Susana Alvarez

Analysis of the conditional stock-return distribution under incomplete specification

Abstract The analysis of the distribution of the stock-returns plays an important role in financial theory since a distributional assumption is required for mean–variance portfolio theory, theoretical models of capital asset prices, determining the price of derivative products, efficient estimation by maximum likelihood procedure and establishing forecasting confidence intervals. Up to now, most of the studies analyze the unconditional distribution of the stock-returns using the likelihood ratio test, the Schwarz Information Criterion or by graphical analysis. However, the analysis of the conditional distribution is very important since most of the empirical financial studies use high-frequency data and these data present dynamic structure. In this paper, we focus on the conditional distribution. We design different bootstrap mechanisms for comparing the goodness-of-fit of several functional forms postulated under the null hypothesis for individual Spanish stocks and for the General Index of the Madrid Stock Market. We use the Cramer–von Mises test statistic, based on the standardized residuals and assuming that the null distribution can depend on some unknown parameters.The analysis of the distribution of the stock-returns plays an important role in financial theory since a distributional assumption is required for mean–variance portfolio theory, theoretical models of capital asset prices, determining the price of derivative products, efficient estimation by maximum likelihood procedure and establishing forecasting confidence intervals. Up to now, most of the studies analyze the unconditional distribution of the stock-returns using the likelihood ratio test, the Schwarz Information Criterion or by graphical analysis. However, the analysis of the conditional distribution is very important since most of the empirical financial studies use high-frequency data and these data present dynamic structure. In this paper, we focus on the conditional distribution. We design different bootstrap mechanisms for comparing the goodness-of-fit of several functional forms postulated under the null hypothesis for individual Spanish stocks and for the General Index of the Madrid Stock Market. We use the Cr amer–von Mises test statistic, based on the standardized residuals and assuming that the null distribution can depend on some unknown parameters. 2003 Elsevier B.V. All rights reserved.

On the accuracy of loss-given-default prediction intervals

Purpose - The purpose of this paper is to critically analyze the common assumption, made by many credit risk models such as the Moodys KMV Loss-Calc model, of a Design/methodology/approach - Simulation experiments were conducted to highlight the potential problems associated with this distributional assumption in constructing prediction intervals for LGD. Findings - The simulation experiments show that, when starting from a different assumption concerning the shape of the population distribution, the beta distribution does not perform well in constructing prediction intervals for LGD. Originality/value - The analysis performed in this study addresses a relevant subject. Indeed, a correct estimate of a credit exposure LGD is particularly relevant not only for internal risk management and management purposes, but also for regulatory reasons within the context of the internal ratings based approach of the recently approved capital regulation framework (Basel II).

A New Multidimensional Measurement of Educational Poverty. An Application to PISA 2012

The consequences that educational underperforming has on both individuals and the society as a whole lead policy makers and planners to focus on how to measure properly the extent of educational poverty. The main aim of this paper is to propose a multidimensional adjusted poverty index (α-MAPI) by considering explicitly not only the individual deprivations, but also the non-deprivation attributes of the poor. It permits to set a precise valuation on school poverty. We apply α-MAPI to the measurement of educational poverty in the OECD countries by using data from PISA 2012 report.

Coverage properties of beta estimated prediction intervals for multimodal recovery rates

In this paper we use bootstrap methodology to achieve accurate estimated prediction intervals for recovery rates. In the framework of the LossCalc model, which is the Moodys KMV model to predict loss given default, a single beta distribution is usually assumed to model the behaviour of recovery rates and, hence, to construct prediction intervals. We evaluate the coverage properties of beta estimated prediction intervals for multimodal recovery rates. We carry out a simulation study, and our results show that bootstrap versions of beta mixture prediction intervals exhibit the best coverage properties.

On the performance of recovery rate modeling

To ensure accurate predictions of loss given default it is necessary to test the goodness-of-fit of the recovery rate data to the Beta distribution, assuming that its parameters are unknown. In the presence of unknown parameters, the Cramer-von Mises test statistic is neither asymptotically distribution free nor parameter free. In this paper, we propose to compute approximated critical values with a parametric bootstrap procedure. Some simulations show that the bootstrap procedure works well in practice.

Hypothesis of Normality in the Context of the Market Model

This paper discusses the normality assumption of the market model errors, convention- ally accepted. Some other possible specifications are proposed and their performance is testing using a test statistic based on the empirical distribution function of the residuals of the model and assuming that the null distribution can depend on some unknown parameters. The parametric boot- strap method is used. Empirical evidence is provided using a sample of thirty companies of the Spanish Stock Market.