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PORTFOLIO CHOICE WITH HEAVY TAILED DISTRIBUTIONS 1
"... Firstly, we examine investor’s optimal choices when we assume respectively either Gaussian or stable nonGaussian unconditional distributed index returns. Then, we approximate discrete time optimal allocations assuming returns following an ARMA process. Secondly we examine different performance meas ..."
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Firstly, we examine investor’s optimal choices when we assume respectively either Gaussian or stable nonGaussian unconditional distributed index returns. Then, we approximate discrete time optimal allocations assuming returns following an ARMA process. Secondly we examine different performance measures alternative to Sharpe Ratio. In particular, we analyze several allocation problems which consider portfolio selection models based on different performance ratios. For each allocation problem, we discuss an expost multiperiod portfolio selection analysis in order to describe and compare the sample path of final wealth processes. Finally, we describe further autoregressive portfolio choice models. Key words: Stable distributions, portfolio selection, ARMA models. Over the last fifty years, the problem of optimal portfolio selection has lost none of its allure or importance for the financial community. Just consider the following reason, which will appeal immediately to every investor. At a time when more than fifty percent of all financial assets in North America are controlled by pension or mutual funds, a lot of people apparently
Proper Conditioning for Coherent VaR in Portfolio Management ∗
"... Value at Risk (VaR) is a central concept in risk management. As stressed by Artzner et al. (1999), VaR may not possess the subadditivity property required to be a coherent measure of risk. The key idea of this paper is that, when tail thickness is responsible for violation of subadditivity, elicitin ..."
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Value at Risk (VaR) is a central concept in risk management. As stressed by Artzner et al. (1999), VaR may not possess the subadditivity property required to be a coherent measure of risk. The key idea of this paper is that, when tail thickness is responsible for violation of subadditivity, eliciting proper conditioning information may restore VaR rationale for decentralized risk management. The argument is threefold. First, since individual traders are hired because they possess a richer information on their specific market segment than senior management, they just have to follow consistently the prudential targets set by senior management to ensure that decentralized VaR control will work in a coherent way. The intuition is that if one could build a fictitious conditioning information set merging all individual pieces of information, it would be rich enough to restore VaR subadditivity. Second, in this decentralization context, we show that if senior management has access expost to the portfolio shares of the individual traders, it amounts to recovering some of their private information. These shares can be used to improve backtesting in order to check that the prudential targets have been enforced by the traders. Finally, we stress that tail thickness required to violate subadditivity, even for small probabilities, remains an extreme situation since it corresponds to such poor conditioning information that expected loss appears to be infinite. We then conclude that lack of coherency of decentralized VaR management, that is VaR nonsubadditivity at the richest level of information, should be an exception rather than a rule.
Criteria
"... In this paper, we analyze momentum strategies that are based on rewardrisk stock selection criteria in contrast to ordinary momentum strategies based on a cumulative return criterion. Rewardrisk stock selection criteria include the standard Sharpe ratio with variance as a risk measure, and alterna ..."
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In this paper, we analyze momentum strategies that are based on rewardrisk stock selection criteria in contrast to ordinary momentum strategies based on a cumulative return criterion. Rewardrisk stock selection criteria include the standard Sharpe ratio with variance as a risk measure, and alternative rewardrisk ratios with the expected shortfall as a risk measure. We investigate momentum strategies using 517 stocks in the S&P 500 universe in the period 1996 to 2003. Although the cumulative return criterion provides the highest average monthly momentum profits of 1.3 % compared to the monthly profit of 0.86 % for the best alternative criterion, the alternative ratios provide better riskadjusted returns measured on an independent riskadjusted performance measure. We also provide evidence on unique distributional properties of extreme momentum portfolios analyzed within the framework of general nonnormal stable Paretian distributions. Specifically, for every stock selection criterion, loser portfolios
The proper use of risk . . .
"... This paper discusses and analyzes risk measure properties in order to understand how a risk measure has to be used to optimize the investor’s portfolio choices. In particular, we distinguish between two admissible classes of risk measures proposed in the portfolio literature: safety risk measures an ..."
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This paper discusses and analyzes risk measure properties in order to understand how a risk measure has to be used to optimize the investor’s portfolio choices. In particular, we distinguish between two admissible classes of risk measures proposed in the portfolio literature: safety risk measures and dispersion measures. We study and describe how the risk could depend on other distributional parameters. Then, we examine and discuss the differences between statistical parametric models and linear fund separation ones. Finally, we propose an empirical comparison among three different portfolio choice models which depend on the mean, on a risk measure, and on a skewness parameter. Thus, we assess and value the impact on the investor’s preferences of three different risk measures even considering some derivative assets among the possible choices.