How To Pick The Best Loan From A Sequence

Game theory

There is a simple mathematical concept known as the “maximum of sequence” that every banker should know in order to increase performance. The concept is derived from the "Marriage Problem" made popular in the 60’s that presents the following issue: Suppose you must choose a spouse out of 100 applicants. You may interview each one once and after each interview you must decide whether to marry that person or not. If you decline, you lose the opportunity forever. For the uninitiated, the odds of finding the best partner are about 1 in 100. However, after reading this article, you can do dramatically better and then you can learn to apply this solution to a variety of problems around the bank.


The solution to this equation is to talk to 37 potential spouses and then choose the first one that comes after that is better than the 37. Yes, the best suitor maybe in the 37, which means you might get stuck with candidate number 100, but those are the breaks in dealing in probabilities, not certainty.


The good news is that this method raises your odds of picking the best candidate to 37%, the highest that can be achieved within the constraints of the situation. The number 37 comes from dividing 100 by e, the base of the natural logarithms which is roughly equal to 2.72. This law works no matter how many options you are looking at, as you simply divide the number of options by 2.72 and then choose the next option that beats those options from the first group.


For example, suppose you see 20 loans each month and you want to pick the best one. You look at the first 7 (20/2.72) and then pick the loan that has the highest risk-adjusted return of the best loan in the first 7. This not only optimizes your choice, but also optimizes your resources as it allows you not to have to review each loan.


The maximum of sequence optimization works in a variety of situations and can be further adapted for thousands more. Other situation this concept works nicely is when you have to pick a vendor, choosing job candidates, choosing what customers to call on, testing fraud or even when to get gas for the lowest price. In fact, one of the best applications is how to deal with time. If you switch the problem around and say you want to hit a target of x loans before the end of the 12th month, you can choose not to make any loans for the first (12/2.72) four months and then start making all loans that are better and the loans seen during the first four months.  


Of course, not all situations call for looking at options in sequence. In other words, some loans you can review and still might be available two weeks from now. In these cases, game theory of maximum of sequence math shows that you want to choose the best loan (or option) when it is about to become unavailable, even thought you might not get to review all the options.


In the future, we will introduce something called Bayesian analytics to simply solve more complicated problems, but bankers can start by applying the maximum of sequence solution to everyday problems.


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