Working paper series / Johann-Wolfgang-Goethe-Universität Frankfurt am Main, Fachbereich Wirtschaftswissenschaften : Finance & Accounting
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199
Gauging risk with higher moments : handrails in measuring and optimising conditional value at risk
(2009)
The aim of the paper is to study empirically the influence of higher moments of the return distribution on conditional value at risk (CVaR). To be more exact, we attempt to reveal the extent to which the risk given by CVaR can be estimated when relying on the mean, standard deviation, skewness and kurtosis. Furthermore, it is intended to study how this relationship can be utilised in portfolio optimisation. First, based on a database of 600 individual equity returns from 22 emerging world markets, factor models incorporating the first four moments of the return distribution have been constructed at different confidence levels for CVaR, and the contribution of the identified factors in explaining CVaR was determined. Following this the influence of higher moments was examined in portfolio context, i.e. asset allocation decisions were simulated by creating emerging market portfolios from the viewpoint of US investors. This can be regarded as a normal decisionmaking process of a hedge fund focusing on investments into emerging markets. In our analysis we compared and contrasted two approaches with which one can overcome the shortcomings of the variance as a risk measure. First of all, we solved in the presence of conflicting higher moment preferences a multi-objective portfolio optimisation problem for different sets of preferences. In addition, portfolio optimisation was performed in the mean-CVaR framework characterised by using CVaR as a measure of risk. As a part of the analysis, the pair-wise comparison of the different higher moment metrics of the meanvariance and the mean-CVaR efficient portfolios were also made. Throughout the work special attention was given to implied preferences to the different higher moments in optimising CVaR. We also examined the extent to which model risk, namely the risk of wrongly assuming normally-distributed returns can deteriorate our optimal portfolio choice. JEL Classification: G11, G15, C61
83
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.
59
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.
94
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.
92
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.
174
We compute the optimal dynamic asset allocation policy for a retiree with Epstein-Zin utility. The retiree can decide how much he consumes and how much he invests in stocks, bonds, and annuities. Pricing the annuities we account for asymmetric mortality beliefs and administration expenses. We show that the retiree does not purchase annuities only once but rather several times during retirement (gradual annuitization). We analyze the case in which the retiree is restricted to buy annuities only once and has to perform a (complete or partial) switching strategy. This restriction reduces both the utility and the demand for annuities.
176
Many tax-codes around the world allow for special taxable treatment of savings in retirement accounts. In particular, profits in retirement accounts are usually tax exempt which allow investors to increase an asset’s return by holding it in such a retirement account. While the existing literature on asset location shows that risk-free bonds are usually the preferred asset to hold in a retirement account, we explain how the tax exemption of profits in retirement accounts affects private investors’ asset allocation. We show that total final wealth can be decomposed into what the investor would have earned in a taxable account and what is due to the tax exemption of profits in the retirement account. The tax exemption of profits can thus be considered a tax-gift which is similar to an implicit bond holding. As this tax-gift’s impact on total final wealth decreases over time, so does the investor’s equity exposure.
170
The tax codes in many countries allow for special tax advantages for investments in special retirement plans. Probably the most important advantage to these plans is that profits usually remain untaxed. This paper deals with the question, which assets are preferable in a taxdeferred account (TDA). Contrary to the conventional wisdom that one should prefer bonds in the TDA, it is shown that especially in early years, stocks can be the preferred asset to hold in the TDA for an investor maximizing final wealth, given a certain asset allocation. The higher the performance of stocks compared to bonds, the higher the tax burden put on stocks compared to bonds. Simultaneously, the longer the remaining investment horizon, the larger the relative outperformance of the optimal asset location strategy compared to the myopic strategy of locating bonds in the TDA. An algorithm is provided to determine the investment strategy that maximizes (expected) funds at the end of a given investment horizon when there is an analytical solution.
169
This paper analyzes the relation between demographic structure and real asset returns on treasury bills, bonds and stocks for the G7-countries (United States, Canada, Japan, Italy, France, the United Kingdom and Germany). A macroeconomic multifactor model is used to examine a variety of different demographic factors from 1951 to 2002. There was no robust relationship found between shocks in demographic variables and asset returns in the framework of these models, which suggests that Asset Meltdown is rather fiction than fact.
067
In this paper we study the benefits derived from international diversification of stock portfolios from German and Hungarian point of view. In contrast to the German capital market, which is one of the largest in the world, the Hungarian Stock Exchange is an emerging market. The Hungarian stock market is highly volatile, high returns are often accompanied by extremely large risk. Therefore, there is a good potential for Hungarian investors to realize substantial benefits in terms of risk reduction by creating multi-currency portfolios. The paper gives evidence on the above me ntioned benefits for both countries by examining the performance of several ex ante portfolio strategies. In order to control the currency risk, different types of hedging approaches are implemented.