DECREASE IN MARKET RISK FOR THE EQUITY MARKET IN COLOMBIA WITH INTERNATIONAL ASSETS

International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 9, September 2018, pp. 1111 1117, Article ID: IJMET_09_09_121 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=9&itype=9 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 IAEME Publication Scopus Indexed DECREASE IN MARKET RISK FOR THE EQUITY MARKET IN COLOMBIA WITH INTERNATIONAL ASSETS Miguel Jiménez-Gómez Departamento de Finanzas, Instituto Tecnológico Metropolitano ITM, Colombia Universidad Nacional de Colombia Natalia Acevedo-Prins Departamento de Finanzas, Instituto Tecnológico Metropolitano ITM, Colombia ABSTRACT Market risk is the effect generated by the change in market prices. In the case of equity investment portfolios, the change in stock prices generates an expected loss, this expected loss is called Value at Risk (VaR). One way to reduce market risk in investment portfolios is through diversification. This paper proposes the international diversification of portfolios, which is more effective than diversification, through ETFs on international indices of the main stock exchanges of the world. The way to determine the benefits of international diversification of portfolios is done with the VaR calculation by several methodologies. The results show that for investment portfolios from the perspective of investor in Colombia, the market risk with international assets decreases more than with national assets. Key words: Market risk, Value at Risk, ETF, investment portfolios, diversification. Cite this Article: Miguel Jiménez-Gómez and Natalia Acevedo-Prins, Decrease in Market Risk for the Equity Market in Colombia with International Assets, International Journal of Mechanical Engineering and Technology 9(8), 2018, pp. 1111 1117. http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=9&itype=8 1. INTRODUCTION The risk is the possibility of losses generated by changes in the factors that affect the value of an asset. The risk associated with an investment portfolio is defined as the probability that the result of the investment may be different than expected [1], [2]. With diversification this risk is mitigated, but if diversification is carried out with international financial assets, Levy and Sarnat [3] affirm that better results are obtained with lower risks of the portfolio. Therefore, with the international portfolio diversification, a lower risk is obtained than locally diversified portfolios [4]. With investment portfolios with only local financial assets, diversifications are not obtained that reduce the risk. Therefore, it is necessary to identify international financial http://www.iaeme.com/ijmet/index.asp 1111 editor@iaeme.com

Decrease in Market Risk for the Equity Market in Colombia with International Assets assets that allow greater diversification, and thus, expand investment options for the Colombian market. The first evidences found in the literature on international diversification, are the works of Grubel [5] and Levy and Sarnat [3] using the methodology of media - variance. Grubel [5] implemented a macroeconomic model in government bonds of two countries to empirically examine the advantages of international diversification for an investor in the United States. This paper aims to demonstrate the benefits of international diversification of portfolios from the point of view of Colombian investors, which make up investment portfolios with local financial assets. The international assets that will be used for the diversification will be exchange-traded funds or ETF (Exchange Traded Fund). An initial portfolio will be formed with only shares of the Colombian market, then it will be diversified with international ETFs and through the quantification of VaR (Value at Risk) the benefits of international diversification of portfolios will be determined. 2. MATERIALS AND METHODS In order to demonstrate the benefits of international diversification of portfolios for the Colombian equity market, an initial portfolio was formed with the most liquid stocks of the Colombian Stock Exchange (BVC), as international assets, were used five ETFs from five continents. The initial portfolio was diversified internationally with each ETF, thus obtaining five internationally diversified portfolios. The VaR by the parametric and non-parametric methods were calculated for each portfolio. The most liquid stocks of the Colombian stock Exchange correspond to the companies ECOPETROL (ECO), Bancolombia preferential stock (PFBCOLOM), Canacol Energy (CNEC), Pacific Rubiales (PREC) and Isagen (ISAGEN). For its part, Morgan Stanley Capital International (MSCI) is a provider of indexes on stocks, bonds and hedge funds. The MSCI ETFs replicate these indices and are the most traded on the New York Stock Exchange. The MSCI brand ETFs were used to internationally diversify the Colombian portfolio and, in addition, the STF SPY that replicates the S & P 500 stock index because it is the first ETF and the one with the highest level of trading and liquidity. We used closing data of the shares and ETFs on a daily and monthly basis, so that daily and monthly data were obtained for the VaR. On the other hand, the limitation that was found with the data was with the action of CNEC, it is the shortest time in the BVC, that is why the data of the closing prices of the shares and the ETFs were used from the 1 from August 2012 until July 31, 2017, resulting in 1,197 observations for the daily series and 60 observations for the monthly series. In this order of ideas, part of an initial portfolio consisting of the five Colombian shares with equal investment proportions, that is, in each action was considered an investment of 20% of the money. This portfolio is called initial portfolio, it is the diversified portfolio, but only with local actions, not internationally diversified. Afterwards, each ETF was added to the initial portfolio to form internationally diversified portfolios. It was not considered to enter all the ETFs at the same time, on the contrary, it was done individually. In this way, with five ETFs, five portfolios were obtained with the same investment proportions in each asset (16.67% of the money invested in each asset). Two conventional methodologies were implemented to calculate the VaR, with parametric and nonparametric VaR methodologies were performed with confidence levels of 99% and 95%, except the Monte Carlo method that was performed with 95%. With six investment portfolios and five VaR calculations, there is 30 VaR and, as the results were applied for daily and monthly data, a total of 60 portfolios were reached, that is, 60 VaR or Securities at Risk. http://www.iaeme.com/ijmet/index.asp 1112 editor@iaeme.com

Miguel Jiménez-Gómez and Natalia Acevedo-Prins 2.1. Value At Risk The risk associated with equity investments is quantified through the volatility or standard deviation of the returns. [6] explains that this type of measure considers both positive and negative changes in share prices as constituting risk, despite the fact that most investors ignore positive changes in a context of risk. The VaR focuses on negative changes and attempts to derive a single measure of possible losses, either in nominal or percentage terms. It provides a measure of the potential loss in portfolio value over a specific period of time, and in doing so, aggregates all risks into a single measure that can be easily understood by portfolio managers and investors [7]. Risk is defined as the volatility of the returns that lead to unexpected losses, high volatility indicates greater risk. The volatility of returns is influenced by some variables called risk factors and by interaction between these risk factors [8]. The VaR of a portfolio is based on two parameters: the time horizon, t, and the confidence level, X%. This is the level of loss over a period of time of length t that will not be exceeded with a confidence level of X%. In relation to the time horizon, [9] states that it must correspond to the time required to cover market risk, however, as the asset trading portfolios are usually subject to change, it is more appropriate to use a time horizon short-term time, like a day. Through the international diversification of portfolios, investors can reduce the risk of portfolios due to low or negative correlations between financial instruments in national and international markets [7], [10]. There are two methodologies to calculate the VaR: Parametric methods and non-parametric methods. The parametric methods are the Monte Carlo simulation and the variance-covariance analysis. The first consists of taking the current yields as a starting point and simulating the expected returns over a period of time, generating thousands of possible alternatives. The variance-covariance analysis method makes assumptions about the distributions of the returns for the market risk, and the variances and the covariances between the variables. Finally, among the nonparametric methods is the historical simulation, which uses historical data to create a distribution of the returns [7] The following describes these three methods to calculate the VaR in an investment portfolio. 2.1.1. Parametric Methods According to [11], the VaR models are composed of two basic parameters: the confidence level and the time horizon. These parameters must be chosen with the objectives of managing the risk. From the perspective of an investor, the choice of level of confidence depends on their level of risk tolerance. Higher confidence levels, such as 99%, are generally applied to VaR estimates for risk-adverse investors. Regarding the time horizon, [9] states that it must correspond to the amount of time necessary to cover market risks. The VaR of an individual asset is calculated with equation 1: Where F corresponds to the value of z or to the confidence level, for a confidence level of 99% it is 2.33 or for a confidence level of 95% it is 1.65. The amount of the investment in the portfolio corresponds to S, σ is the standard deviation of the asset and t is the time horizon in which the VaR is to be calculated. To calculate the VaR of a portfolio there are two forms included in the parametric methods: variance-covariance method or normal delta and the Monte Carlo simulation method. http://www.iaeme.com/ijmet/index.asp 1113 editor@iaeme.com

Decrease in Market Risk for the Equity Market in Colombia with International Assets 2.1.2. Method of Variance-Covariance or Normal Delta Under this method, there are three simplifying assumptions: normality, independence of series and an absence of non-linear positions [12]. The assumption of normality implies that the returns of the risk factors are normally distributed and that their combined distribution is normal multivariate. According to [11], this assumption implies that the covariance matrix of the yields of the risk factors is all that is needed to estimate the VaR. Second, the assumption of series independence means that the magnitude of the VaR estimate on a given day will have no impact on the VaR estimate over a longer horizon. The importance of this assumption is that the VaR for a long time horizon can be obtained by multiplying the VaR estimate of 1 day by the square root of the number of days in the required horizon. Third, the variancecovariance method is only suitable for portfolios that have a linear relationship between risk and portfolio positions [7]. This method estimates the changes in the prices of the assets using their "delta", in other words, the logarithmic changes of the prices. It assumes that the price of the assets are lognormal and that the logarithm of the returns has a normal distribution [13]. 2.1.3. Monte Carlo Simulation Method The Monte Carlo simulation replicates the prices of assets by means of a simulation of random processes. The results of the simulation in a large number of scenarios or iterations, for example, 10,000 scenarios, of the prices that converge to a probability distribution [8]. In an efficient market, the prices of assets behave according to a stochastic process or Brownian Geometric Movement, equation 2 represents this process [14]: Where μ represents the average of the yields and σ the standard deviation of the same dz behaves with normal distribution, standard, zero, and variance, is the instantaneous change in a Wiener process. Applying the Itô motto, equation 2 results in a process of a G function of S and t (see equation 3) (Hull, 2012): ( ) Both S and G are affected by the same uncertainty of the underlying asset, dz. To create random scenarios, random numbers (dz) are generated with standard normal distribution with zero mean and variance 1. Equation 3 determines the price of the asset, which depends on the value obtained in the previous period (t - 1). 2.1.4. Nonparametric Method In this method the yields have empirical distribution, indicating that the historical distribution will remain the same in the following periods. The VaR is estimated by means of the empirical percentiles of the empirical distribution of the historical data of the yields. The fifth percentile corresponds to a level of confidence of 95% and the tenth percentile to a confidence of 90% [15]. 3. RESULTS AND DISCUSSIONS The VaR of the 60 portfolios is shown in Table 1. The diversified portfolios with the ETFs obtained lower magnitudes of VaR with respect to the initial portfolio. With the SPY ETF comes to a diversified portfolio with the lowest risk, this is shown from the normal delta methodologies and historical simulation with a confidence of 99%. With the Monte Carlo simulation and daily data, the diversified portfolio with the EWJ ETF generated the lowest http://www.iaeme.com/ijmet/index.asp 1114 editor@iaeme.com

Miguel Jiménez-Gómez and Natalia Acevedo-Prins risk and with monthly data, with the historical simulation method with 95% confidence, the portfolio with the EWG ETF, both in daily yields as monthly. Otherwise, diversified portfolios with the EWZ ETF (Brazil) did not benefit from international diversification, as demonstrated by most methods except historical simulation with 99% confidence and monthly returns. Table 1 VaR for the 60 portfolios. Daily data Monthly data Method Portfolio VaR Portfolio VaR Normal Delta (95%) Normal Delta (99%) Monte Carlo (95%) Historical simulation (95%) Historical simulation (99%) Initial portfolio 3.36% Initial portfolio 11.81% SPY 2.24% SPY 9.94% FEZ 2.30% FEZ 10.80% EWG 2.30% EWG 10.46% EWJ 2.25% EWJ 10.24% EWZ 2.33% EWZ 11.01% Initial portfolio 3.54% Initial portfolio 14.31% SPY 2.87% SPY 12.76% FEZ 2.96% FEZ 13.86% EWG 2.95% EWG 13.42% EWJ 2.89% EWJ 13.14% EWZ 2.99% EWZ 14.13% Initial portfolio 2.93% Initial portfolio 13.68% SPY 2.45% SPY 11.04% FEZ 2.40% FEZ 11.05% EWG 2.42% EWG 11.00% EWJ 2.39% EWJ 10.73% EWZ 2.47% EWZ 11.53% Initial portfolio 2.52% Initial portfolio 11.88% SPY 2.26% SPY 10.45% FEZ 2.28% FEZ 11.45% EWG 2.23% EWG 10.27% EWJ 2.28% EWJ 10.94% EWZ 2.28% EWZ 11.84% Initial portfolio 3.28% Initial portfolio 13.53% SPY 2.87% SPY 10.81% FEZ 2.99% FEZ 13.34% EWG 2.97% EWG 11.68% EWJ 2.86% EWJ 11.34% EWZ 3.15% EWZ 13.16% 4. CONCLUSIONS The VaR was quantified to 60 investment portfolios to demonstrate the benefits of the international diversification of investment portfolios by means of ETFs for a portfolio of the http://www.iaeme.com/ijmet/index.asp 1115 editor@iaeme.com

Decrease in Market Risk for the Equity Market in Colombia with International Assets Colombian market. Daily and monthly closing prices of shares of the Colombian market and international ETFs were used. A diversified portfolio was formed with local actions and then diversified with ETF, five ETFs were integrated into the Colombian portfolio. The ETFs that best diversify the portfolio are SPY and EWJ, the VaR of the portfolios held by these ETFs was the least significant; however, the EWZ ETF did not reduce the risk for the local market portfolio. The above was determined by calculating the VaR by parametric and nonparametric methods for both daily and monthly returns. Among the five ETFs identified, the SPY had the lowest standard deviation, but it is the ETF most correlated with the Colombian shares, this measured with the correlation coefficient. In contrast, the EWJ ETF showed the highest standard deviation of the ETFs, which is why the internationally diversified portfolios with this asset did not reduce the risk. On the other hand, the actions of the Colombian market have high correlations compared with the correlations of these actions with the ETFs where negative correlation coefficients were obtained. These low correlations and the standard deviations of lower value of the ETF managed to obtain portfolios that were less risky and also diversified internationally. REFERENCES [1] K. Grundy and B. G. Malkiel, Reports of Beta death have been greatly exaggerated. Journal of Portfolio Management., J. Portf. Manag., vol. 22, pp. 36 44, 1996. [2] M. Jiménez-Gómez, N. Acevedo-Prins, and D. Rojas, Cobertura cambiaria con derivados financieros: caso empresa exportadora en Colombia, in Finanzas, modelación y riesgo, N. Marín, Ed. Medellín, 2017, p. 278. [3] H. Levy and M. Sarnat, NoInternational portfolio diversification of investment portfolios., Am. Econ. Rev., vol. 60, pp. 668 675, 1970. [4] Y. Xu, Diversification in the Chinese stock market. School of Management, 2003. [5] H. G. Grubel, Internationally diversified portfolios: welfare gains and capital flows., Am. Econ. Rev., vol. 58, pp. 1299 1314, 1968. [6] P. Jorion, Value at risk: The new benchmark for managing financial risk. USA: McGraw- Hill, 2001. [7] G. Sirr, J. Garvey, and L. Gallagher, Emerging markets and portfolio foreign exchange risk: An empirical investigation using a value-at-risk decomposition technique, J. Int. Money Financ., vol. 30, no. 8, pp. 1749 1772, Dec. 2011. [8] M. Crouhy, D. Galai, and R. Mark, The essentials of risk management. New York: McGraw-Hill, 2006. [9] P. Jorion, Value at risk: the new benchmark for managing financial risk. New York: McGraw-Hill, 2007. [10] M. Jiménez-Gómez and N. Acevedo-Prins, Modelo VAR para medir la relación entre variables Macroeconómicas locales y extranjeras sobre el índice COLCAP, in Gestión del Riesgo Financiero Contribuciones desde Latinoamérica, O. R. Group, Ed. Medellín, 2018, p. 94. [11] C. Alexander, Value-at-risk models. England.: John Wiley & Sons, 2008. http://www.iaeme.com/ijmet/index.asp 1116 editor@iaeme.com

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