30 research outputs found
Risk Minimization through Portfolio Replication
We use a replica approach to deal with portfolio optimization problems. A
given risk measure is minimized using empirical estimates of asset values
correlations. We study the phase transition which happens when the time series
is too short with respect to the size of the portfolio. We also study the noise
sensitivity of portfolio allocation when this transition is approached. We
consider explicitely the cases where the absolute deviation and the conditional
value-at-risk are chosen as a risk measure. We show how the replica method can
study a wide range of risk measures, and deal with various types of time series
correlations, including realistic ones with volatility clustering.Comment: 12 pages, APFA5 conferenc
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
Portfolio Optimization and the Random Magnet Problem
Diversification of an investment into independently fluctuating assets
reduces its risk. In reality, movement of assets are are mutually correlated
and therefore knowledge of cross--correlations among asset price movements are
of great importance. Our results support the possibility that the problem of
finding an investment in stocks which exposes invested funds to a minimum level
of risk is analogous to the problem of finding the magnetization of a random
magnet. The interactions for this ``random magnet problem'' are given by the
cross-correlation matrix {\bf \sf C} of stock returns. We find that random
matrix theory allows us to make an estimate for {\bf \sf C} which outperforms
the standard estimate in terms of constructing an investment which carries a
minimum level of risk.Comment: 12 pages, 4 figures, revte
Financial correlations at ultra-high frequency: theoretical models and empirical estimation
A detailed analysis of correlation between stock returns at high frequency is
compared with simple models of random walks. We focus in particular on the
dependence of correlations on time scales - the so-called Epps effect. This
provides a characterization of stochastic models of stock price returns which
is appropriate at very high frequency.Comment: 22 pages, 8 figures, 1 table, version to appear in EPJ
Accounting for risk of non linear portfolios: a novel Fourier approach
The presence of non linear instruments is responsible for the emergence of
non Gaussian features in the price changes distribution of realistic
portfolios, even for Normally distributed risk factors. This is especially true
for the benchmark Delta Gamma Normal model, which in general exhibits
exponentially damped power law tails. We show how the knowledge of the model
characteristic function leads to Fourier representations for two standard risk
measures, the Value at Risk and the Expected Shortfall, and for their
sensitivities with respect to the model parameters. We detail the numerical
implementation of our formulae and we emphasizes the reliability and efficiency
of our results in comparison with Monte Carlo simulation.Comment: 10 pages, 12 figures. Final version accepted for publication on Eur.
Phys. J.
Dominating Clasp of the Financial Sector Revealed by Partial Correlation Analysis of the Stock Market
What are the dominant stocks which drive the correlations present among stocks traded in a stock market? Can a correlation analysis provide an answer to this question? In the past, correlation based networks have been proposed as a tool to uncover the underlying backbone of the market. Correlation based networks represent the stocks and their relationships, which are then investigated using different network theory methodologies. Here we introduce a new concept to tackle the above question—the partial correlation network. Partial correlation is a measure of how the correlation between two variables, e.g., stock returns, is affected by a third variable. By using it we define a proxy of stock influence, which is then used to construct partial correlation networks. The empirical part of this study is performed on a specific financial system, namely the set of 300 highly capitalized stocks traded at the New York Stock Exchange, in the time period 2001–2003. By constructing the partial correlation network, unlike the case of standard correlation based networks, we find that stocks belonging to the financial sector and, in particular, to the investment services sub-sector, are the most influential stocks affecting the correlation profile of the system. Using a moving window analysis, we find that the strong influence of the financial stocks is conserved across time for the investigated trading period. Our findings shed a new light on the underlying mechanisms and driving forces controlling the correlation profile observed in a financial market
Visual engagement with urban street edges: insights using mobile eye-tracking
This study provides empirical insight into the extent to which pedestrians visually engage with urban street edges and how social and spatial factors impact such engagement. This was achieved using mobile eye-tracking. The gaze distribution of 24 study participants was systematically recorded as they carried out everyday tasks on differing streets. The findings demonstrated that street edges are the most visually engaged component of streets; that street edge visual engagement is impacted by everyday social tasks as well as the spatial and physical materiality of edges on differing streets; and that street edges, which attract a lot of visual engagement while undertaking optional tasks, also attract greater amounts of visual engagement while undertaking necessary tasks. These findings offer new insight into urban street edge engagement from the direct perspective of street inhabitants and in doing so provide greater understanding of how street edges are experienced
On the feasibility of portfolio optimization under expected shortfall
We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As is well known, one can map this problem into a linear programming setting. For some values of the external parameters, when the available time series is too short, portfolio optimization is ill-posed because it leads to unbounded positions, infinitely short on some assets and infinitely long on others. As first observed by Kondor and coworkers, this phenomenon is actually a phase transition. We investigate the nature of this transition by means of a replica approach.Statistical physics, Finance, Portfolio optimization, Quantitative finance, Correlation modelling, Critical phenomena, Risk measures,