Efficient Diversification According to Stochastic Dominance Criteria

Abstract

T his paper develops the first operational tests of portfolio efficiency based on the general stochastic dominance (SD) criteria that account for an infinite set of diversification strategies. The main insight is to preserve the cross-sectional dependence of asset returns when forming portfolios by reexpressing the SD criteria in T -dimensional Euclidean space, with elements representing rates of return in T different states of nature. We characterize subsets of this state-space that dominate a given evaluated return vector by first-and secondorder SD. This allows us to derive simple SD efficiency measures and test statistics, computable by standard mathematical programming algorithms. The SD tests and efficiency measures are illustrated by an empirical application that analyzes industrial diversification of the market portfolio.

Measuring world governance: revisiting the institutions hypothesis

“…The best-case scenario must be …rst-order stochastic dominance e¢ cient for all governance indicators that use a nonsatiable decision maker (see Fishburn 1974;Bawa et al 1985;Post 2003;Kuosmanen 2004; Scaillet and Topaloglou 2010 among many others) which is appropriate for both risk averse and risk lover individuals as utility function may have concave and convex segments respectively. In other words, …rst-order SDE is more general as it corresponds to all types of utility functions as long as they are non-decreasing.…”

“…On the other hand, recently Post (2003) and Kuosmanen (2004) introduced the notion of SDE, which allow for full diversi…cation. Both the Post (2003) and Kuosmanen (2004) approaches are based on derivations of ranked observations under an independent identical distribution (iid) assumption of the asset returns.…”

“…Both the Post (2003) and Kuosmanen (2004) approaches are based on derivations of ranked observations under an independent identical distribution (iid) assumption of the asset returns. In other words, both Post (2003) and Kuosmanen (2004) o¤er a sampling scheme assuming iid observations and therefore do not allow for possible data dependence such as GARCH e¤ects often encountered in high frequency returns (see e.g. Linton and Whang 2012).…”

“…Linton and Whang 2012). Scaillet and Topaloglou (2010), hereafter ST, not only allow for full diversi…cation similar to the Post (2003) and Kuosmanen (2004) methodologies but also extend the Barrett and Donald (2003) and Horvath et al (2006) approaches by allowing for time-dependent data. In other words, the ST methodology allows for full diversi…cation for serially correlated time-dependent data by extending the existing approaches mentioned above.…”

Second Order Stochastic Dominance, Reward-Risk Portfolio Selection and the CAPM

“…The alternatives yield either comparable results (for example g(x) = − 1 γ log (−(1 − exp(−γ)) x + 1)) or a worst fit (g(x) = x γ ). We also used the second-order stochastic dominance tests of Post (2003) and Kuosmanen (2004), which entirely avoid the specification of the transformation function. Interestingly, these tests yield results that are very comparable with the results for the distortion function (3.11).…”