Probable Maximum Loss

Study guides: Exam DISC-RM, Exam 6C

The Probable Maximum Loss (PML) is the loss an insurer's portfolio would suffer from a catastrophe of a specified return period — commonly the 1-in-500 year event for earthquake under OSFI's requirements. It is the central figure in catastrophe risk management: it sizes the reinsurance programme, drives the capital requirement, and is the number the board is asked to accept.

\text{PML}_{p} = \text{VaR}_{p}(\text{Portfolio catastrophe loss})

• In property underwriting the term is used per location. Underwriters and loss control staff use probable maximum loss for one location: the largest loss expected there from a fire, stated in dollars or as a percentage of the location's total values. It sits between two neighbours: the maximum foreseeable loss (MFL), the worst loss likely from a single event, and the maximum possible loss (MPL), the worst that could possibly occur. DISC-RM uses it to determine the potential loss severity of a commercial property, and for business income it is the income lost over the longest probable period of restoration (Business Income Coverage, COPE).
• It is a modelled quantity, not an observed one. PMLs come from catastrophe models built on hazard science (fault maps, ground motion, wind fields), an exposure database (location, construction, occupancy, height, age), a vulnerability function linking hazard intensity to damage, and the financial terms (limits, deductibles, reinsurance).
• Return period language is often misread. A 1-in-500 event has a 0.2\% annual probability; over 30 years the probability of at least one such event is 1 - 0.998^{30} \approx 5.8\%. "Once in 500 years" does not mean "not in our lifetime."
• Gross and net PML are different questions. Gross PML sizes the reinsurance programme; net PML — after reinsurance and after any reinstatement premiums — is what actually hits capital. OSFI's earthquake requirements test whether the insurer's financial resources cover the net exposure.
• Model uncertainty is large. Different vendor models produce materially different PMLs for the same portfolio, and all are sensitive to exposure data quality. Using a single model's output as a precise figure is a Model Risk failure; the defensible practice is multiple models, sensitivity testing, and disclosure of the basis.
• Exposure data quality dominates. A PML computed on unmapped or mis-coded locations is wrong regardless of the model's sophistication — one of the most common and least visible errors in catastrophe management.
• The PML feeds FCT and ORSA: the catastrophe scenario in the financial condition testing report is usually built from it, and the internal target should be set so the ratio survives the net figure.

Sizing a Catastrophe Programme From the PML An insurer's modelled earthquake PMLs are: 1-in-100, \$180 million; 1-in-250, \$310 million; 1-in-500, \$430 million. Its reinsurance programme retains \$40 million and covers up to \$350 million. Capital available is \$390 million and the base solvency buffer is \$230 million.

Assess the adequacy of the programme.

Answer At the 1-in-500 level the programme is exhausted. The insurer retains:

\begin{align*}
\text{Net loss} &= \$40\text{M} + (\$430\text{M} - \$350\text{M}) \\
&= \$40\text{M} + \$80\text{M} \\
&= \$120\text{M}
\end{align*}

Effect on the capital ratio, taking the loss after tax at roughly \$88 million:

\begin{align*}
\text{MCT} &= \frac{\$390\text{M} - \$88\text{M}}{\$230\text{M}} \\
&= 131\%
\end{align*}

The insurer survives — above the 100\% minimum — but falls below the 150\% supervisory target, with an earthquake to pay for, a damaged region, likely reinstatement premium to find, and no easy access to capital markets.

What to consider:

• Buy the top layer. Extending cover from \$350M to \$430M removes the \$80M excess exposure. The question is whether that layer's premium is worth the roughly 26 points of post-event MCT ratio it protects.
• Check reinstatements. If the programme has limited reinstatements and a foreshock or a second event occurs, the analysis above is optimistic.
• Check the model. A single model's 1-in-500 figure carries real uncertainty; a second model might put it at \$550 million, at which point the retained loss is \$240 million and the conclusion changes entirely.
• Reinsurer credit. A \$310 million recovery is only worth what the reinsurers pay. Their credit standing and any concentration among them is part of the assessment, and it matters most in exactly the scenario where every cedant is claiming at once.