volume over the course of the housing bubble years of this decade.  As the Wired article explains, the explosive commercial viability of this formula can be explained by its use of a simple sleight of hand.  Rather than modeling out the default correlation implications of pools of thousands upon thousands of individual mortgage obligations – an extremely complex undertaking requiring powerful algorithms and massively robust computational processing technology – the CDO market’s Wall Street practitioners used a shortcut that appeared elegant but proved deadly: using the market price of credit default swaps (CDSs) as a proxy for the actual historical data.

What happened in essence was that the CDO market ran up against one of the most challenging of quantitative modeling problems: the dimensionality curse.  This refers to what happens in complex environments where numerous variables interact with each other and all of the resulting combinatorial possibilities influence the economic value.  The addition of an incremental variable to the pool exerts an exponential effect on the number of possible outcomes.  Think of a simple case: if you have a pool of two variables then the number of potential outcomes is four: add a third dimension (variable) to the mix and the potential outcomes expand to nine, and so on.  In an environment like pools of thousands of mortgage obligations or credit card receivables influenced by a bevy of macro- and micro-economic, behavioral, seasonal and other random factors there are literally billions of combinatorial outcomes that could affect the incidence, magnitude  and frequency of default events and hence the price of the CDOs whose economic value derives from those pools.   Getting to the right answers – and doing so with enough speed to satisfy the blistering pace of 24-7 investment markets every day – is a daunting challenge to say the least.  So when Daniel X. Li, a quantitative analyst at JPMorgan Chase, posited the use of CDS prices as a proxy for historical data in a 2000 paper published in the Journal of Fixed Income Securities, the CDO market rejoiced and basically punted away the dimensionality curse by using this shortcut.  The reasoning and the assumptions employed proved to be flawed and the disastrous results are entirely visible to the naked eye in all their graphic detail.

In quantitative methods as in life there are no free lunches.  You can’t simply punt away the dimensionality curse – you have to embrace it and try to achieve mastery over it using all the knowledge and technology tools at your disposal.  At Sentrana we deal with dimensionality curse problems every day – the demand markets for the products and services our clients sell are highly complex environments: tens of thousands of products for thousands of customers in hundreds of locations reachable by any number of marketing vehicles and sales channels.  Modeling these environments is not for the faint-hearted: but the problems are not impossible.  The computational technology does exist, as does the modeling science.  The critical ingredient is the will and determination of those who practice quantitative methods in business to forego the easy outs and stay focused on solving the real problems, however daunting.

Perhaps the field of quantitative methods needs a variation of the medical profession’s Hippocratic Oath: First of all, do no harm.  Clearly the Wall Street experiment egregiously failed that standard.  Let’s hope that the next time some arcane mathematical formula figures into the cultural Zeitgeist it will be for better, not for worse.