Solution: The reinsurer gets 75% × 70% = 52.5% of the premium and pays 75% of the loss:

52.5% × $250,000 – 75% × $59,000 = $87,000.

The purpose of the ceding commission is commonly explained that it reimburses the ceding company for its acquisition and underwriting expenses. This sounds good, but it is not correct. No reinsurer simply takes a pro-rata share of the subject premium and returns the amount paid by the ceding company for expenses. If this were true, reinsurers would not need actuaries and they would all be broke.

In fact, the reinsurer determines the amount of premium it needs to cover the losses and backs out what the ceding company would be. Were there no other purpose for the ceding company, the reinsurer would simply charge the adequate premium.

The purpose of the ceding commission is provide surplus relief. The surplus relief stems from the definition of the unearned premium reserve in statutory accounting and the manner of its capitalization and amortization.

To explain this, we first show a logical but incorrect accounting procedure. We then make one small change to get statutory accounting, and the surplus relief is clear.

Suppose the primary insurer writes a $100 million block of auto insurance on December 31 and pays agents commission and other underwriting expenses of $20. It cedes the business 100% to a reinsurer for a premium of $80 million.

Logically, one might say: the cash flows leave the primary insurer with zero dollars. It also has zero liabilities, since everything is ceded, so there is no change in surplus.

This overlooks the definition of the unearned premium reserve. The unearned premium reserve starts as the written premium and declines to zero as the coverage is provided.

The primary company’s UEPR was $100 million at inception of the policies, since the primary premium is $100 million. If the reinsurance premium is $80 million, only $80 million of the UEPR is taken down. The last $20 million runs off over the policy terms. This is a $20 charge to surplus at policy inception, even though the ceding company has no retained business.

The reinsurance ceding commission solves the problem. The reinsurance premium is $100 million, so all $100 million of UEPR is taken down. The ceding commission is plain income, to offset the excessive reinsurance premium.

This is not the same as the standard explanation. The ceding commission is based on the reinsurer’s estimate of the adequate premium, not on the ceding company’s costs. If the ceding company’s costs are 30% of the premium, but the reinsurer needs 80% of the premium to pay the losses and its own costs, the ceding commission is 20%, not 30%. If the ceding commission were 30%, the reinsurer would expect to lose money. Reinsurers sometimes lose money, but they don’t plan on doing so.