Why the ROI Curve is the Right Curve to Look at

n my earlier post I talked about the ROI curve for deposit fraud. It is created using real deposit fraud data and it is for one of our deposit fraud solution queues. This ROI curve shows us the loss avoided (or recovered) minus the cost the organization incurs to find that fraud. Remember, Memento’s advanced analytics more accurately risk-rank the alerts, which helps the fraud prevention team review and investigate alerts with the highest probability and greatest potential for loss first.

So Why is the ROI curve the right curve to look at? Well, for starters it tells a story and illustrates answers to important questions. Using our original graph, I’m going share a couple of these stories. In Figure 1 we see that if an analyst works an average of 800 alerts a day (the solid,magenta vertical line), then the company could expected roughly $1.5 million in annual return on the investment of working this fraud alert queue (the black, horizontal line).

Figure 1: Comparing two strategies based on the number of worked alerts

However, also notice that an analyst could also achieve this same $ 1.5 million in annual return on investment by working an average of 35 alerts per day (the dashed, vertical, magenta line in Figure 1). Obviously, working an average of 35 alerts a day consumes a smaller fraction of a bank’s resources dedicated to working this queue than the 800 cited above. On the other hand, working an average of 800 alerts a day means the analyst will find a lot more fraud, and perhaps discourage fraudsters from attempting to defraud the institution, yet the dollar value of loss prevention the organizations realizes is equal. Each strategy has its advantages, both tangible and intangible.

Every company has limited fraud prevention resources so let’s say we want to know how to optimize the return on investment and our resource utilization. In Figure 2 we see that the analyst should work the number of alerts where the graph indicates the highest peak, here an average of 214 alerts a day (the red, vertical line). At this point, the organization will achieve the optimal ROI of roughly $2 million a year (the blue, horizontal line).

Figure 2: Optimizing ROI based on the number of worked alerts

Why do we like the vantage point that the ROI curve provides? Well, from a practical point of view, if the goal is to optimize and understand the return on investment of fraud prevention, then using the ROI curve gives us a good idea of how much work we need to do and estimates the value our work will bring to the organization. This is very useful information indeed when creating a preferred loss mitigation strategy. But to a mathematician, the situation is even better. If we define the optimal ROI as the payoff, it provides an objective function to measure the effectiveness of a given fraud prevention strategy. Such an objective function provides a principled way to take one’s mathematical gloves off and pummel the problem with tools from the theories of optimization and machine learning. And this is what I do.

Now, even to a mathematician, the ROI curve’s utility doesn’t stop with model development. The ROI curve can be used to tackle problems ranging from comparing different solutions to combining fraud queues to formulating a solid business case. But descriptions of such applications will need to wait for another day…

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