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Applications of Bayesian Econometrics to Financial Economics

Bengtsson, Christoffer LU (2006) In Lund Economics Studies 135.
Abstract (Swedish)
Popular Abstract in Swedish

Denna doktorsavhandling består av fyra fristående artiklar. Artiklarna har det gemensamt att de alla använder Bayesiansk ekonometri, i kombination med s.k. Markov chain Monte Carlo (MCMC) metoder, för att studera olika problem inom finansiell ekonomi. De första två artiklarna är ytterligare relaterade till varandra genom att de båda handlar om portföljvalsteori och skattningsfel, vilket också de två sista artiklarna är genom att de båda handlar om extrema aktieavkastningar ur ett internationellt perspektiv.



Den första artikeln, "The Impact of Estimation Error on Single-Period Portfolio Selection", undersöker effekterna av skattningsfel i ett en-perioders... (More)
Popular Abstract in Swedish

Denna doktorsavhandling består av fyra fristående artiklar. Artiklarna har det gemensamt att de alla använder Bayesiansk ekonometri, i kombination med s.k. Markov chain Monte Carlo (MCMC) metoder, för att studera olika problem inom finansiell ekonomi. De första två artiklarna är ytterligare relaterade till varandra genom att de båda handlar om portföljvalsteori och skattningsfel, vilket också de två sista artiklarna är genom att de båda handlar om extrema aktieavkastningar ur ett internationellt perspektiv.



Den första artikeln, "The Impact of Estimation Error on Single-Period Portfolio Selection", undersöker effekterna av skattningsfel i ett en-perioders portföljoptimeringsproblem. Detta görs under något mer realistiska antaganden än de som används av Chopra och Ziemba (1993, Journal of Portfolio Management 19, 6-12) i en ofta refererad artikel, men samtidigt utnyttjas deras angreppssätt och simuleringsbaserade metod i vilken simulerade skattningsfel adderas till vad som antas vara avkastningarnas sanna medelvärdesvektor och kovariansmatris. För att ta reda på hur stora estimeringsfelen är i verkliga skattningar används en Bayesiansk metod baserad på MCMC metoder. Artikeln analyserar också vilken påverkan blankningsrestriktioner har på effekterna av skattningsfel. De empiriska resultaten skiljer sig från Chopra och Ziembas (1993) och pekar på att effekten av skattningsfel kan ha överdrivits något historiskt sett. Dessutom finner artikeln att när blankning i viss utsträckning tillåts, så gäller inte nödvändigtvis den traditionella uppfattningen att skattningsfel i medelvärdesvektor alltid har större effekt än skattningsfel i kovariansmatrisen.



Den andra artikeln, "A Shrinkage Estimator of the Covariance Matrix for Improved Mean-Variance Optimization", utvecklar en metod för att bättre skatta kovariansmatrisen för avkastningar genom att optimalt väga samman den vanliga stickprovskovariansmatrisen med en K-faktors principalkomponentskovariansmatris. Artikeln undersöker också vad som kan vinnas genom att ta hänsyn till den skattade kovariansmatrisens osäkerhet genom s.k. portföljåtersampling baserad på kovariansmatrisens posteriorfördelning som kvantifieras med MCMC metoder. I en empirisk tävling mellan olika kovariansmatrisskattare, där syftet är att välja portföljer med så låg volatilitet som möjligt, gör den föreslagna skattningsmetoden bäst ifrån sig av alla tävlande skattningsmetoder. Dessutom kan volatiliteten minskas ytterligare genom at använda portföljåtersampling.



Den tredje artikel, "Jump Spillover in International Equity Markets", författad tillsammans med Hossein Asgharian, undersöker i vilken grad som hopp i avkastningar sprider sig mellan olika internationella aktieindex, s.k. jump spillover. För att identifiera de historiska hoppen i olika index estimeras för ett antal index en univariat modell som tillåter hopp i avkastningar och stokastisk volatilitet. Det analyseras dels hur ofta hopp inträffar samtidigt i olika marknader, dels i vilken utsträckning hopp i stora marknader orsakar hopp eller onormalt stora avkastningar i mindre marknader. Artikeln finner starka bevis för att hopp i avkastningar sprider sig mellan marknader, särskilt mellan marknader i samma region och som har liknande industrier, men intressant nog inte nödvändigtvis mellan marknader vars avkastningar i normala fall är högt korrelerade.



Den fjärde artikeln, "International Jumps in Returns", studerar, precis som föregående artikel, extrema aktieavkastningar ur ett internationellt perspektiv, men gör detta på ett ekonometriskt mer formellt sätt. Artikeln föreslår en multivariat modell som tillåter hopp i avkastningar och stokastisk volatilitet, vilken skattas på tre grupper av nordamerikanska, europeiska och asiatiska aktieindex. Modellen antar att hopp i avkastningar antingen är systemiska (samtidiga i olika marknader) eller idiosynkratiska (marknadsspecifika). I alla tre fallen finner artikeln signifikanta bevis för att hopp i avkastningar i viss utsträckning är systemiska. I de nordamerikanska marknaderna (USA och Kanada) är majoriteten av alla hopp systemiska, medan majoriteten av alla hopp i de europeiska marknaderna (Storbritannien, Tyskland och Frankrike) och de asiatiska marknaderna (Japan och Hong Kong) är idiosynkratiska. I samtliga fall är systemiska hopp i genomsnitt signifikant negativa, medan idiosynkratiska hopp inte är signifikant skilda från noll. Lite överraskande är att korrelationerna mellan storlekarna på olika länders systemiska hopp är relativt låga och inte signifikant skilda från noll. (Less)
Abstract
This PhD thesis consists of four separate papers. What these papers have in common is that Bayesian Econometrics, in combination with Markov chain Monte Carlo (MCMC) methods, is applied to study various problems in financial economics. The first two papers are further related in that they both deal with portfolio selection and estimation risk, as are the last two papers in that they both deal with international aspects of extreme stock returns.



The first paper, "The Impact of Estimation Error on Single-Period Portfolio Selection", examines the impact of estimation error on single-period portfolio selection. This is done under slightly more realistic assumptions than those made by Chopra and Ziemba (1993, Journal of... (More)
This PhD thesis consists of four separate papers. What these papers have in common is that Bayesian Econometrics, in combination with Markov chain Monte Carlo (MCMC) methods, is applied to study various problems in financial economics. The first two papers are further related in that they both deal with portfolio selection and estimation risk, as are the last two papers in that they both deal with international aspects of extreme stock returns.



The first paper, "The Impact of Estimation Error on Single-Period Portfolio Selection", examines the impact of estimation error on single-period portfolio selection. This is done under slightly more realistic assumptions than those made by Chopra and Ziemba (1993, Journal of Portfolio Management 19, 6-12) in frequently cited paper, but still using their basic approach and simulation methodology, in which simulated estimation error is added to what are assumed to be the true mean vector and covariance matrix of returns. To obtain estimation error sizes that are more consistent with those in actual estimates, a Bayesian approach based on MCMC methods is used. The paper also looks at what effects short selling constraint have on the impact of estimation error. The empirical results differ from those of Chopra and Ziemba (1993), suggesting that the effect of estimation error may have been overestimated in the past. Furthermore, when some short selling is allowed, the paper finds reason to question the traditional viewpoint that estimating the covariance matrix correctly is always less important than estimating the mean vector correctly.



The second paper, "A Shrinkage Estimator of the Covariance Matrix for Improved Mean-Variance Optimization", proposes a shrinkage estimator of the covariance matrix of returns which shrinks the usual sample covariance matrix towards a K-factor principal component covariance matrix. In addition, the paper examines the gains from taking into account the uncertainty of the estimated covariance matrix when selecting portfolios. This is done through portfolio resampling based on the posterior distribution of the covariance matrix quantified with MCMC methods. In an empirical contest between estimators, where the objective is to pick portfolios with as low out-of-sample volatility as possible, the proposed estimator is found to perform better than all other competing estimators. In addition, it is found that the out-of-sample volatility can be reduced even further through portfolio resampling.



The third paper, "Jump Spillover in International Equity Markets", co-authored with Hossein Asgharian, studies what is referred to as jump spillover effects between a number of international equity indices. In order to identify the latent historical jumps of each index, a univariate stochastic volatility jump-diffusion model is estimated on each index using a Bayesian approach based on MCMC methods. The paper looks at the simultaneous jump intensities of pairs of countries and the probabilities that jumps in large countries cause jumps or unusually large returns in other countries. In all cases, significant evidence of jump spillover is found. In addition, it is found that jump spillover seems to be particularly large and significant between countries that belong to the same regions and have similar industry structures, whereas, interestingly, the sample correlations between the countries have difficulties in capturing the jump spillover effects.



The fourth paper, "International Jumps in Returns", examines, just as the previous paper, the international aspects of jumps in returns, but does so in an econometrically more formal manner. The paper proposes a multivariate stochastic volatility jump-diffusion model which is estimated on three groups of major North American, European, and Asian equity indices. The model assumes that returns are affected by both systemic (simultaneous across markets) and idiosyncratic (market specific) jumps. In all three cases, significant evidence of the existence of systemic jumps is found. In the North American markets (the United States and Canada), the majority of jumps are systemic, whereas in the European markets (the United Kingdom, Germany, and France) and the Asian markets (Japan and Hong Kong), the majority of jumps are idiosyncratic. In all cases, the mean sizes of systemic jumps are significantly negative, while the mean sizes of idiosyncratic jumps are not significantly different from zero. Surprisingly, the finding in all cases is that the correlation coefficients between the sizes of systemic jumps are relatively small and not significantly different from zero. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Eraker, Bjørn, Department of Economics, Duke University
organization
publishing date
type
Thesis
publication status
published
subject
keywords
economic systems, economic theory, econometrics, Economics, systemic risk, stochastic volatility, jump-diffusion, shrinkage, covariance matrix estimation, estimation risk, portfolio selection, mean-variance optimization, Markov chain Monte Carlo, Bayesian econometrics, ekonomisk politik, ekonomiska system, ekonomisk teori, ekonometri, Nationalekonomi, economic policy
in
Lund Economics Studies
volume
135
pages
134 pages
publisher
Department of Economics, Lund Universtiy
defense location
Lund University School of Economics and Management, Room EC3:210, Tycho Brahes väg 1, Lund, Sweden
defense date
2006-08-22 13:15
ISSN
0460-0029
language
English
LU publication?
yes
id
a4c72b5b-c4bf-4320-b91d-23b7784819af (old id 546935)
date added to LUP
2007-09-27 11:12:45
date last changed
2018-05-29 09:23:34
@phdthesis{a4c72b5b-c4bf-4320-b91d-23b7784819af,
  abstract     = {This PhD thesis consists of four separate papers. What these papers have in common is that Bayesian Econometrics, in combination with Markov chain Monte Carlo (MCMC) methods, is applied to study various problems in financial economics. The first two papers are further related in that they both deal with portfolio selection and estimation risk, as are the last two papers in that they both deal with international aspects of extreme stock returns.<br/><br>
<br/><br>
The first paper, "The Impact of Estimation Error on Single-Period Portfolio Selection", examines the impact of estimation error on single-period portfolio selection. This is done under slightly more realistic assumptions than those made by Chopra and Ziemba (1993, Journal of Portfolio Management 19, 6-12) in frequently cited paper, but still using their basic approach and simulation methodology, in which simulated estimation error is added to what are assumed to be the true mean vector and covariance matrix of returns. To obtain estimation error sizes that are more consistent with those in actual estimates, a Bayesian approach based on MCMC methods is used. The paper also looks at what effects short selling constraint have on the impact of estimation error. The empirical results differ from those of Chopra and Ziemba (1993), suggesting that the effect of estimation error may have been overestimated in the past. Furthermore, when some short selling is allowed, the paper finds reason to question the traditional viewpoint that estimating the covariance matrix correctly is always less important than estimating the mean vector correctly.<br/><br>
<br/><br>
The second paper, "A Shrinkage Estimator of the Covariance Matrix for Improved Mean-Variance Optimization", proposes a shrinkage estimator of the covariance matrix of returns which shrinks the usual sample covariance matrix towards a K-factor principal component covariance matrix. In addition, the paper examines the gains from taking into account the uncertainty of the estimated covariance matrix when selecting portfolios. This is done through portfolio resampling based on the posterior distribution of the covariance matrix quantified with MCMC methods. In an empirical contest between estimators, where the objective is to pick portfolios with as low out-of-sample volatility as possible, the proposed estimator is found to perform better than all other competing estimators. In addition, it is found that the out-of-sample volatility can be reduced even further through portfolio resampling.<br/><br>
<br/><br>
The third paper, "Jump Spillover in International Equity Markets", co-authored with Hossein Asgharian, studies what is referred to as jump spillover effects between a number of international equity indices. In order to identify the latent historical jumps of each index, a univariate stochastic volatility jump-diffusion model is estimated on each index using a Bayesian approach based on MCMC methods. The paper looks at the simultaneous jump intensities of pairs of countries and the probabilities that jumps in large countries cause jumps or unusually large returns in other countries. In all cases, significant evidence of jump spillover is found. In addition, it is found that jump spillover seems to be particularly large and significant between countries that belong to the same regions and have similar industry structures, whereas, interestingly, the sample correlations between the countries have difficulties in capturing the jump spillover effects.<br/><br>
<br/><br>
The fourth paper, "International Jumps in Returns", examines, just as the previous paper, the international aspects of jumps in returns, but does so in an econometrically more formal manner. The paper proposes a multivariate stochastic volatility jump-diffusion model which is estimated on three groups of major North American, European, and Asian equity indices. The model assumes that returns are affected by both systemic (simultaneous across markets) and idiosyncratic (market specific) jumps. In all three cases, significant evidence of the existence of systemic jumps is found. In the North American markets (the United States and Canada), the majority of jumps are systemic, whereas in the European markets (the United Kingdom, Germany, and France) and the Asian markets (Japan and Hong Kong), the majority of jumps are idiosyncratic. In all cases, the mean sizes of systemic jumps are significantly negative, while the mean sizes of idiosyncratic jumps are not significantly different from zero. Surprisingly, the finding in all cases is that the correlation coefficients between the sizes of systemic jumps are relatively small and not significantly different from zero.},
  author       = {Bengtsson, Christoffer},
  issn         = {0460-0029},
  keyword      = {economic systems,economic theory,econometrics,Economics,systemic risk,stochastic volatility,jump-diffusion,shrinkage,covariance matrix estimation,estimation risk,portfolio selection,mean-variance optimization,Markov chain Monte Carlo,Bayesian econometrics,ekonomisk politik,ekonomiska system,ekonomisk teori,ekonometri,Nationalekonomi,economic policy},
  language     = {eng},
  pages        = {134},
  publisher    = {Department of Economics, Lund Universtiy},
  school       = {Lund University},
  series       = {Lund Economics Studies},
  title        = {Applications of Bayesian Econometrics to Financial Economics},
  volume       = {135},
  year         = {2006},
}