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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
The direct financial impact of the financial crisis has been to deal a heavy blow to investment-based pensions; many workers lost a substantial portion of their retirement saving. The financial sector implosion produced an economic crisis for the rest of the economy via high unemployment and reduced labor earnings, which reduced household contributions to Social Security and some private pensions. Our research asks which types of individuals were most affected by these dual financial and economic shocks, and it also explores how people may react by changing their consumption, saving and investment, work and retirement, and annuitization decisions. We do so with a realistically calibrated lifecycle framework allowing for time-varying investment opportunities and countercyclical risky labor income dynamics. We show that households near retirement will reduce both short- and long-term consumption, boost work effort, and defer retirement. Younger cohorts will initially reduce their work hours, consumption, saving, and equity exposure; later in life, they will work more, retire later, consume less, invest more in stocks, save more, and reduce their demand for private annuities. Keywords: Financial Crisis , Household Finance , Cycle Portfolio Choice , Labor Supply Classification: D1, G11, G23, G35, J14, J26, J32
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.
How might retirees consider deploying the retirement assets accumulated in a defined contribution pension plan? One possibility would be to purchase an immediate annuity. Another approach, called the "phased withdrawal" strategy in the literature, would have the retiree invest his funds and then withdraw some portion of the account annually. Using this second tactic, the withdrawal rate might be determined according to a fixed benefit level payable until the retiree dies or the funds run out, or it could be set using a variable formula, where the retiree withdraws funds according to a rule linked to life expectancy. Using a range of data consistent with the German experience, we evaluate several alternative designs for phased withdrawal strategies, allowing for endogenous asset allocation patterns, and also allowing the worker to make decisions both about when to retire and when to switch to an annuity. We show that one particular phased withdrawal rule is appealing since it offers relatively low expected shortfall risk, good expected payouts for the retiree during his life, and some bequest potential for the heirs. We also find that unisex mortality tables if used for annuity pricing can make women's expected shortfalls higher, expected benefits higher, and bequests lower under a phased withdrawal program. Finally, we show that delayed annuitization can be appealing since it provides higher expected benefits with lower expected shortfalls, at the cost of somewhat lower anticipated bequests. Klassifikation: G22, G23, J26, J32, H55 . January 2004.
Shares of open-end real estate funds are typically traded directly between the investor and the fund management company. However, we provide empirical evidence for the growth of secondary market activities, i.e., the trading of shares on stock exchanges. We find high trading levels in situations where the fund management company suspends the issue or redemption of shares. Shares trade at a discount when the fund management company suspends the redemption, whereas shares trade at a premium when the fund management company suspends the issue. We also find evidence that secondary market trading activity is increasing since German regulation introduced a minimum holding period and a mandatory notice period for open-end real estate funds.
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.
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.
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.