In this dissertation, I consider a fundamental issue in modern finance, the efficient allocation of assets to a portfolio. Markowitz (1952) developed the mean variance optimal portfolio theory to maximize the investors' mean variance utility function. Later the Capital Asset Pricing Model (CAPM) was proposed by Sharpe (1964) and Lintner (1965) and they argue that the market value-weighted portfolio is the mean variance optimal portfolio of risky assets under certain conditions. The classical approach based on mean variance portfolio theory and the CAPM suggests that investors should either optimize the mean variance portfolio or invest in the market value-weighted portfolio.
A challenge in constructing the optimal mean variance portfolio is the estimation loss due to the difference between the estimated parameters and the true parameters. This results in a substantial difference between the estimated optimal portfolio weights and the true weights. In Essay 1 of the dissertation, I propose a new class of estimators for the optimal portfolio weights under parameter uncertainty without considering any specific benchmark to address the estimation loss issue. I provide a tight upper bound for the estimators and a general theoretical lower bound for any optimal portfolio weights estimators. The upper bound convergence rate achieves the minimax lower bound, which shows that the new estimators are the optimal estimators of the optimal portfolio weights. The distances between the estimator and the true value of the optimal weight and their corresponding utility functions are also discussed. Based on a comprehensive empirical analysis, I demonstrate that portfolios based on the new estimators can consistently outperform the portfolio based on a naive diversification method (1/N Rule). Specifically, the optimized-optimal portfolio improves the out-of-sample Sharpe ratio by 32% compared to the 1/N Rule.
In Essay 2 of the dissertation, I consider the estimation of the optimal portfolio weights to track and outperform a benchmark index using a subset of the underlying stocks. The classical portfolio theory and the CAPM suggest the market value-weighted index is the benchmark for the risky investment portfolio (Sharpe, 1964). Hence index funds have been one of the most popular investment vehicles among investors, with total assets indexed to the S&P500 index exceeding $ 1.4 trillion at the end of 2013. Recently, enhanced index funds, which seek to outperform an index while maintaining a similar risk profile, have grown in popularity. I propose a new enhanced index tracking method that uses the linear absolute shrinkage selection operator (LASSO) method to minimize the Conditional Value-at-Risk (CVaR) of the tracking error. This minimizes the large downside tracking error while keeping the upside. I also theoretically show the oracle property of the estimators. Using a sample of the largest 100 stocks the new method closely tracks the S&P500 Index. In out-of-sample tests using data from 2003-2012, the CVaR-LASSO Enhanced Index Replication (CLEIR) method consistently outperformed the benchmark index by an average of 2.3% per year with a tracking error of 1% and an alpha of 2.33% per year using 50 - 80 large capitalization firms.
|Advisor:||Nimalendran, Mahendrarajah, Ritter, Jay R.|
|Commitee:||Cheng, Kenneth Hsing, Ray, Sugata|
|School:||University of Florida|
|School Location:||United States -- Florida|
|Source:||DAI-A 79/04(E), Dissertation Abstracts International|
|Subjects:||Business administration, Finance|
|Keywords:||enhanced indexation, estimation, investment, optimal estimators|
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