Full rate scenario: premium → loss ratio → exposure → ESG → quoted rate
One end-to-end Workers' Compensation rate scenario: earned premium, loss ratio and payroll exposure feed a loss-ratio indication; a real rate engine — discount factors bootstrapped from today's US Treasury curve (Federal Reserve H.15) and shocked by the seven NAIC prescribed interest-rate scenarios — discounts the payout pattern for investment income; the result is an indicated rate per $100 of payroll and a quoted premium for a sample risk.
Indicated manual rate per $100 payroll
| Value | |
|---|---|
| Current manual rate | $3.37 |
| Indicated — undiscounted | $4.45 |
| Indicated — market Treasury curve | $3.97 |
| Indicated — NAIC 7 · Pop-down −3% (conservative) | $4.34 |
Quoted premium — sample risk
payroll/100 × rate × class relativity × experience mod × (1 + schedule)
| Value | |
|---|---|
| At current rate | 152,423 |
| At indicated (market curve) | 179,571 |
| At indicated (NAIC worst scenario) | 196,318 |
| Change vs. current | 17.8% |
Indication steps
| Step | Formula | Value |
|---|---|---|
| On-level earned premium | 43,555,600 | |
| Developed losses | 37,052,000 | |
| Trended, loaded losses | 43,610,020 | |
| Trended on-level premium | 45,766,155 | |
| Projected loss ratio | 95.3% | |
| Indicated rate change | 32.0% |
Present-value factor under the seven NAIC prescribed scenarios
The WC paid pattern (24%, 26%, 15%, 10%, 7%, 5%, 4%, 3%, 3%, 3%) is discounted along forward rates bootstrapped from the last known Treasury curve, then along each NY Reg 126 scenario (up/down 0.5%/yr, up-then-down, pop-up/pop-down 3%). No random draws: the same curve always gives the same rate.
| Year | Par yield | Spot | Forward | Discount factor | Payout share |
|---|---|---|---|---|---|
| 1 | 3.72% | 3.72% | 3.72% | 0.9641 | 24% |
| 2 | 3.61% | 3.61% | 3.50% | 0.9316 | 26% |
| 3 | 3.63% | 3.63% | 3.68% | 0.8985 | 15% |
| 4 | 3.66% | 3.66% | 3.73% | 0.8662 | 10% |
| 5 | 3.68% | 3.68% | 3.78% | 0.8346 | 7% |
| 6 | 3.76% | 3.77% | 4.21% | 0.8009 | 5% |
| 7 | 3.84% | 3.86% | 4.39% | 0.7672 | 4% |
| 8 | 3.92% | 3.95% | 4.58% | 0.7336 | 3% |
| 9 | 4.00% | 4.04% | 4.78% | 0.7001 | 3% |
| 10 | 4.08% | 4.13% | 4.98% | 0.6669 | 3% |
- Defaults are calibrated to the State Farm WC Schedule P analysis saved earlier (≈$3.38 per $100 indicated on an undiscounted basis) but are editable; replace with your own book.
- Discounting losses for investment income inside the indication lowers the required rate; the conservative bound is the NAIC prescribed scenario with the least investment income (usually the 3% pop-down), and the undiscounted indication is what most WC filings show.
- The rate engine is deterministic and data-driven: par yields come from the Federal Reserve H.15 constant-maturity Treasury series (3-month to 30-year) via FRED, are interpolated to annual tenors, bootstrapped to spot and forward rates, and shocked by the seven NY Regulation 126 scenarios used in NAIC cash-flow testing. Stochastic GOES-style paths remain available on /uncertainty/esg for CTE reserves.
- Results are illustrative for education; a filed indication needs a credentialed actuary's review (ASOP 53, ASOP 56).