A comprehensive portfolio construction under stochastic environment

Prior research has established that idiosyncratic volatility of the securities prices exhibits a positive trend. This trend and other factors have made the merits of investment diversification and portfolio construction more compelling. ^ A new optimization technique, a greedy algorithm, is proposed to optimize the weights of assets in a portfolio. The main benefits of using this algorithm are to: (a) increase the efficiency of the portfolio optimization process, (b) implement large-scale optimizations, and (c) improve the resulting optimal weights. In addition, the technique utilizes a novel approach in the construction of a time-varying covariance matrix. This involves the application of a modified integrated dynamic conditional correlation GARCH (IDCC - GARCH) model to account for the dynamics of the conditional covariance matrices that are employed. ^ The stochastic aspects of the expected return of the securities are integrated into the technique through Monte Carlo simulations. Instead of representing the expected returns as deterministic values, they are assigned simulated values based on their historical measures. The time-series of the securities are fitted into a probability distribution that matches the time-series characteristics using the Anderson-Darling goodness-of-fit criterion. Simulated and actual data sets are used to further generalize the results. Employing the S&P500 securities as the base, 2000 simulated data sets are created using Monte Carlo simulation. In addition, the Russell 1000 securities are used to generate 50 sample data sets. ^ The results indicate an increase in risk-return performance. Choosing the Value-at-Risk (VaR) as the criterion and the Crystal Ball portfolio optimizer, a commercial product currently available on the market, as the comparison for benchmarking, the new greedy technique clearly outperforms others using a sample of the S&P500 and the Russell 1000 securities. The resulting improvements in performance are consistent among five securities selection methods (maximum, minimum, random, absolute minimum, and absolute maximum) and three covariance structures (unconditional, orthogonal GARCH, and integrated dynamic conditional GARCH). ^

A Comprehensive Portfolio Construction Under Stochastic Environment

Prior research has established that idiosyncratic volatility of the securities prices exhibits a positive trend. This trend and other factors have made the merits of investment diversification and portfolio construction more compelling. A new optimization technique, a greedy algorithm, is proposed to optimize the weights of assets in a portfolio. The main benefits of using this algorithm are to: a) increase the efficiency of the portfolio optimization process, b) implement large-scale optimizations, and c) improve the resulting optimal weights. In addition, the technique utilizes a novel approach in the construction of a time-varying covariance matrix. This involves the application of a modified integrated dynamic conditional correlation GARCH (IDCC - GARCH) model to account for the dynamics of the conditional covariance matrices that are employed. The stochastic aspects of the expected return of the securities are integrated into the technique through Monte Carlo simulations. Instead of representing the expected returns as deterministic values, they are assigned simulated values based on their historical measures. The time-series of the securities are fitted into a probability distribution that matches the time-series characteristics using the Anderson-Darling goodness-of-fit criterion. Simulated and actual data sets are used to further generalize the results. Employing the S&P500 securities as the base, 2000 simulated data sets are created using Monte Carlo simulation. In addition, the Russell 1000 securities are used to generate 50 sample data sets. The results indicate an increase in risk-return performance. Choosing the Value-at-Risk (VaR) as the criterion and the Crystal Ball portfolio optimizer, a commercial product currently available on the market, as the comparison for benchmarking, the new greedy technique clearly outperforms others using a sample of the S&P500 and the Russell 1000 securities. The resulting improvements in performance are consistent among five securities selection methods (maximum, minimum, random, absolute minimum, and absolute maximum) and three covariance structures (unconditional, orthogonal GARCH, and integrated dynamic conditional GARCH).

International stock portfolio selection and performance measures recognizing higher moments of return distributions

Since the seminal works of Markowitz (1952), Sharpe (1964), and Lintner (1965), numerous studies on portfolio selection and performance measure have been based upon the mean-variance framework. However, several researchers (e.g., Arditti (1967, and 1971), Samuelson (1970), and Rubinstein (1973)) argue that the higher moments cannot be neglected unless there is reason to believe that: (i) the asset returns are normally distributed and the investor's utility function is quadratic, or (ii) the empirical evidence demonstrates that higher moments are irrelevant to the investor's decision. Based on the same argument, this dissertation investigates the impact of higher moments of return distributions on three issues concerning the 14 international stock markets.^ First, the portfolio selection with skewness is determined using: the Polynomial Goal Programming in which investor preferences for skewness can be incorporated. The empirical findings suggest that the return distributions of international stock markets are not normally distributed, and that the incorporation of skewness into an investor's portfolio decision causes a major change in the construction of his optimal portfolio. The evidence also indicates that an investor will trade expected return of the portfolio for skewness. Moreover, when short sales are allowed, investors are better off as they attain higher expected return and skewness simultaneously.^ Second, the performance of international stock markets are evaluated using two types of performance measures: (i) the two-moment performance measures of Sharpe (1966), and Treynor (1965), and (ii) the higher-moment performance measures of Prakash and Bear (1986), and Stephens and Proffitt (1991). The empirical evidence indicates that higher moments of return distributions are significant and relevant to the investor's decision. Thus, the higher moment performance measures should be more appropriate to evaluate the performances of international stock markets. The evidence also indicates that various measures provide a vastly different performance ranking of the markets, albeit in the same direction.^ Finally, the inter-temporal stability of the international stock markets is investigated using the Parhizgari and Prakash (1989) algorithm for the Sen and Puri (1968) test which accounts for non-normality of return distributions. The empirical finding indicates that there is strong evidence to support the stability in international stock market movements. However, when the Anderson test which assumes normality of return distributions is employed, the stability in the correlation structure is rejected. This suggests that the non-normality of the return distribution is an important factor that cannot be ignored in the investigation of inter-temporal stability of international stock markets. ^

A non-linear discrete stochastic optimization model for Advanced Access patient appointment scheduling

Access to healthcare is a major problem in which patients are deprived of receiving timely admission to healthcare. Poor access has resulted in significant but avoidable healthcare cost, poor quality of healthcare, and deterioration in the general public health. Advanced Access is a simple and direct approach to appointment scheduling in which the majority of a clinic's appointments slots are kept open in order to provide access for immediate or same day healthcare needs and therefore, alleviate the problem of poor access the healthcare. This research formulates a non-linear discrete stochastic mathematical model of the Advanced Access appointment scheduling policy. The model objective is to maximize the expected profit of the clinic subject to constraints on minimum access to healthcare provided. Patient behavior is characterized with probabilities for no-show, balking, and related patient choices. Structural properties of the model are analyzed to determine whether Advanced Access patient scheduling is feasible. To solve the complex combinatorial optimization problem, a heuristic that combines greedy construction algorithm and neighborhood improvement search was developed. The model and the heuristic were used to evaluate the Advanced Access patient appointment policy compared to existing policies. Trade-off between profit and access to healthcare are established, and parameter analysis of input parameters was performed. The trade-off curve is a characteristic curve and was observed to be concave. This implies that there exists an access level at which at which the clinic can be operated at optimal profit that can be realized. The results also show that, in many scenarios by switching from existing scheduling policy to Advanced Access policy clinics can improve access without any decrease in profit. Further, the success of Advanced Access policy in providing improved access and/or profit depends on the expected value of demand, variation in demand, and the ratio of demand for same day and advanced appointments. The contributions of the dissertation are a model of Advanced Access patient scheduling, a heuristic to solve the model, and the use of the model to understand the scheduling policy trade-offs which healthcare clinic managers must make. ^