Luisa Tibiletti

Sharpe thinking in asset ranking with one-sided measures

Abstract If we exclude the assumption of normality in return distributions, the classical risk–reward Sharpe Ratio becomes a questionable tool for ranking risky projects. In line with Sharpe thinking, a general risk–reward ratio suitable to compare skewed returns with respect to a benchmark is introduced. The index includes asymmetrical information on: (1) “good” volatility (above the benchmark) and “bad” volatility (below the benchmark), and (2) asymmetrical preference to bet on potential high stakes and the aversion against possible huge losses. The former goal is achieved by using one-sided volatility measures and the latter by choosing the appropriate order for the one-sided moments involved. The Omega Index (see [Cascon A., Keating, C., Shadwick, W., 2002. Introduction to Omega, The Finance Development Centre]) and the Upside Potential Ratio (see [Sortino, F., Van Der Meer, R., Plantinga, A., 1999. The Dutch triangle. Journal of Portfolio Management, 26 (I, Fall), 50–58]) follow as special cases.

Beneficial Changes in Random Variables Via Copulas: An Application to Insurance

A risk-averse agent does not necessarily decrease the optimal insurance whenever a beneficial change in the distribution of final wealth occurs. This paper provides sufficient conditions to guarantee such a decrease. Beneficial changes can be induced by either a beneficial loss-distribution shift, by a modification of the dependence structure between the randomness sources, or by both of these. Conditions for each case are stated. Hadar-Seo and Meyer results turn out as special cases.

Computational asset allocation using one-sided and two-sided variability measures

Excluding the assumption of normality in return distributions, a general reward-risk ratio suitable to compare portfolio returns with respect to a benchmark must includes asymmetrical information on both “good” volatility (above the benchmark) and “bad” volatility (below the benchmark), with different sensitivities. Including the Farinelli-Tibiletti ratio and few other indexes recently proposed by the literature, the class of one-sided variability measures achieves the goal. We investigate the forecasting ability of eleven alternatives ratios in portfolio optimization problems. We employ data from security markets to quantify the portfolio’s overperformance with respect to a given benchmark.

A Multicriteria Classification: An Application to Italian Mutual Funds

The evaluation problem of the fund performance has been widely debated in the literature during the last twenty years (see for example, Treynor (1965), Levy-Sarnat (1984), Koury-Martel (1990)) and numerous performance measures have been proposed. Since each of them may take into account a different set of factors (such as the investment term, the safe return comparison,..) discordant performance judgment may be formulated by using different indicators. This fact has motivated the attempts to tackle the problem using multicriteria procedures in order to yield a global evaluation. An example in this direction is offered by Cardin et al. (1992), where a PROMETHEE multicriteria method has been employed. The crucial point of this method is the preference functions choice and although, that permits a proper fund classification, it may appear an “unfriendly” approach to users, who are not accustomed to deciding upon analytical expressions.

Internal vs. external risk measures: How capital requirements differ in practice

We compare capital requirements derived from tail conditional expectation (TCE) with those derived from the tail conditional median (TCM). In theory, TCE is higher than TCM for most distributions commonly used in finance and at fixed confidence levels; however, we find that in empirical data, there is no clear-cut relationship between the two. Our results highlight the relevance of TCM as a robust alternative to TCE, especially for regulatory control.

Skewness in hedge funds returns: classical skewness coefficients vs Azzalini's skewness parameter

Purpose - Recent literature discusses the persistence of skewness and tail risk in hedge fund returns. The aim of this paper is to suggest an alternative skewness measure, Azzalinis skewness parameter delta, which is derived as the normalized shape parameter from the skew-normal distribution. The paper seeks to analyze the characteristics of this skewness measure compared with other indicators of skewness and to employ it in some typical risk and performance measurements. Design/methodology/approach - The paper first provides an overview of the skew-normal distribution and its mathematical formulation. Then it presents some empirical estimations of the skew-normal distribution for hedge fund returns and discusses the characteristics of using delta with respect to classical skewness coefficients. Finally, it illustrates how delta can be used in risk management and in a performance measurement context. Findings - The results highlight the advantages of Azzalinis skewness parameter delta, especially with regard to its interpretation. Delta has a limpid financial interpretation as a skewness shock on normally distributed returns. The paper also derives some important characteristics of delta, including that it is more stable than other measures of skewness and inversely related to popular risk measures such as the value-at-risk (VaR) and the conditional value-at-risk (CVaR). Originality/value - The contribution of the paper is to apply the skew-normal distribution to a large sample of hedge fund returns. It also illustrates that using Azzalinis skewness parameter delta as a skewness measure has some advantages over classical skewness coefficients. The use of the skew-normal and related distributions is a relatively new, but growing, field in finance and not much has been published on the topic. Skewness itself, however, has been the subject of a great deal of research. Therefore, the results contribute to three fields of research: skewed distributions, risk measurement, and hedge fund performance.

A target-oriented approach: A "one-size" model to suit humans and econs behaviors

Thaler and Sunstein (2008) introduce two stereotypical decision makers: the Econs, imaginary people who always behave as strictly rational expected utility maximizers, and the Humans, real people subject to ordinary behavioral biases. This note sheds light on how the axiomatic target-oriented approach introduced by Castagnoli and Li Calzi (1996) may fit well the behavior of both of them. We show that although Econs and Humans use a different language, they maximize the same functional, e.g. the probability of meeting the goal. So declaring the probability distribution of the goal permits to elicit the agent value function. A number of different distributions for goals are discussed and the family of the skew normal ones is proposed for its user-friendly flexibility. We show how moving the skewness parameter along its range every stereotypical decision maker’s profile may be modelled.

Mean‐extended Gini portfolios personalized to the investor's profile

Purpose – Shalit and Yitzhaki presented the mean‐extended Gini (MEG) as a workable alternative to the Markowitz mean‐variance approach in 1984. Since then, the challenge has been to extend the MEG approach. The purpose of this paper is to propose a generalization of the MEG approach for making customized optimal asset allocation to control both down‐performance and/or up‐performance.Design/methodology/approach – The MEG approach is used to make strategical allocation tailored to the investor risk aversion and gain propensity measured by characteristic parameters of the extended Gini measures.Findings – The authors set up two optimization problems: the former focused on controlling the risk, the latter on emphasizing the potential gains. Sufficient conditions such that the efficient MEG‐risk frontier coincides with the inefficient MEG‐gain frontier are stated. In the realistic scenarios that portfolios have asymmetrical distributions and/or the investor profile is very conservative or very aggressive, the ...

How skewness influences optimal allocation in a risky asset

This article extends the classic Samuelson (1970) and Merton (1973) model of optimal portfolio allocation with one risky asset and a riskless one to include the effect of the skewness. Using an extended version of Steins Lemma, we provide the explicit solution for optimal demand that holds for all expected utility maximizing investors when the risky asset is skew-normally and normally distributed. A closed expression is achieved for investors with constant absolute risk aversion.

Moment identity for discrete random variable and its applications

In this paper, we obtain a moment identity applicable to a general class of discrete probability distributions. We then derive the corresponding identities for modified power series, Ord and Katz families. It is noted that the proposed identity has potential applications in different fields.