Applications of Bayesian Econometrics to Financial Economics

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.