These two downside risk measures calculate variance using the returns lower than a target return or below a mean return. Markowitz (1959) and then Nawrocki (1999) propose two downside risk measures: a semi-variance (SV) calculated by below-target SV and a SV calculated by below-mean SV. By minimizing the portfolio losses of below-target mean returns, it provides portfolio allocations to minimize the likelihood of below-target mean returns. Thus, the studies of asymmetric risk measures, which are based on the decreasing losses of below-target mean returns, are able to make a more appropriate model of investors’ decision making. However, Markowitz (1959) finds that it does not describe accurately investors’ preferences to minimize portfolio losses. He assumes that investors equally worry to eliminate two sides of their own portfolio return distribution. The downside risk measure is primarily introduced by Markowitz (1959). The majority of the studies focus exclusively on two initial moments of portfolio return distribution, namely, mean and variance. However, due to the publication of Markowitz's (1952) seminal study on portfolio diversification, there are a large number of subsequent studies on portfolio performance. This theory has gradually changed the framework of portfolio theory by focusing on the maximization of expected utility instead of returns maximization on a given risk. The concept of portfolio optimization is grounded on ‘utility theory’, which is a theory of ranking the wealth levels. Variance and below-target-returns variation The section ‘Discussion of results’ discusses the main findings, and the section ‘Concluding remarks’ summarizes the findings, and discusses their implications. The section ‘An empirical study’ discusses and analyzes the empirical purpose of our article, data and research method. The section ‘Proposed methodology’ proposes the methodology of funds’ optimization based on the DRM. The section ‘Theoretical basis and literature review’ explains utility theory as a basic theory in portfolio optimization, and then reviews the MV literature, below-target-returns variation and the DRM development. The evaluation of the US investor's perspective provides initial implications about the issue of how the DRM can be used to affect returns’ drawdown risk decrease. The objective of our article is first to describe the DRM risk measure and its own development, second to propose two new MV models in the DRM form and third to empirically assess the practical indications of portfolio performance from the US investors’ perspective. Specifically, the previous studies do not develop the MV framework based on the DRM in analyzing the changing degrees of risk tolerances. However, previousstudies neglect to consider whether the DRM can flexibly describe the changing degrees of risk tolerances. One the other hand, the development of asymmetric risk measures and the restrictions of MV increase interests in extending the DRM models. However, in spite of the success of the mean variance (hereafter, MV) framework and computational costs, his view on the DRM models is widely neglected. The initial academic interest of the DRM can stem from Markowitz's (1952) seminal paper on portfolio diversification. For instance, Alexander and Baptista (2006), Steiner (2011) and Tavakoli Baghdadabad et al (2011) investigate the DRM measures in investment portfolios. The DRM optimization model reduces investors’ risk more than the conventional models and can be accommodated with risk-averse investors’ approach.Īsymmetric risk studies, in particular the drawdown risk measure (hereafter, DRM), have extensively increased during recent decades. Our findings also show that skewness does not impose any significant problem in the DRM model. We find that it can negatively affect portfolio returns. Our findings increase the importance of risk (tolerance) perception, in particular drawdown risk, when making many investment decisions. ![]() We find that the potential benefits of funds’ diversification may weaken decreases in tolerance levels of drawdown risk. The optimization models in the DRM form are run to optimize the risk measures and investigate the effects of drawdown risk reduction. The monthly returns are applied for 1720 US hedge funds over the period 2000–2011. Unlike prior literatures, we use the drawdown risk measure (DRM), which is a special case of LPM, to study the impacts of drawdown risk decrease on management styles of the US hedge funds. Despite the existence of numerous evidences on the asymmetric distribution of portfolio returns, the asymmetric risk measures have been extensively applied in risk management during recent years with the considerable applications on the lower partial moment (LPM) methodology. We investigate the effects of drawdown risk reduction on the US hedge funds.
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