Optimal Strategies for Asymmetrical Wealth Endowments
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People who build successful businesses often experience asymmetrical wealth endowments, where most of their investments are tied to a particular asset related to their business. In the context of Texas, for example, the recent shale oil and gas development generated a great deal of wealth for many families in Texas, so it possibly has created substantial asymmetry in local investors' asset allocations. According to Modern Portfolio Theory , investors should diversify their portfolio into a mix of different assets in order to achieve an optimal portfolio, in which investors can either minimize the risk given a certain expected return or maximize the expected return given a certain risk. Expected return can be estimated from historical returns on the assets under consideration, while risk is measured by the covariance matrix of the historical returns. However, the tax costs associated with diversification of a dominant asset may mean the portfolio from classical Portfolio Theory is no longer optimal. This thesis has two objectives. First, the classical portfolio optimization methods will be presented, and we will discuss how they can be modified to take tax costs into effect. Then, with the revised optimization tools, we will investigate different strategies for divarication of a portfolio initially consisting only of oil. To quantify the uncertainty in the forecasts, we will use GARCH models based on the historical data to simulate different plausible outcomes
A thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science in the Graduate Mathematics Program, Applied and Computational Mathematics Option from Texas A&M University-Corpus Christi in Corpus Christi Texas.