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- Integrated asset liability modelling for property casuality insurance : a portfolio theoretical approach (2001)
- In this paper we have developed a financial model of the non-life insurer to provide assistance for the management of the insurance company in making decisions on product, investment and reinsurance mix. The model is based on portfolio theory and recognizes the stochastic nature of and the interaction between the underwriting and investment income of the insurance business. In the context of an empirical application we illustrate howa portfolio optimisation approach can be used for asset-liability management.

- Zur Quantifizierung der Risikoprämien deutscher Versicherungsaktien im Kontext eines Multifaktorenmodells (2000)
- Vorgestellt wird eine empirische Studie, welche den Zusammenhang zwischen Rendite und Risiko für ein Sample deutscher Versicherungsaktien im Zeitraum 1975-1998 untersucht. Als Methode wurde ein Multifaktorenmodell mit makroökonomischen Faktoren verwendet. Je nach Untersuchungszeitraum beläuft sich der Anteil der erklärten Varianz auf 9,29% bis 13,62%. Es konnte eine signifikanter negativer Einfluß zwischen der Veränderung des allgemeinen Zinsniveaus und den Risikoprämien von Versicherungsaktien identifiziert werden. Weiterhin ist Wechselkurses der DM zum US-Dollar signifikant.

- How much foreign stocks? : Bayesian approaches to asset allocation can explain the home bias of US investors (2003)
- US investors hold much less foreign stocks than mean/variance analysis applied to historical data predicts. In this article, we investigate whether this home bias can be explained by Bayesian approaches to international asset allocation. In contrast to mean/variance analysis, Bayesian approaches employ different techniques for obtaining the set of expected returns. They shrink sample means towards a reference point that is inferred from economic theory. We also show that one of the Bayesian approaches leads to the same implications for asset allocation as mean-variance/tracking error criterion. In both cases, the optimal portfolio is a combination the market portfolio and the mean/variance efficient portfolio with the highest Sharpe ratio. Applying the Bayesian approaches to the subject of international diversification, we find that substantial home bias can be explained when a US investor has a strong belief in the global mean/variance efficiency of the US market portfolio and when he has a high regret aversion falling behind the US market portfolio. We also find that the current level of home bias can justified whenever regret aversion is significantly higher than risk aversion. Finally, we compare the Bayesian approaches to mean/variance analysis in an empirical out-ofsample study. The Bayesian approaches prove to be superior to mean/variance optimized portfolios in terms of higher risk-adjusted performance and lower turnover. However, they not systematically outperform the US market portfolio or the minimum-variance portfolio.

- Portfolio choice and estimation risk : a comparison of Bayesian approaches to resampled efficiency (2002)
- Estimation risk is known to have a huge impact on mean/variance (MV) optimized portfolios, which is one of the primary reasons to make standard Markowitz optimization unfeasible in practice. Several approaches to incorporate estimation risk into portfolio selection are suggested in the earlier literature. These papers regularly discuss heuristic approaches (e.g., placing restrictions on portfolio weights) and Bayesian estimators. Among the Bayesian class of estimators, we will focus in this paper on the Bayes/Stein estimator developed by Jorion (1985, 1986), which is probably the most popular estimator. We will show that optimal portfolios based on the Bayes/Stein estimator correspond to portfolios on the original mean-variance efficient frontier with a higher risk aversion. We quantify this increase in risk aversion. Furthermore, we review a relatively new approach introduced by Michaud (1998), resampling efficiency. Michaud argues that the limitations of MV efficiency in practice generally derive from a lack of statistical understanding of MV optimization. He advocates a statistical view of MV optimization that leads to new procedures that can reduce estimation risk. Resampling efficiency has been contrasted to standard Markowitz portfolios until now, but not to other approaches which explicitly incorporate estimation risk. This paper attempts to fill this gap. Optimal portfolios based on the Bayes/Stein estimator and resampling efficiency are compared in an empirical out-of-sample study in terms of their Sharpe ratio and in terms of stochastic dominance.

- Bayesian Asset Allocation and U.S. Domestic Bias (2003)
- U.S. investors hold much less international stock than is optimal according to mean–variance portfolio theory applied to historical data. We investigated whether this home bias can be explained by Bayesian approaches to international asset allocation. In comparison with mean–variance analysis, Bayesian approaches use different techniques for obtaining the set of expected returns by shrinking the sample means toward a reference point that is inferred from economic theory. Applying the Bayesian approaches to the field of international diversification, we found that a substantial home bias can be explained when a U.S. investor has a strong belief in the global mean–variance efficiency of the U.S. market portfolio, and in this article, we show how to quantify the strength of this belief. We also found that one of the Bayesian approaches leads to the same implications for asset allocation as the mean–variance/tracking-error criterion. In both cases, the optimal portfolio is a combination of the U.S. market portfolio and the mean–variance-efficient portfolio with the highest Sharpe ratio.

- How much foreign stocks? : classical versus Bayesian approaches to asset allocation (2003)
- The classical approaches to asset allocation give very different conclusions about how much foreign stocks a US investor should hold. US investors should either allocate a large portion of about 40% to foreign stocks (which is the result of mean/variance optimization and the international CAPM) or they should hold no foreign stocks at all (which is the conclusion of the domestic CAPM and mean/variance spanning tests). There is no way in between. The idea of the Bayesian approach discussed in this article is to shrink the mean/variance efficient portfolio towards the market portfolio. The shrinkage effect is determined by the investor's prior belief in the efficiency of the market portfolio and by the degree of violation of the CAPM in the sample. Interestingly, this Bayesian approach leads to the same implications for asset allocation as the mean-variance/tracking error criterion. In both cases, the optimal portfolio is a combination of the market portfolio and the mean/variance efficient portfolio with the highest Sharpe ratio. Applying both approaches to the subject of international diversification, we find that a substantial home bias is only justified when a US investor has a strong belief in the global mean/variance efficiency of the US market portfolio and when he has a high regret aversion of falling behind the US market portfolio. We also find that the current level of home bias can be justified whenever-regret aversion is significantly higher than risk aversion. Finally, we compare the Bayesian approach of shrinking the mean/variance efficient portfolio towards the market portfolio to another Bayesian approach which shrinks the mean/variance efficient portfolio towards the minimum-variance portfolio. An empirical out-of-sample study shows that both Bayesian approaches lead to a clearly superior performance compared to the classical mean/variance efficient portfolio.

- Implications of money-back guarantees for individual retirement accounts: protection then and now (2019)
- In the wake of the financial crisis and continued volatility in international capital markets, there is growing interest in mechanisms that can protect people against retirement account volatility. This paper explores the consequences for savers’ wellbeing of implementing market-based retirement account guarantees, using a life cycle consumption and portfolio choice model where investors have access to stocks, bonds, and tax-qualified retirement accounts. We evaluate the case of German Riester plans adopted in 2002, an individual retirement account produce that includes embedded mandatory money-back guarantees. These guarantees influenced participant consumption, saving, and investment behavior in the higher interest rate environment of that era, and they have even larger impacts in a low-return world such as the present. Importantly, we conclude that abandoning these guarantees could enhance old-age consumption for over 80% of retirees, particularly lower earners, without harming consumption during the accumulation phase. Our results are of general interest for other countries implementing default investment options in individual retirement accounts, such as the U.S. 401(k) defined contribution plans and the Pan European Pension Product (PEPP) recently launched by the European Parliament.

- Putting the pension back in 401(k) plans: optimal versus default longevity income annuities (2016)
- Most defined contribution pension plans pay benefits as lump sums, yet the US Treasury has recently encouraged firms to protect retirees from outliving their assets by converting a portion of their plan balances into longevity income annuities (LIA). These are deferred annuities which initiate payouts not later than age 85 and continue for life, and they provide an effective way to hedge systematic (individual) longevity risk for a relatively low price. Using a life cycle portfolio framework, we measure the welfare improvements from including LIAs in the menu of plan payout choices, accounting for mortality heterogeneity by education and sex. We find that introducing a longevity income annuity to the plan menu is attractive for most DC plan participants who optimally commit 8-15% of their plan balances at age 65 to a LIA that starts paying out at age 85. Optimal annuitization boosts welfare by 5-20% of average retirement plan accruals at age 66 (assuming average mortality rates), compared to not having access to the LIA. We also compare the optimal LIA allocation versus two default options that plan sponsors could implement. We conclude that an approach where a fixed fraction over a dollar threshold is invested in LIAs will be preferred by most to the status quo, while enhancing welfare for the majority of workers.

- How persistent low expected returns alter optimal life cycle saving, investment, and retirement behavior (2017)
- This Chapter explores how an environment of persistent low returns influences saving, investing, and retirement behaviors, as compared to what in the past had been thought of as more “normal” financial conditions. Our calibrated lifecycle dynamic model with realistic tax, minimum distribution, and Social Security benefit rules produces results that agree with observed saving, work, and claiming age behavior of U.S. households. In particular, our model generates a large peak at the earliest claiming age at 62, as in the data. Also in line with the evidence, our baseline results show a smaller second peak at the (system-defined) Full Retirement Age of 66. In the context of a zero-return environment, we show that workers will optimally devote more of their savings to non-retirement accounts and less to 401(k) accounts, since the relative appeal of investing in taxable versus tax-qualified retirement accounts is lower in a low return setting. Finally, we show that people claim Social Security benefits later in a low interest rate environment.

- Putting the pension back in 401(k) retirement plans : optimal versus default longevity income annuities (2018)
- A recent US Treasury regulation allowed deferred longevity income annuities to be included in pension plan menus as a default payout solution, yet little research has investigated whether more people should convert some of the $15 trillion they hold in employer-based defined contribution plans into lifelong income streams. We investigate this innovation using a calibrated lifecycle consumption and portfolio choice model embodying realistic institutional considerations. Our welfare analysis shows that defaulting a small portion of retirees’ 401(k) assets (over a threshold) is an attractive way to enhance retirement security, enhancing welfare by up to 20% of retiree plan accruals.