Fair Price, Optimal Price

Businesses seek to maximize the value they can obtain from their revenue models.  Price is the key lever decision-makers can operate to influence revenue, and in recent years a growing number of businesses have sought to implement strategies for actively managing the price lever – strategies such as demand management and revenue optimization.  However businesses are also highly sensitive to the perception by individual consumers and the society at large that their prices are fair, in other words that they do not violate widely held individual or societal norms.  Fair pricing matters – it matters to me, and to you, and perhaps ever more so in a climate characterized by economic uncertainty, downward pressure on demand and a perceptible decrease in the citizenry’s trust of public and private institutions.

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. Read the rest of this entry »

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Revenue Optimization: Coming Soon to a Big Drug Company Near You

Large brand-name drug companies – Big Pharma in the common vernacular – are not exactly known for competitive pricing or razor-thin margins.  For 2008 the industry was ranked third most profitable in the U.S. according to Fortune magazine, with average profit-to-sales margins of 19.3%.  That’s a pretty fat comfort zone compared to the scorched-earth landscape of many other industries…or is it?  Until recently Big Pharma was pretty consistent at the #1 spot in those rankings. A look under the microscope reveals some troubles bubbling up in the hitherto happy world of magic molecules and blockbuster brands.  These days the whole country seems transfixed by the subject of healthcare, and no matter what does or does not come out of the legislative sausage factory this year, some major trends are afoot that have potentially far-reaching consequences for Big Pharma and may influence the normally lackadaisical approach drug makers have exhibited to the prices they charge for their brand-name drugs – in particular when those drugs reach the end of their exclusivity protection period and go off patent. Read the rest of this entry »

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How Major League Baseball Can Steal Profits Back From Ticket Scalpers Using the Right Pricing Solution

The National Baseball Hall of Fame recently inducted Ricky Henderson, one of baseball’s most prolific base stealers with a record 1,406 bases stolen in his career – yet, Major League Baseball has failed to deal with scalpers who steal millions in profits from their franchises every year. Scalpers have seized the lost opportunity where Baseball franchises lock in their ticket prices months before the season starts and choose not to adjust prices throughout the season. A more efficient secondary market thrives due to the scalpers’ ability to factor in several game variables (e.g. strength of opponent, seat type, starting lineup, weather conditions, etc.), as well as buyer-specific factors (e.g. age, attitude, clothing, jewelry, etc.) to determine the maximum (and therefore optimal from the seller’s perspective) price that each person is willing to pay. Another advantage for scalpers is their ability to immediately negotiate if the buyer doesn’t accept the first price, carefully moving the price down until both the buyer and seller agree upon a satisfactory price. To help reclaim these lost profits, the San Francisco Giants are now testing dynamic pricing software to help adjust ticket prices based on the expected consumer demand for each game. So what exactly is dynamic pricing, and is it powerful enough to replace the individualized pricing, negotiation, and sales effectiveness of ticket scalpers? Read the rest of this entry »

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Finding Pricing Excellence on a Roulette Wheel

One of my recent posts, “You Are Not At the Mercy of the Market…”, attracted a rather thought-provoking response posted directly to the blog.  The crux of this response, and others sent directly to me, have all revolved around a similar theme:  With so much uncertainty surrounding consumer behavior, words such as “pinpoint” or “optimize” should not be uttered when it comes to the decisions that pricing and marketing managers must make.  This is indeed a compelling sentiment, and has stirred much discussion amongst my colleagues in industry and in academia (our research organization collaborates closely with professors within the University of Chicago and Carnegie Mellon University).  This discussion has taken on many twists and turns, which we hope to summarize in future posts.  But, there is one particular question that has resonated throughout our discussions:

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? Read the rest of this entry »

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You are Not at the Mercy of the Market: You Have All the Power to Make Your Price

If figuring out how to maximize your revenues by charging the right price is hard when people actually need your product, imagine how much harder it is when they don’t need your product or don’t necessarily even need to pay to enjoy your product.  The lessons learned from how to maximize revenue in this regard, which is a much more formidable challenge, can profoundly impact your ability to maximize earnings in the less difficult situation where people have no alternate choice but to pay for your product.  In a stroll down a busy street, we will once in a great while receive a good that can stir our soul yet require no payment.  We receive this good from the ubiquitous street musician who earns his income as a mendicant who lets you set the price (which is often nil), rather than setting his own price for “services tendered.”

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. Read the rest of this entry »

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Forget Your Competitors, The Power to Consistently Lead Your Market Lies In Understanding How Every Customer Values Your Product

Far too often, we have companies seeking our expertise to ascertain their competitors’ competitive strategy vis-à-vis their pricing, as if this will provide the magical insight they need to help them maximize their own revenues. My advice: save the detective work for Colombo and forget about your competitors! Your bottom line profits should not hinge upon a competitive response strategy that reacts to your competitors’ price moves, where you surrender control over your revenue structure and end up locking your firm into a race-to-the-bottom pricing with the rest of the industry. Escaping this destructive cycle lies in focusing relentlessly on your customers rather than your competitors. If you’ve read the news in the last 10 years, you may have realized that your customers are the most informed consumers in the history of the world! They are utilizing every available resource, from various news and industry websites to trade magazines to word-of-mouth gossip to Oprah to… well, even your price helps them determine their perceived value of your product. They are better informed about their purchases than ever before, but I wonder if you are learning as much about them and how they view your products?

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.

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You Can’t Punt Away the Dimensionality Curse

A single mathematical formula brought ruin to the global financial markets.  What happened was not a failure of quantitative methods per se but rather a lesson in the perils of ignoring real-world complexities in favor of deceptively elegant shortcuts.

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.

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What Happens When We Can’t Keep Up with Information

I ran into a former colleague the other day who, as it turns out, recently left his job and presently spends his days building options pricing models and trading from home on his own accounts. In turn, I described to him some of the recent work that we have done in revenue optimization and particularly the breakthroughs that we have engineered for processing data. His face scrunched up a bit, and his response was uncharacteristically blunt: “You can always process numbers quickly if you need to,” he smirked.

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.

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The Price You Pay for Not Changing Price

The WSJ ran a story on 3/10/09 on the financial success of McDonald’s Corp. throughout the present recession. Since the company is one of only two DJIA members (the other being Wal-Mart Stores, Inc.) to have ended 2008 by posting a gain for the year, it is perhaps only fitting that the Journal devote a few inches to McDonald’s. The only student to pass a difficult exam rightly deserves a gold star. But amidst the discussion of McDonald’s zeal for succession planning, controlled expansion and keeping a lid on costs in the face of the last year’s commodity price swings, one item deserves more attention than it received: McDonald’s is encouraging individual locations to experiment with prices.

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.

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