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Value Creation and Solvency: A Simple Approach to Deriving a Non-Life Insurer’s Optimal Growth Strategy

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Abstract

Strategic planning in non-life insurance companies must consider differing demands from the company’s various stakeholders. While investors and shareholders require growth in equity market value, rating agencies, costumers and the authorities focus on the company’s solvency, that is, the amount of capital covering the business risks. In that regard, growth in premium income and business profitability are critical, but opposing drivers for operative management. In this article, we model profitability in the insurance business in dependence on premium growth and analyse the impact of the underlying growth strategy on shareholder value and solvency for a non-life insurance company. In a multi-period framework, we find that an optimal growth strategy, maximising net present value and fulfilling a solvency constraint can be derived in dependence on the initial insurance portfolio mix of new and renewal business. The results of the analysis further demonstrate that higher growth rates can lead to lower equity values and vice versa, and that the solvency constraint can prohibit a shareholder-value-maximising strategy. Therefore, the approach is useful in supporting strategic decision-taking and value-based management in non-life insurance companies.

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Notes

  1. See, for example, the Investors’ Day presentations of the big European insurers Allianz (www.allianz.com), Assicurazioni Generali (www.generali.com) or AXA (www.axa.com).

  2. Nakada et al. (1999); Malmi and Ikäheimo (2003); Diers (2011); Diers et al. (2012).

  3. Stewart (1994); O’Hanlon and Peasnell (1998).

  4. Kraus (2013).

  5. Cummins and Sommer (1996); Wakker et al. (1997).

  6. Butsic (1994).

  7. European Commission (2009).

  8. A comprehensive overview on quantile-based risk measures is provided by Dowd and Blake (2006).

  9. Wang et al. (2011) show the importance of cycle management for an insurer’s growth strategy.

  10. Ma and Ren (2012).

  11. D’Arcy and Doherty (1989, 1990); Feldblum (1996); Cohen (2005); Wu and Lin (2009).

  12. Fu (2012).

  13. D’Arcy and Gorvett (2004).

  14. Inselbag and Kaufold (1997).

  15. Oletzky and Graf von der Schulenburg (1998).

  16. For full compatibility with the NPV in (3) at different periods t, the value of already realized residual income (TVRI) must be added to PVRI t (O’Hanlon and Peasnell, 2002): .

  17. Sharpe (1964); Lintner (1965); Mossin (1966))

  18. Biger and Kahane (1978); Fairley (1979); Hill (1979); Cummins and Harrington (1985).

  19. Reinsurance is excluded for simplification reasons.

  20. We use an amended version of the approach introduced by Fu (2012).

  21. Wu and Lin (2009).

  22. More complex functions describing non-linear relationships could easily be incorporated instead.

  23. D’Arcy and Doherty (1989, 1990).

  24. Cohen (2005).

  25. Tasche (2002); Eling and Parnitzke (2007); Eling et al. (2007); Schmautz and Lampenius (2013).

  26. EIOPA (2014).

  27. Using the formula for the equilibrium state of new business percentage provided by Fu (2012), we obtain .

  28. For simplification reasons, we assume LR0/CR0=LR t /CR t =const and ER0/CR0=ER t /CR t , when developing the financial statements. Alternatively, fixed percentages for the business expenditure or cost functions, in dependence on growth, could be applied.

  29. Data obtained from www.allianz.com/investor_relations at 1 April 2015.

  30. In the technical specifications for non-life underwriting risk modelling, EIOPA (2013, section SCR.9.2.) defines constant standard deviations for premium and reserve risk for different lines of business. In our model framework, v represents all risks of the insurer and is therefore assumed to have a value exceeding those specified by EIOPA (2013, section SCR.9.2.) for the single lines of business.

  31. The premium growth rates in the German non-life insurance market range from -0.9 per cent to 3.5 per cent in the years 2003-2013 (German Insurance Association, 2014).

  32. In the model framework, the impact of the initial parameter values on the results, and therefore, possible levers for strategic measures for management could be observed by a sensitivity analysis. Accordingly, we provide a sensitivity analysis of the model outcomes by varying the initial parameter values in Table 1 with +1 per cent. The related impact on (optimal) growth, net present value (at its maximum) and solvency level is depicted in relation to the results of the base scenario as a percentage. Figure A1 visually illustrates the results of the sensitivity analysis.

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Authors and Affiliations

  1. Risk Management & Auditing, International Insurance Group, Vienna, 1010, Austria

    Matthias Schmautz

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Appendix

Appendix

See Figure A1.

Figure A1
figure 5

Sensitivity analysis.

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SeeTable A1, A2, A3, A4 and A5

Table A1 Financial statement
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Table A2 Periodic CE distribution and periodic solvency level
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Table A3 Base scenario g=1.50 per cent and q rb,0=0.80
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Table A4 Scenario g=1.50% and q rb,0=0.85
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Table A5 Simulation results: NPV0 in dependence of g and q rb ,0 (v=0.40)
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Schmautz, M. Value Creation and Solvency: A Simple Approach to Deriving a Non-Life Insurer’s Optimal Growth Strategy. Geneva Pap Risk Insur Issues Pract 40, 701–719 (2015). https://doi.org/10.1057/gpp.2015.20

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