Simone Farinelli

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.

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.

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.

Portfolio Management and Stochastic Optimization in Discrete Time: An Application to Intraday Electricity Trading and Water Values for Hydroassets

Hydro storage system optimization is becoming one of the most challenging task in Energy Finance. Following the Blomvall and Lindberg (2002) interior point model, we set up a stochastic multiperiod optimization procedure by means of a “bushy” recombining tree that provides fast computational results. Inequality constraints are packed into the objective function by the logarithmic barrier approach and the utility function is approximated by its second order Taylor polynomial. The optimal solution for the original problem is obtained as a diagonal sequence where the first diagonal dimension is the parameter controlling the logarithmic penalty and the second is the parameter for the Newton step in the construction of the approximated solution. Optimimal intraday electricity trading and water values for hydroassets are computed. The algorithm is implemented in Mathematica.