By Blaise Jeutang Ndongmo Kendah, Deputy General Manager
Activa Vie Cameroon
Teacher at IIA and ESSFAR
In recent years, life insurance companies in the CIMA zone have gradually gained a positive reputation because they almost always fulfill their commitments to policyholders. This result is not random, but rather the result of rigorous actuarial management. To ensure the fulfillment of these commitments, actuaries use an essential mechanism called mathematical provisions (PM), which allows life insurance companies to have the necessary funds to honor their contractual obligations.
According to the CIMA Code in its article 334-2, Mathematical Provisions are defined as the difference between the probable current values of the commitments respectively made by the insurer and the policyholders. This definition is the prospective definition adopted by CIMA.
In simple terms, Mathematical Provisions (PM) are defined as an amount of money that the life insurance company sets aside to be able to meet its present and future commitments to policyholders.
In principle, the actuary evaluates the PM according to the method prescribed by the regulator or the method chosen by their organization (for their own analyses), and the question is whether the company has this amount or not. If it does not have this amount, it will have to establish it.
In the daily activities of a life insurance company, several questions are generally asked about PMs: Why provision? When should we evaluate the PMs? Why evaluate them? Their importance? The method used? Why are some PMs negative? and how to manage negative PMs? How do they evolve over time? What is their impact on the annual result?
WHEN TO EVALUATE MATHEMATICAL PROVISIONS?
Mathematical Provisions can be evaluated at any time while a contract is in force, that is, at any time after its subscription and before its expiration. It is recommended to evaluate the PMs once a year, but it is necessary to evaluate them at least every quarter to assess their consistency and also as part of the quarterly evaluations of the company’s performance.
They are also evaluated during the profit testing period, a phase where we ensure that the product is profitable (or that it meets certain specific conditions) before being marketed. Actuarial teams are responsible for evaluating the PMs.
NEGATIVE MATHEMATICAL PROVISIONS
According to the definition mentioned above, we can have negative PMs only if the insured’s commitment is higher than that of the insurer.
We generally observe these cases in the early years of contract life or in cases where the covered risk is decreasing (for example, Decreasing Term with decreasing capital) or also when we apply the Zilmérisation principle (This is a principle that consists of partially or totally taking into account the commissions prefinanced to the sales force during the early years of a contract’s life in the evaluation of PMs. Zilmérisées PMs are generally lower than classical PMs. Zilmériser comes from German AUGUST ZILMER [1831 – 1893]) in the evaluation of PMs. This principle is generally applied to mixed products.
Negative Mathematical Provisions are a danger for life insurance companies, as they reduce the company’s commitment. This is why conventionally all negative PMs are systematically set to zero in order not to reduce the company’s commitment. However, when they are negative, it does not necessarily mean that the company’s commitment is zero, therefore, life insurance companies would benefit from establishing provisions for contracts that generate negative PMs.
WHAT METHODS ARE USED FOR THE EVALUATION OF MATHEMATICAL PROVISIONS?
The validated method for the evaluation of Mathematical Provisions by CIMA is the prospective method mentioned above. There is also the retrospective method, the recurrence method, the cash flow method, and many others.
In general, the chosen method is not the most important, but the one that is mathematically coherent, logical, and allows the company to ensure its contractual commitments is the most important. Companies would benefit from evaluating PMs with different methods and assumptions adapted to their portfolio and environment in order to identify the best method for their portfolio, without forgetting the method prescribed by the regulator.
DO TARIFF ASSUMPTIONS NEED TO BE EQUAL TO PROVISIONING ASSUMPTIONS?
In our environment, we apply the same tariff assumptions to provisioning assumptions when calculating PMs. Is this logical? Why is it so?
In reality, tariff assumptions should be different from provisioning assumptions, as we are in an environment that changes over time and sometimes drastically: life expectancy, inflation, the evolution of scientific discoveries in genetics, etc.
The conditions under which we took out a contract ten years ago are no longer the same today.
For example, life expectancy at birth in Cameroon was 53.88 years in 2010 and in 2020 it is 60.33 years. These statistics are even better in 2026. Thus, we observe a considerable improvement in life expectancy. The same goes for the cost of living, which has changed significantly over time.
For example, life insurance contracts taken out before 2011 in our portfolios are not on the same basis. The tariff is based on the CIMA TD table, while the PMs are based on the CIMA H table. This is the result of the change in mortality tables in 2012 by CIMA (which stemmed from the fact that CIMA estimated that the tables used were no longer adapted to the population).
Are the mortality tables used today suitable for our portfolios? Only a study can confirm this assertion.
The management loadings planned ten years ago in the tariffs should ideally have experienced inflation. The same goes for life expectancy at birth as mentioned above.
Based on this observation, we believe that these pricing bases should be different from the provisioning bases for long-term products. Below, you will see the impact on PMs when we modify the provisioning bases.
EVOLUTION OF MATHEMATICAL PROVISIONS AND PARAMETERS THAT IMPACT PMs
In this section, we will present simulations of PMs for a classic mixed product. That is, a contract that guarantees a capital sum in case of death during the contract period or in case of survival at the end of the contract. For this simulation, we used a 50-year-old insured person for a capital sum of 1 franc at the end of the contract for a duration of 10 years. The PMs are evaluated based on the prospective method.
– PM Single Premium CIMA H: These are the classic PMs evaluated based on the CIMA H mortality table.
– PM Annual CIMA H Classic: These are the classic PMs with annual premium evaluated based on the CIMA H mortality table.
– PM Annual CIMA TD: These are the classic PMs with annual premium evaluated based on the CIMA TD mortality table (old mortality table).
– PM Annual Zilmérisé CIMA H: These are the classic PMs with annual premium evaluated based on the CIMA H mortality table taking into account the total prefinancing of due commissions.
– PM CIMA H +20%: These are the classic PMs with annual premium evaluated based on the CIMA H mortality table with the provision assumption of +20% of management and acquisition loadings.
– PM CIMA H -20%: These are the classic PMs with annual premium evaluated based on the CIMA H mortality table with the provision assumption of -20% of management and acquisition loadings.
Observations:
– Zilmérisées PMs are the lowest (they are generally lower);
– Increasing management and acquisition loadings generally increase PMs, while decreasing loadings decrease PMs;
– For this case, there is not a big difference between classic PMs CIMA H and CIMA TD;
– Single premium PMs are the highest;
– Regardless of the method used, all PMs converge towards the guaranteed capital (a measure of consistency to always validate).
This is just a simulation to illustrate how PMs can evolve over time and based on chosen assumptions. As an actuary, we should practice this exercise on all types of products in our portfolio and assess the impact on results (Stress Test).
WHY EVALUATE MATHEMATICAL PROVISIONS?
1. To determine the minimum solvency margin of the company.
In article 337-3, the CIMA code defines the minimum solvency margin amount as equal to 5%*85%*PM. Therefore, a poor evaluation of PMs will have an impact on the minimum solvency margin. This is why actuarial teams are generally advised to be pessimistic (to be cautious in evaluation assumptions) in their approach to PM evaluation. Because a margin of error of (+/-) 5% can have a considerable impact on the minimum solvency margin.
2. To evaluate surrender values.
In article 76, the CIMA code defines the determination of the surrender value as equal to a maximum of 5% of the PM if the contract duration is less than 10 years, and equal to the PM if the duration is 10 years or more.
3. To determine the profitability of the portfolio’s claims.
For example, each time we market a product with a death benefit, the ultimate risk is to pay the guaranteed capital during the coverage period, so it is necessary to evaluate the PM of this contract at all times. The profit on claims over the period is defined by the following formula:
4. To determine if a product is profitable before marketing (during the profit testing phase).
In a profit testing module, we assess the product’s profitability based on tariff and provisioning assumptions in order to achieve a required profitability.
5. To determine the company’s profitability.
In a company’s general income statement, it is clear that the PM charge (closing PM minus opening PM) is an integral part of the calculation of the company’s annual profitability. The higher the charge, the more the company should provision. Of course, a poor evaluation would have an impact on the annual result.
This is why it is always important to have your PMs validated by external firms to challenge the results obtained internally.
By convention, a difference of (+/-) 5% between the work of the external firm and the company is generally validated. In reality, this gap should be minimized. Prudently, one should always test the company’s profitability by oscillating the PM charge by (+/-) 5%, especially if there is a gap between the results of the external firm’s work and the company.
Identifying the ideal method for evaluating our PMs can be operationally tricky, especially for mixed products. Having high PMs allows the company to have a high minimum solvency margin, enough liquidity for investments, more cash on investment returns, and high surrender values.
However, having high PMs is a risk for companies with high lapses in the early years of contracts, as they will pay high surrender values on contracts where they may have prefinanced commissions without always having the possibility of recovering them.
On the other hand, having low PMs means a low minimum solvency margin, little cash to invest, little return on investment, and consequently low surrender values. Low surrender values can discourage policyholders from subscribing to contracts.
Therefore, it is up to the actuary to find the right method and assumptions for the company, shareholders, and policyholders.
BK
