Zipf’s Law and Your Lenders

April 13, 2016 Dallas Wells


In the mid-1930s, George Kinsley Zipf, a linguist at Harvard University, made the first of a series of fascinating discoveries. After tallying the frequency of word use in many different languages, Zipf noticed a nearly universal distribution. In almost all languages, the frequency of a word is inverse to its rank. In other words, the second most common word is used ½ as much as the most common, and the tenth most common word is used 1/10 as the most common. When plotted on a curve, it looks like this:

Zipf Curve

The really interesting part, though, was that this relationship wasn’t just true for entire languages. It was also true for words in individual books. The frequency table would be very different for Huckleberry Finn than for the King James Bible, but the distribution remained intact.

As Zipf dug deeper, he found that this power law curve applied to much more than language. It also applied to things like city populations, as the most populous city would be twice as big as the second largest city, and 100 times as big as the 100th largest city. Interestingly, the distribution remained over time, so even as the largest cities grew, the entire curve shifted. What started as a language phenomenon is now known as a Zipfian distribution, and it can be applied to far ranging things such as frequency of proteins in a genome sequence or even the number of Twitter followers for NBA teams.

How Zipf Applies to Your Bank

So what does this have to do with your lenders?

Earlier this year, we wrote a blog post about the importance of the top lenders at banks, or “alpha lenders” as we call them at PrecisionLender. We attached some data to a phenomenon that all bankers are already very familiar with, namely that the best lenders in any bank produce the majority of the results. In banking we often call it the “80/20 rule,” which is really just shorthand for the Pareto principle (for you math nerds, a Zipfian distribution is just the discrete version of the continuous Pareto distribution, so the two concepts are mathematical cousins of sorts).

The more we played with this data, though, the more a familiar pattern started to emerge. First, we ranked all lenders that use our tool by portfolio size, and the result was a nearly perfect Zipfian distribution (noticed, of course, by our resident math nerd, Carl Ryden).

Much like individual books, though, individual banks also showed the same distribution. Below is a detailed look at one bank. Its top lender has a portfolio balance over $200 million. Meanwhile, the average balance for all the bank’s lenders with a portfolio (49 in total) is $26 million.

Lender Portfolio Distribution (Individual Bank)

That Zipfian data story repeated itself over and over among the banks we studied. Each column in the chart below represents an individual bank like the one above. The lenders’ portfolio sizes are represented by the colors listed on the right. All of these banks have a few big producers at the top (the aquas, greens, yellow and oranges in each bar) and most of their lenders producing relatively small portfolios (all those shades of purple).

(Bonus: The banks are listed left to right by their number of lenders. This creates – you guessed it – a basic Zipfian distribution.)

Lender Portfolio Distributions (Multiple Banks)

Getting More From Your Best Lenders

While this was an interesting find, we initially thought of it as one of our classic “vanity metrics.” In other words, it was something that was interesting, but didn’t provide much value. But, as we discussed it with a few lenders from the top of those charts, that sentiment changed. In fact, it started to sound a lot like another business from Carl’s background, venture capital.

Fred Wilson, a well-known partner at VC firm Union Square Ventures, published a great post on his AVC blog last week called Losing Money. Here was the part that resonated:

Our first USV fund, our 2004 vintage, has turned out to be the single best VC fund that I have ever been involved in. We made 21 investments. We made money on twelve of those investments. We lost money on nine of them. And we lost our entire investment on most of those nine failed investments. The reason that fund performed so well has pretty much nothing to do with the losses. It was all about five investments in which we made 115x, 82x, 68x, 30x, and 21x.

In other words, if you chart out the returns, there were a couple of massive homeruns, a few middling successes, and then a bunch of zeroes. Fred’s point was that while the zeroes were valuable learning experiences, ALL OF THE PERFORMANCE came from the top of the curve, and his fund succeeded because they used time, money, and resources accordingly.

Loan portfolios in banks are built on similar distributions (FYI, customer profitability also happens to follow a Zipfian distribution in most of the banks we checked), and yet banks focus time, money, and resources at the exact other end of the curve from Fred. In this case I’m not talking about loan losses. Those absolutely need time and attention. I’m talking about all of the rules, systems, and management time put into “corralling” the bank’s least productive lenders.

Carl describes the curve like this. If a bank’s top lender generates a $1.00 of returns, then the fourth best lender would generate $0.25, and the 100th best lender would generate $0.01. In other words, you have dollar lenders, quarter lenders, and so on, all the way down to your penny lenders. The issue is that banks put rules in place to keep their penny lenders from making penny mistakes. And since there are a LOT more penny lenders, that takes a ton of effort and resources from management. In addition, those rules do very little to help your dollar lenders. In fact, the rules put in place to keep penny lenders from making mistakes are actually a hindrance to your dollar lenders being creative and responsive for their borrowers.

For example, in our world of pricing, we see banks spend inordinate amounts of energy trying to avoid pricing exceptions for their penny lenders. “Don’t do any loans over 7 years. Don’t do non-recourse loans under any circumstances. Don’t offer ANY pricing below the hurdle rates.”

The frustration comes from the red tape that bogs down dollar lenders trying to serve the bank’s best clients. Philosophically, the bank would be willing to bend the rules and be responsive to its most important borrowers, but in reality, the structures set in place for the penny lenders make it very difficult to have that flexibility.

Think of it this way. Would it be easier to take a typical nickel lender, and double their production, or take a dollar lender, and make them a $1.05 producer? Also, if you want to move the needle on portfolio performance or asset mix, where are you more likely to make a dent? The focus should be at the top of the curve.

The Rising Tide Lifts All Boats

And the really cool part? Remember that the distributions tend to remain intact, so if you improve the performance at the top of the curve, they don’t put distance between themselves and everyone else. Instead, they lift the performance of the entire curve.

Want to learn more about how these top lenders do it? Check out the latest chapters of our book, Earn It: Building Your Bank’s Brand One Relationship at a Time.

The post Zipf’s Law and Your Lenders appeared first on PrecisionLender.


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