Comparación de comisiones por flujo y por saldo en sistemas de pensiones con cuentas individuales de capitalización

Comparison between Charges on Flow and Charges on Balance in Individual-Account Pension Systems 61 Comparison between Charges on Flow and Charges on Balance in Individual-Account Pension Systems Luis Chávez-Bedoya Nelson Ramírez Rondán* ESAN, Lima Banco Central de Reserva del Perú, Lima Abstract In this present article, we develop a discrete-time methodology to compare front-end load and balance fees in the accumulation phase of a definedcontribution pension fund under a system of individual accounts. Using this methodology, we study the effect of risk aversion and other relevant variables in the performance and suitability of the aforementioned types of fees. Finally, we carry out a practical application and show the results for the Peruvian Private Pension System, including indifference values between fees and certainty equivalent ratios. Key words: Pension funds; front-end load fee; balance fee; individual accounts. * Article received on April 17, 2015; final version approved on March 11, 2016. The authors thank Guillermo Moloche and the Apuntes reviewer for their valuable comments, as well as the participants of the Central Reserve Bank of Peru’s (Banco Central de Reserva del Perú, BCRP) research seminar, the 31st Meeting of BCRP Economists, and the 2014 Annual Congress of the Peruvian Association of Economics (Asociación Peruana de Economía, APE) for the comments and discussions that enriched this study. Any possible errors are the responsibility of the authors. Luis Chávez-Bedoya holds a Ph.D. in Management Sciences from Northwestern University. He is currently professor of finances at the ESAN Graduate School of Business. His research has been published in Quantitative Finance, Journal of Pension Economics and Finance, CEPAL Review, Estudios de Economía de la Universidad de Chile and Journal of Asset Management, among other specialized journals. Email: Nelson Ramírez Rondán holds a Ph.D. in Economics from the University of Wisconsin-Madison. He is currently a researcher at the BCRP Department of Economic Research. His areas of interest are theoretical econometrics and empirical macroeconomics. Email: Vol. XLIII, N° 78, First Semester 2016: pages 61-88 / ISSN 0252-1865 DOI: http://dx.doi.org/10.21678/apuntes.78.835 Copyright 2016: Centro de Investigación de la Universidad del Pacífico 62 Apuntes 78, First Semester 2016 / Chávez-Bedoya and Ramírez Rondán Acronyms AFP APE BCRP CRRA GBM IA SDE SBS SPP Pension fund management company (Administradora de fondos de pensiones) Peruvian Association of Economics (Asociación Peruana de Economía) Central Reserve Bank of Peru (Banco Central de Reserva del Perú) Constant relative risk aversion Geometric Brownian movement Individual account Stochastic differential equation Superintendence of Banking, Insurance, and AFPs (Superintendencia de Banca, Seguros y AFP) Private Pension Pystem (Sistema Privado de Pensiones) Comparison between Charges on Flow and Charges on Balance in Individual-Account Pension Systems 63 1. INTRODUCTION During the final quarter of the last century, many Latin American countries reformed their pension systems, switching from public pay-as-you-go (PAYG) systems to private systems based on individual accounts (IAs).1 According to Escrivá et al. (2010), these new systems constitute an attempt to adapt to the new risks and challenges faced by countries in the region, including factors such as: the vulnerability of public finances, changes in birth rates, greater life expectancy, problems of efficiency in public administration, and greater potential development of financial markets. However, a new series of reforms are now being proposed, whose fundamental objectives, discussed by Kritzer et al. (2011), are to increase coverage and competition in pension systems while reducing administrative costs. Two important characteristics of IA pension systems are, on the one hand, the fact that affiliates assume the risk associated with fluctuation in the value of administrative assets; and on the other, the fact that the administrative fees (commissions) charged by pension fund management companies (administradoras de fondos de pensiones, AFPs) have a significant impact on the final balance of IAs.2 Furthermore, as stated in James et al. (2001), Whitehouse (2001), and Mitchell (1998), one of the main criticisms of IA systems is their high cost, since this does nothing to encourage participation, damages the image of the systems as a whole, reduces the value of future pensions, and increases the future costs to the government of a guaranteed minimum pension. According to Kritzer et al. (2011), the most common type of administrative fees in IA pension systems are: proportional charges on flow (expressed as a percentage of income or contribution), fixed charges on flow, and charges on excess returns.3 This article analyzes 1. 2. 3. The most documented case is Chile. For the main aspects of this reform, see: Arrau et al. (1993); Diamond and Valdés-Prieto (1994); Edwards (1998); and Arenas de Mesa and Mesa-Lago (2006). In the case of Peru, a complete analysis of pension system reform and its current status is provided in Marthans and Stok (2013). Queisser (1998), Sinha (2000), Kay and Kritzer (2001), Mesa-Lago (2006), and Kritzer et al. (2011) are good references for the study of the reform, status, and perspective of Latin American pension systems. Devesa-Carpio et al. (2003) argue that the levy scheme adopted in IA systems is very important because the accumulation process is exponential and directed toward long time horizons. For example, Murthi et al. (2001) estimate that in the United Kingdom, 40% of the value of IAs is dissipated by administrative fees, while Whitehouse (2001) finds that an annual levy of 1% of assets represents nearly 20% of the final pension value. Analyses and comparison of administrative fees across different countries can be found in: James et al. (2001); Whitehouse (2001); Gómez-Hernández and Stewart (2008); Corvera et al. (2006); Tapia and Yermo (2008); Devesa-Carpio et al. (2003). Moreover, Sinha (2001), Masías and Sánchez (2007), and Martínez and Murcia (2008) perform a detailed analysis (notwithstanding the changes that have since been made) of administrative fees in Mexico, Peru, and Colombia, respectively. 64 Apuntes 78, First Semester 2016 / Chávez-Bedoya and Ramírez Rondán only proportional charges on flow and income, which are the most common and important types of levy in Latin America. For Queisser (1998), charges on flow are more advantageous to AFPs during the initial phase of the system, and despite the fact that income-based commission is aligned to AFPs’ objectives in terms of increasing fund profitability, they tend to be more expensive in the long run given that IAs increase in value. Meanwhile, Shah (1997) argues that charges on flow give rise to distortions and undesirable tendencies, such as engend (...truncated)