Stochastic dominance and risk measure: A decision-theoretic foundation for VaR and C-VaR

Abstract

Is it possible to obtain an objective and quantifiable measure of risk backed up by choices made by some specific groups of rational investors? To answer this question, in this paper we establish some behavior foundations for various types of VaR models, including VaR and conditional-VaR, as measures of downside risk. Though supported to some extent with unanimous choices by some specific groups of expected or non-expected utility investors, VaRs as profiles of risk measures at various levels of risk tolerance are not quantifiable-they can only provide partial and incomplete risk assessments for risky prospects. Also included in our discussion are the relevant VaRs and several alternative risk measures for investors; these alternatives use somewhat weaker assumptions about risk-averse behavior by incorporating a mean-preserving-spread. For this latter group of investors, we provide arguments for and against the standard deviation vs. VaR and conditional VaRs as objective and quantifiable measures of risk in the context of portfolio choice.

A Bayesian approach to excess volatility, short-term underreaction and long-term overreaction during financial crises

“…One may incorporate other information, for example, the economic and financial environment (Fong, Lean, and Wong, 2008), the mean-variance rule (Wong and Ma, 2008;Bai, Hui, Wong, and Zitikis, 2012), CAPM statistics (Leung, Ng and Wong, 2012), VaR rule (Ma and Wong, 2010), portfolio optimization (Bai, Liu, and Wong, 2009), and portfolio diversification (Egozcue and Wong, 2010) into the theory developed in the paper to make better investment decisions.…”

Market Efficiency of Oil Spot and Futures: A Mean-Variance and Stochastic Dominance Approach

“…In addition, the conclusion drawn from SD is equivalent to many other non-normal approaches. For example, it is well known that the finding from FSD is equivalent to that from VaR, and the finding from SSD is equivalent to that from CVaR (Ogryczak and Ruszczynski, 2002;Leitner, 2005;Ma and Wong, 2006). Thus, it is not necessary to consider other non-normal approaches.…”

The Impacts of Joint Energy and Output Prices Uncertainties in a Mean-Variance Framework

“…We note that the theory developed in our paper could be used in many areas, for example, Vorotnikova and Asci [35] developed an empirical estimation for multi-output production decision using multiple inputs in the profit maximizing We also note that mean-variance framework is related to stochastic dominance (SD) theory, see, for example, Wong [43] and Wong and Ma [44] for more information. Nonetheless, Rrisk measures are found to be interesting because they could be related to stochastic dominance theory and thus it is wellknown that domination by risk measures could be related to expected utility maximization, see, for example, Ma and Wong [44].…”