Profit Testing and Analysis of Surplus for Life Insurance Contracts
Profit testing
This domain tests whether a contract is profitable after allowing for premiums, claims, expenses, reserves, interest and risk discount. A profit test projects cashflows by duration. A common formula is profit before interest equals premiums minus expenses minus claims minus increase in reserves. The result is accumulated with interest to the end of the year. The profit signature is the sequence of projected profits by policy year. Discounting the signature at a risk discount rate gives NPV; the internal rate of return is the discount rate giving zero NPV. Profit margin is NPV divided by EPV of premiums.
Analysis of surplus
Analysis of surplus explains why actual surplus differs from expected. Sources include interest, mortality or morbidity, expenses, persistency, tax and miscellaneous items. Each source is measured by holding other assumptions at expected values and varying one factor. This helps management identify which assumptions are driving results.
Worked example
A one-year contract has premium 1,000 and expenses 100 at the start, expected claim 600 at the end, and a required reserve of 200 at the end. Interest is 5%. Start cashflow is 900. Accumulated to year end: 900(1.05)=945. End outgo is claim plus reserve, 600+200=800. Profit is 145. If the risk discount rate is 5%, the NPV is 145/1.05=138.10. If actual claims are 550, the mortality surplus is 50 before interest.
Traps
Discounting profits at the valuation interest rate rather than the risk discount rate; omitting the increase in reserves; mixing start-of-year and end-of-year cashflows; and treating a positive profit signature in early years as automatically profitable without discounting.