Loss Triangle Labyrinth - chain ladder practice
The upper-left is history. The dashed cells are money you owe and have not paid - what you must hold reserves against today.
What are the volume-weighted link ratios?
For each step, add up every origin year where both columns are known, then divide.
About Loss Triangle Labyrinth
Develop a run-off triangle with chain ladder link ratios, set the total reserve, and know when to switch to Bornhuetter-Ferguson.
You are handed a run-off triangle of cumulative paid claims in thousands: five origin years (2021 to 2025) as rows, development years as columns. 2021 is fully developed through five columns (1000, 1500, 1750, 1875, 1900); each later year has one fewer entry, down to 2025 with a single figure of 1400. The dashes in the lower-right are money you owe but have not paid, and the game is about estimating it.
Phase 1 asks for the four volume-weighted link ratios, one per development step: for each step, sum the later column across every origin year where both columns are known, sum the earlier column over the same years, and divide. Each ratio is checked within 0.01. Phase 2 asks for the total chain ladder reserve: project each origin year's latest figure to ultimate using the product of remaining link ratios, subtract what is already paid, and sum across years (tolerance 40).
Phase 3 focuses on 2025, the year with one data point and a cumulative development factor near 1.9. You choose a method - stay with chain ladder or switch to Bornhuetter-Ferguson - and then compute the 2025 reserve given a premium of 2,600 and an expected loss ratio of 72%. The value is checked against the BF answer within 40. All answers lock after one check; you can rerun the triangle at the end.
Why quant interviews test this
Every P&C reserving interview starts with a triangle, and this is the standard sequence: compute volume-weighted link ratios, chain the CDFs, state the reserve as ultimate minus paid. Getting the ratio-of-sums estimator right (and saying why it beats a simple average) is the baseline; the differentiator is knowing the one situation where chain ladder blows up.
"When would you not use chain ladder?" is the classic follow-up, and the answer this game drills is the one interviewers want: an immature year with high leverage, where you switch to Bornhuetter-Ferguson and can explain it as a credibility weighting between the development-based estimate and an a-priori expectation, with Z = 1/CDF. This material maps directly to the reserving portions of the actuarial exam track and to case questions at consulting and insurance employers.
The Loss Triangle Labyrinth guide covers how scoring works, the strategy that wins, a worked example and the mistakes most players make.
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