Date of Graduation
Chambers College of Business and Economics
Douglas W. Mitchell.
The dissertation explores the effect of different constrained portfolio strategies on investors' welfare. A constrained portfolio strategy gives investors a sub-optimal asset allocation that results in investors' welfare losses. To measure those welfare losses I compare constrained portfolios with optimal portfolios by using the concept of the proportionate opportunity cost along with various CRRA utility functions.;Chapter 1 discusses reasons the investors use constrained portfolio strategies, describes the different constrained portfolio strategies that are used in the dissertation, derives the proportionate opportunity cost, describes the derivation of the joint probability distribution functions for asset returns, and describes the way the historical extreme asset returns values are exaggerated to check the robustness of the estimates of the proportionate opportunity cost.;The first essay, in Chapter 2, analyzes investors' welfare losses from being constrained to choose a mean-variance efficient portfolio. I show that the mean-variance strategy shows a moderately good approximation to the optimal portfolio strategy. When extreme values of returns are not exaggerated in the returns distribution, investors' welfare losses do not exceed 5.6% of initial wealth. With extreme returns values exaggerated in the returns distribution, investors' welfare losses do not exceed 11% of initial wealth.;The second essay, in Chapter 3, analyzes investors' welfare losses from investing in a non-well-diversified number of assets. The analysis is performed with and without a short-selling constraint. I show that without the short-selling constraint and with no exaggeration of extreme values of asset returns the lowest well-diversified number of assets for an investor with low risk aversion is 24. The number decreases as the level of risk aversion increases, and when the short-selling constraint is introduced.;The second part of the chapter explores investors' welfare losses when they restrict themselves to either stocks or bonds but not both. I show that for investors with low levels of risk aversion welfare losses do not exceed 1.5% of initial wealth when they invest in only one type of assets. For investors with medium and high levels of relative risk aversion, constrained portfolios that include only one type of assets, stocks only or bonds only, along with Treasury bills, give expected utility about as high as unconstrained portfolios that include both types of assets, stocks and bonds.;The third essay, in Chapter 4, analyzes investors' welfare losses from being restricted from short selling. I show that with a nominally risk-free asset the optimal portfolio strategy with the short-selling constraint performs almost as well as the unconstrained portfolio strategy for investors with medium levels of risk aversion, and performs as well as the unconstrained portfolio strategy for investors with high levels of risk aversion. The results, derived from the original historical asset returns data set with no exaggeration of extreme returns, show that investors' welfare losses reach 12.8% of initial wealth when risk aversion is low. With extreme returns exaggerated in the returns distribution, investors' welfare losses reach 13.5% of initial wealth.;Chapter 5 provides the summary of the dissertation and discusses the directions for possible future research.
Melkumian, Alla Anatolyevna, "Essays on the opportunity cost of constrained portfolio strategies" (2003). Graduate Theses, Dissertations, and Problem Reports. 1831.