Analysis of Bank Leverage via Dynamical Systems and Deep Neural Networks

We consider a model of a simple financial system consisting of a leveraged investor that invests in a risky asset and manages risk by using value-at-risk (VaR). The VaR is estimated by using past data via an adaptive expectation scheme. We show that the leverage dynamics can be described by a dynamical system of slow-fast type associated with a unimodal map on [0,1] with an addi-tive heteroscedastic noise whose variance is related to the portfolio rebalancing frequency to target leverage. In absence of noise the model is purely deterministic and the parameter space splits into two regions: (i) a region with a globally attracting fixed point or a 2-cycle; (ii) a dynamical core region, where the map could exhibit chaotic behavior. Whenever the model is randomly perturbed, we prove the existence of a unique stationary density with bounded variation, the stochastic stability of the process, and the almost certain existence and continuity of the Lyapunov exponent for the stationary measure. We then use deep neural networks to estimate map parameters from a short time series. Using this method, we estimate the model in a large dataset of US commercial banks over the period 2001--2014. We find that the parameters of a substantial fraction of banks lie in the dynamical core, and their leverage time series are consistent with a chaotic behavior. We also present evidence that the time series of the leverage of large banks tend to exhibit chaoticity more frequently than those of small banks

Unimodal maps perturbed by heteroscedastic noise: an application to a financial systems

We investigate and prove the mathematical properties of a general class of one-dimensional unimodal smooth maps perturbed with a heteroscedastic noise. Specifically, we investigate the stability of the associated Markov chain, show the weak convergence of the unique stationary measure to the invariant measure of the map, and show that the average Lyapunov exponent depends continuously on the Markov chain parameters. Representing the Markov chain in terms of random transformation enables us to state and prove the Central Limit Theorem, the large deviation principle, and the Berry-Ess\`een inequality. We perform a multifractal analysis for the invariant and the stationary measures, and we prove Gumbel's law for the Markov chain with an extreme index equal to 1. In addition, we present an example linked to the financial concept of systemic risk and leverage cycle, and we use the model to investigate the finite sample properties of our asymptotic results.Comment: 31 pages, 8 figure

Genotypic and phenotypic consequences of reintroduction history in the black-footed ferret (Mustela nigripes)

Abstract Population augmentation with translocated individuals has been shown to alleviate the effects of bottlenecks and drift. The first step to determine whether restoration for genetic considerations is warranted is to genetically monitor reintroduced populations and compare results to those from the source. To assess the need for genetic restoration, we evaluated genetic diversity and structure of reintroduced (n = 3) and captive populations of the endangered black-footed ferret (Mustela nigripes). We measured genotypic changes among populations using seven microsatellite markers and compared phenotypic changes with eight morphometric characters. Results indicated that for the population which rapidly grew postreintroduction, genetic diversity was equivalent to the captive, source population. When growth languished, only the population that was augmented yearly maintained diversity. Without augmentation, allelic diversity declined precipitously and phenotypic changes were apparent. Ferrets from the genetically depaupertate population had smaller limbs and smaller overall body size than ferrets from the two populations with greater diversity. Population divergence (F ST = 0.10 ± 0.01) was surprisingly high given the common source of populations. Thus, it appears that 5-10 years of isolation resulted in both genotypic divergence and phenotypic changes to populations. We recommend translocation of 30-40 captive individuals per annum to reintroduction sites which have not become established quickly. This approach will maximize the retention of genetic diversity, yet maintain the beneficial effects of local adaptation without being swamped by immigration

Testicular masses in association with Adrenogenital syndrome: US findings

Adrenogenital syndrome (AGS) is the result of inborn enzymatic defects in the synthesis of steroid hormones. The production of cortisol is deficient and that of adrenocorticotropic hormone is increased. Sometimes male patients have clinically detectable testicular lesions, known as testicular tumors of AGS (TTAGS). From 1985 to 1991, scrotal ultrasonography (US) was performed in 30 consecutive pubertal and postpubertal patients with AGS to investigate the prevalence and US characteristics of TTAGS. Eight of 30 patients had a testicular lesion (27%); six of the eight lesions were clinically undetected. The mean diameter of the lesions was 16.44 mm (range, 2-28 mm). The lesions were hypoechoic in all cases, with well-defined margins in six cases. The nodules were multifocal in all patients and bilateral in six (75%). If testicular lesions are present in a patient with AGS, TTAGS are likely, and frequent US monitoring is adequate for diagnostic evaluation

Adding Cycles into the Neoclassical Growth Model

We propose a stochastic Solow growth model where a cyclical component is added to the total factor productivity process. Theoretically, an important feature of the model is that its main equation takes a state space representation where key parameters can be estimated via an unobserved component approach without involving capital stock measures. In addition, the dynamic properties of the model are mostly unaffected by the newly introduced cyclical component. Empirically, our novel framework is consistent with secular U.S. empirical evidenc

ENANTIOSELECTIVE MUKAIYAMA-ALDOL REACTION BETWEEN ENOL SILANES AND KETOMALONATE CATALYZED BY THE COPPER(II) COMPLEX OF TIPS-SUBSTITUTED BIS-OXAZOLINE

The stable complex [(4'S,5'S)-4b/Cu(Tf)(2)/H2O] (5), obtained from TIPS-Box and Copper triflate, catalyzes enantioselectively the Mukaiyama-aldol reactions between two silyl enol ethers (1a,b) and diethyl ketomalonate (2). Yields are very good and the ee of (R)-3b is up to 94%. When the reaction was catalyzed by 4-Ph-Box complex [(4'R)-4a/Cu(Tf)(2)], in which the configuration at the C-4 centre is opposite to that of 5, the same enantiomer was obtained. The undistorted square pyramidal structure of complex 5, determined by crystallographic structure, and the effect of water and molecular sieves on efficiency and selectivity of the catalyst, suggest some proposals to rationalize the resulting stereoselectivity

A closed-form formula characterization of the Epps effect

In this study we provide an analytical characterization of the impact of zero returns on the popular realized covariance estimator of Barndorff-Nielsen and Shephard [Econometric analysis of realized covariation: High frequency based covariance, regression, and correlation in financial economics. Econometrica, 2004, 72(3), 885-925]. In our framework, efficient price processes evolve as a semimartingale with some likelihood of repeated prices. We show that the standard realized covariance estimator is asymptotically affected by a downward bias, and the size of the bias depends on these likelihoods. We demonstrate that this result can be used to construct a consistent estimator of the integrated covariance of a vector semimartingale. The advantages with respect to other estimators are discussed with data

On the role of domestic and international financial cyclical factors in driving economic growth

We investigate the effects of (domestic and international) financial cyclical factors on the US business cycle over the period 1890–2013 using an augmented stochastic version of the neoclassical growth model. In our setting, financial factors enter as determinants of the total factor productivity cyclical pattern. By means of static and dynamic estimations we find that (i) the inclusion of financial cyclical factors improves the model’s performance; (ii) the sensitivity of economic growth to financial factors is time-varying; (iii) domestic financial factors have a key role in explaining short-run output fluctuations only in the first half of the 20th century; (iv) (i.e., financial integration) over the last three decades. JEL CODES: O40, E32, C32

Landscape features influence postrelease predation on endangered black-footed ferrets

Predation can be a critical factor influencing recovery of endangered species. In most recovery efforts lethal and nonlethal influences of predators are not sufficiently understood to allow prediction of predation risk, despite its importance. We investigated whether landscape features could be used to model predation risk from coyotes (Canis latrans) and great horned owls (Bubo virginianus) on the endangered black-footed ferret (Mustela nigripes). We used location data of reintroduced ferrets from 3 sites in South Dakota to determine whether exposure to landscape features typically associated with predators affected survival of ferrets, and whether ferrets considered predation risk when choosing habitat near perches potentially used by owls or near linear features predicted to be used by coyotes. Exposure to areas near likely owl perches reduced ferret survival, but landscape features potentially associated with coyote movements had no appreciable effect on survival. Ferrets were located within 90 m of perches more than expected in 2 study sites that also had higher ferret mortality due to owl predation. Densities of potential coyote travel routes near ferret locations were no different than expected in all 3 sites. Repatriated ferrets might have selected resources based on factors other than predator avoidance. Considering an easily quantified landscape feature (i.e., owl perches) can enhance success of reintroduction efforts for ferrets. Nonetheless, development of predictive models of predation risk and management strategies to mitigate that risk is not necessarily straightforward for more generalist predators such as coyotes