I85PREP
⌘ K
CRM Risk study materials
CRM Risk study resources

Forecasting Retained Loss with a Thin Five-Year History

CRM Risk · Put your knowledge to work in context.

All case studies

Forecasting Retained Loss with a Thin Five-Year History

Ryder Fleet Services operates 120 power units; the fleet will be 132 next budget year. Over the last five accident years the auto liability program produced 240 claims and $26.4M of ground-up incurred losses, of which $14.2M fell in the layer above the $250,000 per-occurrence self-insured retention (18 claims). Claim frequency has tracked fleet size. Average severity, driven by litigation and medical costs in the markets served, has risen about 5% a year. Losses in the $250,000 to $500,000 range have run at 14 claims and $4.9M ground-up over the five years, an average of $170,000 per claim that would move into the company's retention if the SIR rose to $500,000. The insurer offers a 12% credit on the $4.1M liability premium for that change and wants $1.2M of collateral. The CFO wants next year's retained and transferred loss figures with assumptions stated.

1. Forecast next year's retained and transferred losses, showing each step and the arithmetic.

Read the worked answer

Step 1 - split the five-year history

  • Ground-up incurred: $26.4M; layer above the $250k SIR: $14.2M; retained portion: $26.4M - $14.2M = $12.2M.
  • Annual average retained: $12.2M / 5 = $2.44M, or $20,333 per power unit.
  • Annual average transferred: $14.2M / 5 = $2.84M, or $23,667 per unit.

Step 2 - scale to the exposure

The stated assumption is frequency proportional to fleet size, so unit cost scales linearly.

  • Retained: $2.44M x (132/120) = $2.68M.
  • Transferred: $2.84M x (132/120) = $3.12M.

Step 3 - trend severity to the budget year

The average accident year sits around mid-2022; the budget year is 2026, roughly 3.5 years of trend.

  • 1.05^3.5 = 1.19 (at 3 years it is 1.16; at 4 years, 1.22).
  • Retained: $2.68M x 1.19 = about $3.2M (range $3.1M-$3.3M).
  • Transferred: $3.12M x 1.19 = about $3.7M.

Sanity check: total ground-up of roughly $6.9M against $4.1M of excess premium is a plausible 90% loss ratio on the transferred layer once expenses and risk margin are added - if the answer had the insurer paying more than it collects, the trend or the layer split would need re-examination.

What this is not

It is an expected value, not a budget. It says nothing about the 90th percentile, which is what the CFO actually needs, and it assumes the 14 claims in the $250k-$500k band stay in that band.

2. Which assumption would most damage the forecast if it were wrong, and what would you do before letting anyone rely on the number?

Read the worked answer

The fragile assumptions, ranked

  1. Development of the $14.2M above-SIR total. Incurred includes case reserves; a handful of large claims dominate the layer. One claim developing like the open files in this book can move the transferred figure by 10-15% and the retained figure less. Ask for paid-versus-incurred triangles on the 18 large claims and the age of the largest reserves.
  2. Constant 5% severity trend. Three years of 5% versus 8% changes the answer by roughly 10%. Trend fitted to five noisy years is weakly identified, and the mix can shift independently (new territories, heavier trucks, a plaintiff-friendly venue).
  3. Frequency proportional to units. Adding 12 units is not neutral if they run new routes, new drivers, or higher-mileage duty cycles.
  4. No coverage or retention changes. Confirm the SIR and limits are identical across all five years; a limits change mid-period corrupts the layer split.

What to do before signing off

  • Present the CFO with a range, not a point: rerun at 3% and 7% trend and at flat versus per-unit frequency.
  • If a 90% confidence budget is genuinely needed, fit a frequency-severity model (Poisson count, lognormal severity) rather than trending an average, and validate it against the observed volatility of annual retained loss.
  • Test the model by back-forecasting one year you already know.
  • State explicitly that five years is thin: one bad year is 20% of the dataset, so the estimate should be refreshed quarterly as the year develops and never presented without its range.

3. Should Ryder raise the SIR to $500,000? Set out the arithmetic and the conditions under which you would say yes.

Read the worked answer

The arithmetic

  • Additional expected retention: $4.9M of band losses over five years, but only the slice above $250k shifts, at $170k per claim x 14 claims = $2.38M, or $0.48M a year.
  • Trend and exposure adjust: $0.48M x 1.10 x 1.19 = about $0.63M a year of additional expected retained loss.
  • Premium credit offered: 12% x $4.1M = $0.49M.
  • Net expected cost of the change: roughly $140k a year worse, before collateral.
  • Collateral: $1.2M tied up; at a 6% opportunity cost that is another $72k a year.

So on expected value the offer fails, and it also increases variance, because the $250k-$500k band is lumpy - a year with three such claims costs $0.5M more than the average. The insurer is pricing the transfer above its expected cost, which is normal, but at 12% it is pricing it well above.

When I would say yes

  • Credit rises to roughly $0.75M-$0.80M (18-20%), which covers expected retention plus a margin for variance.
  • The company can demonstrate better in-house claims handling on the retained layer (early reporting, nurse triage, return-to-work) that actually reduces the band's severity.
  • Collateral is cheap or can be posted with letters of credit the treasury already holds.
  • The CFO wants to trade premium spend for self-funding as a deliberate step toward a captive, in which case the SIR decision is a trial run rather than a cost play.

Otherwise: decline, and use the analysis to renegotiate. Asking the insurer to justify a credit below the marginal expected loss is a legitimate and productive conversation.