Olay, Nivea, Neutrogena and L’Oreal are all established beauty products brands with a broad array of medium-priced product lines and multiple product offerings in each.  More to the point, for purposes of this thought exercise of mine, is that each of them offers a range of good quality facial cleansers, a product I buy on average about once every two months.  The exercise was to determine what, if any, brand loyalty existed in my facial cleanser purchases over the last 2 years.  The answer appeared to be: none.  Nada.  At some point over those past 24 months and (give or take) 12 purchases, my domestic shelf space has been occupied by at least one representative facial cleanser SKU from each of those brands.  I wondered why this was the case.  And then I remembered that it was not always thus.  Long ago (more years than I care to disclose) there was a rather splendid product by Neutrogena called the Facial Cleansing Bar.

a simpler time for consumers

It was a large amber, translucent bar of pure goodness, I thought at the time, and for many years it was the only thing that would ever come to mind in association with facial cleansing. That product still exists, but the last time I bought a bar was back in an era when folks were marveling over the newfound wonders of that thing called email… I wondered: what had happened along this journey from the devoted, faithful me of old to this fickle consumer circa 2010?  What could any one of these companies do to win back my loyalty, and presumably that of many others like me?

Brand success depends on both walletshare and mindshare. If a brand manager wants to get to my wallet then he or she has to first get to my mind and convince me why, out of all the marketing messages that assault me with mind-numbing regularity throughout the changing venues and vistas of my daily routine, this is the one that is most worthy of my time and money.  The problem is that our economy is awash in multiple products, multiple messaging formats and multiple physical & digital marketing channels.  More brands than ever before vie for our attention and our dollars (or rupees, or renminbi); and in so doing the ability of any given brand to make a meaningful impact is diluted by the sheer magnitude and frequency of audio-visual-textual images clamoring to engage our senses.  This, it seems, is what happened to that wonderful amber cleansing bar by Neutrogena – it got lost in the proliferation of categories, products and beauty care messages that exploded into our lives over the last 20-odd years.  This proliferation explosion has engendered many results both positive and negative – one of the latter of which has been to weaken the brand’s ability to connect heart and mind.

If mindshare leads to walletshare, then heartshare leads to mindshare. I don’t believe this paradigm has changed – I think it is no less true today than it was in the golden age of brand advertising (see any episode of Mad Men for a useful reference point).  But the path to the heart is different today, and much trickier.  It’s not all about the brilliant ad that manages to imprint the differentiating qualities of its product so firmly in the cultural mindset that whole households could recite them in their sleep (it is still partly about that, but much less so than the days when the Don Drapers of the world dreamed up the copy over three-martini lunches).  In fact it is not about any one thing, but rather about multiple things – things that form a complex multi-dimensional mathematical equation that would have those ad men of old reaching for the Scotch bottles they kept in their office credenzas.  Namely: how do you match the right message with the right format, for the right geographic region and customer segment via the right marketing channel, for optimal effect? The answer to this equation is not obvious – in fact it is entirely unknowable to the unaided human brain.  To solve it requires vast computational power and advanced scientific methods for solving multivariable problems where many of the variables are interdependent (which adds several levels of complexity to the math needed to get to the solution).

To put it more mundanely, it requires disentangling the clues from that vast sea of transactional information that form a composite picture of the customer-product interaction leading to my walking to the CVS checkout counter with a particular facial cleanser in hand.  What are the demand chain activities that could make this customer-product interaction more predictable; and more personally satisfying for me, the customer?  Is it a pricing question, or a product mix question, or a channel promotions question or an image question?  Traditionally, marketing managers have viewed these as separate issues rather than forming an integrated portfolio of activities around which to optimize a particular objective (like brand value).  But they are not separate, and they cannot be optimally solved in the isolation tanks of marketing department silos.

Fortunately for the beleaguered brand decision-makers of the world there are holistic quantitative marketing solutions that can help them leverage the insights necessary to build and sustain their brand’s value by treating these questions as components of an integrated whole.  The starting point for these solutions is the recognition that what happens in one part of the demand chain affects things that happen in other parts.  As a consumer, my world is more complex now than it used to be and most likely my attention span for any one message is shorter.  But some configuration of activities undertaken by a company – or more than one company along a supply chain – can have a significant impact on me at that reinforces the value of the brand and gives it a meaning more closely aligned with how I actually make purchasing decisions today.

These solutions may lack the simple goodness of that old facial cleansing bar – but they may yet win the heartshare of facial cleanser (and many other) consumers all the world over.

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.

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.