What Are Investors Afraid of? Finding the Big Bad Wolf

open2The aim of financial institutions and regulators is to find an effective way to measure the risk profile of different segments of investors. Both economists and psychologists developed several methodologies to elicit and assess individual risk attitude, but these are not perfect and show several drawbacks when used in practice. Thanks to a unique database of around 15,000 investors,thispapercombinessurvey-basedevidencewithrevealedpreferencesbaseduponobserved asset allocation. This paper confirms some results known in the literature like the gender and age differencesinrisk-taking. Moreover,thebehavioralclusteringapproachusedfortheanalysisisuseful in an inferential framework. The segments built starting from the questionnaire permit to “forecast” the individual risk attitude that is described by the individual choices in terms of asset allocation. Loss aversion per se is a relevant variable in explaining financial risk-taking.openBarbara Alemanni; Pierpaolo UbertiAlemanni, Barbara; Uberti, Pierpaol

A singular value decomposition based approach to handle ill-conditioning in optimization problems with applications to portfolio theory.

We identify a source of numerical instability of quadratic programming problems that is hidden in its linear equality constraints. We propose a new theoretical approach to rewrite the original optimization problem in an equivalent reformulation using the singular value decomposition and substituting the ill-conditioned original matrix of the restrictions with a suitable optimally conditioned one. The proposed novel approach is showed, both empirically and theoretically, to solve ill-conditioning related numerical issues, not only when they depend on bad scaling and are relative easy to handle, but also when they result from almost collinearity or when numerically rank-deficient matrices are involved. Furthermore, our strategy looks very promising even when additional inequality constraints are considered in the optimization problem, as it occurs in several practical applications. In this framework, even if no closed form solution is available, we show, through empirical evidence, how the equivalent reformulation of the original problem greatly improves the performances of MatLab®’s quadratic programming solver and Gurobi®. The experimental validation is provided through numerical examples performed on real financial data in the portfolio optimization context

Proper measures of connectedness

The concept of connectedness has been widely used in financial applications, in particular for systemic risk detection. Despite its popularity, at the state of the art, a rigorous definition of connectedness is still missing. In this paper we propose a general definition of connectedness introducing the notion of proper measures of connectedness (PMCs). Based on the classical concept of mean introduced by Chisini, we define a family of PMCs and prove some useful properties. Further, we investigate whether the most popular measures of connectedness available in the literature are consistent with the proposed theoretical framework. We also compare different measures in terms of forecasting performances on real financial data. The empirical evidence shows the forecasting superiority of the PMCs compared to the measures that do not satisfy the theoretical properties. Moreover, the empirical results support the evidence that the PMCs can be useful to detect in advance financial bubbles, crises, and, in general, for systemic risk detection

Focolaio di COVID-19 in un campo estivo nella Regione Piemonte (2021): descrizione, lezioni apprese e raccomandazioni per futuri campi estivi

COVID-19 outbreak at a summer camp in Piedimont region in 2021: description, lessons learned and recommendations for future summer camps Introduction In August 2021, an outbreak of coronavirus disease 2019 (COVID-19) occurred in a summer camp in Piedmont region, Italy, affecting primarily campers aged ≤16 years. We conducted a retrospective cohort study among campers and personnel (attendees) to determine the attack rate (AR), evaluate possible factors associated with transmission and propose recommended measures for the organization of future summer camps. Materials and methods A de-identified database including demographic, role of attendees, cohorting, means of transportation to the camp, inter-camper interactions, SARS-CoV-2 testing results and symptomatology was used. All analysis data came from a collection of data carried out by the organizing private company and the information related to the mitigation protocol put in place was provided by the health care personnel. All campers were asked to have an antigen/molecular test within 72 hours before departure. Nine dedicated buses departed from different Italian regions towards the camp. All travellers wore a surgical mask during the trip. Upon arrival, regardless of the bus used, the campers were divided into 11 subgroups with no further contact between them unless they were blood relatives. No SARS-CoV-2 screening tests were scheduled for campers after arrival and during the camp period. On the other hand, personnel had a screening test at each shift change. During the camp period, antigen tests were performed at cases with symptoms suggestive of infection. Only attendees enrolled in the private company and those who received at least one test since arrival at the camp were considered in the study. We calculated overall AR and relative risk (RR) along with specific, transmission-focused risk factors. Results Among the 187 study participants, the median age was 14 years (range: 6-45). Seven days after arrival at the camp, 8 campers developed symptoms and tested positive. The overall AR was 33.7% (63 out of 187), and 34.2% (50/146) for campers and 31.7% (13/41) for staff, respectively. Among those with available symptoms information, 72% (36/50) were asymptomatic at the time of testing. Only 17.1% of campers had direct contact with blood relatives from other subgroups. The AR of participants using a bus was 36.2% (59/163) with an RR of 1.18 (95% CI = 0.51-2.73,) and the AR of those belonging to a subgroup was 35% (62/177) with an RR of 3.5 (95% CI = 0.54-22.7). For personnel, participation to a subgroup gave an AR of 38.7% (12/31) and an RR of 3.87 (95% CI = 0.57-26.18). All but four subgroups had a high AR (>33,3). Conclusions Getting tested prior to traveling and campers separation into low-contact subgroups was not sufficient enough to avoid a high number of infections in this summer camp. Analysis did not allow the identification of an index case or helped to understand whether the outbreak originated from the attendees who travelled on the same bus. The high AR observed in all subgroups suggest that there was frequent contact between attendees belonging to different subgroups. Sharing of common areas such as the canteen and contact between attendees are possible factors that have contributed to the spread of the outbreak. The experience gained by the analysis of this data was used for the review of measures for the organization of summer camps in 2022

UNCERTAINTY INTERVAL TO ASSESS PERFORMANCES OF CREDIT RISK MODELS

reserved2In this paper, we propose a novel approach to compare the performances of binary classification models with an application on a real data set on credit risk provided by Unicredit bank. Starting from the probability of default estimated by each predictive model under comparison, the idea is to derive an uncertainty interval comparing the predictions with the observed target variable. A model is considered to have good performances if the associated uncertainty interval is small. The shape of the uncertainty interval provides also some information about the model performances in terms of classification errors, false positive and false negative. The uncertainty interval permits to compare different models without selecting a binarization threshold and it applies both for parametric and non parametric predictive models.mixedSilvia Figini; Pierpaolo UbertiFigini, Silvia; Uberti, Pierpaol

How to measure single-name credit risk concentrations

Credit risk concentration is one of the leading topics in modern finance, as the bank regulation has made increasing use of external and internal credit ratings. Concentration risk in credit portfolios comes into being through an uneven distribution of bank loans to individual borrowers (single-name concentration) or in a hierarchical dimension such as in industry and services sectors and geographical regions (sectorial concentration). To measure single-name concentration risk the literature proposes specific concentration indexes such as the Herfindahl-Hirschman index, the Gini index or more general approaches to calculate the appropriate economic capital needed to cover the risk arising from the potential default of large borrowers. However, in our opinion, the Gini index and the Herfindahl-Hirschman index can be improved taking into account methodological and theoretical issues which are explained in this paper. We propose a new index to measure single-name credit concentration risk and we prove the properties of our contribution. Furthermore, considering the guidelines of Basel II, we describe how our index works on real financial data. Finally, we compare our index with the common procedures proposed in the literature on the basis of simulated and real data.Credit risk Concentration Gini index Herfindahl-Hirschman index Granularity adjustment

Connectedness versus diversification: two sides of the same coin

In the financial framework, the concepts of connectedness and diversification have been introduced and developed respectively in the context of systemic risk and portfolio theory. In this paper we propose a theoretical approach to bring to light the relation between connectedness and diversification. Starting from the respective axiomatic definitions, we prove that a class of proper measures of connectedness verifies, after a suitable functional transformation, the axiomatic requirements for a measure of diversification. The core idea of the paper is that connectedness and diversification are so deeply related that it is possible to pass from one concept to the other. In order to exploit such correspondence, we introduce a function, depending on the classical notion of rank of a matrix, that transforms a suitable proper measure of connectedness in a measure of diversification. We point out general properties of the proposed transformation function and apply it to a selection of measures of connectedness, such as the well-known Variance Inflation Factor