Assessing the risk-return trade-off in loan portfolios

This paper analyses the risk and return of loans portfolios in a joint setting. I develop a model to obtain the distribution of loans returns. I use this model to describe the investment opportunity set of lenders using mean-variance analysis with a Value at Risk constraint. I also obtain closed form expressions for the interest rates that banks should set in compensation for borrowers’ credit risk under absence of arbitrage opportunities and I use these rates as a benchmark to interpret actual loans’ prices. Finally, I study the risk-return trade-off in an empirical application to the Spanish banking syste

Testing non-linear dependence in the hedge fund industry

This paper proposes a parsimonious approach to test non-linear dependence on the conditional mean and variance of hedge funds with respect to several market factors. My approach introduces non-linear dependence by means of empirically relevant polynomial functions of the factors. For comparison purposes, I also consider multifactor extensions of tests based on piecewise linear alternatives. I apply these tests to a database of monthly returns on 1,071 hedge funds. I fi nd that non-linear dependence on the mean is highly sensitive to the factors that I consider. However, I obtain a much stronger evidence of non-linear dependence on the conditional varianc

Volatility-related exchange traded assets : an econometric investigation

En este trabajo comparamos expansiones seminoparamétricas de la distribución Gamma con expansiones de Laguerre alternativas, demostrando que amplían sustancialmente el rango de momentos factibles de variables aleatorias positivas. Posteriormente, combinamos dichas expansiones con una versión con componentes de un Modelo de Error Multiplicativo, con el fin de capturar la reversión a la media característica de series temporales positivas y estacionarias. Finalmente, llevamos a cabo una aplicación empírica en la que comparamos distintas estrategias de selección de cartera para Exchange Traded Notes, que son activos financieros cada vez más populares a pesar de sus riesgos que replican índices sobre futuros del VIX. Los resultados demuestran que las estrategias basadas en nuestro modelo econométrico producen rendimientos superioresWe compare semi-nonparametric expansions of the Gamma distribution with alternative Laguerre expansions, showing that they substantially widen the range of feasible moments of positive random variables. Then we combine those expansions with a component version of the Multiplicative Error Model to capture the mean reversion typical in positive but stationary fi nancial time series. Finally, we carry out an empirical application in which we compare various asset allocation strategies for Exchange Traded Notes tracking VIX futures indices, which are increasingly popular but risky financial instruments. We show the superior performance of the strategies based on our econometric mode

Distributional tests in multivariate dynamic models with normal and student t innovations

We derive Lagrange Multiplier and Likelihood Ratio specifi cation tests for the null hypotheses of multivariate normal and Student t innovations using the Generalised Hyperbolic distribution as our alternative hypothesis. We decompose the corresponding Lagrange Multiplier-type tests into skewness and kurtosis components, from which we obtain more powerful one-sided Kuhn-Tucker versions that are equivalent to the Likelihood Ratio test, whose asymptotic distribution we provide. We conduct detailed Monte Carlo exercises to study our proposed tests in finite samples. Finally, we present an empirical application to ten US sectoral stock returns, which indicates that their conditional distribution is mildly asymmetric and strongly leptokurti

Valuation of VIX derivatives

We conduct an extensive empirical analysis of VIX derivative valuation models before, during and after the 2008-2009 fi nancial crisis. Since the restrictive mean reversion and heteroskedasticity features of existing models yield large distortions during the crisis, we propose generalisations with a time varying central tendency, jumps and stochastic volatility, and analyse their pricing performance, and implications for term structures of VIX futures and volatility «skews». We fi nd that a process for the log of the observed VIX combining central tendency and stochastic volatility reliably prices VIXRealizamos un extenso análisis empírico de los modelos de valoración de los derivados sobre el VIX antes, durante y después de la crisis fi nanciera de 2008-2009. Como las características restrictivas de reversión a la media y heteroscedasticidad de los modelos existentes generan grandes distorsiones durante la crisis, proponemos generalizaciones con una tendencia central cambiante en el tiempo, saltos y volatilidad estocástica, analizando la adecuación de sus precios y sus implicaciones sobre la estructura temporal de los futuros del VIX y las curvas de volatilidad implícita. Nuestros resultados indican que un proceso para el logaritmo del VIX que combina una tendencia central y volatilidad estocástica valora adecuadamente los derivados sobre el VIX. Asimismo, hallamos una prima de riesgo signifi cativa que desplaza el nivel de la volatilidad a largo plaz

What drives sovereign debt portfolios of banks in a crisis context?

Estudiamos los determinantes de las tenencias de bonos soberanos de los bancos españoles sobre un período prolongado, que comienza en 2008. Nuestros resultados cuestionan la hipótesis de que los bancos decidieron sus estrategias de inversión en función de factores de riesgo moral, explotando el tratamiento regulatorio de las exposiciones soberanas. En concreto, mostramos que no hay relación entre un nivel bajo de capitalización bancaria y unas tenencias más elevadas de deuda soberana nacional. Aunque existe un fuerte vínculo entre el apoyo del banco central, a través de sus programas de liquidez, y las tenencias de deuda soberana, los comportamientos de tipo oportunista, o de búsqueda de rentabilidad, parecen limitarse a la cartera de deuda soberana extranjera de los bancos mejor capitalizados. Estos podrían haberse beneficiado de su mayor capacidad de absorción de riesgos para aumentar su exposición (vía liquidez del banco central) a los bonos soberanos más arriesgados. Por otro lado, también documentamos que la fragmentación financiera en los mercados de la zona del euro ha desempeñado un papel clave en la composición de las carteras soberanas. Nuestros resultados tienen implicaciones importantes para la discusión en curso sobre el diseño óptimo del tratamiento regulatorio de las exposiciones soberanasWe study determinants of sovereign portfolios of Spanish banks over a long time-span, starting in 2008. Our findings challenge the view that banks engaged in moral hazard strategies to exploit the regulatory treatment of sovereign exposures. In particular, we show that being a weakly capitalized bank is not related to higher holdings of domestic sovereign debt. While a strong link is present between central bank liquidity support and sovereign holdings, opportunistic strategies or reach-for-yield behavior appear to be limited to the non-domestic sovereign portfolio of well-capitalized banks, which might have taken advantage of their higher risk-bearing capacity to gain exposure (via central bank liquidity) to the set of riskier sovereign bonds. Furthermore, we document that financial fragmentation in EMU markets has played a key role in reshaping sovereign portfolios of banks. Overall, our results have important implications for the ongoing discussion on the optimal design of the risk-weighted capital framework of bank

Sovereign bond-backed securities as European reference safe assets: a review of the proposal by the ESRB-HLTF

Artículo de revistaA High-Level Task Force (HLTF ) of the European Systemic Risk Board (ESRB) has recently put forward a proposal aimed to increase the supply of low-risk financial assets in Europe through the securitisation of national euro area sovereign debt. This article reviews the proposal from different angles, including regulatory and financial stability considerations, as well as current market practices relevant to safe assets. We conclude that the proposal has some positive elements that would help to foster financial integration in the euro area, although it would also pose challenges related to financial stability in times of stress. All the pros and cons of the proposal should be properly accounted for if further steps are taken to develop this proposal

Macroprudential policy : objectives, instruments and indicators

Este documento presenta el marco analítico desarrollado recientemente por el Banco de España para la puesta en marcha de su política macroprudencial. La metodología descrita incorpora un amplio conjunto de indicadores que permiten realizar un seguimiento de los riesgos macroprudenciales a través de un mapa de riesgos. El marco servirá de soporte para definir la orientación general de la política macroprudencial del Banco de EspañaThis document presents the analytical framework recently developed by the Banco de España for the implementation of its macroprudential policy. The methodology described uses a broad set of indicators that enables macroprudential risks to be monitored through risk mapping. This framework will provide support for the Banco de España’s broad macroprudential policy stanc

Modelling the distribution of credit losses with observable and latent factors

This paper develops a flexible and computationally efficient model to estimate the credit loss distribution of the loans in a banking system. We consider a sectorial structure, where default frequencies and the total number of loans are allowed to depend on macroeconomic conditions as well as on unobservable credit risk factors, which can capture contagion effects between sectors. In addition, we also model the distributions of the Exposure at Default and the Loss Given Default. We apply our model to the Spanish credit market, where we find that sectorial default frequencies are affected by a persistent latent factor. Finally, we also identify the potentially riskier sectors and perform stress test

Sovereign risk and financial stability

Artículo de revist