By Eric Maniable *
We propose a little soap opera on the theme of the redemption rate curve. This first article shows the need for the actuary to provide the right answers to the right questions. A first trap, very common and yet rarely raised. The purchase of a life insurance policy is an option widely used by policyholders. This faculty contributes to the attractiveness of life insurance by offering flexibility and liquidity to contracts. Its counterpart is the liquidity risk for the insurer, as well as the change in the profitability profile of the contracts.
The Chief Financial Officer wants to know how much can be bought back in the coming months. The Chief Executive Officer and the Shareholder will want to know the future profitability of his portfolio. And also the potential profitability of a new product. The question asked to the actuary is “build us a redemption rate curve”.
The executives entrusted the study of the total repurchase of a portfolio (more than 15,000 repurchases over more than 20 years and relating to nearly 70,000 contracts) to two actuaries, Mr. Junior and Mrs. Senior. The youngest actuary, Mr. Junior, then starts analyzing his data, uses the usual actuarial methods, … and quickly produces a nice curve. And the leaders are very happy.
But they would like the second actuary, Ms. Senior, to confirm these results. Ms. Senior is experienced. A few days later, it produces two curves, but very different from each other. The first curve is identical to that of Mr. Junior.
This disturbs very strongly the DG, the DAF, … They doubt the intelligence of their employees, the utility of having an actuary, and worse two actuaries who give results as dissimilar. So Senior tells them that her younger brother’s work is just as well as his own. The two curves were built according to several methods (Kaplan-Meier, Nelson-Alaen) which give very close results, whose tests are very good. So she is certain of both results. But, … she is not certain of data.
Indeed, she has noticed that about 15,000 contracts do not have very reliable information, … and therefore she does not know if these contracts are still in force or not. If they are no longer “active,” they are unlikely to be redeemed. This is Hypothesis 1, and Ms. Senior has excluded them from the field of study, as Mr. Junior did. But Mrs. Senior thought that we should not stop at this logic. The second approach, or Hypothesis 2, is to consider that this lack of information does not indicate the inactivity of these contracts. She has kept all contracts in the field of study, assuming they are all still in force. The conclusion is that the truth is between the two curves. The rest of the story is that we had to requalify a large part of the portfolio.
The moral of this story is that the leaders could have had only Mr. Junior, who presented only one of the curves. Only because he made an implicit choice, without referring to his hierarchy, and without evaluating the impact of the choice to make. And so without measuring the impact of this choice on the management and management of the company. But this story of redemption curve was just beginning. Of course, following the next episode.
