Portfolio selection problems in practice: a comparison between linear and quadratic optimization models

Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACVaR) models, where the assets are limited with the introduction of quantity and cardinality constraints. We propose a completely new approach for solving the LAM model, based on reformulation as a Standard Quadratic Program and on some recent theoretical results. With this approach we obtain optimal solutions both for some well-known financial data sets used by several other authors, and for some unsolved large size portfolio problems. We also test our method on five new data sets involving real-world capital market indices from major stock markets. Our computational experience shows that, rather unexpectedly, it is easier to solve the quadratic LAM model with our algorithm, than to solve the linear LACVaR and LAMAD models with CPLEX, one of the best commercial codes for mixed integer linear programming (MILP) problems. Finally, on the new data sets we have also compared, using out-of-sample analysis, the performance of the portfolios obtained by the Limited Asset models with the performance provided by the unconstrained models and with that of the official capital market indices

The Genetic Structure and History of Africans and African Americans.

Africa is the source of all modern humans, but characterization of genetic variation and of relationships among populations across the continent has been enigmatic. We studied 121 African populations, four African American populations, and 60 non-African populations for patterns of variation at 1327 nuclear microsatellite and insertion/deletion markers. We identified 14 ancestral population clusters in Africa that correlate with self-described ethnicity and shared cultural and/or linguistic properties. We observed high levels of mixed ancestry in most populations, reflecting historical migration events across the continent. Our data also provide evidence for shared ancestry among geographically diverse hunter-gatherer populations (Khoesan speakers and Pygmies). The ancestry of African Americans is predominantly from Niger-Kordofanian (approximately 71%), European (approximately 13%), and other African (approximately 8%) populations, although admixture levels varied considerably among individuals. This study helps tease apart the complex evolutionary history of Africans and African Americans, aiding both anthropological and genetic epidemiologic studies

Patterns of male-specific inter-population divergence in Europe, West Asia and North Africa

We typed 1801 males from 55 locations for the Y-specific binary markers YAP! DYZ3, SRY10831 and the (CA)n microsatellites YCAII and DYS413. Phylogenetic relationships of chromosomes with the same binary haplotype were condensed in seven large one-step networks! which accounted for 95% of all chromosomes. Their coalescence ages were estimated based on microsatellite diversity. The three largest and oldest networks undergo sharp frequency changes in three areas. The more recent network; 3.1A clearly discriminates between Western and Eastern European populations. Pairwise Pst showed an overall increment with increasing geographic distance but with a slope greatly reduced when compared to previous reports. BI sectioning the entire data set according to geographic and linguistic criteria, we found higher Fst-on-distance slopes within Europe than in West Asia or across the tno continents

Y-Chromosome Based Evidence for Pre-Neolithic Origin of the Genetically Homogeneous but Diverse Sardinian Population: Inference for Association Scans

The island of Sardinia shows a unique high incidence of several autoimmune diseases with multifactorial inheritance, particularly type 1 diabetes and multiple sclerosis. The prior knowledge of the genetic structure of this population is fundamental to establish the optimal design for association studies in these diseases. Previous work suggested that the Sardinians are a relatively homogenous population, but some reports were contradictory and data were largely based on variants subject to selection. For an unbiased assessment of genetic structure, we studied a combination of neutral Y-chromosome variants, 21 biallelic and 8 short tandem repeats (STRs) in 930 Sardinian males. We found a high degree of interindividual variation but a homogenous distribution of the detected variability in samples from three separate regions of the island. One haplogroup, I-M26, is rare or absent outside Sardinia and is very common (0.37 frequency) throughout the island, consistent with a founder effect. A Bayesian full likelihood analysis (BATWING) indicated that the time from the most recent common ancestor (TMRCA) of I-M26, was 21.0 (16.0–25.5) thousand years ago (KYA) and that the population began to expand 14.0 (7.8–22.0) KYA. These results suggest a largely pre-Neolithic settlement of the island with little subsequent gene flow from outside populations. Consequently, Sardinia is an especially attractive venue for case-control genome wide association scans in common multifactorial diseases. Concomitantly, the high degree of interindividual variation in the current population facilitates fine mapping efforts to pinpoint the aetiologic polymorphisms