arXiv subjects

Fabio Caccioli

Publications and source records attributed to Fabio Caccioli.

At least 55 records · Page 3Linked to original sources

arXiv2018

Quantification of systemic risk from overlapping portfolios in the financial system

Financial markets are exposed to systemic risk, the risk that a substantial fraction of the system ceases to function and collapses. Systemic risk can propagate through different mechanisms and channels of contagion. One important form of financial contagion arises from indirect interconnections between financial institutions mediated by financial markets. This indirect interconnection occurs when financial institutions invest in common assets and is referred to as overlapping portfolios. In this work we quantify systemic risk from indirect interconnections between financial institutions. Having complete information of security holdings of major Mexican financial intermediaries and the ability to uniquely identify securities in their portfolios, allows us to represent the Mexican financial system as a bipartite network of securities and financial institutions. This makes it possible to quantify systemic risk arising from overlapping portfolios. We show that focusing only on direct exposures underestimates total systemic risk levels by up to 50%. By representing the financial system as a multi-layer network of direct exposures (default contagion) and indirect exposures (overlapping portfolios) we estimate the mutual influence of different channels of contagion. The method presented here is the first objective data-driven quantification of systemic risk on national scales that includes overlapping portfolios.

q-fin.RM↗

arXiv2017

Network models of financial systemic risk: A review

The global financial system can be represented as a large complex network in which banks, hedge funds and other financial institutions are interconnected to each other through visible and invisible financial linkages. Recently, a lot of attention has been paid to the understanding of the mechanisms that can lead to a breakdown of this network. This can happen when the existing financial links turn from being a means of risk diversification to channels for the propagation of risk across financial institutions. In this review article, we summarize recent developments in the modeling of financial systemic risk. We focus in particular on network approaches, such as models of default cascades due to bilateral exposures or to overlapping portfolios, and we also report on recent findings on the empirical structure of interbank networks. The current review provides a landscape of the newly arising interdisciplinary field lying at the intersection of several disciplines, such as network science, physics, engineering, economics, and ecology.

q-fin.RM↗

arXiv2017

Excess reciprocity distorts reputation in online social networks

The peer-to-peer (P2P) economy relies on establishing trust in distributed networked systems, where the reliability of a user is assessed through digital peer-review processes that aggregate ratings into reputation scores. Here we present evidence of a network effect which biases digital reputation, revealing that P2P networks display exceedingly high levels of reciprocity. In fact, these are much higher than those compatible with a null assumption that preserves the empirically observed level of agreement between all pairs of nodes, and rather close to the highest levels structurally compatible with the networks' reputation landscape. This indicates that the crowdsourcing process underpinning digital reputation can be significantly distorted by the attempt of users to mutually boost reputation, or to retaliate, through the exchange of ratings. We uncover that the least active users are predominantly responsible for such reciprocity-induced bias, and that this fact can be exploited to obtain more reliable reputation estimates. Our findings are robust across different P2P platforms, including both cases where ratings are used to vote on the content produced by users and to vote on user profiles.

physics.soc-ph↗

arXiv2017

The effect of heterogeneity on financial contagion due to overlapping portfolios

We consider a model of financial contagion in a bipartite network of assets and banks recently introduced in the literature, and we study the effect of power law distributions of degree and balance-sheet size on the stability of the system. Relative to the benchmark case of banks with homogeneous degrees and balance-sheet sizes, we find that if banks have a power-law degree distribution the system becomes less robust with respect to the initial failure of a random bank, and that targeted shocks to the most specialised banks (i.e. banks with low degrees) or biggest banks increases the probability of observing a cascade of defaults. In contrast, we find that a power-law degree distribution for assets increases stability with respect to random shocks, but not with respect to targeted shocks. We also study how allocations of capital buffers between banks affects the system's stability, and we find that assigning capital to banks in relation to their level of diversification reduces the probability of observing cascades of defaults relative to size based allocations. Finally, we propose a non-capital based policy that improves the resilience of the system by introducing disassortative mixing between banks and assets.

q-fin.GN↗

arXiv2017

Reverse stress testing interbank networks

We reverse engineer dynamics of financial contagion to find the scenario of smallest exogenous shock that, should it occur, would lead to a given final systemic loss. This reverse stress test can be used to identify the potential triggers of systemic events, and it removes the arbitrariness in the selection of shock scenarios in stress testing. We consider in particular the case of distress propagation in an interbank market, and we study a network of 44 European banks, which we reconstruct using data collected from Bloomberg. By looking at the distribution across banks of the size of smallest exogenous shocks we rank banks in terms of their systemic importance, and we show the effectiveness of a policy with capital requirements based on this ranking. We also study the properties of smallest exogenous shocks as a function of the largest eigenvalue $λ_{\rm max}$ of the matrix of interbank leverages, which determines the endogenous amplification of shocks. We find that the size of smallest exogenous shocks reduces and that the distribution across banks becomes more localized as $λ_{\rm max}$ increases.

q-fin.RM↗

arXiv2017

Pathways towards instability in financial networks

Following the financial crisis of 2007-2008, a deep analogy between the origins of instability in financial systems and complex ecosystems has been pointed out: in both cases, topological features of network structures influence how easily distress can spread within the system. However, in financial network models, the details of how financial institutions interact typically play a decisive role, and a general understanding of precisely how network topology creates instability remains lacking. Here we show how processes that are widely believed to stabilise the financial system, i.e. market integration and diversification, can actually drive it towards instability, as they contribute to create cyclical structures which tend to amplify financial distress, thereby undermining systemic stability and making large crises more likely. This result holds irrespective of the details of how institutions interact, showing that policy-relevant analysis of the factors affecting financial stability can be carried out while abstracting away from such details.

q-fin.RM↗

arXiv2017

Relation between regional uncertainty spillovers in the global banking system

We report on time-varying network connectedness within three banking systems: North America, the EU, and ASEAN. The original method by Diebold and Yilmaz is improved by using exponentially weighted daily returns and ridge regularization on vector autoregression (VAR) and forecast error variance decomposition (FEVD). We compute the total network connectedness for each of the three banking systems, which quantifies regional uncertainty. Results over rolling windows of 300 days during the period between 2005 and 2015 reveal changing uncertainty patterns which are similar across regions, with common peaks associated with identifiable exogenous events. Lead-lag relationships among changes of total network connectedness of the three systems, quantified by transfer entropy, reveal that uncertainties in the three regional systems are significantly causally related, with the North American system having the largest influence on EU and ASEAN.

q-fin.ST↗

arXiv2017

Analytic solution to variance optimization with no short-selling

A large portfolio of independent returns is optimized under the variance risk measure with a ban on short positions. The no-short selling constraint acts as an asymmetric $\ell_1$ regularizer, setting some of the portfolio weights to zero and keeping the out of sample estimator for the variance bounded, avoiding the divergence present in the non-regularized case. However, the susceptibility, i.e. the sensitivity of the optimal portfolio weights to changes in the returns, diverges at a critical value $r=2$. This means that a ban on short positions does not prevent the phase transition in the optimization problem, it merely shifts the critical point from its non-regularized value of $r=1$ to $2$. At $r=2$ the out of sample estimator for the portfolio variance stays finite and the estimated in-sample variance vanishes. We have performed numerical simulations to support the analytic results and found perfect agreement for $N/T<2$. Numerical experiments on finite size samples of symmetrically distributed returns show that above this critical point the probability of finding solutions with zero in-sample variance increases rapidly with increasing $N$, becoming one in the large $N$ limit. However, these are not legitimate solutions of the optimization problem, as they are infinitely sensitive to any change in the input parameters, in particular they will wildly fluctuate from sample to sample. We also calculate the distribution of the optimal weights over the random samples and show that the regularizer preferentially removes the assets with large variances, in accord with one's natural expectation.

q-fin.PM↗

arXiv2016

Distress propagation in complex networks: the case of non-linear DebtRank

We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of the DebtRank algorithm, recently introduced in the literature. The mechanics of distress propagation is very simple: When a bank suffers a loss, distress propagates to its creditors, who in turn suffer losses, and so on. The original DebtRank assumes that losses are propagated linearly between connected banks. Here we relax this assumption and introduce a one-parameter family of non-linear propagation functions. As a case study, we apply this algorithm to a data-set of 183 European banks, and we study how the stability of the system depends on the non-linearity parameter under different stress-test scenarios. We find that the system is characterized by a transition between a regime where small shocks can be amplified and a regime where shocks do not propagate, and that the overall stability of the system increases between 2008 and 2013.

q-fin.RM↗

arXiv2016

Replica approach to mean-variance portfolio optimization

We consider the problem of mean-variance portfolio optimization for a generic covariance matrix subject to the budget constraint and the constraint for the expected return, with the application of the replica method borrowed from the statistical physics of disordered systems. We find that the replica symmetry of the solution does not need to be assumed, but emerges as the unique solution of the optimization problem. We also check the stability of this solution and find that the eigenvalues of the Hessian are positive for $r=N/T<1$, where $N$ is the dimension of the portfolio and $T$ the length of the time series used to estimate the covariance matrix. At the critical point $r=1$ a phase transition is taking place. The out of sample estimation error blows up at this point as $1/(1-r)$, independently of the covariance matrix or the expected return, displaying the universality not only of the critical index, but also the critical point. As a conspicuous illustration of the dangers of in-sample estimates, the optimal in-sample variance is found to vanish at the critical point inversely proportional to the divergent estimation error.

q-fin.PM↗

arXiv2016

Optimal growth trajectories with finite carrying capacity

We consider the problem of finding optimal strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a non-linear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases compute optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

q-fin.PM↗

arXiv2016

Emergence of strongly connected giant components in continuum disk-spin percolation

We propose a continuum model of percolation in two dimensions for overlapping disks with spin. In this model the existence of bonds is determined by the distance between the centers of the disks, and by the scalar product of the (randomly) directed spin with the direction of the vector connecting the centers of neighboring disks. The direction of a single spin is controlled by a "temperature", representing the amount of polarization of the spins in the direction of an external field. Our model is inspired by biological neuronal networks and aims to characterize their topological properties when axonal guidance plays a major role. We numerically study the phase diagram of the model observing the emergence of a giant strongly connected component, representing the portion of neurons that are causally connected. We provide strong evidence that the critical exponents depend on the temperature.

cond-mat.stat-mech↗

arXiv2015

Portfolio Optimization under Expected Shortfall: Contour Maps of Estimation Error

The contour maps of the error of historical resp. parametric estimates for large random portfolios optimized under the risk measure Expected Shortfall (ES) are constructed. Similar maps for the sensitivity of the portfolio weights to small changes in the returns as well as the VaR of the ES-optimized portfolio are also presented, along with results for the distribution of portfolio weights over the random samples and for the out-of-sample and in-the-sample estimates for ES. The contour maps allow one to quantitatively determine the sample size (the length of the time series) required by the optimization for a given number of different assets in the portfolio, at a given confidence level and a given level of relative estimation error. The necessary sample sizes invariably turn out to be unrealistically large for any reasonable choice of the number of assets and the confidence level. These results are obtained via analytical calculations based on methods borrowed from the statistical physics of random systems, supported by numerical simulations.

q-fin.RM↗

arXiv2015

Taming the Basel Leverage Cycle

Effective risk control must make a tradeoff between the microprudential risk of exogenous shocks to individual institutions and the macroprudential risks caused by their systemic interactions. We investigate a simple dynamical model for understanding this tradeoff, consisting of a bank with a leverage target and an unleveraged fundamental investor subject to exogenous noise with clustered volatility. The parameter space has three regions: (i) a stable region, where the system always reaches a fixed point equilibrium; (ii) a locally unstable region, characterized by cycles and chaotic behavior; and (iii) a globally unstable region. A crude calibration of parameters to data puts the model in region (ii). In this region there is a slowly building price bubble, resembling a "Great Moderation", followed by a crash, with a period of approximately 10-15 years, which we dub the "Basel leverage cycle". We propose a criterion for rating macroprudential policies based on their ability to minimize risk for a given average leverage. We construct a one parameter family of leverage policies that allows us to vary from the procyclical policies of Basel II or III, in which leverage decreases when volatility increases, to countercyclical policies in which leverage increases when volatility increases. We find the best policy depends critically on three parameters: The average leverage used by the bank; the relative size of the bank and the fundamentalist, and the amplitude of the exogenous noise. Basel II is optimal when the exogenous noise is high, the bank is small and leverage is low; in the opposite limit where the bank is large or leverage is high the optimal policy is closer to constant leverage. We also find that systemic risk can be dramatically decreased by lowering the leverage target adjustment speed of the banks.

econ.GN↗

arXiv2015

DebtRank: A microscopic foundation for shock propagation

The DebtRank algorithm has been increasingly investigated as a method to estimate the impact of shocks in financial networks, as it overcomes the limitations of the traditional default-cascade approaches. Here we formulate a dynamical "microscopic" theory of instability for financial networks by iterating balance sheet identities of individual banks and by assuming a simple rule for the transfer of shocks from borrowers to lenders. By doing so, we generalise the DebtRank formulation, both providing an interpretation of the effective dynamics in terms of basic accounting principles and preventing the underestimation of losses on certain network topologies. Depending on the structure of the interbank leverage matrix the dynamics is either stable, in which case the asymptotic state can be computed analytically, or unstable, meaning that at least one bank will default. We apply this framework to a dataset of the top listed European banks in the period 2008 - 2013. We find that network effects can generate an amplification of exogenous shocks of a factor ranging between three (in normal periods) and six (during the crisis) when we stress the system with a 0.5% shock on external (i.e. non-interbank) assets for all banks.

q-fin.RM↗

arXiv2015

Contour map of estimation error for Expected Shortfall

The contour map of estimation error of Expected Shortfall (ES) is constructed. It allows one to quantitatively determine the sample size (the length of the time series) required by the optimization under ES of large institutional portfolios for a given size of the portfolio, at a given confidence level and a given estimation error.

q-fin.RM↗

arXiv2014

$L_p$ regularized portfolio optimization

Investors who optimize their portfolios under any of the coherent risk measures are naturally led to regularized portfolio optimization when they take into account the impact their trades make on the market. We show here that the impact function determines which regularizer is used. We also show that any regularizer based on the norm $L_p$ with $p>1$ makes the sensitivity of coherent risk measures to estimation error disappear, while regularizers with $p<1$ do not. The $L_1$ norm represents a border case: its "soft" implementation does not remove the instability, but rather shifts its locus, whereas its "hard" implementation (equivalent to a ban on short selling) eliminates it. We demonstrate these effects on the important special case of Expected Shortfall (ES) that is on its way to becoming the next global regulatory market risk measure.

q-fin.PM↗

arXiv2013

How interbank lending amplifies overlapping portfolio contagion: A case study of the Austrian banking network

In spite of the growing theoretical literature on cascades of failures in interbank lending networks, empirical results seem to suggest that networks of direct exposures are not the major channel of financial contagion. In this paper we show that networks of interbank exposures can however significantly amplify contagion due to overlapping portfolios. To illustrate this point, we consider the case of the Austrian interbank network and perform stress tests on it according to different protocols. We consider in particular contagion due to (i) counterparty loss; (ii) roll-over risk; and (iii) overlapping portfolios. We find that the average number of bankruptcies caused by counterparty loss and roll-over risk is fairly small if these contagion mechanisms are considered in isolation. Once portfolio overlaps are also accounted for, however, we observe that the network of direct interbank exposures significantly contributes to systemic risk.

q-fin.GN↗