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The contribution of this article is to present an investment process that allows the asset manager to limit risk exposure to macro-factors - including expectations on correlation dynamics - whilst allowing for selective exposure to risk factors using factor-portfolios that emulate the risk and return profile of market micro-factors.

As a natural extension to Leon and Vivas (2010) and Leon and Reveiz (2010) this paper briefly describes the Cholesky method for simulating Geometric Brownian Motion processes with long-term dependence, also referred as Fractional Geometric Brownian Motion (FBM). Results show that this method generates random numbers capable of replicating independent, persistent or antipersistent time-series depending on the value of the chosen Hurst exponent. Simulating FBM via the Cholesky method is (i) convenient since it grants the ability to replicate intense and enduring returns, which allows for reproducing well-documented financial returns’ slow convergence in distribution to a Gaussian law, and (ii) straightforward since it takes advantage of the Gaussian distribution ability to express a broad type of stochastic processes by changing how volatility behaves with respect to the time horizon. However, Cholesky method is computationally demanding, which may be its main drawback. Potential applications of FBM simulation include market, credit and liquidity risk models, option valuation techniques, portfolio optimization models and payments systems dynamics. All can benefit from the availability of a stochastic process that provides the ability to explicitly model how volatility behaves with respect to the time horizon in order to simulate severe and sustained price and quantity changes. These applications are more pertinent than ever because of the consensus regarding the limitations of customary models for valuation, risk and asset allocation after the most recent episode of global financial crisis.

This paper builds upon previous research on currency bands, and provides a model for the Colombian peso. Stochastic differential equations are combined with information related to the Colombian currency band to estimate competing models of the behaviour of the Colombian peso within the limits of the currency band. The resulting moments of the density function for the simulated returns describe adequately most of the characteristics of the sample returns data. The factor included to account for the intra-marginal intervention performed to drive the rate towards the Central Parity accounts only for 6.5% of the daily change, which supports the argument that intervention, if performed by the Central Bank, it is not directed to push the currency towards the limits. Moreover, the credibility of the Colombian Central Bank, Banco de la Republica’s ability to defend the band seems low.

Financial basics and intuition stresses the importance of investment horizon for risk management and asset allocation. However, the beta parameter of the Capital Asset Pricing Model (CAPM) is invariant to the holding period. Such contradiction is due to the assumption of long-term independence of financial returns; an assumption that has been proven erroneous. Following concerns regarding the impact of the long-term dependence assumption on risk (Holton, 1992), this paper quantifies and fixes the CAPM’s bias resulting from this abiding –but flawed- assumption. The proposed procedure is based on Greene and Fielitz (1980) seminal work on the application of fractional Brownian motion to CAPM, and on a revised technique for estimating time-series’ fractal dimension with the Hurst exponent (León and Vivas, 2010; León and Reveiz, 2011a). Using a set of 85 stocks from the S&P100, this paper finds that relaxing the long-term independence assumption results in significantly different estimations of beta. According to three tests herein implemented with a 99% confidence level, more than 60% of the stocks exhibit significantly different beta parameters. Hence, expected returns are biased; on average, the bias is about ±60bps for a contemporary one-year investment horizon. Thus, as emphasized by Holton (1992), risk is a two-dimensional quantity, with holding period almost as important as asset class. The procedure herein proposed is valuable since it parsimoniously achieves an investment

Financial basics and intuition stresses the importance of investment horizon for risk management and asset allocation. However, the beta parameter of the Capital Asset Pricing Model (CAPM) is invariant to the holding period. Such contradiction is due to the assumption of long-term independence of financial returns; an assumption that has been proven erroneous. Following concerns regarding the impact of the long-term dependence assumption on risk (Holton, 1992), this paper quantifies and fixes the CAPM´s bias resulting from this abiding -but flawed- assumption. The proposed procedure is based on Greene and Fielitz (1980) seminal work on the application of fractional Brownian motion to CAPM, and on a revised technique for estimating time-series´ fractal dimension with the Hurst exponent (Leon and Vivas, 2010; Leon and Reveiz, 2011a). Using a set of 85 stocks from the SP on average, the bias is about ± 60bps for a contemporary one-year investment horizon. Thus, as emphasized by Holton (1992), risk is a two-dimensional quantity, with holding period almost as important as asset class. The procedure herein proposed is valuable since it parsimoniously achieves an investment horizon dependent CAPM.

Financial basics and intuition stresses the importance of investment horizon for risk management and asset allocation. However, the beta parameter of the Capital Asset Pricing Model (CAPM) is invariant to the holding period. Such contradiction is due to the assumption of long-term independence of financial returns; an assumption that has been proven erroneous.Following concerns regarding the impact of the long-term dependence assumption on risk (Holton, 1992), this paper quantifies and fixes the CAPM’s bias resulting from this abiding – but flawed – assumption. The proposed procedure is based on Greene and Fielitz (1980) seminal work on the application of fractional Brownian motion to CAPM, and on a revised technique for estimating time-series’ fractal dimension with the Hurst exponent (Leon and Vivas, 2010; Leon and Reveiz, 2011a).Using a set of 85 stocks from the SP on average, the bias is about

As a natural extension to León and Vivas (2010) and León and Reveiz (2010) this paper briefly describes the Cholesky method for simulating Geometric Brownian Motion processes with long-term dependence, also referred as Fractional Geometric Brownian Motion (FBM). Results show that this method generates random numbers capable of replicating independent, persistent or antipersistent time-series depending on the value of the chosen Hurst exponent. Simulating FBM via the Cholesky method is (i) convenient since it grants the ability to replicate intense and enduring returns, which allows for reproducing well-documented financial returns’ slow convergence in distribution to a Gaussian law, and (ii) straightforward since it takes advantage of the Gaussian distribution ability to express a broad type of stochastic processes by changing how volatility behaves with respect to the time horizon. However, Cholesky method is computationally demanding, which may be its main drawback. Potential applications of FBM simulation include market, credit and liquidity risk models, option valuation techniques, portfolio optimization models and payments systems dynamics. All can benefit from the availability of a stochastic process that provides the ability to explicitly model how volatility behaves with respect to the time horizon in order to simulate severe and sustained price and quantity changes. These applications are more pertinent than ever because of the consensus regarding the limitations of customary models for valuation, risk and asset allocation after the most recent episode of global financial crisis.

As a natural extension to Leon and Vivas (2010) and Leon and Reveiz (2010) this paper briefly describes the Cholesky method for simulating Geometric Brownian Motion processes with long term dependence, also referred as Fractional Geometric Brownian Motion (FBM). Results show that this method generates random numbers capable of replicating independent, persistent or antipersistent time‐series depending on the value of the chosen Hurst exponent. Simulating FBM via the Cholesky method is (i) convenient since it grants the ability to replicate intense and enduring returns, which allows for reproducing well‐documented financial returns’ slow convergence in distribution to a Gaussian law, and (ii) straightforward since it takes advantage of the Gaussian distribution ability to express a broad type of stochastic processes by changing how volatility behaves with respect to the time horizon. However, Cholesky method is computationally demanding, which may be its main drawback. Potential applications of FBM simulation include market, credit and liquidity risk models, option valuation techniques, portfolio optimization models and payments systems dynamics. All can benefit from the availability of a stochastic process that provides the ability to explicitly model how volatility behaves with respect to the time horizon in order to simulate severe and sustained price and quantity changes. These applications are more pertinent than ever because of the consensus regarding the limitations of customary models for valuation, risk and asset allocation after the most recent episode of global financial crisis.

Frente al enfasis tradicional en la dependencia de corto plazo de los retornos, la dependencia de largo plazo permanece ignorada. Pese a que la literatura financiera provee evidencia de la existencia de memoria de largo plazo, el supuesto de independencia serial subsiste. La cuantificacion de la dependencia de largo plazo que presenta este documento se basa en la metodologia de rango re-escalado (R/S), que es una metodologia popular y robusta disenada por geofisicos, pero de extenso uso en la literatura financiera. Los resultados coinciden con gran parte de la evidencia previa sobre la presencia de dependencia de largo plazo significativa, particularmente para mercados de tamano reducido o de poca liquidez, donde la persistencia es su forma mas usual. Esta persistencia implica que el rango de posibles valores futuros de una variable es mas amplio que aquel que supone el comportamiento aleatorio e independiente de estas. Como una extension a la literatura financiera sobre R/S, los autores estiman un exponente de Hurst ajustado para estimar de manera adecuada la matriz de covarianza a horizontes de inversion mayores, con lo cual se evita recaer en el supuesto de independencia que subyace en la regla de la raiz cuadrada del tiempo. Ignorar la dependencia de largo plazo en el modelo de optimizacion de portafolio basado en media-varianza resulta en la subestimacion del riesgo; de este modo, al realizar el ajuste propuesto la ponderacion de activos con alta (baja) persistencia disminuye (aumenta) al extenderse el horizonte de inversion. Esto mitiga algunas deficiencias tipicas de los modelos tradicionales de optimizacion de portafolio para inversionistas de largo plazo (e.g. bancos centrales, fondos de pensiones), tales como la toma de riesgos excesivos en portafolios de largo plazo, asignaciones extremas, sesgos locales, y la propension a mantener activos denominados en moneda local exclusivamente

It is widely known that the Markowitz formulation of the portfolio optimization problem, based on maximizing expected return and minimizing risk, is the main pillar of the portfolio management theoretical foundations. Nevertheless, its limited impact in investment management practice is also widely recognized1, which has fostered new approaches to the portfolio optimization problem.

Operational Risk (OR) results from endogenous and exogenous risk factors, as diverse and complex to assess as human resources and technology, which may not be properly measured using traditional quantitative approaches. Engineering has faced the same challenges when designing practical solutions to complex multifactor and non-linear systems where human reasoning, expert knowledge, and imprecise information are valuable inputs. One of the solutions provided by engineering is a Fuzzy Logic Inference System (FLIS). The choice of a FLIS for OR assessment results in a convenient and sound use of qualitative and quantitative inputs, capable of effectively articulating risk management’s identication, assessment, monitoring, and mitigation stages. Different from traditional approaches, the proposed model allows for evaluating mitigation efforts ex-ante, thus avoiding concealed OR sources from system complexity build-up and optimizing risk management resources. Furthermore, because the model contrasts effective with expected OR data, it is able to constantly validate its outcome, recognize environment’s shifts, and issue warning signals.

Este trabajo desarrolla un modelo de simulación para estimar el flujo de caja de un pensionado que tiene su cuenta individual en una Administradora de Fondos de Pensiones (AFP) colombiana. Se proyecta el flujo a partir de las sendas salariales y densidades de cotización estimadas por la Dirección de Estudios Económicos del Departamento Nacional de Planeación (DNP) y, basado en lo anterior, se calcula el valor de la pensión que se podría obtener a partir de la riqueza acumulada al final de la vida laboral. Los resultados muestran que, de no adoptar medidas tendientes a aumentar las densidades y las tasas de cotización, un gran porcentaje de la fuerza laboral obtendrá pensiones inferiores a la mínima establecida por ley, sin siquiera cumplir con los requisitos para acceder a la garantía estatal para obtener la misma.

Este trabajo desarrolla un modelo de simulacion para estimar el flujo de caja de un pensionado que tiene su cuenta individual en una administradora de fondos de pensiones (AFP) colombiana. Aquel se proyecta a partir de las sendas salariales y densidades de cotizacion estimadas por la Direccion de Estudios Economicos del Departamento Nacional de Planeacion (DNP) y, con base en lo anterior, se calcula el valor de la pension que se podria obtener a partir de la riqueza acumulada al final de la vida laboral. Los resultados muestran que, de no adoptar medidas encaminadas a aumentar las densidades y las tasas de cotizacion, un gran porcentaje de la fuerza laboral obtendria pensiones inferiores a la minima establecida por ley, pero no cumpliria con los requisitos para acceder a la garantia estatal para obtener la misma.

This essay evaluates the regulation related with Colombian Compulsory Pension Funds’ (FPO) portfolio management. Based on authors’ previous research and the analysis herein presented, it is concluded that applicable FPO’s regime requires certain modifications. Main modifications would consist of: i) easing FPO’s investments regime, since it limits managers’ ability to reach superior risk return combinations with greater diversification benefits; ii) to adopt a multifund scheme, which would allow managers to offer portfolios that replicate beneficiary’s risk profile, and iii) to reform manager’s minimum required return and remuneration mechanisms, insofar they foster inefficient investment strategies. The authors consider these modifications key in order to align beneficiary’s and administrators’ economic incentives, resulting in a more efficient pension system. Este documento evalúa la regulación vigente relacionada con la administración de los portafolios de los fondos de pensiones obligatorias (FPO) en Colombia. Con base en investigaciones previas de los autores y en el análisis de este documento, se concluye que el régimen aplicable a los FPO requiere de ciertas modificaciones. Los principales cambios consistirían en: i) ampliar el régimen de inversiones de los FPO, ya que impide a los administradores acceder a niveles superiores de retorno por unidad de riesgo con mayores beneficios de diversificación; ii) adoptar un esquema de multifondos, el cual permitiría al administrador ofrecer portafolios que repliquen el perfil de riesgo del afiliado, y iii) reformar la fórmula de rentabilidad mínima y de remuneración al administrador, por cuanto incentivan estrategias de inversión ineficientes. Los autores consideran que con estas modificaciones se logra alinear de mejor manera los incentivos económicos de los aportantes y de los administradores, lo cual resultaría en un sistema pensional más eficiente. Este documento avalia a regulação vigente relacionada com a administração dos portafolios dos fundos de pensões obrigatórias (FPO) em Colômbia. Com base em investigações prévias dos autores e na análise deste documento, conclui-se que o regime aplicable aos FPO requer de certas modificações. As principais mudanças consistiriam em: i) ampliar o regime de investimentos dos FPO, já que impede aos administradores aceder a níveis superiores de volta por unidade de risco com maiores benefícios de diversificación; ii) adoptar um esquema de multifondos, o qual permitiria ao administrador oferecer portafolios que repliquem o perfil de risco do filiado, e iii) reformar a fórmula de rentabilidad mínima e de remuneración ao administrador, porquanto incentivam estratégias de investimento ineficientes. Os autores consideram que com estas modificações se consegue alinear de melhor maneira o objectivo de maximización de riqueza dos aportantes com os incentivos económicos dos administradores, o qual resultaria num sistema pensional mais eficiente.

Este documento evalua la regulacion vigente relacionada con la administracion de los portafolios de los Fondos de Pensiones Obligatorios (FPO), para esto revisa la literatura relacionada con la eficiencia del Sistema dadas sus actuales restricciones. Se concluye que el marco regulatorio de las inversiones de los FPO restringen el retorno esperado y hace que los administradores de portafolios no accedan a niveles superiores de retorno por unidad de riesgo con 05res beneficios de diversificacion. Asi mismo se limita la capacidad del administrador de construir portafolios que reflejen el perfil de riesgo del afiliado. Se muestra que la formula de rentabilidad minima genera incentivos perversos para que las AFP´s no incurran en riesgo llevando a los Administradores a estrategias que sincronicen los retornos de los portafolios para minimizar el impacto de la incertidumbre generado por la formula de rentabilidad minima. Las propuestas van en el sentido de flexibilizar las inversiones y adecuarlas de acuerdo al perfil de riesgo de los cotizantes utilizando el esquema de Multifondos implementando en otros paises de la region.

The focus of this study is to build, from the ‘bottom-up’, a market with artificially intelligent adaptive agents based on the institutional arrangement of the Colombian Foreign Exchange Market (1994-1999) in order to determine simple agents’ design, rules and interactions that are sufficient to create interesting behaviours at the macroscopic level - emerging patterns that replicate the properties of the time series from the case study. Tools from artificial intelligence research, such as genetic algorithms and fuzzy logic, are the basis of the agents’ mental models, which in turn are used for forecasting, quoting and learning purposes in a double auction market. Sets of fuzzy logic rules yield adequate, approximately continuous risk and utility preferences without the need to fix their mathematical form ex-ante. Statistical properties of financial time series are generated by the artificial market, as well as some additional non-linearity linked to the existence of a crawling band. Moreover, the behaviour of the simulated exchange rate is consistent with currency band theory. Agent’s learning favours forecasting rules based on regulatory signals against rules based on fundamental information. Also, intra-day volatility is strongly linked to the rate of arrival and size of real sector trades. Intra-day volatility is also a function of the frequency of learning and search specialisation. It is found that when a moderately low frequency of learning is used, volatility increases.

Este documento evalúa la regulación vigente relacionada con la inversión de los recursos de los Fondos de Pensiones Obligatorios (FPO), para lo cual se analiza el perfil de eficiencia del sistema dadas sus actuales restricciones. De acuerdo con los resultados obtenidos, se observa que el marco regulatorio de las inversiones de los FPO restringen el retorno esperado y hace que los administradores de portafolios no accedan a niveles superiores de retorno por unidad de riesgo con mayores beneficios de diversificación. Las propuestas apuntan hacia la flexibilización de las restricciones a las inversiones y a su adecuación al perfil de riesgo de los cotizantes, utilizando para ello el esquema de multifondos implementado en otros países de la región.

We present an investment process that: (i) decomposes securities into risk factors; (ii) allows for the construction of portfolios of assets that would selectively expose the manager to desired risk factors; (iii) perform a risk allocation between these portfolios, allowing for tracking error restrictions in the optimization process and (iv) give the flexibility to manage dinamically the transfer coeffficient (TC). The contribution of this article is to present an investment process that allows the asset manager to limit risk exposure to macro-factors - including expectations on correlation dynamics - whilst allowing for selective exposure to risk factors using mimicking portfolios that emulate the behaviour of given specific. An Artificial Intelligence (AI) optimisation technique is used for risk-budget allocation to factor-portfolios.

Este documento evalua la regulacion vigente relacionada con la inversion de los recursos de los Fondos de Pensiones Obligatorios (FPO), para lo cual se analiza el perfil de eficiencia del sistema dadas sus actuales restricciones. De acuerdo con los resultados obtenidos, se observa que el marco regulatorio de las inversiones de los FPO restringen el retorno esperado y hace que los administradores de portafolios no accedan a niveles superiores de retorno por unidad de riesgo con 05res beneficios de diversificacion. Las propuestas apuntan hacia la flexibilizacion de las restricciones a las inversiones y a su adecuacion al perfil de riesgo de los cotizantes, utilizando para ello el esquema de multifondos implementado en otros paises de la region.

The focus of this study is to build, from the ‘bottom-up’, a market with artificially intelligent adaptive agents based on the institutional arrangement of the Colombian Foreign Exchange Market (1994-1999) in order to determine simple agents’ design, rules and interactions that are sufficient to create interesting behaviours at the macroscopic level - emerging patterns that replicate the properties of the time series from the case study. Tools from artificial intelligence research, such as genetic algorithms and fuzzy logic, are the basis of the agents’ mental models, which in turn are used for forecasting, quoting and learning purposes in a double auction market. Sets of fuzzy logic rules yield adequate, approximately continuous risk and utility preferences without the need to fix their mathematical form ex-ante. Statistical properties of financial time series are generated by the artificial market, as well as some additional non-linearity linked to the existence of a crawling band. Moreover, the behaviour of the simulated exchange rate is consistent with currency band theory. Agent’s learning favours forecasting rules based on regulatory signals against rules based on fundamental information. Also, intra-day volatility is strongly linked to the rate of arrival and size of real sector trades. Intra-day volatility is also a function of the frequency of learning and search specialisation. It is found that when a moderately low frequency of learning is used, volatility increases.

We present an investment process that: (i) decomposes securities into risk factors; (ii) allows for the construction of portfolios of assets that would selectively expose the manager to desired risk factors; (iii) perform a risk allocation between these portfolios, allowing for tracking error restrictions in the optimization process and (iv) give the flexibility to manage dinamically the transfer coeffficient (TC). The contribution of this article is to present an investment process that allows the asset manager to limit risk exposure to macro-factors - including expectations on correlation dynamics - whilst allowing for selective exposure to risk factors using mimicking portfolios that emulate the behaviour of given specific. An Artificial Intelligence (AI) optimisation technique is used for risk-budget allocation to factor-portfolios.

This paper approaches active management of baskets of currencies from the perspectiveof Complexity theory, where the market is analysed as a Complex Adaptive system. Abasket of currencies is constructed using objective probabilities (propensities) and anartificial intelligence optimization technique that allows for implicit learning ofcorrelations dynamics. Statistical tests of the diversification benefit are presented.

Las monedas locales de los paises en vias de desarrollo, ademas de no ser libremente convertibles a nivel internacional, suelen experimentar niveles de inflacion superiores y mas volatiles, al tiempo que tienden a sufrir periodos de fuerte apreciacion y depreciacion. Estas bien conocidas caracteristicas no solo implican un reto para las autoridades economicas de estos paises, sino que tambien llaman la atencion sobre la capacidad de las monedas locales para cumplir cabalmente con sus funciones. Colombia, a pesar de ser reconocida por su historial de manejo monetario disciplinado, no ha escapado a ocasionales cuestionamientos sobre la conveniencia de mantener el peso para cumplir con las funciones de la moneda. Estos esporadicos cuestionamientos coinciden con periodos de fuerte apreciacion o depreciacion de la moneda, en los cuales se han escuchado interrogantes sobre la conveniencia de llevar a cabo una dolarizacion total o parcial de la economia. Al respecto, son pocos los paises que han optado por reemplazar totalmente la moneda local por una extranjera para que esta ultima cumpla con todas las funciones de la moneda, pero si son muchos los paises que han permitido la dolarizacion parcial de la economia. Basado en la experiencia internacional, y en especial por las caracteristicas de la economia colombiana, este documento concluye que la dolarizacion financiera conllevaria costos elevados, en especial si se comparan con unos beneficios limitados y apenas potenciales.

The set of objectives in reserves management are normally predifined and include: Protecting the economy against potential external shocks on the current account or on capital flows; invest the reserves minimizing the potential of a loss and ensuring the availability of international liquidity when necessary. Whereas the adoption of a floating exchange rate in theory reduces the need for reserves to protect against external shocks, in the context of free capital movements it will be a function of the efficiency of international markets.

The set of objectives in reserves management are normally predefined and include: protecting the economy against potential external shocks on the current account or on capital flows; invest the reserves minimizing the potential of a loss and ensuring the availability of international liquidity when necessary. Whereas the adoption of a floating exchange rate in theory reduces the need for reserves to protect against external shocks, in the context of free capital movements it will be a function of the efficiency of international markets. In practical terms, Reserves Management is a process with a high effective complexity. The manager is confronted with the randomness of markets – including its own through the impact on the Reserves of Central Bank intervention – and the regularities that arise from its guidelines (i.e. credit and market risk, as well as liquidity policies) and the foreign exchange intervention mechanisms. Recently, given the increase in the size of the foreign reserves in recent decades for some central banks, as a result and in response to globalization and more volatility on currency flows, portfolio foreign investment and other related factors as contagion effects, the pressure to generate long-term returns has increased. However, the goal of increased returns is subdued to the security and liquidity objectives in international reserves management. As a result, the process of asset allocation and the construction of an efficient set of investment guidelines, as well as a risk policy, must be framed by a liquidity policy and, generally, to an asymmetric exposure to risk where capital loses are to be avoided in specific time horizons; i.e. a fiscal year.

En este articulo se discute la importancia de la curva spot (cero cupon), asi como las consideraciones que deben realizarse para escoger un conjunto de metodos de estimacion que suplan las multiples necesidades a las que se enfrenta un inversionista o especulador – valoracion de activos y de productos contingentes, medicion de riesgo, analisis multifactoriales de la curva de rendimientos, etc. Adicionalmente, se presenta una metodologia de estimacion basa en splines cubicos suavizados, con validacion cruzada, con la cual se estima la curva spot de los Tes B tasa fija. Esta estimacion es posteriormente utilizada para ilustrar los problemas que pueden surgir al estimar curvas spot, con cualquier metodologia, en un mercado ineficiente en terminos de arbitraje, asi como para estimar los Key Rate Durations – una descomposicion lineal por tramos de la curva de la duracion efectiva – para titulos especificos o portafolios de bonos. Esto con el fin de mostrar como movimientos no paralelos de la curva, cambios en la pendiente o en la curvatura, pueden afectar portafolios con la misma duracion. En la ultima seccion se presentan las conclusiones, haciendo enfasis principalmente en el hecho de que las herramientas que surgen de la estimacion de esta curva y la sofisticacion de los mercados financieros han llevado a las instituciones financieras y los inversionistas institucionales de tamano importante a nivel global a modificar su proceso de toma de decisiones, trabajando en base a un presupuesto de riesgo definido por los niveles mas altos de las instituciones que es distribuido selectivamente por tipos de riesgo definido por los niveles mas altos de las instituciones que es distribuido selectivamente por tipos de riesgo tales como riesgo de tasa de interes, crediticio o de prepago entre otros.