Search

The aim of the paper is to identify unobservable factors that may significantly determine the level of gold and silver returns and to assess the risk of investment in these metals. To measure risk, the value at risk and other, less popular measures are used: the ES, MS, Rachev ratio and GlueVaR risk measure. Normal and Student’s t‑distributions are used as theoretical distributions. The results of the study show that we can identify latent factors based on observable variables that have a significant impact on the level of gold and silver returns. In addition, it was observed that the risk measures would vary depending on the period of research. It was shown that the estimates of the risk measures using Student’s t‑distribution have a lower estimation error than those based on the normal distribution.

The enhanced index tracking problem (EITP) calls for the determination of an optimal portfolio of assets with the bi-objective of maximizing the excess return of the portfolio above a benchmark and minimizing the tracking error. The EITP is capturing a growing attention among academics, both for its practical relevance and for the scientific challenges that its study, as a multi-objective problem, poses. Several optimization models have been proposed in the literature, where the tracking error is measured in terms of standard deviation or in linear form using, for instance, the mean absolute deviation. More recently, reward-risk optimization measures, like the Omega ratio, have been adopted for the EITP. On the other side, shortfall or quantile risk measures have nowadays gained an established popularity in a variety of financial applications. In this paper, we propose a class of bi-criteria optimization models for the EITP, where risk is measured using the weighted multiple conditional value-at-risk (WCVaR). The WCVaR is defined as a weighted combination of multiple CVaR measures, and thus allows a more detailed risk aversion modeling compared to the use of a single CVaR measure. The application of the WCVaR to the EITP is analyzed, both theoretically and empirically. Through extensive computational experiments, the performance of the optimal portfolios selected by means of the proposed optimization models is compared, both in-sample and, more importantly, out-of-sample, to the one of the portfolios obtained using another recent optimization model taken from the literature. [ABSTRACT FROM AUTHOR]

In the present paper, we study quantile risk measures and their domain. Our starting point is that, for a probability measure Q on the open unit interval and a wide class L Q of random variables, we define the quantile risk measure ϱ Q as the map that integrates the quantile function of a random variable in L Q with respect to Q. The definition of L Q ensures that ϱ Q cannot attain the value + ∞ and cannot be extended beyond L Q without losing this property. The notion of a quantile risk measure is a natural generalization of that of a spectral risk measure and provides another view of the distortion risk measures generated by a distribution function on the unit interval. In this general setting, we prove several results on quantile or spectral risk measures and their domain with special consideration of the expected shortfall. We also present a particularly short proof of the subadditivity of expected shortfall.

The paper presents a copula-based extension of Conditional Value-at-Risk and its application to portfolio optimization. Copula-based conditional value-at-risk (CCVaR) is a scalar risk measure for multivariate risks modeled by multivariate random variables. It is assumed that the univariate risk components are perfect substitutes, i.e., they are expressed in the same units. CCVaR is a quantile risk measure that allows one to emphasize the consequences of more pessimistic scenarios. By changing the level of a quantile, the measure permits to parameterize prudent attitudes toward risk ranging from the extreme risk aversion to the risk neutrality. In terms of definition, CCVaR is slightly different from popular and well-researched CVaR. Nevertheless, this small difference allows one to efficiently solve CCVaR portfolio optimization problems based on the full information carried by a multivariate random variable by employing column generation algorithm. [ABSTRACT FROM AUTHOR]

The paper introduces a new risk measure called Conditional Average (CAVG), which was designed to cover typical attitudes towards risk for any type of distribution. It can be viewed as a generalization of Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), two commonly used risk measures. The preference structure induced by CAVG has the interpretation in Yaari’s dual theory of choice under risk and relates to Tversky and Kahneman’s cumulative prospect theory. The measure is based on the new stochastic ordering called dual prospect stochastic dominance, which can be considered as a dual stochastic ordering to recently developed prospect stochastic dominance. In general, CAVG translates into a nonconvex quadratic programming problem, but in the case of a finite probability space it can also be expressed as a mixed-integer program. The paper also presents the results of computational studies designed to assess the preference modeling capabilities of the measure. The experimental analysis was performed on the asset allocation problem built on historical values of S&P 500 sub-industry indexes. [ABSTRACT FROM AUTHOR]