Financial Applications of Markov Chain Monte Carlo Methods

Abstract: This thesis consists of four empirical studies on financial economics. The first chapter contains a short summary of the thesis. The second chapter Dynamic Portfolio Selection: The Relevance of Switching Regimes and Investment Horizon (co-authored with Birger Nilsson) investigates the questions of dynamic portfolio selection and intertemporal hedging within a Markovian regime-switching framework. The investment opportunity set is spanned by a well-diversified home-market portfolio and the risk-free asset. Our results highlight the economic importance of regimes, as optimal portfolio weights are clearly dependent on the prevailing regime. We present evidence that the question of intertemporal hedging is a more complex issue than is hinted in the previous literature, since demand for intertemporal hedging is present in some regimes, but not in others. Finally, our findings are qualitatively unchanged across the four largest stock markets in the in the world, the US, Japan, the UK and Germany. The third chapter, Empirical Probability Distributions of Real Return from Swedish Stock and Bond Portfolios, introduces a new non-parametric approach to integrate empirical probability functions of the real return for different investment horizons for five portfolios of Swedish stocks and bonds. In our setting the problem reduces to generating new generalizations from a known empirical Markov chain. We find that the stocks yield a real return of about 7.5 percent and bonds about 3.0 percent. Our results suggest that an investor ought to avoid bonds in the long run. Finally if the investors’ goal is to minimize the risk of capital destruction the preferable long run passive portfolio is a mix of bonds and stocks. The fourth chapter, A Bayesian Inference Approach to Testing Mean Reversion in the Swedish Stock Market, utilize a Bayesian approach to test for mean reversion in the Swedish stock market on monthly data 1918-1998. By simply account for the heteroscedasticity of the data with a two-state hidden Markov model of normal distributions and taking estimation bias into account via Gibbs sampling we cannot find support of mean reversion. This is a contradiction to previous result from Sweden. We find that a tranquil and a volatile regime can characterize the Swedish stock market and within the regimes the stock market is random. This finding of randomness is in line with recent evidence for the U.S. stock market. In the final chapter, A Swedish Real Estate Stock Market Index, 1939-1998, presents a new index for Sweden computed using a new time-series of 60 years of monthly returns of real estate stocks from 1939 to the present. The computation of the index is explained along with some general statistics. We find that the financial crisis of 1990-92 and the subsequent economic turmoil had a devastating effect on the real estate stock market. The returns are subject to kurtosis and skewness, especially during the last decade of the period. The Swedish real estate stock market was less sensitive than the Swedish stock market index. This new index offers a valuable data set for future research in financial economics as well as other disciplines.