Asset/Liability Management of German Life Insurance Companies: A Value-at-Risk Approach in the Presence of Interest Rate Guarantees

This contribution analyses the implications of two major determinants influencing the asset allocation decision of German life insurers, which are the capital market development on the one hand and the interest rate guarantees of the traditional life insurance policies on the other hand. The adverse development of the stock prices between 2000 and 2002 asks for a consideration of not only the �normal� volatility but also the worst-case developments in an asset/liability management. In order to meet the latter requirement, we technically apply the risk measures of Value-at-Risk and Conditional Value-at-Risk. German life insurance policies incorporate interest rate guarantees, which are granted on an annual basis. This specific �myopic� nature of guarantees creates � beyond the control of the shortfall risk in general � the necessity to manage the asset allocation on an annual basis to match the time horizon of assets and liabilities. A quantitative approach analyses the impacts on the asset allocation decision. In our research we do not only consider market valuation, but also institutional peculiarities (such as hidden reserves and accounting norms) of German life insurers. We reveal the possibility of a riskless one-year investment, either based on market values or on book values, to be crucial for guaranteeing interest rates on an annual basis.

A Stochastic Linear Programming Model for Asset Liability Management: The Case of an Indian Insurance Company

Asset - Liability management is one of the most critical tasks for any financial institution for determining its cushion against the risk and the net returns. The problem of asset liability management for an insurance company requires matching the cash inflows from premium collections and investment income with the cash outflows due to casualty and maturity claims. Thus, what is required is a prudent investment strategy such that the returns earned on the assets match the liability claims at all points of time in future. Conventionally, the asset allocation has been done using the Mean Variance approach due to Markowitz (1952, 1959). While such a strategy ensures that the asset value always match or are greater than the liability for the next year, it does not maximise the net worth of the firm nor does it take care of all the cash inflows and outflows over a long term period. A stochastic linear programming model (on the lines of Pirbhai, 2004) maximises the net worth of the firm and also takes care of the uncertainties. While there are instances of stochastic linear programming being applied for ALM in financial institutions in developed markets, no such practical application has been reported in this area in Indian context as yet. In this paper, we describe the development of a multi stage stochastic linear programming model for insurance companies. The multi-stage stochastic linear programming model was developed on the modelling language AMPL (Fourer, 2002).

Money-back guarantees in individual pension accounts : evidence from the German pension reform

The German Retirement Saving Act instituted a new funded system of supplementary pensions coupled with a general reduction in the level of state pay-as-you-go old-age pensions. In order to qualify for tax relief, the providers of supplementary savings products must offer a guarantee of the nominal value at retirement of contributions paid into these saving accounts. This paper explores how this "money-back" guarantee works and evaluates alternative designs for guarantee structures, including a life cycle model (dynamic asset allocation), a plan with a pre-specified blend of equity and bond investments (static asset allocation), and some type of portfolio insurance. We use a simulation methodology to compare hedging effectiveness and hedging costs associated with the provision of the money-back guarantee. In addition, the guarantee has important implications for regulators who must find an appropriate solvency system for such saving schemes. This version June 17, 2002 . Klassifikation: G11, G23, G2

Dynamic asset (and liability) management under market and credit risk

We introduce a modelling paradigm which integrates credit risk and market risk in describing the random dynamical behaviour of the underlying fixed income assets. We then consider an asset and liability management (ALM) problem and develop a mul- tistage stochastic programming model which focuses on optimum risk decisions. These models exploit the dynamical multiperiod structure of credit risk and provide insight into the corrective recourse decisions whereby issues such as the timing risk of default is appropriately taken into consideration. We also present a index tracking model in which risk is measured (and optimised) by the CVaR of the tracking portfolio in relation to the index. Both in- and out-of-sample (backtesting) experiments are undertaken to validate our approach. In this way we are able to demonstrate the feasibility and flexibility of the chosen framework

Horizon-unbiased Investment with Ambiguity

In the presence of ambiguity on the driving force of market randomness, we consider the dynamic portfolio choice without any predetermined investment horizon. The investment criteria is formulated as a robust forward performance process, reflecting an investor's dynamic preference. We show that the market risk premium and the utility risk premium jointly determine the investors' trading direction and the worst-case scenarios of the risky asset's mean return and volatility. The closed-form formulas for the optimal investment strategies are given in the special settings of the CRRA preference

Multi-Period Trading via Convex Optimization

We consider a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. We describe a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades off expected return, risk, transaction cost and holding cost such as the borrowing cost for shorting assets. We then describe a multi-period version of the trading method, where optimization is used to plan a sequence of trades, with only the first one executed, using estimates of future quantities that are unknown when the trades are chosen. The single-period method traces back to Markowitz; the multi-period methods trace back to model predictive control. Our contribution is to describe the single-period and multi-period methods in one simple framework, giving a clear description of the development and the approximations made. In this paper we do not address a critical component in a trading algorithm, the predictions or forecasts of future quantities. The methods we describe in this paper can be thought of as good ways to exploit predictions, no matter how they are made. We have also developed a companion open-source software library that implements many of the ideas and methods described in the paper

A robust asset–liability management framework for investment products with guarantees

This paper suggests a robust asset–liability management framework for investment products with guarantees, such as guaranteed investment contracts and equity-linked notes. Stochastic programming and robust optimization approaches are introduced to deal with data uncertainty in asset returns and interest rates. The statistical properties of the probability distributions of uncertain parameters are incorporated in the model through appropriately selected symmetric and asymmetric uncertainty sets. Practical data-driven approaches for implementation of the robust models are also discussed. Numerical results using generated and real market data are presented to illustrate the performance of the robust asset–liability management strategies. The robust investment strategies show better performance in unfavorable market regimes than traditional stochastic programming approaches. The effectiveness of robust investment strategies can be improved by calibrating carefully the shape and the size of the uncertainty sets for asset returns

Differential Evolution for Multiobjective Portfolio Optimization

Financial portfolio optimization is a challenging problem. First, the problem is multiobjective (i.e.: minimize risk and maximize profit) and the objective functions are often multimodal and non smooth (e.g.: value at risk). Second, managers have often to face real-world constraints, which are typically non-linear. Hence, conventional optimization techniques, such as quadratic programming, cannot be used. Stochastic search heuristic can be an attractive alternative. In this paper, we propose a new multiobjective algorithm for portfolio optimization: DEMPO - Differential Evolution for Multiobjective Portfolio Optimization. The main advantage of this new algorithm is its generality, i.e., the ability to tackle a portfolio optimization task as it is, without simplifications. Our empirical results show the capability of our approach of obtaining highly accurate results in very reasonable runtime, in comparison with quadratic programming and another state-of-art search heuristic, the so-called NSGA II.Portfolio Optimization, Multiobjective, Real-world Constraints, Value at Risk, Expected Shortfall, Differential Evolution

Assessing Investment and Longevity Risks within Immediate Annuities

Life annuities provide a guaranteed income for the remainder of the recipient’s lifetime, and therefore, annuitization presents an important option when choosing an adequate investment strategy for the retirement ages. While there are numerous research articles studying annuities from a pensioner’s point of view, thus far there have been few contributions considering annuities from the provider’s perspective. In particular, to date there are no surveys of the general risks within annuity books. The present paper aims at filling this gap: Using a simulation framework, it provides a long-term analysis of the risks within annuity books. In particular, the joint impact of mortality risks and investment risks as well as their respective influences on the insurer’s financial situation are studied. The key finding is that, under the model specifications and using annuity data from the United Kingdom, the risk premium charged for aggregate mortality risk seems to be very large relative to its characteristics. Possible reasons as well as economic implications are provided, and potential caveats are discussed