Loss Picks Explained: LDF, Bornhuetter-Ferguson, and Credibility Blending for PEO Books

A loss pick is the number a PEO's workers' comp program is built on. It is the estimate of what a policy year's claims will ultimately cost, made before most of those claims have been reported and long before any of them have closed. The loss fund is sized from it. Client pricing is derived from it. The carrier's collateral demand is negotiated against it. If the pick is low, the PEO finds out two or three years later, when the fund runs dry on claims that were already in the system the day the pick was made.

Most PEO operators know the pick matters and treat its production as something that happens at the actuary's office. This post is for the operator who wants to understand what comes back, and the underwriter who wants to build a defensible one. We cover the three standard methods, the way they get blended, and the reasons a PEO book should carry loads a single-employer book does not. The method descriptions follow the standard casualty actuarial treatments, including Friedland's reserving text as reproduced in the chainladder documentation and the original 1972 Bornhuetter-Ferguson paper, "The Actuary and IBNR."

At any valuation date, a policy year's reported losses are incomplete. Claims have occurred that have not been reported. Claims that have been reported carry case reserves that will develop, usually upward. Some claims will reopen. The gap between what is on the loss run today and what the year will finally cost is the thing being estimated, and it has two components: development on known claims and incurred-but-not-reported claims. Practitioners often fold both into the term IBNR.

The estimate relies on a loss development factor, or LDF: the ratio of ultimate losses to losses reported at a given age. A 12-month-to-ultimate LDF of 2.00 means that, historically, a year's losses at twelve months of age have doubled by the time the year closes. The reciprocal of the LDF is the percent reported; at an LDF of 2.00, half the ultimate has emerged. LDFs come from the book's own triangles if it has enough history, from bureau or industry patterns if it does not, or from a blend.

Everything that follows is a different way of using the LDF.

Chain-ladder: trust the data

The chain-ladder method, also called the development method, multiplies reported losses by the LDF. Ultimate equals reported times LDF. If a year has $520,000 reported at twelve months and the 12-to-ultimate factor is 2.00, the chain-ladder ultimate is $1,040,000.

Its virtue is that it uses only the year's own experience. Its flaw is the same thing. At early ages, the reported figure is small and volatile, and the LDF is large, so a single claim reported or not reported in the first few months swings the ultimate by its full developed value. A year with one early large claim projects to a disaster; a year where the large claim is reported in month thirteen projects to a dream. Neither is likely true.

Chain-ladder is most reliable for mature years, where most of the ultimate has emerged and the LDF is close to 1.00, and least reliable for the year the PEO is actually trying to price.

Bornhuetter-Ferguson: trust the expectation, adjusted for what has emerged

The Bornhuetter-Ferguson method addresses the immature-year problem by splitting the ultimate into two pieces. The reported piece is taken as is. The unreported piece is estimated from an a priori expected loss, not from the reported figure. Ultimate equals reported losses plus expected losses times the percent unreported, where percent unreported is one minus the reciprocal of the LDF.

The a priori expectation is usually an expected loss ratio applied to the year's premium or exposure. In a PEO context the exposure is the workers' comp charges collected from clients for the year, or classified payroll times manual rates, and the expected loss ratio comes from the program's history, the carrier's pricing, or an industry benchmark.

Continuing the hypothetical: suppose the year's premium is $2,000,000 and the expected loss ratio is 65 percent, so expected losses are $1,300,000. Percent unreported at an LDF of 2.00 is 50 percent. The BF ultimate is $520,000 plus $1,300,000 times 0.50, which is $1,170,000.

Notice that the reported figure contributed only itself. If reported losses had been $300,000 instead of $520,000, chain-ladder would have dropped to $600,000, while BF would have dropped only to $950,000. BF is stable where chain-ladder is volatile, and the price of that stability is that BF leans on an assumption, the expected loss ratio, which may be wrong.

Cape Cod: derive the expectation from the book

The Cape Cod method, also known as the Stanard-Bühlmann method, is BF with the expected loss ratio estimated from the data rather than selected. Reported losses across all years are divided by the "used-up" premium across all years, where each year's used-up premium is its premium times its percent reported, or equivalently premium divided by LDF. That ratio is the expected loss ratio, and it is then applied in the BF formula.

Extend the hypothetical with a prior year: premium $1,800,000, reported losses at twenty-four months $1,050,000, 24-to-ultimate LDF 1.25. Its used-up premium is $1,440,000. The current year's used-up premium is $1,000,000. Combined, reported losses of $1,570,000 over used-up premium of $2,440,000 gives an expected loss ratio of about 64.3 percent. The Cape Cod ultimate for the current year is $520,000 plus 64.3 percent of $2,000,000 times 0.50, or roughly $1,163,000.

Cape Cod's strength is that the expectation is grounded in the program's own results. Its weaknesses, which Friedland's text lays out, are that it assumes one loss ratio applies across years unless trended or adjusted, and that it can be distorted by changes in case reserving strength or in the mix of business. For a PEO book whose client composition changes every year, that second weakness is not theoretical.

Credibility blending: how much to trust each

With three estimates on the table, the underwriter has to pick, and the honest answer is usually a weighted combination. Credibility weighting assigns a weight Z to the data-driven estimate and one minus Z to the expectation-driven estimate, with Z rising as the data matures.

The simplest and most common form uses the percent reported as the weight, which is the logic behind the Benktander approach: at twelve months with 50 percent reported, Z is 0.50, so the blend is half chain-ladder and half BF. In the hypothetical that is 0.50 times $1,040,000 plus 0.50 times $1,170,000, or $1,105,000. At thirty-six months with 85 percent reported, chain-ladder would carry most of the weight, which is right, because by then the year's own data is telling most of the story.

Other credibility formulas scale with claim counts or exposure volume rather than age. The principle is the same. A small, young book should lean on expectations; a large, mature one should lean on its own experience; and the weight should move smoothly between them rather than switching.

The result of all this, for the hypothetical, is a pick in the range of $1.10 to $1.17 million depending on method and blend, against reported losses of $520,000. That spread is the defensible range, and an underwriter who can show how each number was produced can argue for any point in it.

Why PEO books carry upward loads

A loss pick for a single employer is an estimate of that employer's year. A loss pick for a PEO is an estimate of a portfolio that is changing while the year runs, and that structural difference calls for loads the standard methods do not supply on their own. In our own program, three are applied routinely, and we build them into ModIQ's loss pick for the same reason.

The first is client concentration. A PEO book with four hundred clients where the top ten account for a third of payroll is not as diversified as its client count suggests. A single large client's bad year moves the whole book, and the expected loss ratio drawn from the portfolio's history understates the variance. A concentration load raises the pick to reflect that the book's outcome depends on fewer independent risks than it appears.

The second is payroll-growth IBNR. A PEO adds clients through the year, so the exposure at year end is larger than the exposure at the start, and the clients added late have contributed almost nothing to reported losses. Methods that apply a single LDF to the year's reported losses implicitly assume exposure was level. A growing book needs an adjustment for the portion of the year's exposure that has had no time to generate reported claims, or the IBNR is understated in proportion to the growth.

The third is open-reserve margin. Case reserves on open claims are the adjuster's estimate and they develop. A book with a high share of its reported losses in open reserves, rather than paid, carries more uncertainty than the LDF alone captures, especially if the claims operation has recently changed or the claims are in states with long-tail medical. A margin on open reserves acknowledges that the reported figure is softer than it looks.

Applying illustrative loads to the hypothetical blend, say 5 percent for concentration, 3 percent for growth, and 2 percent for open-reserve margin, moves the $1,105,000 pick to about $1,219,000. Those percentages are for illustration only; the right loads depend on the book, and the point is that the unloaded pick was not the answer.

Why "defensible" is the standard

A loss pick is argued over. The carrier's actuary wants it high, because collateral follows it. The PEO's CFO wants it low, because the fund contribution follows it. The sales team wants it low, because client pricing follows it. The number that survives is the one whose derivation can be shown: which LDFs, from what source, which expected loss ratio, from what history, which blend, which loads, and why.

That is the design principle behind ModIQ's loss pick. It runs chain-ladder, Bornhuetter-Ferguson, and Cape Cod on the aggregated, policy-year loss data, applies a credibility blend with the weights visible, applies the PEO loads as named line items, and produces a range with every input exposed. An operator can change the expected loss ratio and see the BF and blend move. A carrier actuary can see where the number came from and argue about an assumption rather than about the number.

Loss picks will never be precise. The goal is for them to be explicit about their reasoning, so that when the year closes and the actual comes in, the PEO knows which assumption was wrong and fixes it for the next pick, rather than discovering that nobody remembers how the last one was built.