4,705 research outputs found
Optimal leverage from non-ergodicity
In modern portfolio theory, the balancing of expected returns on investments
against uncertainties in those returns is aided by the use of utility
functions. The Kelly criterion offers another approach, rooted in information
theory, that always implies logarithmic utility. The two approaches seem
incompatible, too loosely or too tightly constraining investors' risk
preferences, from their respective perspectives. The conflict can be understood
on the basis that the multiplicative models used in both approaches are
non-ergodic which leads to ensemble-average returns differing from time-average
returns in single realizations. The classic treatments, from the very beginning
of probability theory, use ensemble-averages, whereas the Kelly-result is
obtained by considering time-averages. Maximizing the time-average growth rates
for an investment defines an optimal leverage, whereas growth rates derived
from ensemble-average returns depend linearly on leverage. The latter measure
can thus incentivize investors to maximize leverage, which is detrimental to
time-average growth and overall market stability. The Sharpe ratio is
insensitive to leverage. Its relation to optimal leverage is discussed. A
better understanding of the significance of time-irreversibility and
non-ergodicity and the resulting bounds on leverage may help policy makers in
reshaping financial risk controls.Comment: 17 pages, 3 figures. Updated figures and extended discussion of
ergodicit
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
Recommended from our members
OPM Schema Editor 2—A Graphical Editor for Specifying Object-Protocol Structures
Noise Dressing of Financial Correlation Matrices
We show that results from the theory of random matrices are potentially of
great interest to understand the statistical structure of the empirical
correlation matrices appearing in the study of price fluctuations. The central
result of the present study is the remarkable agreement between the theoretical
prediction (based on the assumption that the correlation matrix is random) and
empirical data concerning the density of eigenvalues associated to the time
series of the different stocks of the S&P500 (or other major markets). In
particular the present study raises serious doubts on the blind use of
empirical correlation matrices for risk management.Comment: Latex (Revtex) 3 pp + 2 postscript figures (in-text
An Evolutionary Optimization Approach to Risk Parity Portfolio Selection
In this paper we present an evolutionary optimization approach to solve the
risk parity portfolio selection problem. While there exist convex optimization
approaches to solve this problem when long-only portfolios are considered, the
optimization problem becomes non-trivial in the long-short case. To solve this
problem, we propose a genetic algorithm as well as a local search heuristic.
This algorithmic framework is able to compute solutions successfully. Numerical
results using real-world data substantiate the practicability of the approach
presented in this paper
Rapid X-ray Variability of Seyfert 1 Galaxies
The rapid and seemingly random fluctuations in X-ray luminosity of Seyfert
galaxies provided early support for the standard model in which Seyferts are
powered by a supermassive black hole fed from an accretion disc. However, since
EXOSAT there has been little opportunity to advance our understanding of the
most rapid X-ray variability. Observations with XMM-Newton have changed this.
We discuss some recent results obtained from XMM-Newton observations of Seyfert
1 galaxies. Particular attention will be given to the remarkable similarity
found between the timing properties of Seyferts and black hole X-ray binaries,
including the power spectrum and the cross spectrum (time delays and
coherence), and their implications for the physical processes at work in
Seyferts.Comment: To appear in From X-ray Binaries to Quasars: Black Hole Accretion on
All Mass Scales, ed. T. J. Maccarone, R. P. Fender, and L. C. Ho (Dordrecht:
Kluwer
The scaling of X-ray variability with luminosity in Ultra-luminous X-ray sources
We investigated the relationship between the X-ray variability amplitude and
X-ray luminosity for a sample of 14 bright Ultra-luminous X-ray sources (ULXs)
with XMM-Newton/EPIC data, and compare it with the well established similar
relationship for Active Galactic Nuclei (AGN). We computed the normalised
excess variance in the 2-10 keV light curves of these objects and their 2-10
keV band intrinsic luminosity. We also determined model
"variability-luminosity" relationships for AGN, under several assumptions
regarding their power-spectral shape. We compared these model predictions at
low luminosities with the ULX data. The variability amplitude of the ULXs is
significantly smaller than that expected from a simple extrapolation of the AGN
"variability-luminosity" relationship at low luminosities. We also find
evidence for an anti-correlation between the variability amplitude and L(2-10
keV) for ULXs. The shape of this relationship is consistent with the AGN data
but only if the ULXs data are shifted by four orders of magnitudes in
luminosity. Most (but not all) of the ULXs could be "scaled-down" version of
AGN if we assume that: i) their black hole mass and accretion rate are of the
order of ~(2.5-30)x 10E+03 Msolar and ~ 1-80 % of the Eddington limit, and ii)
their Power Spectral Density has a doubly broken power-law shape. This PDS
shape and accretion rate is consistent with Galactic black hole systems
operating in their so-called "low-hard" and "very-high" states.Comment: 10 pages, 5 figures, 2 tables, accepted for publication in A&
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.
A Closed-Form Solution of the Multi-Period Portfolio Choice Problem for a Quadratic Utility Function
In the present paper, we derive a closed-form solution of the multi-period
portfolio choice problem for a quadratic utility function with and without a
riskless asset. All results are derived under weak conditions on the asset
returns. No assumption on the correlation structure between different time
points is needed and no assumption on the distribution is imposed. All
expressions are presented in terms of the conditional mean vectors and the
conditional covariance matrices. If the multivariate process of the asset
returns is independent it is shown that in the case without a riskless asset
the solution is presented as a sequence of optimal portfolio weights obtained
by solving the single-period Markowitz optimization problem. The process
dynamics are included only in the shape parameter of the utility function. If a
riskless asset is present then the multi-period optimal portfolio weights are
proportional to the single-period solutions multiplied by time-varying
constants which are depending on the process dynamics. Remarkably, in the case
of a portfolio selection with the tangency portfolio the multi-period solution
coincides with the sequence of the simple-period solutions. Finally, we compare
the suggested strategies with existing multi-period portfolio allocation
methods for real data.Comment: 38 pages, 9 figures, 3 tables, changes: VAR(1)-CCC-GARCH(1,1) process
dynamics and the analysis of increasing horizon are included in the
simulation study, under revision in Annals of Operations Researc
Superconductivity and Antiferromagnetism: Hybridization Impurities in a Two-Band Spin-Gapped Electron System
We present the exact solution of a one-dimensional model of a spin-gapped
correlated electron system with hybridization impurities exhibiting both
magnetic and mixed-valence properties. The host supports superconducting
fluctuations, with a spin gap. The localized electrons create a band of
antiferromagnetic spin excitations inside the gap for concentrations x of the
impurities below some critical value x_c. When x = x_c the spin gap closes and
a ferrimagnetic phase appears. This is the first example of an exactly solvable
model with coexisting superconducting and antiferromagnetic fluctuations which
in addition supports a quantum phase transition to a (compensated)
ferrimagnetic phase. We discuss the possible relevance of our results for
experimental systems, in particular the U-based heavy-fermion materials.Comment: 4 page
- …