arXiv subjects

Pierpaolo Uberti

Publications and source records attributed to Pierpaolo Uberti.

7 recordsLinked to original sources

arXiv2026

Lower spectrum of financial correlation matrices: a new perspective on market synchronization

In this paper we investigate the information content of the lower part of the spectrum of financial correlation matrices, as a source of information on market synchronization. In a financial context, a classical application of Principal Component Analysis and Random Matrix Theory identifies the largest eigenvalues as indicators of dominant market factors and synchronization patterns. We complement this perspective by showing that the smallest eigenvalues also contain relevant information about the effective structure of financial markets. The paper presents the methodological proposal and validates its effectiveness through comprehensive real data experiments in both descriptive and predictive settings.

q-fin.ST↗

arXiv2026

Measuring the risk or reducing it, that is the question: is risk measurement necessary for risk reduction?

In this research, starting from a widely accepted definition of risk, we support the idea that risk reduction is a more realistic objective than risk minimization, which represents a theoretical utopia. Furthermore, significant risk reduction can be achieved without relying on risk measurement and risk minimization. To this end, we propose a generalization of the numerical rank and the condition number of a matrix, specifically the return matrix in this application. This generalization considers the entire matrix spectrum instead of focusing only on the smallest eigenvalue, as the condition number does. The approach directly provides an order among a finite number of risky scenarios. Risk reduction is obtained by identifying the riskiest scenarios and reducing investment exposures corresponding to them. The validity of this theoretical proposal is supported by a comprehensive experiment performed on real data. The capacity of the proposed approach to effectively reduce risk is proven by measuring the variability of out-of-sample returns for benchmark portfolios-constructed by minimizing standard risk measures-compared to the strategy of reducing exposure in high-risk scenarios. Finally, preventing large losses with limited active management-thereby controlling the impact of transaction costs-not only reduces risk but also preserves the average return and, consequently, the portfolio's Sharpe ratio.

q-fin.RM↗

arXiv2026

Some general results on risk budgeting portfolios

Given a reference risk measure, the risk budgeting is the portfolio where each asset contributes a predetermined amount to the total risk. We propose a novel approach, alternative to the ones proposed in the literature, for the calculation of the risk budgeting portfolio. This different perspective on the problem has several interesting consequences. For the calculation of the portfolio, we define a Cauchy sequence within the simplex of R^n, whose limit corresponds to the risk budgeting portfolio. This construction allows for the straightforward implementation of an efficient algorithm, avoiding the need to solve auxiliary, equivalent optimization problems, which may be computationally challenging and hard to interpret in the decision theory context. We compare our algorithm with the standard optimization-based methods proposed in the literature. From a theoretical point of view, starting from the Cauchy sequence, we define a function for which the risk budgeting portfolio is a fixed point. Therefore, sufficient conditions for the existence and uniqueness of the fixed point can be used. The methodology is developed for general risk measures and implemented in detail in the case of standard deviation.

q-fin.PM↗

arXiv2025

Local and Global Balance in Financial Correlation Networks: an Application to Investment Decisions

The global balance is a well-known indicator of the behavior of a signed network. Recent literature has introduced the concept of local balance as a measure of the contribution of a single node to the overall balance of the network. In the present research, we investigate the potential of using deviations of local balance from global balance as a criterion for selecting outperforming assets. The underlying idea is that, during financial crises, most assets in the investment universe behave similarly: losses are severe and widespread, and the global balance of the correlation-based signed network reaches its maximum value. Under such circumstances, standard diversification (mainly related to portfolio size) is unable to reduce risk or limit losses. Therefore, it may be useful to concentrate portfolio exposures on the few assets - if such assets exist-that behave differently from the rest of the market. We argue that these assets are those for which the local balance strongly departs from the global balance of the underlying signed network. The paper supports this hypothesis through an application using real financial data. The results, in both descriptive and predictive contexts, confirm the proposed intuition.

q-fin.PM↗

arXiv2025

Global Balance and Systemic Risk in Financial Correlation Networks

The global balance index is used in the network literature to quantify how balanced a signed network is. In this paper we show that the global balance index of financial correlation networks can be used as a systemic risk measure. We define the global balance index of a network starting from a diffusive process that describes how the information spreads across nodes in a network, providing an alternative derivation to the usual combinatorial one. The steady state of this process is the solution of a linear system governed by the exponential of the replication matrix of the process. We provide a bridge between the numerical stability of this linear system, measured by the condition number in an opportune norm, and the structural predictability of the underlying signed network. The link between the condition number and related systemic risk measures, such as the market rank indicators, allows the global balance index to be interpreted as a new systemic risk measure. A comprehensive empirical application to real financial data finally confirms that the global balance index of financial correlation networks represents a valuable and effective systemic risk indicator.

q-fin.RM↗

arXiv2020

A new approach in model selection for ordinal target variables

This paper introduces a novel approach to assess model performance for predictive models characterized by an ordinal target variable in order to satisfy the lack of suitable tools in this framework. Our methodological proposal is a new index for model assessment which satisfies mathematical properties and can be easily computed. In order to show how our performance indicator works, empirical evidence achieved on a toy examples and simulated data are provided. On the basis of results at hand, we underline that our approach discriminates better for model selection with respect to performance indexes proposed in the literature.

stat.ME↗

arXiv2018

A note on normality of $\sqrt{2}$ in base 2

In this paper we study the property of normality of a number in base 2. A simple rule that associates a vector to a number is presented and the property of normality is stated for the vector associated to the number. The problem of testing a number for normality is shown to be equivalent to the test of geometrical properties of the associated vector. The paper provides a general approach for normality testing and then applies the proposed methodology to the study of particular numbers. The main result of the paper is to prove that an infinite class of numbers is normal in base 2. As a further result we prove that the irrational number $\sqrt{2}$ is normal in base 2.

math.NT↗