Portfolio Selection and the Analysis of Risk and Time Diversification

University dissertation from Department of Economics

Abstract: This thesis is devoted to the analysis of three important issues in financial economics in general and portfolio selection in particular: the risk measure, estimation risk and time diversification. Besides a short introductory chapter the thesis consists of four empirical essays. In the second chapter, the effect of estimation risk on the efficient frontier in the lower partial moment framework is analyzed. A simulation approach is employed for the analysis of estimation risk in the MLPM-model because it can directly show the effect and magnitude of the estimation error on the portfolios. The results of the average difference between the actual and estimated portfolios show that the estimated portfolios are biased predictors of the actual portfolios in that they underestimate the risk in the portfolios and overestimate the portfolio mean returns. However, the estimates of the optimal portfolios can be improved. If our concern is the uncertainty in the optimal portfolio weights, then a bootstrap approach should be used to improve the optimizations since this approach produces the lowest root-mean squared errors in the study. In the third chapter, a downside risk approximation for calculating optimal portfolios in the discrete-time dynamic investment model is compared to the exact power function formulation that springs from the dynamic reinvestment model. The results show that the downside risk model approximates the dynamic model surprisingly well under both quarterly and annual revisions. However, the approximation seems to be correlated with the target rate of return in the downside risk formulation. In addition, the results suggest that the approximation perform best when the target rate of return is set high as compared to the mean returns of the basic assets. The fourth chapter analyzes whether or not mean-variance efficient portfolio weights for stocks and bills vary significantly with the investment horizon in a buy-and-hold strategy. Real returns from the U.S. asset market on a monthly basis from 1900 to 1997 were used in the analysis. As far as the question of estimation risk is concerned, the results showed that the estimation errors increased with the risk tolerance and with the investment horizon. However, the results in this study indicate that the optimal weights in stocks are not independent of the investment horizon, and that whether or not investors should tilt their portfolio weight towards or away from stocks in long horizon portfolios depends on the investor's risk aversion. The fifth chapter contains an analysis of whether the portfolio weights for stocks and bills, which are formed on the basis of direct expected utility maximization for a set of utility functions, vary significantly with the investment horizon. A non-parametric bootstrap approach is employed, which allows us to draw conclusions on whether or not differences between optimal portfolios are significant. Our analysis shows that the weights for stocks are significantly higher for long horizon investment as compared to the one-year horizon. We conclude that time diversification exists, and that the allocation decision seems to be independent of the utility function.

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