Main Determinants of Profit-Sharing Policy in the French Life Insurance Industry


The current low interest rate environment and the coming into force of Solvency II raise questions about the stability of the life insurance industry in Europe and the sustainability of traditional insurance products. We use a data set built from French supervisory reports to investigate the drivers of the participation rates (equivalent to annual yields) served on euro-denominated life insurance contracts over the period from 1999 to 2013. Our analysis confirms practitioners’ intuition on the alignment with the 10-year French government bond; we later analyse the deviation of the participation rates from this reference. Our data indicate that financial margins are more strictly targeted than participation. We find evidence that surrenders are fairly uncorrelated with participation, suggesting that other levers are used to monitor them. While higher asset returns can imply better yield for policyholders, riskier portfolios do not necessarily translate into better participation.

This is a preview of subscription content, access via your institution.

Figure 1


  1. 1.

    Swiss Re (2012); Hieber et al. (2015); Berdin and Gründl (2015); Moody’s (2015).

  2. 2.

    see e.g. Schmeiser and Wagner (2015).

  3. 3.

    In France in 2013, the mathematical reserves (MRs) for life insurance with participation added up to more than EUR 1.4 trillion, i.e. about 70 per cent of the French gross domestic product—see

  4. 4.

    An official general definition of surrenders is provided in the delegated acts of the Solvency II Directive (see Commission Européenne (2015), p. 21), yet a proper definition of lapse could not be found. In the academic literature on life insurance, both terms are broadly used as synonyms (see Eling and Kochanski 2013). In the context of this article, for clarity reasons, we choose to use exclusively the word surrender, which we define as the policyholder’s decision to fully or partially terminate his policy and withdraw the corresponding surrender value.

  5. 5.

    see e.g. Eling and Holder (2013).

  6. 6.

    Grosen and Jørgensen (2000).

  7. 7.

    Hansen and Miltersen (2002).

  8. 8.

    Ballotta et al. (2006).

  9. 9.

    Planchet and Thérond (2007).

  10. 10.

    Bauer et al. (2006).

  11. 11.

    Hainaut (2009).

  12. 12.

    Gandolphe (2014).

  13. 13.

    Bacinello (2001)

  14. 14.

    Gerstner et al. (2008).

  15. 15.

    Milhaud et al. (2010)

  16. 16.

    Loisel and Milhaud (2011).

  17. 17.

    see e.g. Eling and Kochanski (2013).

  18. 18.

    Note that we indicated the current binding constraint, but the Code des Assurances stipulates that after eight years the technical rate is also subject to an upper limit of 3.5 per cent. These limits were set in their current form in 1995. See Code des Assurances:

  19. 19.

    See Darpeix (2016).

  20. 20.

    As of 2014, 75 per cent of mathematical provisions for individual euro-denominated life insurance products were associated with a 0 per cent technical rate, and 84 per cent had technical rates lower than 1 per cent.

  21. 21.

    Other contractual mechanisms exist (e.g. promotional rates) but the taux minimum garanti is clearly the most common.

  22. 22.

    Before 1995, this limit was 90 per cent [Arrêté du 28 mars 1995, JORF no. 83 du 7 avril 1995, entrée en application au 1er juin 1995]. See Arrêté du 28 mars:

  23. 23.

    Other limitations were included in 2010 with reference to the maximal technical rate and the average rate served to the policyholders over the previous two years.

  24. 24.

    The C21 tabs of the prudential reports are used by controllers to investigate each firm’s guarantees, but this information is not standardised and therefore not necessarily comparable between firms at the macro level.

  25. 25.

    Article A.132-7 of the Code des Assurances stipulates that the amounts stored in the PPB be released within eight years. See Code des Assurances:

  26. 26.

    For instance, the Contributions sociales were established in 1990 and did not apply to life insurance interests before 1997. The tax rate on the accrued interests rose from 0 per cent before 1996 to 15.5 per cent in 2014, but the largest part of the increase occurred between 1996 and 1998 when the tax rate was already 10 per cent. Similarly, since 1983, contracts of more than six years benefitted from a full income tax exemption. In 1990, this exemption was only granted after eight years, and in 1998, the full exemption became a reduced taxation at a rate of 7.5 per cent. Since then, the tax brackets have not changed. Consequently, with our database covering the period 1999 to 2013, we are not able to assess the impact of these major fiscal changes.

  27. 27.

    The expression “insurance undertaking” should be understood in its broadest sense as it includes all the undertakings in the insurance sector that are under ACPR supervision. For the life insurance market, there are three main French insurance legislation regimes, namely the Insurance Code (Code des Assurances), the Mutual Insurance Code (Code de la Mutualité) and the Social Security Code (Code de la Sécurité Sociale), all regimes falling under ACPR supervision. See Code des Assurances:; Code de la Mutualité; Code de la Sécurité Sociale

  28. 28.

    See for a description (in French) of the reporting templates. In short, undertakings must submit an annual report including general information, accounting documents (balance sheet, P&L, etc.) and data for prudential needs, i.e. credit, reinsurance, solvency, reserves reports.

  29. 29.

    Technically speaking, we consider contracts classified in categories 1 (Contrats de capitalisation à prime unique), 2 (Contrats de capitalisation à prime périodique), 4 (Autres contrats individuels d’assurance vie à prime unique) and 5 (Autres contrats individuels d’assurance vie à prime périodique) according to article A.344-2 of the Code des Assurances. Note that these categories are only variations on the French individual saving contracts. In the categories 1 and 4, contracts with a single premium are considered, whereas the categories 2 and 5 are dedicated to regular premiums. The categories 1 and 4 have different fiscal features. In practice, category 4 is clearly the most important in terms of mathematical reserves and drives the results. See Code des Assurances:

  30. 30.

    Note that the final scope excludes the undertakings specialised in providing pension, disability or healthcare insurance (Institutions de prévoyance) which are ruled by the Code de la Sécurité Sociale: see

  31. 31.

    Milhaud et al. (2011).

  32. 32.

    Eling and Kiesenbauer (2011).

  33. 33.

    Lorson and Wagner (2014).

  34. 34.

    Defined here as the ratio of the financial profits not distributed to policyholders relative to the mathematical reserves since the financial products generated by the company can either be stored in the PPB for future use or distributed to the policyholders via the participation rate, or be included in the company’s financial income (with potential distribution to the shareholders), analogous to the optimal dividend strategies surveyed in Avanzi (2009).

  35. 35.

    This duration is largely driven by the fiscal advantage to policyholders after eight years.

  36. 36.

    Bonnin et al. (2014).

  37. 37.

    Consistent with Article 45 of the Solvency II Directive, the Own Risk Solvency Assessment is a fundamental part of the internal risk management system for an insurer, taking into account its specific risk profile, its risk tolerance and its strategy. This system allows continuous compliance with the Solvency II requirements and monitoring of the relevance of the capital calculation model. See also Guibert et al. (2014).

  38. 38.

    See e.g. Baltagi (2013) for a description of classic techniques used for panel data.

  39. 39.

    Bond (2002).

  40. 40.

    Judson and Owen (1999).

  41. 41.

    Computations are carried out with Stata.

  42. 42.

    See e.g. Arrondel et al. (2013).

  43. 43.

    A tentative categorisation of strategic “patterns” is explained in Appendix 4.

  44. 44.

    For example, in Germany life insurance products have high fixed guarantees throughout the duration of the contract. The main part of the guarantees is attached to this fixed guarantee level that was set when the contract was underwritten. Indeed, this upper guaranteed level is regulated and is fixed at 60 per cent of the average returns of the 10Y government bonds. From 01 January 2015, the German parliament decreased the upper bound level from 1.75 to 1.25 per cent for new business and the future premiums on the ongoing contracts.

  45. 45.

    Note, however, that one subtlety of the French legislation is that there are so-called “mutual insurers” that are ruled by the Code des Assurances rather than by the Code de la Mutualité (the Sociétés d’assurance mutuelle, or mutual insurance corporations), which are often sub-branches of large insurance corporations. We do have several undertakings of this type in our sample.

  46. 46.

    In the past, there have been concerns about the PPB management. For example, the highest French public law court, the Conseil d’État (“CE”) confirmed several times ACPR’s decision that PPB should neither be monitored nor mitigated (see CE, 5 May 2010, no 307089 or CE, 30 March 2007, no 277991). Those rulings indicate that insurance companies might already have tried to implement such schemes. Note, however, that in the case of liabilities’ portfolio transfer, CE ruled that companies do have leeway to reallocate the PPB, except for ring-fenced funds (see CE, 24 November 1989, nos. 92619 or 92621).


  1. Arrondel, L., Debbich, M. and Savignac, F. (2013) ‘Financial literacy and financial planning in France’, Numeracy 6(2).

    Article  Google Scholar 

  2. Avanzi, B. (2009) ‘Strategies for dividend distribution: A review’, North American Actuarial Journal 13(2): 217–251.

    Article  Google Scholar 

  3. Bacinello, A. (2001) ‘Fair pricing of life insurance participating policies with a minimum interest rate guaranteed’, ASTIN Bulletin 31(2): 275–297.

    Article  Google Scholar 

  4. Ballotta, L., Haberman, S. and Wang, N. (2006) ‘Guarantees in with-profit and unitized with-profit life insurance contracts: Fair valuation problem in presence of the default option’, Journal of Risk and Insurance 73(1): 97–121.

    Article  Google Scholar 

  5. Baltagi, B.H. (2013) Econometric Analysis of Panel Data, 5th edn, New York: John Wiley.

    Google Scholar 

  6. Bauer, D., Kiesel, R., Kling, A. and Ruß, J. (2006) ‘Risk-neutral valuation of participating life insurance contracts’, Insurance: Mathematics and Economics 39(2): 171–183.

    Google Scholar 

  7. Berdin, E. and Gründl, H. (2015) ‘The effects of a low interest rate environment on life insurers’, The Geneva Papers on Risk and InsuranceIssues and Practice 40(3): 385–415.

    Article  Google Scholar 

  8. Bond, S.R. (2002) ‘Dynamic panel data models: A guide to micro data methods and practice’, Portuguese Economic Journal 1(2): 141–162.

    Article  Google Scholar 

  9. Bonnin, F., Planchet, F. and Juillard, M. (2014) ‘Best estimate calculations of savings contracts by closed formulas: Application to the ORSA’, European Actuarial Journal 4(1): 181–196.

    Article  Google Scholar 

  10. Commission Européenne (2015) Réglement Délégué (EU) 2015/35 du 10 octobre 2014 complétant la directive 2009/138/CE du Parlement européen et du Conseil sur l’accès aux activités de l’assurance et de la réassurance et leur exercice (solvabilité II), OJ L.12/1.

  11. Darpeix, P.-E. (2016) Le taux technique en assurance vie (Code des Assurances), Analyses et Synthèses 66, Paris: Autorité de Contrôle Prudentiel et de Résolution.

    Google Scholar 

  12. Eling, M. and Holder, S. (2013) ‘Maximum Technical Interest Rates in Life Insurance in Europe and the United States: An Overview and Comparison’, The Geneva Papers on Risk and InsuranceIssues and Practice 38(2): 354–375.

    Article  Google Scholar 

  13. Eling, M. and Kiesenbauer, D. (2011) ‘Does surplus participation reflect market discipline? An analysis of the German Life Insurance Market’, Journal of Financial Services Research 42(3): 159–185.

    Article  Google Scholar 

  14. Eling, M. and Kochanski, M. (2013) ‘Research on lapse in life insurance: What has been done and what needs to be done?’, The Journal of Risk Finance 14(4): 392–413.

    Article  Google Scholar 

  15. Gandolphe, S. (2014) Etude sur les taux de revalorisation des contrats individuels d’assurance vie au titre de 2013. Analyses et Synthèses 26, Paris: Autorité de Contrôle Prudentiel et de Résolution.

    Google Scholar 

  16. Gerstner, T., Griebel, M., Holtz, M., Goschnick, R. and Haep, M. (2008) ‘A general asset-liability management model for efficient simulation of portfolios of life insurance policies’, Insurance: Mathematics and Economics 42(2): 704–716.

    Google Scholar 

  17. Grosen, A. and Jørgensen, P.L. (2000) ‘Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies’, Insurance: Mathematics and Economics 26(1): 37–57.

    Google Scholar 

  18. Guibert, Q., Juillard, M., Nteukam Teuguia, O. and Planchet, F. (2014) Solvabilité prospective en assurance: Méthodes quantitatives pour l’ORSA, Assurance Audit Actuariat, Paris: Economica.

    Google Scholar 

  19. Hainaut, D. (2009) Profit sharing: a stochastic control approach, Bulletin Français d’Actuariat, 9(18): 65–78.

    Google Scholar 

  20. Hansen, M. and Miltersen, K.R. (2002) ‘Minimum rate of return guarantees: The Danish case’, Scandinavian Actuarial Journal 2002(4): 280–318.

    Article  Google Scholar 

  21. Hieber, P., Korn, R. and Scherer, M. (2015) ‘Analyzing the effect of low interest rates on the surplus participation of life insurance policies with different annual interest rate guarantees’, European Actuarial Journal 5(1):11–28.

    Article  Google Scholar 

  22. Judson, R.A. and Owen, A. (1999) ‘Estimating dynamic panel data models: A guide for macroeconomists’, Economics Letters 65(1): 9–15.

    Article  Google Scholar 

  23. Loisel, S. and Milhaud, X. (2011) ‘From deterministic to stochastic surrender risk models: Impact of correlation crises on economic capital’, European Journal of Operational Research 214(2): 348–357.

    Article  Google Scholar 

  24. Lorson, J. and Wagner, J. (2014) ‘Sales efficiency in life insurance: The drivers for growth in the German market’, The Geneva Papers on Risk and InsuranceIssues and Practice 39(3): 493–524.

    Article  Google Scholar 

  25. Milhaud, X., Gonon, M.-P. and Loisel, S. (2010) ‘Les comportements de rachat en Assurance Vie en régime de croisière et en période de crise’, Risques 83(83): 76–81.

    Google Scholar 

  26. Milhaud, X., Loisel, S. and Maume-Deschamps, V. (2011) ‘Surrender triggers in life insurance: what main features affect the surrender behavior in a classical economic context?’ Bulletin Français d’Actuariat 11(22): 5–48.

    Google Scholar 

  27. Moody’s (2015) Low Interest Rates are Credit Negative for Insurers Globally, but Risks Vary by Country, Technical report, from

  28. Planchet, F. and Thérond, P.-E. (2007) Mesure et gestion des risques d’assurance: Analyse critique des futurs référentiels prudentiel et d’information financière, Assurance Audit Actuariat, Paris: Economica.

    Google Scholar 

  29. Schmeiser, H. and Wagner, J. (2015) ‘A proposal on how the regulator should set minimum interest rate guarantees in participating life insurance contracts’, The Journal of Risk and Insurance 82(3): 659–686.

    Article  Google Scholar 

  30. Swiss Re (2012) Facing the interest rate challenge, sigma No. 4/2012, Zurich: Swiss Reinsurance Company Ltd.

Download references


The authors are very thankful to An Chen for her thorough reading and discussion of an earlier version of this paper. They wish to thank participants of an internal ACPR seminar and the 2015 IAA colloquium for their helpful comments and suggestions. They are also grateful to their colleagues at the research department of the ACPR for their help in improving the paper. Eventually, the paper benefited from the excellent research assistance of Farida Azzi, thrilling discussions with Pierre Valade and the astute remarks of George Overton. The comments and suggestions brought by the two anonymous reviewers greatly improved the paper from its first version. The remaining mistakes are the responsibility of the authors. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Autorité de Contrôle Prudentiel et de Résolution (ACPR), nor those of the Banque de France.

Author information



Corresponding author

Correspondence to Pierre-Emmanuel Darpeix.


Appendix 1: panel selection and treatment of outliers

To the best of our knowledge, we are the first to build such a database for the French life insurance business. The raw supervisory data need to be cleaned and tabulated. The treatments and filters applied are summarised in the following paragraphs.

First, we extract all relevant information from the regulatory databases, selecting all undertakings with mathematical reserves larger than EUR 50 million for at least five years. Atypical observations and outliers are corrected, either with expert judgement—e.g. obvious reporting mistakes—or using the paper files. Mergers and acquisitions are relatively common in the French insurance market for the period under study and can bias the analysis significantly since they impact the profit-sharing policy. Using ACPR records on these operations, we decompose the entities before and after the operation, and consider them as distinct undertakings.

The aforementioned operations provide us with a sample of 91 undertakings and 965 observations over the period from 1999 to 2013. The database includes only four “pure” mutual insurers (Mutuelles, ruled under the Code de la Mutualité), corresponding to 32 observations, and no providence institution (Institution de Prévoyance, ruled under the Code de la Sécurité Sociale).Footnote 45 The observations’ overall consistency is evaluated a posteriori with, firstly, a study of the departure of the asset returns from the OAT-10Y, then an analysis of the distribution of the spread between the participation rate and the OAT-10Y and, finally, an inspection of the variable coding for the stock of profit participation reserve (PPB) relative to the mathematical reserves (MRs).

Appendix 2: additional controls for the static model

Building on Model 4, we try and add other potential explanatory candidates in order to see whether they can explain part of the remaining variance, and check the stability of our coefficients for the introduction of these variables. We first look at the soundness variables (Models 5.a and 5.b) and at the size variable (Model 6). The results of the estimations are presented in Table 6.

Table 6 Estimating the static model with impact of the soundness and size variables

The coefficients on the reference model’s variables do not change much with the introduction of the additional terms, except for the one on asset returns which is reduced by an amount equivalent to the value of the coefficient on the newly introduced UCGL variable. We therefore merely decompose part of the variance previously attributed to the financial performance. Due to missing data, our sample is marginally reduced with the solvency ratio variable, although the coefficients of the baseline model are stable. While the coverage ratio is significant at the 10 per cent level in the FE specification, the impact is extremely small. The size variable (the natural logarithm of the mathematical reserves) does not alter the baseline model coefficients. The variable itself is only significant under the pooled OLS specification, as there is not much variation for a given individual over time. The coefficient is positive, as expected, yet extremely small as it indicates that an increase in the MRs by 1 per cent is associated with an increase in the participation by 5bps.

Second, we study the effect of the introduction of several reserving variables (the Provision pour risque d’exigibilité—PRE, the Provision pour dépréciation durable—PDD and the Réserve de capitalisation—RC) on our reference model (Model 4). The results reported in Table 7 indicate clearly that PRE and PDD have no effect on the regression, whereas the RC comes out as statistically significantly correlated with the participation rate under the FE specification. The order of magnitude of the coefficient is small, about the same as the one on the PPB. The coefficients of the baseline model are not affected by the new variable.

Table 7 Estimating the static model with impact of the asset reserves variables

In a last step, we consider in Table 8 two ALM variables in addition to the asset return variable: the asset structure (Model 8.a), and the capital gain ratio (Model 8.b).

Table 8 Estimating the static model with impact of the ALM variables

It appears that more investment in equity generally implies a lower participation (both under OLS and FE specifications). This is rather surprising, as one would expect that more risk should be associated with higher yields over the long term. The coefficients of the baseline model are not affected much by the introduction of this asset allocation variable, except unsurprisingly and only marginally the one for the return variable. The capital gains ratio has no significant impact on the model.

Appendix 3: Robustness checks

In order to check the consistency of our estimates, we run the model over two sub-periods of seven years to assess the time stability of the coefficients. Note that 2006 belongs to the two sub-periods. The results are fairly encouraging, as the point estimates are rather stable across the two sub-periods.

Indeed, as can be seen in Table 9, in both the OLS and fixed-effects specifications with static target rate, the signs and orders of magnitude are preserved from one sub-period to the other. More precisely, it appears that the coefficient on the financial performance relative to the French government bond stays positive and statistically significant, yet decreases in magnitude from one sub-period to the other (from 0.12 to 0.07 under FE). Good financial performance seems to translate less and less into a better participation rate. The coefficient on the OAT-10Y remains negative and large. The continuous decrease of the government bond rates over the period could explain the increase in the absolute value of the coefficient, as it becomes more complicated to serve less than the OAT-10Y while staying above the legal 0 bound. As the OAT-10Y gets close to zero, the mean of participation spread can only increase. The coefficient for the surrender rate—negative and statistically significant in the first period—becomes insignificant in the second. The coefficient on the stock of PPB stays consistently around 0.9.

Table 9 Time stability of the static model (Model 4)

We extract the content of the fixed effects to see whether they were coherent from one period to another. A simple OLS regression of the coefficients for the first period on the coefficients for the second yields a point estimate of 0.98 significant at the 1 per cent confidence level and an adjusted R2 of 0.52: this tends to confirm that the fixed effects do capture idiosyncratic characteristics which are stable over time.

These robustness checks seem to confirm the main findings of the paper concerning the static model. We obtain similar results with the dynamic model (see Table 10).

Table 10 Time stability of the dynamic model (Model 4′)

Appendix 4: cluster analysis

This appendix presents an empirical clustering analysis for insurers in our data. The schemes are detected empirically through an analysis of the respective variations of the financial margin and participation rates as a function of the asset returns spreads.

Figures 2 and 3 exhibit three different behavioural patterns for a sample of anonymised insurers. The three undertakings presented in Figure 2 (Type 1) are characterised by an extremely smooth financial margin (second row) and a participation very close to the OAT-10Y (first row). The PPB varies in parallel with the assets’ performances (third row), but the observations are slightly below the 45° line. All this seems to indicate that the behavioural rule of these undertakings is (1) take the targeted financial margin; (2) serve the OAT-10Y; (3) store the rest of the assets’ return in the PPB for later participation. Note, however, that over the 15 years under study, the PPB was not much released, which can raise questions about the enforcement of the legal obligation not to retain the PPB for more than eight years.Footnote 46 In contrast, for the three insurers of panel 2 (Type 2), the participation rate is largely driven by the assets’ performance: indeed, in the first row, it appears that the observations parallel the 45° line. However, this does not mean that the policy is necessarily to the advantage of the policyholder, despite the overall good financial performance of these undertakings: the parallel behaviour of the participation is sometimes considerably below the assets’ returns and even below the OAT-10Y (see for instance X2 and Y2). The financial margins (second row) are fairly stable, as well as the PPB. All this seems to indicate that the behavioural rule of these undertakings is (1) take the targeted financial margin; (2) conserve the PPB; (3) serve what is left to the policyholders, even if below the OAT-10Y.

Figure 2

Each column corresponds to a distinct undertaking and each observation (dot) to a given year. All X-axes represent the difference between the assets’ returns and the OAT-10Y rate. Thus, an abscissa of 0.02 means that the assets yielded 2 percentage points (200bps) more than the OAT-10Y. In the first row, the ordinate is the difference between the participation served and the OAT-10Y. In the second row, it represents the financial margin, and in the third, it corresponds to the relative change in the PPB. In each graph, the 45° line is marked with dashes

Figure 3

Type 3 pattern. Each column corresponds to a distinct undertaking and each observation (dot) to a given year. All X-axes represent the difference between the assets’ returns and the OAT10Y rate. In the first row, the ordinate is the difference between the participation served and the OAT-10Y. In the second row, it represents the financial margin, and in the third, it corresponds to the relative change in the PPB. In each graph, the 45° line is marked with dashes

For others, with a more “mutual insurance” type, the bad financial performances are absorbed through a lower financial margin, and the participation rates are maintained close to the OAT-10Y. The three insurers presented in Figure 3 (Type 3—two out of three happen to be ruled by the Code de la Mutualité) display an extremely smooth participation around the OAT-10Y (first row) despite rather poor financial performances (returns often lower than the government bonds rates) and a PPB that does not vary much (third row). One can actually see in the second row that all bad financial performances are absorbed by the financial margins, which become negative when the assets yield less than the OAT-10Y. Together these considerations seem to indicate that the behavioural rule of these undertakings is (1) serve the OAT-10Y to the policyholders; (2) conserve the PPB; (3) absorb the poor performances with negative financial margins.

The definition of “standard patterns” is natural for our analysis, but the small average number of observations per company makes the categorisation difficult or very dependent on an expert judgement’s classification.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Borel-Mathurin, F., Darpeix, PE., Guibert, Q. et al. Main Determinants of Profit-Sharing Policy in the French Life Insurance Industry. Geneva Pap Risk Insur Issues Pract 43, 420–455 (2018).

Download citation


  • participation rate
  • profit-sharing policy
  • life insurance
  • panel data
  • regulatory database