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"... Contaduría y Administración, No. 235, septiembre-diciembre 2011: [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] Minimización del tracking error con solución analítica para portafolios indizados Fecha de recepción: 26.05.2010 Fecha de aceptación: 06.08.2010 Resumen Este artícu ..."

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Contaduría y Administración, No. 235, septiembre-diciembre 2011: [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] Minimización del tracking error con solución analítica para portafolios indizados Fecha de recepción: 26.05.2010 Fecha de aceptación: 06.08.2010 Resumen Este artículo presenta dos resultados: por una parte, desarrolla una solución analítica (también conocida como "forma cerrada") para la minimización del llamado tracking error; por otra, demuestra que si bien dicha minimización es relativamente fácil de lograr con métodos numéricos, la solución analítica reduce considerablemente el tiempo de cálculo computacional. La minimización se hace sobre el universo de acciones sobre un subconjunto arbitrario de esas emisiones y, por lo tanto, es utilizable en un contexto heurístico para la selección de emisiones en número restringido que minimicen el tracking error. Palabras clave: tracking error, optimización, portafolios Homero Zambrano Mañueco Closed-form solution for tracking error minimization for indexed portfolios Abstract This paper has a twofold result: 1) It develops an analytical solution (closed-form solution) for the minimization of tracking error. 2) It shows that, notwithstanding that minimization is relatively easy to achieve with numerical algorithms, the analytical solution considerably reduces CPU time. Minimization is done over the whole population of stocks issuances or over an arbitrary sample of them; therefore, the solution is applicable within a heuristic context for selecting a definite number of stocks issuances with which to minimize the tracking error.

### 15+ MILLION TOP 1% MOST CITED SCIENTIST 12.2% AUTHORS AND EDITORS FROM TOP 500 UNIVERSITIES Iterations for a General Class of Discrete-Time Riccati-Type Equations: A Survey and Comparison

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### Iterations for a General Class of Discrete-Time Riccati-Type Equations: A Survey and Comparison

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### A ROBUST OPTIMIZATION APPROACH FOR INDEX TRACKING PROBLEM

"... Index tracking is an investment approach where the primary objective is to keep portfolio return as close as possible to a target index without purchasing all index components. The main purpose is to minimize the tracking error between the returns of the selected portfolio and a benchmark. In this s ..."

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Index tracking is an investment approach where the primary objective is to keep portfolio return as close as possible to a target index without purchasing all index components. The main purpose is to minimize the tracking error between the returns of the selected portfolio and a benchmark. In this study, quadratic as well as linear models are presented for minimizing the tracking error. The uncertainty is considered in the input data using a tractable robust framework that controls the level of conservatism while maintaining linearity. The linearity of the proposed robust optimization models allows a simple implementation of an ordinary optimization software package to find the optimal robust solution. The proposed model of this study employs Morgan Stanley Capital International Index as the target index and the results are reported for six

### Portfolio Modeling, Analysis and Management by

, 2010

"... A systematic top down approach to minimize risk and maximize the profits of an investment over a given period of time is proposed. Macroeconomic factors such as Gross Domestic Product (GDP), Consumer Price Index (CPI), ..."

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A systematic top down approach to minimize risk and maximize the profits of an investment over a given period of time is proposed. Macroeconomic factors such as Gross Domestic Product (GDP), Consumer Price Index (CPI),

### Investigation of Portfolio Choice that Tracks a Continuously Moving Target

, 2008

"... We investigate the problem of tracking a moving target, specifically a given continuously com-pounded, deterministic growth rate by using linear quadratic control theory. We first present some preliminaries and then derive and solve the corresponding Riccati equations for our problem. We then implem ..."

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We investigate the problem of tracking a moving target, specifically a given continuously com-pounded, deterministic growth rate by using linear quadratic control theory. We first present some preliminaries and then derive and solve the corresponding Riccati equations for our problem. We then implement our findings in MATLAB by using one stock from the FTSE100 and a risk-less asset and analyze the results. Furthermore, we focus on situations when the performance of our tracking is not the expected and highlight when this can happen and what the risks involved are. We also present situations when we would need to borrow or short sell, like in the case of aggressively tracking a target. We then briefly present the extension to multi asset portfolios. Finally, we discuss the case of tracking a market index.