# Participating Life Insurance Products with Alternative Guarantees: Reconciling Policyholders’ and Insurers’ Interests

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Considered Products

- -
- Traditional, cliquet-style product: ${i}_{g}={i}_{p}={i}_{r}=1.75\%$
- -
- Alternative 1 product with a 0% year-by-year guarantee: ${i}_{p}={i}_{r}=1.75\%$, ${i}_{g}=0\%$
- -
- Alternative 2 product without any year-by-year guarantee: ${i}_{p}={i}_{r}=1.75\%$, ${i}_{g}=-100\%$

## 3. Stochastic Modeling and Assumptions

#### 3.1. The Financial Market Model

#### 3.2. The Asset-Liability Model

#### 3.3. The Projection Setup

## 4. Results

#### 4.1. Analysis of the Insurer’s Profit

#### 4.2. Analysis of the Insurer’s Risk

#### 4.3. Analysis of Policyholder’s Risk-Return Profiles

#### 4.4. Sensitivity Analyses

#### 4.4.1. Asset Allocation

#### 4.4.2. Capital Market Assumptions

## 5. Conclusions and Outlook

## Author Contributions

## Conflicts of Interest

## References

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^{1}For example, Zurich Deutscher Herold Lebensversicherung stopped new business in participating life insurance in 2013, and now offers so-called “select products” (cf. Alexandrova et al. [16]). Generali Deutschland announced in a press release in May 2015 their target to discontinue participating life insurance and focus on offering unit-linked insurance. The Talanx group announced in July 2015 to sell new business from the end of 2016 on with only a return-of-premium guarantee (instead of a guaranteed interest rate).^{2}Note that these products have different surplus participation rates due to the aforementioned construction of the iso-profit products.^{3}For these types of products—different than, for example, for US-style variable annuities—typically no hedging strategies for the guarantees are in place. Under current regulation, all policyholders (who have contracts with different levels of guarantee that started at different points in time and will mature at different points in time) participate in the return of the same pool of assets. Hence, hedge assets could not be attributed to certain guarantees that mature at a certain time, which limits the potential for micro-hedging. Therefore, we do not consider any hedging strategies in our paper.^{4}Reuß et al. [13] pointed out some restrictions on the choice of the three interest rates: “only combinations fulfilling ${i}_{g}\le {i}_{p}\le {i}_{r}$ result in suitable products: If the first inequality is violated, then the year-to-year minimum guaranteed interest rate results in a higher (implicitly) guaranteed maturity benefit than the (explicit) guarantee resulting from the pricing rate. If the second inequality is violated then at t = 0, additional reserves (exceeding the first premium) are required.”^{6}Since for all product designs the account value (and hence the surrender value) never falls below the prospective reserve for the guaranteed maturity benefit, this is, in our opinion, consistent with guaranteed minimum surrender benefits specified by German insurance contract law (§169 “Versicherungsvertragsgesetz” (VVG)).^{7}Without these regulatory requirements, the insurer might make even better use of time diversification of asset returns (see, for example, the results on optimal pension insurance and time diversification in the life cycle model in Aase [19]). However, the alternative products proposed in this paper are designed to allow a higher degree of time diversification than the traditional product. The Alternative 2 product even comes with the maximum degree of time diversification possible under existing regulation for participating contracts.^{8}Note that 1.75% is the maximum reserving rate allowed in Germany until 31 December 2014. On 1 January 2015, it has been lowered to 1.25%. In order to make our results comparable to the results in Reuß et al. [13], we still use a reserving rate of 1.75%.^{9}cf. Vasicek [20].^{12}As in Reuß et al. [13] we perform our analyses for the insurance portfolio on a stand-alone basis, and therefore do not explicitly consider the shareholders’ equity or other reserves on the liability side. This is due to the fact that the valuation of liabilities from insurance contracts is typically independent of the amount of shareholders’ equity held by the insurance company. Consequently, our framework measures the contribution of a specific portfolio of insurance contracts to the own funds of the insurance company in a risk-based solvency framework. Of course, shareholder’s equity is another important component of the own funds (but does not depend on the product design).^{13}The distribution algorithm is explained in more detail in Reuß et al. [13].^{14}As stated in Reuß et al. ([13], p. 196): “We do not consider the shareholders’ default put option resulting from their limited liability, which is in line with both, Solvency II valuation standards and the Market Consistent Embedded Value framework (MCEV), cf. e.g., Bauer et al. [25] or DAV [26], Section 5.3.4 (p. 30ff).”^{15}cf. Reuß et al. ([13], p. 199): “Note that due to mortality before $t=0$, the number of contracts for the different remaining times to maturity is not the same.”^{17}For instance, the German life insurer Allianz has introduced a product with alternative guarantees in the German market that compensates the policyholder for lower and weaker guarantees by an increase in surplus distribution. Also, several insurers have introduced products that are similar to our Alternative 1 product with ${i}_{g}=0\%$, ${i}_{p}=x\%$, and ${i}_{r}=1.75\%,$ where $x$ is chosen such that the guaranteed benefit coincides with the sum of all premiums paid. In these products, as a compensation for the lower and weaker guarantee, the policyholders may choose annually to invest their surplus distribution in some equity option generating an annual return on the policy that depends on some equity index, cf. Alexandrova et al. [16].^{18}The concept of PVFP is introduced as part of the MCEV Principles in the CFO-Forum [28].^{19}In our numerical analyses, we always vary the equity ratio q in steps of 0.25% and then calculate the PVFP for a given profit participation rate p or the profit participation rate p for a given PVFP. Therefore, in what follows, equity ratios are always given as multiples of 0.25%.^{20}Note that other market risk modules, such as property risk and spread risk, are not relevant in our simplified asset-liability model. However, the analysis could be extended using more complex asset models.^{21}A description of the version of the standard formula that has been applied during the preparatory phase of Solvency II can be found in EIOPA [30].^{22}It is common practice in some insurance markets to use risk-return profiles in order to present the characteristics of insurance products to policyholders. E.g., German regulation requires a risk-return classification of government subsidized old-age provision products based on risk-return profiles derived from a “simulation model” (cf. “Altersvorsorgeverträge-Zertifizierungsgesetz” (AltZertG), §7). Therefore, we will focus on risk-return profiles. Of course, it would also be interesting to perform utility optimizations or to analyze for which types of clients (characterized by their utility functions and parameters) certain product designs are particularly appealing.^{23}The following measures for risk and return are being used in the framework mentioned in Footnote 22.^{24}It must be noted that the observed changes and their size generally depend on the choice of the risk measures. The CTE20 was chosen as a measure for policyholders’ risk because it has been used in a framework implemented by product rating firms and will be used in the risk-return classifications required by German regulation. Therefore, the focus of market participants is on this measure and it might coincide with perceived risk. However, it does not reflect all aspects of risk, and by applying other risk measures different size changes might be observed.^{25}We particularly observe that the CTE20 for the Alternative 2 product shows very little variation (also in the values shown in Table 5 and Table 6). This is the result of two opposing effects that occur if the risk level (and hence also the equity ratio) is increased: on the one hand, this increases the returns also for some scenarios in the lower tail (causing the higher CTE20 for Alternative 1 in the two lower rows of Table 4 since for the Alternative 1 product, this effect dominates). On the other hand, it causes a higher volatility in the asset portfolio which increases the number of years where a negative return is credited to the account for the Alternative 2 contract. As a result, in a larger portion of scenarios, only the guaranteed benefit is paid, which reduces the CTE20. For Alternative 2, these two effects almost exactly cancel each other out.^{26}Such cross-generational effects are similar to those analyzed by Hieber et al. [31]. They analyze the attractiveness of traditional policies for different generations of policyholders in a case where all assets are pooled, and in a case where assets covering the different generations are segregated.^{27}cf. e.g., the results in Aase [19], where a life cycle model of a consumer with recursive utility is used, and conclusions on optimal pensions and life insurance contracts are drawn that lead to smoother consumption paths.

**Figure 1.**Iso-profit curves with $\mathit{P}\mathit{V}\mathit{F}\mathit{P}=\mathbf{3.62}\%$ (based on the traditional product with $\mathit{p}=\mathbf{90}\%$ and $\mathit{q}=\mathbf{5}\%$).

**Figure 3.**Benefit distribution of products with the

**same PVFP**and the

**same SCR**, based on the traditional product with

_{mkt}**q = 5%**.

**Figure 4.**Comparison of products with the

**same PVFP**and

**reduced**$\mathit{S}\mathit{C}{\mathit{R}}_{\mathit{m}\mathit{k}\mathit{t}}$, based on the traditional product with $\mathit{q}=\mathbf{5}\%$.

**Figure 5.**Benefit distribution of products with the

**same PVFP**and

**reduced**$\mathit{S}\mathit{C}{\mathit{R}}_{\mathit{m}\mathit{k}\mathit{t}}$, based on the traditional product with $\mathit{q}=\mathbf{5}\%$.

**Figure 6.**Comparison of products with the

**same PVFP**and the

**same**$\mathit{S}\mathit{C}{\mathit{R}}_{\mathit{m}\mathit{k}\mathit{t}}$, based on traditional products with $\mathit{q}=\mathbf{2.5}\%$ ($\mathit{S}\mathit{C}{\mathit{R}}_{\mathit{m}\mathit{k}\mathit{t}}=\mathbf{2.3}\%$) and $\mathit{q}=\mathbf{7.5}\%$ ($\mathit{S}\mathit{C}{\mathit{R}}_{\mathit{m}\mathit{k}\mathit{t}}=\mathbf{4.9}\%$).

G | T | α | β | P |
---|---|---|---|---|

20,000 € | 20 years | 4% | 3% | 896.89 € |

r_{0} | θ | $\mathit{\kappa}$ | σ_{r} | λ | μ | σ_{s} | ρ |
---|---|---|---|---|---|---|---|

2.5% | 3.0% | 30.0% | 2.0% | −23.0% | 6.0% | 20.0% | 15.0% |

Assets | Liabilities |
---|---|

$B{V}_{t}^{S}$ | ${X}_{t}$ |

$B{V}_{t}^{B}$ | $A{V}_{t}$ |

**Table 4.**IRR and CTE20 for products with the

**same asset allocation**, with the

**same**$\mathit{S}\mathit{C}{\mathit{R}}_{\mathit{m}\mathit{k}\mathit{t}}$, and with

**reduced**$\mathit{S}\mathit{C}{\mathit{R}}_{\mathit{m}\mathit{k}\mathit{t}}$ for alternative products, based on the traditional product with $\mathit{q}=\mathbf{5}\%$ (PVFP = 3.62%).

IRR/CTE20 | Traditional Product | Alternative 1 | Alternative 2 |
---|---|---|---|

Same asset allocation | 2.49%/1.96% | 2.47%/1.83% | 2.48%/1.83% |

Same risk level (SCR_{mkt} = 3.4%) | 2.65%/1.87% | 2.75%/1.85% | |

Reduced risk for alternatives 1/2 (SCR_{mkt} = 2.5%) | 2.59%/1.86% | 2.66%/1.85% |

**Table 5.**IRR and CTE20 for products with the

**same**$\mathit{S}\mathit{C}{\mathit{R}}_{\mathit{m}\mathit{k}\mathit{t}}$, and with

**reduced**$\mathit{S}\mathit{C}{\mathit{R}}_{\mathit{m}\mathit{k}\mathit{t}}$ for alternative products, for base case and sensitivities of asset allocation.

IRR/CTE20 | Risk Level | Traditional Product | Alternative 1 | Alternative 2 |
---|---|---|---|---|

“Less equity” (q = 2.5%) | Same risk level (SCR_{mkt} = 2.3%) | 2.41%/1.91% | 2.56%/1.85% | 2.62%/1.85% |

Reduced risk for Alternatives 1/2 (SCR_{mkt} = 1.8%) | 2.51%/1.84% | 2.52%/1.84% | ||

Base case (q = 5%) | Same risk level (SCR_{mkt} = 3.4%) | 2.49%/1.96% | 2.65%/1.87% | 2.75%/1.85% |

Reduced risk for Alternatives 1/2 (SCR_{mkt} = 2.5%) | 2.59%/1.86% | 2.66%/1.85% | ||

“More equity” (q = 7.5%) | Same risk level (SCR_{mkt} = 4.9%) | 2.56%/2.00% | 2.72%/1.88% | 2.86%/1.85% |

Reduced risk for Alternatives 1/2 (SCR_{mkt} = 3.5%) | 2.65%/1.87% | 2.76%/1.85% |

**Table 6.**IRR and CTE20 for products with the

**same**$\mathit{S}\mathit{C}{\mathit{R}}_{\mathit{m}\mathit{k}\mathit{t}}$, and with

**reduced**$\mathit{S}\mathit{C}{\mathit{R}}_{\mathit{m}\mathit{k}\mathit{t}}$ for alternative products, for base case and capital market sensitivities (± 50 bps).

IRR/CTE20 | Risk Level | Traditional Product | Alternative 1 | Alternative 2 |
---|---|---|---|---|

“Cap.Mkt. −50 bps” | Same risk level (SCR_{mkt} = 4.7%) | 2.28%/1.93% | 2.42%/1.84% | 2.51%/1.84% |

Reduced risk for Alternatives 1/2 (SCR_{mkt} = 3.6%) | 2.35%/1.84% | 2.41%/1.84% | ||

Base case | Same risk level (SCR_{mkt} = 3.4%) | 2.49%/1.96% | 2.65%/1.87% | 2.75%/1.85% |

Reduced risk for Alternatives 1/2 (SCR_{mkt} = 2.5%) | 2.59%/1.86% | 2.66%/1.85% | ||

“Cap.Mkt. +50 bps” | Same risk level (SCR_{mkt} = 2.7%) | 2.86%/2.21% | 3.02%/2.15% | 3.13%/2.13% |

Reduced risk for Alternatives 1/2 (SCR_{mkt} = 2.0%) | 2.97%/2.15% | 3.04%/2.14% |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Reuß, A.; Ruß, J.; Wieland, J. Participating Life Insurance Products with Alternative Guarantees: Reconciling Policyholders’ and Insurers’ Interests. *Risks* **2016**, *4*, 11.
https://doi.org/10.3390/risks4020011

**AMA Style**

Reuß A, Ruß J, Wieland J. Participating Life Insurance Products with Alternative Guarantees: Reconciling Policyholders’ and Insurers’ Interests. *Risks*. 2016; 4(2):11.
https://doi.org/10.3390/risks4020011

**Chicago/Turabian Style**

Reuß, Andreas, Jochen Ruß, and Jochen Wieland. 2016. "Participating Life Insurance Products with Alternative Guarantees: Reconciling Policyholders’ and Insurers’ Interests" *Risks* 4, no. 2: 11.
https://doi.org/10.3390/risks4020011