Funny Story About Selecting LDFs

My first job as an actuary in 1995 was as a summer intern at an auto insurer in Winston-Salem, NC. It used to be called Integon Insurance, but it changed names a few times over the years and now it's called National General Insurance. I started in the pricing department but at the end of the summer they hired me full-time and I transferred to reserving.

Anyway, one of my tasks in reserving was assisting the chief actuary in making LDF selections for the quarterly reserve review. We had data by accident quarter and development quarter so our triangles were huge. We were active in roughly 20 states at the time and our standard auto policy had I think 7 coverages. Then each of those roughly 140 combinations had its own set of triangles: paid loss, reported loss, paid counts, reported counts, ALAE, salvage & subrogation. That's a huge number of triangles of LDFs where we had to make selections.

Our procedure was that I would make the first pass at selecting LDFs and this would take me a couple of weeks of early mornings and late nights. I would analyze the various triangles to try to understand what was going on. Was there a catastrophe? Tort reform? Adverse selection from a change in risk classification? Do I need to talk with product managers? It went on and on. And then how should I incorporate all of this information to make sensible LDF selections. To do this for a small number of triangles could be an interesting project, but with amount of data we had it was completely overwhelming.

When I'd finished, I'd pass several thick binders along to the chief actuary. In those days we still printed everything out. Then for the next week or so, I'd watch him in his office, thumbing through the pages, smoking his cigarettes, marking it up with a red pen. (Yes, smoking was still allowed in offices North Carolina back in the 1990s.). Then he'd dump it back on my desk so I could type the his changes into Lotus 123. (Lotus 123 is another throwback to the 1990s, an old spreadsheet program that doesn't exist anymore.)

After a few quarters of this mind-numbingly boring task I couldn't take it anymore and here's what I did. I played around and created what I thought was a reasonable algorithm for the computer to select LDFs. I then went back a 2 quarters and used my algorithm to make all the LDFs selections, which took about an hour. All I had to do was write a macro to copy the formulas into the right place in all the different files that contained the triangles. When I summarized the results, I got a total reserve roughly equal to the official value. No real surprise as I had basically reversed engineered the algorithm. The real test was the following quarter.

When the new quarter's data arrived, I ran my macro. The computer selected all the LDFs and I got the estimate of the total reserves in about half a day. It was 100% automated and the results looked completely reasonable. It seemed to easy. So I wrote another macro to flag estimates based on criteria like changes in loss ratio, frequency, severity versus the prior quarter in excess of a certain percentage. That helped me pinpoint potential problems areas without having to look through thousands of numbers myself. I spent another day or two looking very closely at the segments that were flagged or segments with the highest reserves. Most of what I did was adjust LDF selections for the most recent 1 or 2 quarters, making sure the results ultimate loss ratio, severity, frequency, and pure premium still all looked reasonable. I was basically done but I still had another week or two before the chief actuary was expecting me to pass it along to him. I spent the time looking it over, tweaking my code, writing a few more macros to make the process more efficient. At the end of the 2 weeks, I printed everything out and handed him the binders.

He said...nothing. A week later, he handed the binders back to me with notes on the LDF selections he wanted changed. And he hadn't made any more changes to my work than he had done in prior quarters. I spent a few hours typing them in then reran the summaries. There didn't seem to me to be any material difference in the final result. He never did ask my any questions about my process so I kept quiet. It isn't that I did less work overall – the nature of my work changed. I spent more time focusing on bigger-picture issues and far less time agonizing over things like an LDF selection for the 24-27 month development period for collision triangles in Rhode Island.

This story had a part 2 and a part 3 but I'll save that for another time.