Benchmark-adjusted performance of US equity mutual funds and the issue of prospectus benchmarks

This study examines the impact of mismatch between prospectus benchmark and fund objectives on benchmark-adjusted fund performance and ranking in a sample of 1281 US equity mutual funds. All funds in our sample report S&P500 index as a prospectus benchmark, yet 2/3 of those are placed in the Morningstar category with risk and objectives different to those of the S&P500 index. We identify more appropriate ‘category benchmarks’ for those mismatched funds and obtain their benchmark-adjusted alphas using recent Angelidis et al. (J Bank Finance 37(5):1759–1776, 2013) methodology. We find that S&P500-adjusted alphas are higher than ‘category benchmark’-adjusted alphas in 61.2% of the cases. In terms of fund quartile rankings, 30% of winner funds lose that status when the prospectus benchmark is substituted with the one better matching their objectives. In the remaining performance quartiles, there is no clear advantage of using S&P 500 as a benchmark. Hence, the prospectus benchmark can mislead investors about fund’s relative performance and ranking, so any reference to performance in a fund’s prospectus should be treated with caution

An Algorithmic Metatheorem for Directed Treewidth

The notion of directed treewidth was introduced by Johnson, Robertson, Seymour and Thomas [Journal of Combinatorial Theory, Series B, Vol 82, 2001] as a first step towards an algorithmic metatheory for digraphs. They showed that some NP-complete properties such as Hamiltonicity can be decided in polynomial time on digraphs of constant directed treewidth. Nevertheless, despite more than one decade of intensive research, the list of hard combinatorial problems that are known to be solvable in polynomial time when restricted to digraphs of constant directed treewidth has remained scarce. In this work we enrich this list by providing for the first time an algorithmic metatheorem connecting the monadic second order logic of graphs to directed treewidth. We show that most of the known positive algorithmic results for digraphs of constant directed treewidth can be reformulated in terms of our metatheorem. Additionally, we show how to use our metatheorem to provide polynomial time algorithms for two classes of combinatorial problems that have not yet been studied in the context of directed width measures. More precisely, for each fixed $k,w \in \mathbb{N}$, we show how to count in polynomial time on digraphs of directed treewidth $w$, the number of minimum spanning strong subgraphs that are the union of $k$ directed paths, and the number of maximal subgraphs that are the union of $k$ directed paths and satisfy a given minor closed property. To prove our metatheorem we devise two technical tools which we believe to be of independent interest. First, we introduce the notion of tree-zig-zag number of a digraph, a new directed width measure that is at most a constant times directed treewidth. Second, we introduce the notion of $z$-saturated tree slice language, a new formalism for the specification and manipulation of infinite sets of digraphs.Comment: 41 pages, 6 figures, Accepted to Discrete Applied Mathematic

Weakly complete axiomatization of exogenous quantum propositional logic

A weakly complete finitary axiomatization for EQPL (exogenous quantum propositional logic) is presented. The proof is carried out using a non trivial extension of the Fagin-Halpern-Megiddo technique together with three Henkin style completions.Comment: 28 page