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1 Electric Companies and Downside Risk Portfolio Analysis ABSTRACT This Paper Aims to Compare the Optimization Models by MV

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Electric Companies and Downside Risk Portfolio Analysis Autoria: Alcides Carlos de Araújo, Alessandra de Ávila Montini ABSTRACT This paper aims to compare the optimization models by MV, LPM and Conditional Value-at- Risk to study their different forms of allocation in investment portfolios consisting of shares of electric companies in the Brazilian stock exchange. The innovativeness in this paper is comparing the models MV, CVaR (ROCKAFELLAR; URYASEV, 2000) and LPM (NAWROCKI; CUMOVA, 2011) in a same work with the metric these authors. As contributions, a portfolio analyses for a specific sector in an exclusive moment of Brazilian economy. Proposing possible ways to fund managers focused in sectors balanced the portfolios when the investors risk preferences are highly pessimists. 1 INTRODUCTION The pioneer article of Markowitz (1952) caused a radical change on how to analyze the problem of the formation of portfolios (groups or portfolios) of financial assets. Over the past decades, authors such as Rom and Ferguson (1994), Grootveld and Hallerbach (1999) and Roman and Mitra (2009) argue that this theory is in a transition stage to the so-called Post Modern Portfolio Theory. According to the authors, the development of new ways to optimize investment portfolios enabled by the computational capabilities brings new dilemmas and issues to managers of portfolios. The present work is an extension of the paper proposed by Araújo and Montini (2012); these authors did comparisons between the risk metrics proposed by Markowitz (1952), Estrada (2008) and Nawrocki and Cumova (2011). The results demonstrated that measure proposed by Estrada (2008) have a significant bias regarding the original metric proposed by Hogan and Warren (1974); thus, the metric proposed by Nawrocki and Cumova (2011) demonstrated best convergence and results focused in a risk and return analysis. The purpose of this paper is to investigate the allocations of investments in shares using different metrics to minimize risks, seeking to answer the following question: What are the characteristics of the portfolios when different metrics to measure risks are used in a specific sector? The analyses focused on understanding whether the risk metrics could form different compositions in the portfolios, besides verifying if these portfolios would present different characteristics of risk and return. The risk metrics were: standard-deviation (MARKOWITZ, 1952), semivariance – which is also related to the L.P.M. family (NAWROCKI; CUMOVA, 2011) and CVaR (ROCKAFELLAR, URYASEV, 2000); the choice of these risk measures was based on the study of Roman and Mitra (2009) which indicated the importance of the use of the so-called downside risk measures. The sector selected was the Brazilian Electric Energy sector. 1.1 Justifications for the research Jarrow (2006) mentions three reasons for the increasing attention to the downside risk measures. The first refers to the current discussions caused by the numerous financial catastrophes and Basel agreements. In these discussions, the downside risk measures, such as CVaR, have considerable importance. The second is related to the use of derivatives in portfolio management, which modify the probability distribution of the portfolio, changing from symmetric to asymmetric. In September of 2012, the Brazilian government decreed the provisional measure 579 which regulates the new concessions for “Distributors” and “Generators” of electric energy, a point in this rule is the tariff reduction for consumers. Second analysts, these regulatory measures had negative effects in the sector; it’s estimated that companies lost R$34 billions of market value (KAHIL, 2013). Second Souza (2012), after the decree the analysts estimated that electric companies revenues can be dropped at R$13 billions. After this shock in the Brazilian economy Souza (2012) cites what assets can be good investments second market analysts; some of them are the companies TAEE11, CPFE3, COCE5 and TBLE3. The analysts observed 4 criteria: regulatory impacts, balance sheet, 2 dividends and management capacity. Regarding these data, this study analyzed, in a context of risk and returns, what stocks would be selected. For practical applications in the portfolio management, there are many funds focused in specific sectors of economy, for example the “Dividend Portfolios”, these portfolios consist mainly of shares of companies in the Brazilian electricity sector. After the provisional measure 579, the “dividend funds” were harmed because these portfolios are concentrated in stocks with high liquidity. With these problems, many analysts asked some questions as: “Is it worth paying a management fee and performance for a manager who invests in a concentrated portfolio with high liquidity?”; “Can do a balanced portfolio by a specific sector a better performance?” (ROCHA, 2013). This study analyses the questions for a different view, i.e, a better performance will be achieved by a portfolio more balanced or a portfolio balanced by a coherent measure of risk? The provisional measure proposed by government changed the investors risk preferences, these risk preferences are reflected on probability distributions of the assets. So, it’s important to align the new probability distribution with a method for portfolio selection that to consider the possible asymmetry in the investors risk preference. The innovativeness in this paper is comparing the models MV (MARKOWITZ, 1952), CVaR (ROCKAFELLAR; URYASEV, 2000) and LPM (NAWROCKI; CUMOVA, 2011) in a same work with the metric these authors. As contributions, a portfolio analyses for a specific sector in an exclusive moment of Brazilian economy. Proposing possible ways to fund managers focused in sectors balanced the portfolios when the investors risk preferences are highly pessimists. Next topics are focused in the literature review (portfolio models and comparisons), methodology, analysis and results. 2 LITERATURE REVIEW It’s necessary present the concepts related with the objectives constructed, in this way, the paper shows the discussions regarding to the portfolio models that will be analyzed and the results of comparisons of the several authors. 2.1 Portfolio models and comparisons The story of risk fascinates the financial world. One of the main studies in this line is the best seller: Against the Gods: The Remarkable Story of Risk, by Peter L. Berstein (1996). Other researchers have published interesting articles, such as Nawrocki (1999), who made a literature review to describe the development of the measurements of the so-called downside risk. Roman and Mitra (2009) also make a brief history of the risk measures. In this topic will be discussed the risk measures utilized in this work in respect to comparisons from the others authors in the theme of optimization of asset portfolio. It is worthy to highlight that only in the work of Konno et al. (2002) the analysis of the three measures was found. One of the works to be mentioned about the comparison between MV vs. LPM (in the work called downside risk) regarding the portfolio efficiency was conducted by Rom and Ferguson (1994). In this work, it was used, possibly for the first time, the expression "post- modern portfolio theory". One of the greatest points of this work is the results about the efficient frontier. In this case, the curve in the graphic “Return vs. Risk” showed more dominance when the optimization model which had the LPM measure was used. It was also verified more allocations, in the LPM model, in variable income assets, when the MV executed more positions in fixed income assets. That was explained by greater degree of 3 positive asymmetry of variable income assets, showing the LPM superiority when the portfolios are formed with assets with the above mentioned characteristics. Works which defend the results presented by Rom and Fergunson (1994) were also found. Grootveld and Hallerbach (1999) and Nawrocki and Cumova (2011) can be quoted when the fact that the portfolio return is greater when the risks (characterized by LPM) are minimized is mentioned. In Brazil, there are the articles by Andrade (2006), Araújo and Montini (2011); in these papers, the defense occurs when the ex-post portfolio returns, that is, the portfolio returns after the period of implementation are greater by LPM in relation to MV. Regarding the comparison MV vs. CVaR, the works by Rockafellar and Uryasev (2000) and Bertsimas (2004) can be metioned. In the first article, returns were generated by simulation, and the comparisons occurred by portfolio composition through selected confidence level (90%, 95% and 99%) and by VaR and CVaR calculations in both models of optimization. By the results of Rockafellar and Uryasev (2000), the portfolio and VaR and CVaR calculations tend to the convergence in both methods. In Bertsimas' work (2004), the author sought to deepen the analyses by varying, through simulations, the asymmetric degree of asset returns distribution to be imposed on the portfolio. By simulation the asymmetric distributions, the model with CVaR showed dominance in relation to MV, being the differences considered significant. Konno et al. (2002), as mentioned in the beginning, the authors compared the three measures. However, they omitted the results between MV vs. LPM/CVaR, claiming that there were no significant differences. But, the comparisons between LPM vs. CVaR could be presented in detail. The analyses were conducted with data from 1995 to 1999 in assets of Tokyo stock exchange. As it was
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