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). ^

The relationship between educational placement, instructional practices, and achievement gains of Black students with specific learning disabilities in secondary urban school settings

Black students, in general, are underserved academically (Darling-Hammond, 2000; Townsend, 2002) and overrepresented in special education (Donovan & Cross, 2002). Black students with disabilities are further overrepresented in more restrictive educational environments (Skiba, Poloni-Staudinger, Gallini, Simmons & Feggins-Azziz, 2006). Although the National Longitudinal Transition Study 2 (NLTS2) revealed that the academic performance of students with learning disabilities is positively related to the percentage of courses taken in the general education setting (Newman, 2006), the research specifically on placement of Black students with disabilities, particularly at the secondary level, as it relates to academic achievement is lacking. While previous studies have sought to determine which placement is better for students with disabilities, no study was found that specifically examined the impact of placement specific to Black students with specific learning disabilities (SLD) in urban settings (Fore, III, Hagan-Burke, Burke, Boon & Smith, 2008; Rea, McLaughlin & Walther-Thomas, 2002). This study examined educational placement, instructional best practices, and achievement gains of Black students with SLD in urban secondary settings using an ex post facto research design. Achievement, placement, and demographic data were collected and analyzed on approximately 314 Black eighth grade students with SLD. The Teacher Instructional Practices Survey was developed and used to collect and analyze data from the teachers of 78 of these students as it relates to instructional best practices. Results indicate no significant difference in reading but a significant difference in math gains of students served in inclusive settings as compared to resource settings with a small effect size. Also, no significant relationship was found between achievement gains and the reported use of instructional best practices. However, there was a relationship between educational placement and the use of instructional best practices. The results implied that there is a need for training with both general and special education teachers on instructional best practices for SWD and that there should be certain IEP team considerations when making placement decisions for this population of students with disabilities. It is recommended that future research in this area include classroom observations and factors other than test scores to measure growth in achievement.

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).