تجزیه و تحلیل عملکرد مشارکت قراردادهای بیمه عمر

Participating life insurance contracts are one of the most important products in the European life insurance market. Even though these contract forms are very common, only very little research has been conducted in respect to their performance. Hence, we conduct a performance analysis to provide a decision support for policyholders. We decompose a participating life insurance contract in a term life insurance and a savings part and simulate the cash flow distribution of the latter. Simulation results are compared with cash flows resulting from two benchmarks investing in the same portfolio of assets but without investment guarantees and bonus distribution schemes, in order to measure the impact of these two product features. To provide a realistic picture within the two alternatives, we take transaction costs and wealth transfers between different groups of policyholders into account. We show that the payoff distribution strongly depends on the initial reserve situation and managerial discretion. Results indicate that policyholders will in general profit from a better payoff distribution of the participating life insurance compared to a mutual fund benchmark but not compared to an exchange-traded fund benchmark portfolio.

As a consequence of the financial crisis, private investors currently seek safe investments with low downside risks. In this context, minimum interest rate guarantees embedded in financial products are one option for investors. Insurance companies offer investment products with such a downside protection and are often perceived as a safe harbor.2 Participating life insurance (PLI hereafter) is one of the most important products in the life insurance sector with a built in minimum interest rate guarantee. In most European countries, these contracts are typically characterized by an embedded term life insurance, a cliquet-style interest rate guarantee,3 and bonus participation rules with regard to the insurer’s reserve situation (surplus fund). However, administrative costs and complex profit distribution schemes between policyholders and shareholders make it difficult to measure the performance of this product from the policyholder’s point of view. We model PLI based on contract forms offered in the German market4 and simulate the complete payoff distribution on an ex ante basis. Subsequently, we compare the cash flow distribution of the PLI with two passive portfolios which invests into the same assets. We show how the payoff distribution depends on the initial reserve situation (the surplus fund in our model) and management’s discretion. The characteristics of PLI contracts make it difficult to measure their performance. A PLI embeds various (explicit and implicit) options as well as complex bonus distribution schemes between policyholders and shareholders. In addition, an insurance company’s management has a certain discretion with respect to some parameters. Furthermore, wealth transfers between different groups of policyholders take place. In order to get over these difficulties, we measure the performance of PLI contracts from an ex ante perspective while taking embedded options, bonus distribution, and management’s discretion into account. We empirically calibrate our model with market data and simulate various insurance collectives to incorporate wealth transfer effects. In previous research on PLI, we can distinguish between two major streams of literature. The first one addresses fair pricing of participating life insurance policies based on option pricing theory. Amongst others, bonus distribution rules are often modeled and reproduced in this area of research (see, for example, Grosen and Jørgensen (2000), Bacinello (2001), Hansen and Miltersen (2002), Haberman et al. (2003), and Kling et al. (2007)). For instance, Kling et al. (2007) analyze the numerical impact of interest rate guarantees found in PLI contracts on the shortfall probability of a life insurance company. Gatzert (2008) provides a general framework for pricing and risk management of participating life insurance contracts under different assumptions in respect to asset management and surplus distribution strategies. Gatzert and Schmeiser (2008) assess, in particular, the risk of different premium payment options typically offered in participating life insurance contracts. However, these fair pricing approaches generally only work under the assumption of perfect and frictionless markets. The second stream of literature mainly analyzes performance by means of the internal rate of return, accounting ratios, and similar performance ratios based on historical cash-flows or numerical examples provided by insurance companies (see, e.g., Ferrari (1968) and Levy and Kahane (1970)). However, these approaches generally ignore embedded options and do not consider the risk-return profile of the investment. Exceptions are Waldow (2003) and Stehle et al. (2003). In these contributions, not only one single performance ratio is derived, but also historical cash flows of PLI contracts are compared with those of an alternative portfolio composed of an annual term life insurance and different investment products. Nevertheless, as most of these performance analyses are conducted from an ex post perspective, they can only indicate whether PLI contracts were advantageous in the past. Implications for the future, however, are limited. In order to get a clear picture of the performance of PLI, we decompose PLI in a term life insurance and an investment part and simulate the cash flow distribution of the investment part under the real world measure PP. Further, we create two benchmark portfolios based on the same underlying to measure the impact of the interest rate guarantee and the bonus distribution rules on the cash flows of the portfolio. By calibrating our model with empirical market data, we are able to show in which cases the interest rate guarantee and the mechanisms applied by the insurance company can be beneficial to the policyholder. In addition, we show how the payoff distribution depends on the initial reserve situation and management’s discretion. We do not benchmark the PLI using a fair (risk-neutral) pricing approach, which would mean to compare the observed market price with the calculated fair price, because we believe that the underlying assumption of perfect and frictionless markets is rather not fulfilled in this context. We doubt that instruments exist that enable policyholders to replicate the PLI’s cash flows. We think that consumers will rather judge products depending on personal preferences and actually available alternatives. The contribution of this paper is that we neither rely on a single performance measurement ratio nor do we provide an ex post analysis. Instead, our framework allows a comparison of the complete payoff distribution on an ex ante basis. This general framework is subsequently not bonded to one specific subjective preference scheme. Further, we model an insurance company with various insurance collectives in order to incorporate wealth transfer effects between different groups of policyholders. Only Hansen and Miltersen (2002) analyzed PLI with pooled accounts before, but just for a two-policyholders case. In addition, the influence of the initial level of the pooled surplus fund on the performance of one single contract is analyzed. Furthermore, we examine how management’s discretion, in terms of a change of the target rate of return, affect the payoff distribution. Results indicate that all of the elements we incorporate have a strong impact on payoffs and should subsequently not be neglected. We find that if the initial level of the surplus fund is high, a PLI contract will in general yield a better payoff distribution compared to the mutual fund (MF hereafter) benchmark but not compared to the exchange-traded fund (ETF hereafter) benchmark portfolio. The remainder of the paper is organized as follows: In Section 2, we introduce our general framework. Results from Monte Carlo simulations are discussed in Section 3. We conclude in Section 4.

PLI contracts are popular–especially in the context of old-age provisions. This popularity might be to a large extent attributable to the downside protection. However, it is controversial if these products are actually beneficial for policyholders. More precisely, even though these contract forms are very common in insurance practice, only very little research has been conducted in respect to their performance in comparison to feasible investment alternatives. In this paper, we develop, in a first step, a framework to estimate payoffs from PLI contracts from the point of view of policyholders. We decompose PLI into an investment part and a term life insurance. Thus we are able to analyze the benefits of the minimum interest rate guarantee in combination with the profit distribution rules separately from the term life insurance. In addition, we model more than one single contract which allows us to incorporate distribution effects between policyholders. In a second step, we simulate the payoff distributions and benchmark the complete payoff distribution on an ex ante basis. We show how the payoff distribution depends on the level of the surplus fund at inception of the contract and analyze the effect of management’s discretion. We show that PLI can be beneficial to policyholders depending on the initial reserve situation. A low initial reserve situation of the insurer appears to be disadvantageous. Individuals continuing their contract until maturity without death or surrender will in general profit from a better payoff distribution compared to the MF benchmark portfolio but not compared to the ETF benchmark portfolio. Our preference dependent performance analysis shows that, in most cases, an ETF portfolio will perform better than each possible PLI contract if taxes are ignored. If taxes are accounted for, the PLI could perform better than the ETF benchmark but this will always depend on a specific investors marginal tax rate. However, if the surplus fund is already built up, the PLI tends to perform better than the MF benchmark