Blame for the global financial crisis has been cast upon government leaders, bankers, home owners, and quantitative analysts. In fact, mathematical models and formulas such as Black Scholes, Gaussian Copula, and VAR have received particular attention as culprits in this financial mess.


And while these financial models had flaws, a more egregious error was the blind faith and lack of critical thinking in the adoption of these models. Executives are realizing that when it comes to modeling complexity–there are no magic beans, there are no magic formulas. But have we learned these lessons too late?

From the dawn of time, humans have wrestled with, and tried to explain the unknown. From myths of how the sun and moon were formed, to why it rains some days and not others, ancients have tried to pin a "cause" on every "effect". But sometimes, complexity defies simplification.

Case in point, a recent Wired Magazine article describes the rise and fall of David X. Li, a senior Wall Street quantitative analyst who tried to simplify a very complex issue (probability of default on a pool of mortgages) through mathematical modeling.

Li's formula was known as a Gaussian Copula function and it worked like this. Based on historical data of people similar to me, it might be pretty easy for a banker to discern the probability that I will default on my home loan (assuming a normal distribution and independence). Now let's add my neighbor to the mix. What are the probabilities that our fortunes are somehow tied together? Are we correlated at all? If I default on my mortgage, will he default on his?

Adding more complexity to the mix, Wall Street often bundled packages of mortgages together, 150-200 at a time, and sold the pool of mortgages to investors. Obviously, a method was needed to identify the overall "risk" of a particular package so that the pool could be priced and sold. With hundreds of mortgages in a particular pool, correlation was extremely difficult–after all, there are nearly an "infinite amount of relationships between various loans that make up a pool." Yikes!

Now without getting into a messy discussion about how Li modeled correlation on the prices of credit default swaps–instead of historical data on actual mortgage defaults–I'll sum it up this way: Li's formula put a pretty bow on a very complex problem.

Armed with Li's formula, Wall Street was able to build an entire industry of packaged mortgage pools (known as collateralized debt obligations, or CDOs). Using this simple formula, all kinds of bonds and loans could be packaged together (securitized) and priced for investors. It was a nice, neat solution to a messy challenge.

Wall Street bankers ate up the output of the Gaussian Copula formula. They had their magic numbers for assessing risk. That's all they needed to get a trillion dollar machine moving. Few asked questions, most just wanted their magic numbers. And critical thinking went out the window.

Complex systems often defy a simple mathematical explanation, but what does this have to do with marketing management?

Mathematical modeling isn't just for financial companies. In fact, analytically savvy companies are now using analytical modeling to discern customer value, reduce customer churn, examine the effect of price changes on demand, and divine the right mix of marketing investments. So modeling–in marketing–is a valuable function. But we can certainly apply some lessons learned from this debacle on modeling default correlation.

First, we cannot turn off our brains. It's tempting to think we've found the magic beans–the single answer that solves an intractable problem. David X. Li and the Wall Street bankers thought they found it. Magic beans cannot replace thinking, questioning, and challenging assumptions.

Second, complex systems are hard to model. Markets, weather–or any system where hundreds, thousands, if not millions of interactions take place at any one time is very difficult to accurately model. If you think you've found the magic beans, be careful.

Third, don't mistake the model for the system. A model is simply a representation of the system. Sometimes a model will predict the behavior of a system correctly and maybe 99% of the time it will get it right. But watch out for the impact of the 1% outliers. They often pack a knockout punch.

For most complex challenges, there are no magic beans, there are no magic formulas. If you think you've finally discovered those magic beans–think of David X. Li, and consider going back to the drawing board.