Funny Story About Selecting LDFs
My first job as an actuary in 1995 was as a summer intern at an auto insurance company. 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. That multiplies out to 140 segments to analyze each with 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 which would take me a couple of weeks of early mornings and late nights. I'd have to 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 cigarettes, red pen in hand. (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 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 2 quarters and used my algorithm to make all the LDFs selections, which took about an hour, total. 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 too easy. So I wrote another macro to flag estimates based on criteria like changes in loss ratio, frequency, and severity versus the prior quarter that were in excess of a certain percentage. That helped me pinpoint potential problem areas without having to wade 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 resulting loss ratios, severities, frequencies, and pure premiums 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 double and triple-checking, 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 which LDF selections he wanted changed. And somewhat surprisingly he hadn't made any more changes to my work than he had in prior quarters. I spent a few hours typing everything in then reran the summaries, and there didn't seem to be any material difference in the final result. I was very relieved! And he never asked any questions about my process so I kept quiet. It isn't that I did less work overall but 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. My new process helped me understand the overall business far better.
This story has a part 2 and a part 3 but I'll save that for another time. Part of the reason I had the opportunity to do all this is that the chief actuary gave me a lot of freedom. He didn't look over my shoulder and I have always appreciated supervisers like that. I don't really know whether he had great trust in me or whether he was just plain lazy! But whatever, it all worked out. :-)
