Jose Olmo

Growth in a Cross-Section of Cities: Location, Increasing Returns or Random Growth?

Abstract This article analyses empirically the main existing theories on income and population city growth: increasing returns to scale, locational fundamentals and random growth. To do this we consider a large database of urban, climatological and macroeconomic data from 1,173 US cities observed in 1990 and 2000. The econometric model is robust to the presence of spatial effects. Our analysis shows the existence of increasing returns and two distinct equilibria in per-capita income and population growth. We also find important differences in the structure of productive activity, unemployment rates and geographical location between cities in low-income and high-income regimes.

Backtesting Parametric Value-at-Risk with Estimation Risk

One of the implications of the creation of the Basel Committee on Banking Supervision was the implementation of Value-at-Risk (VaR) as the standard tool for measuring market risk. Since then, the capital requirements of commercial banks with trading activities are based on VaR estimates. Therefore, appropriately constructed tests for assessing the out-of-sample forecast accuracy of the VaR model (backtesting procedures) have become of crucial practical importance. In this article we show that the use of the standard unconditional and independence backtesting procedures to assess VaR models in out-of-sample composite environments can be misleading. These tests do not consider the impact of estimation risk, and therefore, may use wrong critical values to assess market risk. The purpose of this article is to quantify such estimation risk in a very general class of dynamic parametric VaR models and to correct standard backtesting procedures to provide valid inference in out-of-sample analyses. A Monte Carlo study illustrates our theoretical findings in finite-samples and shows that our corrected unconditional test can provide more accurately sized and more powerful tests than the uncorrected one. Finally, an application to the S&P 500 Index shows the importance of this correction and its impact on capital requirements as imposed by the Basel Accord.

Threshold Quantile Autoregressive Models

This article studies estimation and asymptotic properties of Threshold Quantile Autoregressive processes. In particular, we show the consistency of the threshold and slope parameter estimators for each quantile and regime, and derive the asymptotic normality of the slope parameter estimators. A Monte Carlo experiment shows that the standard ordinary least squares estimation method is not able to detect important nonlinearities produced in the quantile process. The empirical study concentrates on modelling the dynamics of the conditional distribution of unemployment growth after the second world war. The results show evidence of important heterogeneity associated with unemployment and strong asymmetric persistence of unemployment growth in the higher quantiles.

Bank characteristics and the interbank money market: a distributional approach

Abstract This paper studies the relationship between bank characteristics, such as size, nationality, operating currency and sovereign debt in the parent country, and the distribution of funding spreads observed in the e-MID interbank money market during the Great financial crisis. Our setup is a pseudo-panel with a random number of international banks acting in the interbank market in each period. We develop new econometric tools for panel data with random effects and discrete covariates, such as a nonparametric kernel estimator of the distribution function of the response variable conditional on a set of covariates and a consistent test of first order stochastic dominance. Our empirical results, based on these tests, shed light on the survivorship bias in the e-Mid market, and reveal the existence of a risk premium on small banks, banks with currencies different from the Euro, and banks based on countries under sovereign debt distress in the periphery of the European Union. Finally we assess the impact of policy intervention in the aftermath of the financial crisis.

Conditional stochastic dominance tests in dynamic settings

This paper proposes nonparametric consistent tests of conditional stochastic dominance of arbitrary order in a dynamic setting. The novelty of these tests resides on the nonparametric manner of incorporating the information set into the test. The test allows for general forms of unknown serial and mutual dependence between random variables, and has an asymptotic distribution under the null hypothesis that can be easily approximated by a p-value transformation method. This method has a good finite-sample performance. These tests are applied to determine investment efficiency between US industry portfolios conditional on the performance of the market portfolio. Our analysis suggests that Utilities are the best performing sectors in normal as well as distress episodes of the market.

Early Detection Techniques for Market Risk Failure

The implementation of appropriate statistical techniques (backtesting) for monitoring conditional VaR models is the mechanism used by financial institutions to determine the severity of departures of the VaR model from market results and subsequently, the tool used by regulators to determine the penalties imposed for inadequate risk models. So far, however, there has been no attempt to determine the timing of this rejection and with it to obtain some guidance regarding the cause of failure in reporting an appropriate VaR. This paper corrects this by proposing U-statistic type processes that extend standard CUSUM statistics widely employed for change-point detection. In contrast to CUSUM statistics these new tests are indexed by certain weight functions that enhance their statistical power to detect the timing of the market risk model failure. These tests are robust to estimation risk and can be devised to be very sensitive to detection of market failure produced early in the out-of-sample evaluation period, in which standard methods usually fail due to the absence of data.

Investing in the size factor

This paper investigates the role of the size factor for constructing investment portfolios and proposes a dynamic extension that accommodates the risk-free asset and time-varying weights. These weights are determined by a set of state variables given by the term structure of sovereign interest rates, variables describing market risk aversion such as the VIX index and the CRB Industrial return, and indexes reflecting investor sentiment towards the economic outlook. The empirical section explores the suitability of these state variables and analyses the out-of-sample performance of size factors idiosyncratic to the US, the UK and European financial markets that are compared against the dynamic version that optimizes the weights in each period. The results provide support to the different size factors except for periods of economic distress in which the optimal dynamic strategies are clearly superior.

A Nonlinear Threshold Model for the Dependence of Extremes of Stationary Sequences

Abstract We propose a TAR(3,1)-GARCH(1,1) model able to describe two different types of extreme events: a first type generated by large uncertainty regimes and a second type where extremes come from isolated dread/joy events. The novelty of this model resides on the definition of the regimes, motivated by the occurrence of extreme values, and of the threshold variable, defined by the shock affecting the process one period lagged. The model is able to uncover dependence and clustering of extremes in high and low volatility periods. A Wald type test to detect nonlinearities on the conditional mean process defined by an unobservable threshold variable is introduced. In the empirical application, we find evidence of predictability for extreme returns on SPDR S&P500 fund during the recent crisis period, July 2008 to March 2011. This finding seems to support the presence of some persistence and mean reversion in the dynamics of returns after the occurrence of extreme shocks.

On the role of volatility for modelling risk exposure

We show in this paper that volatility measures can be misleading indicators of risk if returns do not follow a Gaussian distribution. A more reliable measure of risk is the probability distribution of the return on an asset. Estimators for these measures are usually challenging and need of nonparametric and semi-parametric techniques. The aim of this paper is twofold. First, it proposes the use of semi-parametric estimators of the distribution function of the return on an asset based on extreme value theory for computing Value-at-Risk; and second, it discusses the validity of different volatility models in this semi-parametric framework. The conclusion is that different volatility models can yield different valid risk measures if coupled with the appropriate distribution function. Hence the puzzle in the choice of volatility measures. This is shown in an empirical exercise for data of financial indexes from USA, UK, Germany, Japan and Spain.

The Role of High-Frequency Prices, Long Memory and Jumps for Value-at-Risk Prediction

This study investigates the practical importance of several VaR modeling and forecasting issues in the context of intraday stock returns. Value-at-Risk (VaR) predictions obtained from daily GARCH models extended with additional information such as the realized volatility and squared overnight returns, are confronted with those from ARFIMA realized volatility models. The out-of-sample evaluation is based on a novel difference-in-proportions test that exploits the frequency of individual VaR rejections and a block-bootstrap unconditional coverage test that is robust to estimation uncertainty and model risk. ARFIMA models produce better backtesting results than GARCH models but fare worse in terms of independence of the hits sequence. Encompassing tests further suggest that GARCH and ARFIMA models can be fruitfully combined to produce more competitive VaR measures. We find evidence that intraday jumps also have forecasting potential. The techniques are illustrated for a small portfolio of large-cap stocks.