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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
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.
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.
In diesem Beitrag wird ein Vorschlag vorgestellt, wie es trotz langfristiger Niedrigzinsen möglich ist, die vor 18 Jahren eingeführte Riester-Rente so umzugestalten, dass alle Beteiligten davon profitieren. Wird die Mindestauszahlung am Ende der Vertragslaufzeit nur für die Eigenbeiträge, nicht aber für die staatlichen Zulagen garantiert, können deutlich höhere Renditen erzielt werden. Unter dem Strich haben dann nicht nur Privatleute mehr Geld aus ihrer Altersvorsorge, sondern der Staat wird mehr Steuern einnehmen und die Anbieter haben mehr Spielraum für bedarfsgerechte Produktgestaltung.
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.
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.
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.
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.
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.
Do required minimum distribution 401(k) rules matter, and for whom? Insights from a lifecylce model
(2021)
Tax-qualified vehicles helped U.S. private-sector workers accumulate $25Tr in retirement assets. An often-overlooked important institutional feature shaping decumulations from these retirement plans is the “Required Minimum Distribution” (RMD) regulation, requiring retirees to withdraw a minimum fraction from their retirement accounts or pay excise taxes on withdrawal shortfalls. Our calibrated lifecycle model measures the impact of RMD rules on financial behavior of heterogeneous households during their worklives and retirement. We show that proposed reforms to delay or eliminate the RMD rules should have little effects on consumption profiles but more impact on withdrawals and tax payments for households with bequest motives.
This paper investigates retirees’ optimal purchases of fixed and variable longevity income annuities using their defined contribution (DC) plan assets and given their expected Social Security benefits. As an alternative, we also evaluate using plan assets to boost Social Security benefits through delayed claiming. We determine that including deferred income annuities in DC accounts is welfare enhancing for all sex/education groups examined. We also show that providing access to well-designed variable deferred annuities with some equity exposure further enhances retiree wellbeing, compared to having access only to fixed annuities. Nevertheless, for the least educated, delaying claiming Social Security is preferred, whereas the most educated benefit more from using accumulated DC plan assets to purchase deferred annuities.
Many nations incentivize retirement saving by letting workers defer taxes on pension contributions, imposing them when retirees withdraw their funds. Using a dynamic life cycle model, we show how ‘Rothification’ – that is, taxing 401(k) contributions rather than payouts – alters saving, investment, consumption, and Social Security claiming patterns. We find that taxing pension contributions instead of withdrawals leads to delayed retirement, somewhat lower lifetime tax payments, and relatively small reductions in consumption. Indeed, the two tax regimes generate quite similar relative inequality metrics: the relative consumption inequality ratio under TEE is only four percent higher than in the EET case. Moreover, results indicate that the Gini measures are also strikingly similar under the EET and the TEE regimes for lifetime consumption, cash on hand, and 401(k) assets, differing by only 1-4 percent. While tax payments are higher early in life under the TEE regime, they are slightly lower in the long run. Moreover, higher EET tax payments are also accompanied by higher volatility. We therefore find few reasons for policymakers to favor either tax approach on egalitarian or revenue-enhancing grounds.
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.
Social Security rules that determine retirement, spousal, and survivor benefits, along with benefit adjustments according to the age at which these are claimed, open up a complex set of financial options for household decisions. These rules influence optimal household asset allocation, insurance, and work decisions, subject to life cycle demographic shocks, such as marriage, divorce, and children. Our model-based research generates a wealth profile and a low and stable equity fraction consistent with empirical evidence. We confirm predictions that wives will claim retirement benefits earlier than husbands, while life insurance is mainly purchased by younger men. Our policy simulations imply that eliminating survivor benefits would sharply reduce claiming differences by sex while dramatically increasing men’s life insurance purchases.
Dieser Artikel behandelt das Zusammenspiel von staatlich organisierten sozialen Sicherungssystemen und der privaten Eigenvorsorge durch Vermögensbildung als Grundpfeiler der sozialen Marktwirtschaft in Deutschland. Die jährlichen Ausgaben der verschiedenen staatlichen Sicherungssysteme belaufen sich auf rund ein Drittel des erwirtschafteten Bruttosozialprodukts, wobei die umlagefinanzierten Alterssicherungssysteme für die Arbeitsnehmer den größten Anteil ausmachen. Sachvermögen in Form von selbst genutzten Wohnungen sowie Finanzvermögen in Form von Bankeinlagen und Ansprüche gegen private Versicherungen machen den größten Anteil der Eigenversorge aus. Aufgrund des niedrigen Zinsniveaus sowie des demografischen Wandels der Gesellschaft wird die Eigenvorsorge durch Anlagen an den internationalen Wertpapiermärkten sowohl für Selbständige als auch Arbeitsnehmer immer bedeutender.
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.
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.
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.
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.