Technical methods · Advanced · ⏱ 12 min
The reserving methods map: ELR, chain ladder, BF, Cape Cod
Four methods, one decision framework. What each assumes, when each wins, and how real reserving actuaries actually blend them across a triangle.
No reserving actuary uses one method. They run several, watch where the answers disagree, and interrogate the disagreement. Here’s the map.
The four workhorses
Expected Loss Ratio (ELR): ultimate = premium × expected loss ratio. Ignores actual claims entirely. Sounds naive: is exactly right when experience is too green to mean anything (a brand-new line, the first months of an accident year).
Chain Ladder: history’s development pattern, projected forward. Trusts actual experience completely: powerful on mature, stable years; unhinged on immature ones. Full build here.
Bornhuetter-Ferguson: the credibility bridge: actuals for what’s emerged, prior for what hasn’t. The default for middle-aged years. Intuition here.
Cape Cod (Stanard-Bühlmann): BF, but instead of assuming an ELR, it estimates one from the triangle’s own reported experience, weighted by how developed each year is. Answers BF’s weakness (“where did that prior come from?”) with “from the data, systematically.”
The pattern behind the choice
Notice the spectrum: ELR trusts the prior 100% → BF/Cape Cod blend → chain ladder trusts experience 100%. The real decision variable is how much the emerged experience deserves to be believed: which is why a standard reserve review often uses ELR for the newest year, BF or Cape Cod through the middle, and chain ladder for mature years, on the same triangle.
The interview question this answers
“Your chain ladder and BF estimates differ by 20% for last accident year. What do you do?” Weak answer: average them. Strong answer: the gap itself is information. Either early experience is genuinely unusual (investigate the large claims) or the prior ELR is stale (investigate pricing changes). The methods aren’t competing calculators; they’re cross-examining witnesses.
Where judgment lives
Factor selection, tail estimation, prior loss ratios, treatment of the weird year: the arithmetic is a spreadsheet, but the reserve is a professional opinion. Take those judgment calls yourself on five triangles, then argue against your own answer the way a reviewing actuary would.