What is the formula for Expected Reinsurer Deficit (ERD)?

• A. ERD = 1% of premium.
• B. ERD = Premium × Loss Ratio.
• C. ERD = Probability (NPV U/W loss to reinsurer) x Avg Severity (U/W loss).
• D. ERD = Probability of any loss × Exposure.

Answer: (C)

The idea here is to capture the reinsurer’s expected monetary shortfall from underwriting losses by combining how often such a deficit might happen with how large the deficit tends to be when it does occur. ERD is essentially the probability that the reinsurer faces a deficit (the underwriting loss event) multiplied by the average size of that deficit when it happens. In formula form, that is a probability of the loss event times the severity of the loss (for the reinsurer), often thought of as the NPV of the underwriting loss to the reinsurer.

Why this form fits best: if deficits occur only with a certain likelihood, and when they occur the loss has a typical, average magnitude, the expected deficit is their product. It properly ties both the chance of adverse outcomes and their typical impact into a single measure.

Contrast with the other ideas: a fixed percentage of premium ignores how large losses can be or how likely deficits are; premium × loss ratio gives an expected claim cost but not the probability-weighted deficit magnitude; and just probability of any loss × exposure estimates how often losses occur and how big the exposure is, but not how large the deficit would be when a loss happens.