Fortunately for business decision-makers, fair pricing and optimal pricing are not at odds with each other but can comfortably coexist.  Over the course of the coming weeks my colleagues at Sentrana and I will be approaching the rich topic of fair pricing in a series of exchanges on this blog.

debating the age-old question of fair price

What is a fair price?  This question has perplexed humanity throughout history.  Leading thought output of the ages, from Aristotle’s Nicomachean Ethics to the Summa Theologicae of  Thomas Aquinas, Pierre de Fermat’s probability proofs and Adam Smith’s classsical economics, have all weighed in with considered opinions on the fairness and justness of alternative ways to price economic goods and services, and the debate continues today.  A series of letters exchanged between Blaise Pascal and Pierre de Fermat in 1654 is often regarded as a primal cause of the development of modern probability theory: this exchange was actually an attempt to establish a scientific basis for the notion of fair price.  In his paper “The Unity and Diversity of Probability” Rutgers professor Glenn Shafer shows how these letters created hypothetical games of value that we today can recognize as the application of probability methods to defend a price as ‘fair’ under conditions of uncertainty.

Uncertainty is the 800-pound gorilla in the room when it comes to price-making decisions.  Buyers and sellers operate from positions of considerable uncertainty in approaching transactions with each other: buyers have only partial information about the features of what they are buying such as quality, reliability, service support and the extent to which a given offered price may be reasonable in relation to these features, while sellers have a limited perspective on what demand exists for their products and what combination of levers such as price, assortment and marketing could influence that demand.  Buyers thus face the risk of inequity in their exchange – paying more than the intrinsic worth of the object acquired, while sellers face the risk of their transactions being unprofitable and, if persistently so, driving them out of business.

Having worked for a number of years in the investment industry I offer up a useful model from this corner of the economy for dealing with uncertainty.  In the investment world uncertainty commands a price: investors demand more compensation, in the form of return on investment, for assets that exhibit higher levels of short term volatility.  Participants widely view this as fair: it is not thought ‘unfair’ that an investor in, say, a 5-year U.S. Treasury note earns a dependable return of 5% whereas someone who takes a punt on the shares of a small-cap biotechnology company may potentially earn over 25% in the same time period.  There is more likelihood that the value of the biotech shares will plunge in the wake of unexpected news or that the company will go out of business than there is of the U.S. government failing to honor its legal obligations to bondholders.  A capitalist economy offers the potential for greater rewards to the investor willing to assume greater risk.

what matters is the customers who don't come

How is this concept analogous to the uncertainty faced by businesses that sell in markets for real (i.e. non-financial) goods and services?  I thought about that the other day while dining out at one of my favorite Northern Italian restaurants, located in a trendy urban area chock-full of good eats.  As I looked around the dining room on a late September Tuesday evening it occurred to me that the uncertainty this business experiences on a daily basis is plainly visible: the number of empty seats during peak dining hours.  Restaurant patronage is a notoriously fickle notion to quantify and is subject to considerable fluctuation in real time.  I wondered about the methodology through which this restaurant’s owner translates the uncertainty of empty seats into the revenue model. It seems to me that the real art to the formulation of this model is not based on the tables that have patrons sitting at them, but rather the ones that are empty.  The hard part of revenue calculation is not figuring out what the average occupied table will spend on any given night – it is dealing with the uncertainty of those empty tables.

Now in theory, the owner could simply build an ‘uncertainty factor’ into menu prices as a partial compensation for the prospect of empty tables.  In practice this is unlikely, and the reason why it is unlikely brings us back to the concept of fairness.  Prospective restaurant patrons (including yours truly) are very unlikely to be sympathetic to the notion that they should have to pay a higher price for the verze e luganega because it helps the owner’s revenue model – to us patrons, that is an unfair offloading of the owner’s problem onto us.  We don’t even have to explicitly know the owner’s motivation.  Discerning customers have plenty of access to comparative information – from other restaurants in the area, our social networks, Internet reviews and so forth – to form strong perceptions of the fairness or unfairness of prices at any given spot.  We will wield our verdict of ‘fair or unfair?’ with much self-righteous certitude in making future dining out decisions.

So what is a ‘fair’ way for our poor restauranteur to manage uncertainty toward a more profitable outcome?   Rather than accepting empty tables as a given fact of life the owner can try to figure out intelligent ways to fill them.  Who may be walking by the restaurant in the late afternoon, or working in a nearby office building and considering an after-work dining outing with colleagues?  What combination of factors might entice these and other prospective patrons to choose this establishment over numerous other choices?  Is there a way to figure out attractive deals that would lure certain prospective customers and to surgically target each such customer with a unique offer?  Yes – it is possible through scientific micromarketing techniques that optimize at the granular level of the customer-product interaction.  The next question – if it is possible, is it also fair?

All those centuries of debate on the notion of fairness and justice in economic commerce now come back into this discussion.  Paul Krugman expressed a concern about this in a New York Times op-ed piece titled “What Price Fairness?” all the way back in October 2000, when price optimization methods were in a much, much earlier stage of development.  His remark (related to the notion of dynamic pricing in general) was that while it may be “arguably good for the economy,” dynamic pricing is also “…unfair: some people pay more just because of who they are.”  Sitting in the restaurant, I imagined a hypothetical case where the gnocchi with sweet basil pesto, which I ordered for the menu-listed price of $14.50, was being enjoyed by the gentleman at a nearby table for $11.30 simply because the restaurant’s micromarketing system contacted his iPhone with a targeted discount offer just before he left his office just down the road.

Is that unfair?  I don’t think so.  Who wins and who loses in this scenario?  The gentleman who receives the offer wins – he gets the opportunity to enjoy a dining experience targeted to his personal preferences.  The restauranteur wins by filling a table that would otherwise be empty, reducing uncertainty and improving the nightly profit intake.  I am still enjoying the gnocchi I ordered at full price and am no worse off than I would have been otherwise; having already concluded that $14.50 is a reasonable price for the dish and ordered on that basis.  On a broader social scale the notion of micromarket pricing does not discriminate between the two of us in a way that I would deem unfair.  I have my own set of preferences that may benefit me with a different offer set on a different day.  In fact, were I to be made aware of the circumstances under which the gentleman got his gnocchi for a lower price, I may well be inclined to leave my own contact information with the establishment in anticipation of future benefits.

There is a road ahead before scientific micromarketing becomes a more accepted feature of B2C commerce situations like that of my hypothetical imaginings while dining out (no doubt helped along by the delights of a 2003 Castello di Camigliano Brunello).  And I expect that a vigorous debate about the question of fairness versus optimality will be part and parcel of this journey.  At day’s end, though, I believe the two are fundamentally compatible.

Health care policymakers may agree on little else, but they do largely agree that the industry’s cost structure is unsustainable.  The whole process of providing health care – including the prescription drugs that account for about 10% of total health care spending – is under the green eyeshade scrutiny of the cost cutting crowd.  Meanwhile insurance companies are increasingly uninclined to pick up the tab for a prescription drug where generic alternatives exist.  And end-consumers themselves are becoming a more central part of the economic equation, as even those with stable employee benefits find their health plans passing on more costs to them.  Prescription drugs then wind up a direct expense item on the monthly household budget, taking a place alongside traditionally more price-sensitive household staple categories like groceries and personal care products.  Those cheery pharmaceutical ads with happy, beautiful people attesting to the wonders of the latest anti-coagulant or cholesterol reducer that saturate the TV channels may seem a bit less compelling to families that have to weigh whether the factors that make those brands more expensive are actually worth the added burden to the household budget.

In particular, I see this as presenting a looming challenge to some of the current practices in managing one of the most (if not the single most) signal economic events for drug manufacturers: the transition of a brand-name drug from on patent to off patent.  Over $60 billion of on patent drugs are scheduled to go off patent between now and 2011, including such widely-known blockbusters as Pfizer’s Lipitor and Aricept, Merck’s Singulair and Sanofi-Aventis’s Xalatan.  If the fate of past blockbusters – Eli Lilly’s off patent experience with Prozac in 2001 comes to mind – is any indication of what is in store for these drug makers then we can expect to see revenue declines of 80% or more when the day of reckoning comes.

That almost looks like the pharmaceutical industry’s equivalent of the “liquidation event” so well-known in the consumer retail sector – but there is a major difference.  Virtually all of those off patent revenue declines come from volume reductions, not changes in price.  In fact, a variety of academic studies show evidence that, to the extent the drug companies actually change their prices in the approach to and immediate aftermath of exclusivity expiration, those are actually price increases, not decreases.  The calculus behind the industry’s preferred mode of competition to date has been based largely on maintenance of a significant price differential with generics based on brand loyalty and certain other means of differentiation.

This price differential is intuitively surprising given the relatively narrow scope of area for competition between originator drugs and generics (by law, generics in any molecular specification must have the same active ingredients as the originator drug, the same route of administration, similar bioequivalence and must have been produced in facilities that meet manufacturing process standards of adequacy).  However, much of the academic inquiry into generic drug price competition has affirmed the success of the drug firms to date in maintaining that differential, labeling it the “generic paradox”.  Essentially, the strategy is to identify that subset of the market to which it can continue to maintain brand differentiation, throw substantial amounts of marketing and sales dollars at that target segment, and live with the predictable revenue declines for off patent drugs while at the other end of the pipeline seeking to shepherd lots of new molecules through the FDA approval process in the hopes that the next Prozac or Lipitor will emerge onto the scene with a 14 year-plus patent protection.

What challenges this status quo more than anything else is the rise of the generic drug industry and its growing acceptance among healthcare providers, insurers and patients alike.  Generics account for about 60% of the drug market today and this sector is growing at just under 10% per year.  Wall Street analysts predict now that Teva Pharmaceutical, the world’s largest generics manufacturer, will see profits growth of 14% annually for the next five years as compared to generally flat earnings for the five largest pharmaceutical concerns.  This implies market share gains at Big Pharma’s expense.  Israel-based Teva already has a market cap ($45 billion) larger than Bristol Myers Squibb or Eli Lilly.  The company’s 37 production facilities generate over 8 billion pills each year.  The smart money seems to be saying that in a world where cost considerations dominate the healthcare landscape, the leading generic makers like Teva and Canonsburg, PA-based Mylan stand to reap the lion’s share of the benefits at the expense of the big brand names.

Unless, that is, Big Pharma figures out a different way to fight back.  The industry does not lack for the size of its marketing budgets, but those dollars are not necessarily being spent in the right places today given the trends described above – heavy sales force deployments to the offices of physicians and other health care providers, and those interminable ads we all have the dubious pleasure of viewing during virtually any prime time television experience.  The real question is: what is the most optimal way to squeeze the most revenue out of every marketing dollar allocated, factoring in the relationship between all the demand levers at the company’s disposal – price, product mix, sales force mechanisms and marketing spend vehicles?  There are potentially rewarding answers to this question, and those answers can be found through innovations in revenue optimization and micromarket science.  I don’t expect to see Big Pharma’s leaders collectively sit back and watch Teva and its ilk cut their markets further down to size.  A relentless focus on optimizing revenue may not be the industry’s historic strength, but I’ll be surprised if it isn’t a fixture in its immediate future.

To answer this question, let’s take a closer look at the solution itself. Dynamic pricing is a form of yield management (also called targeted pricing, flexible pricing, tailored pricing or discriminatory pricing), which formally emerged in the mid-1980s as a means for airlines to capture some value from plane seats that would otherwise go empty by offering, for example, lower than published fares for customers willing to forego other benefits (such as the ability to change a flight date or cancel the ticket). This breakthrough science allows organizations to understand, anticipate and influence consumer behavior in order to maximize revenue or profits from a fixed, perishable resource (e.g. airline seats, hotel room reservations, etc.). In the case of the San Francisco Giants, dynamic pricing is being implemented to allow them to dynamically adjust prices by weighing ticket sales data, weather forecasts, upcoming pitching matchups and other variables to help decide whether the team should raise or lower prices right up until the day of the game.

The problem with dynamic pricing is that it doesn’t enable organizations to truly understand the needs, preferences and spending propensities of each and every customer they serve. For example, the problem I see with dynamic pricing for baseball franchises is that it relies on a basic set of variables (e.g. weather, starting lineup, etc.) to determine how to price to the masses, instead of focusing on – and pricing to – each customer’s specific needs. Let’s say I want to go to a baseball game on my birthday. Will the dynamic pricing system offer me a discounted ticket (or should it predict that I am more spendthrift on my birthday)? If my favorite pitcher is starting will the system recognize my willingness to pay more and increase my ticket price? If I regularly attend games throughout the season will the system consider my loyalty and offer me discounts to other games? The respective answers are no, no and no. The advantage here clearly goes to scalpers, as they can still adjust and negotiate prices with each customer they interact with directly. However, where I see the limitations of dynamic pricing end, the benefit of revenue optimization begins.

Revenue optimization technology can provide baseball franchises an accurate picture of demand down to the single customer-level, where the software can codify each customer’s preferences and adjust prices according to their needs, total amount spent and even longevity as a fan (i.e. brand loyalty). Baseball teams already capture tons of customer data through the MLB web portal, where fans can upload and track their favorite teams/players and purchase tickets and merchandise. All of this data can be mined to figure out each customer’s specific price point for every seat of every game! The technology enables baseball franchises to increase ticket sales volume for less popular games, reduce the number of tickets resold in the secondary market, and increase profits for every game. In addition, baseball teams can begin to cross-sell other items like concessions and merchandise to these loyal fans, or even optimize the sale of bundled tickets and/or merchandise. With this increased ability to effectively market to each fan, baseball franchises will become more adept at selling tickets than the scalpers and can soon “steal” their profits back – forcing scalpers to buy tickets if they want to see Major League Baseball’s most prolific stealers.

What are the implications of the words “pinpoint” and “optimal” when market behavior is so uncertain?

In other words, is it possible to find a single decision that will maximize the odds of earning a handsome payoff when the outcome of any decision is uncertain?  In a rather extreme example, in the highly uncertain world of gambling, can I make some decisions that are clearly better than others in light of the uncertainty?

Let’s say that all of a sudden I have the urge to gamble, and head for Monaco.  I don my tuxedo, and enter the Monte Carlo casino, where I see 3 different tables offering 3 different games.  I have €1,000 to spend, but the house has imposed the constraint that I must pick a single table and commit myself to that table for the entire evening.  Now, let’s say that at each one of the 3 tables, the wager amount for a single bet is €10 (admittedly, a far-cry from what I should be prepared to spend at Monte Carlo), which allows me to play 100 games (€1000 total wallet size ÷ €10 per game) at each table.  So, how does the evening unfold?

Since I am not a gambler, I will have to fabricate some numbers to convey the point.  Let’s say that Table A offers a 49% chance of winning, and each win produces €18 (for a gain of €8 based on my €10 bet); Table B offers a 10% chance of winning, and each win produces €85; whilst Table C offers a 32% chance of winning and each win produces €25.  Needless to say, everything is all but certain inside Monte Carlo, and as a rational man I should stay out.  But if I do venture in and wish to risk my money, can I pinpoint the table that will optimize my returns?

To answer this question, I must travel through several centuries of mathematical thought, and invoke the laws of probability.  I know that if I flip a coin a sufficient number of times, I can say with great certainty that 50% of the outcome will be heads, and the other 50% of the time will be tails).  Notice, the key here is that I must flip the coin a “sufficient” number of times.  Due to the vagaries of random chance, a small number of throws may not reveal the true nature of the coin – with just 7 coin tosses it is possible that all 7 times I see heads.  But, with 700 throws, it is quite unlikely that I’ll see 700 heads.  Instead, I’ll probably see close to 350 heads and close to 350 tails.  This conclusion is driven by a theorem known as the Central Limit Theorem, which was originally put forward by the French-born mathematician Abraham de Moivre.  It states that if we know the probability of an outcome from some event (like a coin toss), we will see that outcome occur as often as the probability multiplied by the number of times the event occurs.

In our hypothetical Monte Carlo excursion, the gambling event can occur 100 times (given my €1,000 allowance and €10 per gamble – i.e., per event).  This means I can expect the following (as I hear de Moivre’s voice from centuries past):

Table A: 100 Events x €18 Won per Event x 0.49 Chance of Win per Event = €882 Expected Winnings

Table B: 100 Events x €85 Won per Event x 0.10 Chance of Win per Event = €850 Expected Winnings

Table C: 100 Events x €25 Won per Event x 0.32 Chance of Win per Event = €800 Expected Winnings

With this arithmetic, de Moivre guides us to Table A – indeed, once can say that he has pinpointed Table A for not in spite of the uncertainty, but in light of the uncertainty. Now, it’s important for us to recognize that the power of de Moivre’s insights rest on understanding the uncertainty – i.e., on “quantifying the chance” of an outcome.  Let’s say that Table A is a Roulette Wheel.  As the host spins the Wheel and we all place our bets, it is impossible to state exactly whether or not I will win or whether or where the ball will land.  There are too many factors to humanely consider:

1. The bounciness of the ball
2. The initial rate of spin with which the host turns the wheel
3. The amount of lubrication in the bearings that bind the wheel to the axle
4. The amount of humidity in the room which can slow down the wheel
5. The air currents in the room when the Air Conditioning comes on
6. The initial height from which the ball is dropped onto the wheel
7. Etc, etc, etc.

And even after knowing all of these factors, the equation used to predict the balls final resting position is nonlinear and the solution is going to be chaotic, as shown in the figure above.  We simply cannot predict where the ball will land.  But, there is hope!

We can predict the probability of winning, and we can do so using 2 different methods.  First, we can look at the fact that there are 37 pockets on a European Roulette wheel, and the odds that our ball will land in any pocket is therefore 1/37 = 0.027, which means we have almost a 3% chance of winning.  Alternatively, we can take a sample of all the previous people that have played in the prior 6 months and look at what fraction have won.  This gives us what is known as a “Frequentist Probability”, and can be used within the context of de Moivre’s principles to help guide us to the “optimal table” on which to place our bets.  The discovery of these probabilities is one of the fundamental pursuits of the entire discipline of Econometrics, and has become pivotal to achieving Pricing excellence (further exposition on this important topic can be found in the “Modeler’s Mechanics” of our blogs, and within our white papers).  As shown in the figure to the left, this probability discovery process leans heavily on historical market data (and remember, the past does not provide a definitive glimpse into the future, but does provide a very good glimpse into the probabilities of many different futures), with a heavy dose of computing power to produce predictions that have so far proven to dramatically improve the pricing manager’s decisions when compared to using their human instincts alone.

For instance, companies will often either adopt an Every Day Low Pricing (EDLP) or a High-Low Pricing (HLP) strategy.  The former seeks to keep prices low by achieving enormous economies of scale and tight supply-chain operations, whilst the latter seeks to lower prices to almost unprofitable levels a few times per month for select products in the hope that it will consumer attention and fuel the sales of additional products in the store.  A major problem with HLP strategies is that the momentary dip in price can wreak havoc on demand predictions for not only the low-price product, but for other products that are swept up within the consumer frenzy.  In one of Canada’s largest retailer, we found that their ability to predict demand to within +/-15% of actual demand occurred only 32% of the time.  But, with probabalistic methods and the recent advances of scientific pricing, this same retailer was able to predict demand to within +/- 15% of actual demand about 87% of the time!  Note, we are not pinpointing the demand value here, nor are we optimizing which specific products to invent and stock.  Rather, we are pinpointing a price that will maximize demand and revenue by understanding the probability of the market’s needs.

I believe that in order to respect the important points that several respondents to the “At the Mercy of the Market” blog have raised, it is important for us to be careful and augment words such as “pinpoint” and “optimal” with the phrase “expected returns.”  In a world of uncertainty, predicting the expected results using the Laws of Probability rather than the absolute results using a Crystal Ball is indeed the best we can do.  It is extremely important for us, and all other scientists / modelers, to inform the audience that we are in no way aspiring to peddle a crystal ball.

And then there are those rare occasions where we encounter a street musician whose music soars so high that we are forced to refer to him simply as a “musician,” for using the adjective “street” would be nothing short of a criticism.  About 2 years ago, this is what I encountered at one of Washington D.C.’s busiest Metro (subway) stations during the morning rush hour.  It wasn’t until much later in the day that I discovered the musician in whose masterly hands the violin “sobbed and laughed and sang” was the great virtuoso Josh Bell.  In the middle of the morning rush hour, 1,097 commuters passed by and all heard soul-stirring music at a price of their own choosing that just a few days earlier fetched more than $100 a seat at Boston’s Symphony Hall.  Josh Bell played to a rush hour herd, and demanded no price for priceless music.

His income depended not on the value he provided to those 1,097 passersby, but the overwhelming value he provided – for, if he failed to stir, we listless commuters would feel no compunction to pause and forfeit even a meager fraction of our purse.  And stir he did, with a masterly performance of Bach’s Chaconne from Partita No.2 in D Minor.  Of the almost 2,000 pedestrians that filed by, only 27 gave money for a total of $32.  In other words, for a performance that was described by the Washington Post as “pearls before breakfast,” less than 3% of us offered any payment (for “a man whose talents can command $1,000 a minute”).  Did the service deserve such scant payment, or was there more to the revenue than just the greatness of the service itself.  This is a question that goes right to the root of just how complex the endeavor of pricing can be.

Beyond Josh Bell’s performance and the payment it merited, there is a litany of other factors that affected his earnings power (or pricing power if he were to charge a price).  First and foremost, there were 3 possible locations at which Bell could have positioned himself (see figure below):

1. At a location of high transient pedestrian traffic (between the entrance door to the subway station and the escalator bank that leads to the underground train platform).
2. At a location of stationary traffic waiting for a subway train to arrive (i.e., on the underground platform).
3. At a location where the acoustics of the Metro arcade would create the most perfect sound possible within the subway station.

Of the 3 possible locations, Bell perhaps chose the worst location to generate earnings.  No matter how good his music, rush hour traffic has no time to stop.  It wasn’t their purse that the commuters failed to contribute, but their precious time.

The attributes that govern your power to generate revenue transcend the product itself.  Bell’s performance at the L’Enfant Plaza Metro stop highlights several fundamental truths of pricing science:

1. Could being situated at one of the locations where stationary traffic was high have yielded more revenue?
2. Or, perhaps could being situated at a location where the sound would be even more magnificent have yielded more revenue?
3. What if the perfect acoustic spot had only scant stationary traffic?  Then, sadly, we can surmise his income would be lower even though the quality of the product would be it’s highest.
4. To complicate matters even further, what if Bell chose a different day for his performance?
5. What if he played on a sunny, spring day where spirits are higher instead of a dreary winter morning?
6. What if he played on payday (in the Federal government, payday typically lands on the 2nd and 4th Friday of the month) instead of an arbitrary day?
7. What if Bell advertised with a sign around his neck that he was indeed Josh Bell?
8. What if underneath the sign, Bell posted a requested donation of $5 for his performance?

By not focusing on these questions, and concentrating solely on his music (i.e., the tangible product itself), Bell failed to create a high market price for his product, and earned only $32 dollars from a 43 minute performance that in a proper venue would have earned 6 figures.   All of these factors would have dramatically affected the revenues Bell earned that morning.  But, identifying the 12 square inch box out of the 15,000 square feet of space in which Bell would have obtained maximum revenue (i.e., gotten an “optimal price” for his public performance) is an optimization problem of mind-boggling complexity, and simply cannot be solved without data and quantitative analysis.  After all, the analysis is not just about where Bell should stand to optimally balance sound quality with foot traffic, but also about how this optimal location varies with changes in any of the above 8 questions.  The lessons here are deep, and profoundly shape our responsibilities as pricing managers.

Before you jump to match your competitor’s price, you should recognize the market’s willingness to offer you payment that goes beyond the value of the product itself.  It is important for you to optimize the marketing attributes of the product in order to optimize the price of the product.  You are not at the mercy of the market. Through your actions you can greatly influence the market price of your product. As a pricing manager, you should not just view the setting of price as your only responsibility.  You have access to much data about your market and your previous sales and your customers, which you can leverage to determine the interplay between all of the marketing attributes of the product and the price of the product.  The price you are able to make is inextricably linked to the actions of your marketing managers, your category managers, and your product and sales managers.  And once those actions are executed, you can digest all of your data to pinpoint the optimal price you can charge in the market.  Last but not least, as a pricing manager, you are the final decider of the trade-offs your enterprise should make to maximize immediate earnings and establish a long-term competitive advantage:  Should you play your violin where it sounds the best but generates the least income or do you play it where it sounds the worst but stands to generate the most income because of high foot traffic?  If you do the latter, will those that pay you today have the loyalty to pay you again tomorrow?

So, before you give in to the seduction of lowering your prices to beat your competitors, remember to identify and carefully influence all of the attributes (i.e., don’t just make great music, stand in a great location) that will compel the market to pay you your just reward for the goods and services you provide.  The crux of price optimization is not about touching price at all, but touching all the other things that make a price.

Here’s an example to help you understand the magnitude of the problem your organization is facing: you sell thousands of products to tens of thousands of different customers each and every day, which is equivalent to millions (if not billions) of distinct customer-product interactions every day – impossible for even the most experienced sales managers to analyze individually. Now grab a pen and some paper and write this down: every sale is an interaction whose revenue can be uniquely maximized! Most companies fail to detect the subtle changes in their customers’ preferences over time, leaving significant profits on the table. And hence the reason for the detective work we’re often called to do; companies don’t realize they have all of the necessary data to maximize revenues right under their noses.

The solution here is Scientific Micromarket Management, which makes it possible for organizations to assess how each customer values your product and offer exactly that price every day in every market. Sure, we may be talking pennies and nickels here, but if you multiply these adjustments by the millions of potential customer-product combinations, then multiply these daily adjustments over the course of a year, and you will realize the significant amount of impact this will have on your bottom-line. Capitalizing on these billions of tiny demand shifts with a dynamic pricing system more targeted than human intuition enables companies to finally understand why every single customer buys what they buy from you and what they are willing to pay for it every time. This is far more comprehensive than any pricing strategy; this is a complete revenue optimization solution. Your customers are getting smarter about you, I think its time you got smarter about them.

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.

Not so, in fact. When you start asking extremely detailed questions that require combing through years of detailed historical data and then performing mathematical transformations on each of those figures, you will find out rather quickly the limits of processing speed when your results finish compiling in a week or so. The thing is that most of us never push up against the processing speed frontier. We can see that every year computers get faster, chips get smaller, and Excel seems to have more rows. Moore’s Law prevails. The trouble is that all the while the rate at which the data universe expands is screaming past advances in processing capabilities, and that rate does not fluctuate with the economic downturn. Consider the markets for microprocessors, which allow us to perform those calculations and manipulate data, and hard drives, which allow for storage of data. Microprocessor sales have been dealt a sharp blow by the global downturn as computer sales have slowed, but worldwide shipments of hard disk drives (HDDs) roughly maintained 2007 levels even in the worst quarters of the recession (and the drives themselves contain more memory). Solid state and flash memory shipments were down, but the evidence suggests that this is due to consumers substituting HDDs for other types of memory, rather than simply not storing more information. The demand for data storage, while not completely recession-proof, is nonetheless of the hardier variety.

Simply put, information of all kinds accumulates faster than we can analyze it. We are losing the race, and the gap is widening, not shrinking. As for what this ultimately means, I will now make a rather dour point. A fashionable explanation for the recession among both politicians and many “Main Street” types is that greed is what did us in. The greed of the bankers, the hedge funds, the fat cats, the small cats, whomever – greed is the culprit. But that doesn’t explain everything by a long shot. Even the greediest person doesn’t want the party to end and the money to stop coming in. Might it be possible that they weren’t able to ask the questions that might have led to certain debt instruments having never been created? Financial services employees have more information available to them than decision makers any other industry, and still here we find ourselves. Think about how many times each day similarly misinformed decisions are made inside corporations all across the world. The information is there, but we are more often than not letting it rot on the docks.

Restaurants sit at the crossroads of both cost and demand volatility. Much to their detriment, companies such as McDonald’s often buffer both their customers and their upstream suppliers from feeling the financial impact of this volatility. Now McDonald’s is at least hinting that it wants out of this arrangement, and our experiences working with multi-billion dollar partners in the food distribution industry points to this being a wise move. We have long observed significant daily fluctuations in food prices across all categories. Couple this with the effect that a strong dollar can have on McDonald’s overseas business, and it quickly becomes clear that understanding how much a customer is truly willing to pay for a menu item is of huge value for a company so proud of its billions and zillions served.

The real question is why don’t more restaurants (or any number of businesses for that matter) treat their price as the valuable asset that it is? It is not overly difficult for a restaurant to approximate a schedule of demand and create several different menus with prices tailored to different Cost of Goods Sold (COGS) environments. For a restaurant grossing $500,000 in revenues annually, every 1% increase in sales corresponds to a $5,000 improvement to the top line (subtracting the printing costs later). In our experiences in food distribution, a 1-2% increase in the organization’s top line can translate into a bottom line improvement of over 8% – an observation that we have seen replicated in numerous industries. Projecting forward a few years, I would be willing to bet that the majority of companies with the highest valuations among their industry peer groups will also be the ones that are trying to actively shape demand through their pricing strategies.