Divergent estimation error in portfolio optimization and in linear regression

The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and diverges for a critical value of this parameter. This divergence is the manifestation of an algorithmic phase transition, it is accompanied by a number of critical phenomena, and displays universality. As the structure of a large number of multidimensional regression and modelling problems is very similar to portfolio optimization, the scope of the above observations extends far beyond finance, and covers a large number of problems in operations research, machine learning, bioinformatics, medical science, economics, and technology.Comment: 5 pages, 2 figures, Statphys 23 Conference Proceedin

Statistics of Atmospheric Correlations

For a large class of quantum systems the statistical properties of their spectrum show remarkable agreement with random matrix predictions. Recent advances show that the scope of random matrix theory is much wider. In this work, we show that the random matrix approach can be beneficially applied to a completely different classical domain, namely, to the empirical correlation matrices obtained from the analysis of the basic atmospheric parameters that characterise the state of atmosphere. We show that the spectrum of atmospheric correlation matrices satisfy the random matrix prescription. In particular, the eigenmodes of the atmospheric empirical correlation matrices that have physical significance are marked by deviations from the eigenvector distribution.Comment: 8 pages, 9 figs, revtex; To appear in Phys. Rev.

Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models

Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An ecologically superior invader and a resident species compete for space preemptively. Our general model includes the basic contact process and a variant of the Eden model as special cases. We employ the concept of a "roughened" front to quantify effects of discreteness and stochasticity on invasion; we emphasize the probability distribution of the front-runner's relative position. That is, we analyze the location of the most advanced invader as the extreme deviation about the front's mean position. We find that a class of models with different assumptions about neighborhood interactions exhibit universal characteristics. That is, key features of the invasion dynamics span a class of models, independently of locally detailed demographic rules. Our results integrate theories of invasive spatial growth and generate novel hypotheses linking habitat or landscape size (length of the invading front) to invasion velocity, and to the relative position of the most advanced invader.Comment: The original publication is available at www.springerlink.com/content/8528v8563r7u2742

Are benchmark asset allocations for Australian private investors optimal?

In this article we examine whether the benchmark asset allocations recommended by financial planning groups for Australian private investors are optimal when measured against the mean-variance criterion of Modern Portfolio Theory. Using historical data for the relevant indices, the mean-variance properties of the various asset classes are determined. Portfolios containing the various asset classes are formed according to the allocations or weightings recommended by financial planning groups. The return-risk characteristics of the portfolios formed on the basis of the recommended asset class allocations are determined and a simple method of iso-risk maximum return calculation using the Excel Solver command is utilised to determine whether portfolios could be formed that are characterised by the same levels of risk but higher levels of return. These are ‘optimal portfolios’ that yield the maximum return for a given level of risk. Applying this methodology, the portfolios resulting from the financial planning groups’ benchmark asset allocations are found to be significantly suboptimal. On each occasion, a better portfolio (yielding a higher expected return for the same risk) could be found by adjusting the allocations