PORTFOLIO THEORY BASED APPROACH TO RISK MANAGEMENT IN ELECTRICITY MARKETS: COLOMBIAN CASE STUDY. Yaneth C. Correa Martinez Leonardo Bedoya Valencia

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1 Proceedings of the 2003 Systems and Information Engineering Design Symposium Matthew H. Jones, Barbara E. Tawney, and K. Preston White, Jr., eds. PORTFOLIO THEORY BASED APPROACH TO RISK MANAGEMENT IN ELECTRICITY MARKETS: COLOMBIAN CASE STUDY Yaneth C. Correa Martinez Leonardo Bedoya Valencia Engineering Management and Systems Engineering Department 129 Kaufman Hall Old Dominion University Norfolk, VA 23529, USA ABSTRACT Since 1994, the Colombian electricity market has been operating under a new structure. The Colombian government undertook a liberalization process, and trading activity was created. The traders face not only increasing competition, but also high-risk levels due to factors not considered previously. In the trading system, the agents are implicitly undertaking the risk associated with market variations and are demanding for new procedures to manage risk. This work is an initial attempt to introduce an existing financial methodology (portfolio theory) to develop a risk management strategy for the electricity trading in Colombia which was developed in three steps. 1 THE ENERGY MARKET IN COLOMBIA In this restructuring of utilities in Colombia, new roles have been created and a liberalized market has arisen. In this new structure, energy trading in the electricity market has become a risky activity. Public and private organizations (named agents in this work), which trade in this market, are facing higher levels of uncertainty due to both its economic and physical structure. On the other hand, in this new market structure, these risks and uncertainties are accepted by the electricity traders and managed by using both long and short-term contracts. The long-term contracts that are signed by the traders over the counter and the short-term contracts that are signed in the spot market and traded hourly. 2 FEATURING THE CONTRACTS In general, a long term contract is a financial figure that assures a defined quantity of an economic good, electricity in this case, on a specific date in the future, during a given period of time at an agreed price fixed in the contract (contract price). Based on this definition, certain features of the contract can be given in order to define groups of contracts that exhibit a similar relation risk/return (i.e. those contracts having similar risk for a given level of return). Contract price is chosen as a response variable and some others variables are defined as influencing factors. Two generic kinds of long term contracts are defined in the Colombian energy market, take or pay (PC) and pay for the demand (PD). By modifying quantity and terms of delivery, multiple types of contracts are created. Considering the transition status to the new market, brainstorming was chosen to identify which factors were influencing the contract price. Two sessions with traders and one with market coordinator representatives were carried out. As result, the next factors were selected and the corresponding factor levels were defined in order to obtain the groups of contracts having similar behavior, each of these sets were named investment opportunities: Contract Type: In order to know variations due to the type of contract. Term of Investment: In order to determine if the contract price is influenced by the duration of the contract. Spot Price Level: In order to verify if the spot price level is considered by electricity traders to fix the contract price. Market share: In order to determine if the market share level of electricity traders is influencing the contract price. Relative contract size: In order to gather possible variations on contract price due to the size of the contract. ANOVA was used for featuring the different types of contracts. This method attempts to explain the variation of the contract price based on components linked to the levels of the factors provided above. A mixed multi-factorial design (2 3 and 3 2 ) were proposed to conduct an analysis over the 35

2 contract price. Direct effects and interactions between factors were sought. Finally, groups of contracts (i.e. investment opportunities) were defined. The results obtained in this analysis are summarized as follows: The contract price is affected by the term of investment, the relative contract size, and the contract type. When electricity traders are fixing the contract price their decision is based upon the spot price level for the previous month. The term of investment is hidden by the spot price effect. The relative contract size has a considerable effect on the contract price. The contract type has a significant effect on the contract price. The interaction between the spot price level and the term of investment are hiding the effect that the latter has on the contract price. Because of this interaction, the change between levels in the term of investments was not gathered. However, based in the Figures 1 and 2, an effect between the contract price and term of investment can be observed. Precio Interaction Plot Horizonte Corto Largo Medio N.P.Bolsa Figure 1: Interaction between spot price level and term of investment. Precio Means and 95.0 Percent LSD Intervals Corto Largo Medio Horizonte Figure 2: Means levels for term of investment. 3 GENERAL RETURNS MULTI-INDEX MODELS USING ARBITRAGE PRICE THEORY (APT) The general returns multi-index models (Elton and Gruber; 1995) were developed in order to determine the returns behavior based upon the investment opportunities in the market. The assumption underlying these models is that investment opportunities prices move because of both movement of the market and variations of the additional sources. By incorporating these additional sources into the models, it is possible to know the return of the investment opportunities as well as the impact of external events on their behavior. The arbitrage theory states a general multi-index model based on an unique price law named the APT model (multi-index equilibrium model). The general multi-index return equation is: R i = R i11 i22 + K i( j 1) j 1 ij j + K i( L 1) L 1 ill (1) Where: j = R j R is the expected additional return for the electricity trader, based on the responsiveness of the investment opportunities to the index j. In other words, j s are the returns obtained when the trader decides to take the risk associated with the index j. R represents the risk free rate. The L-dimensional hyper plane is represented by Equation 1 is used to obtain the investment opportunities return. Many of the world s energy markets are changing their structure in order to ease the risk management process (Fleten, 2000). They are attempting to become more financially based markets as exemplified by both the English and Norwegian markets (Fleten, 2000). The Colombian energy market is also moving toward this direction, therefore, more financial tools and a more structured market is the likely result. Based on this statement, the arbitrage price theory is used to derive the general return multi-index model. In order to use the APT theory for determining the investment opportunities return, historical return were measured, then a set of economic and physical indexes were defined, and finally, the risk free rate was determined. By utilizing the orthogonalization process (Elton and Gruber; 1995), a return multi-index model was applied for the set of investment opportunities. This model is shown in the equation 2: R i = RF (2) i itrm ic C TRM idtf isoi DTF SOI iea ipib EA PIB iqb ipb QB PB iqc QC 36

3 This process consists of fitting the n-dimensional hyper plane (ten in this case, nine indexes and the return) to the available historical information for the twelve sets of investment opportunities. The ij, coefficients to be estimated, are the increment (or decrement) of the return in the investment opportunity i, due to a variation in the index j gained for the electricity trader. Relying on these results, just the index corresponding to the inflow to reservoirs was significant and its estimated coefficient was These results are reasonable because about of 70 percent of the electricity generation in Colombia is based on hydraulic power plants (ISA, 1997). Also, an informal statement, which has been circulating in the Colombian energy market, is supported by this theoretical model. Additionally, these results could demonstrate faults in the model s adjustment due to several reasons: Both economic and physical variables may not have been measured appropriately. The Colombian energy market has not yet defined methodologies and procedures to quantify the risk of the different factors affecting the market. This field is open for further research. Given the novelty of the Colombian energy market, there is not enough historical information about some of the investment opportunities. Therefore, the reliability of the model s results could be questionable. 4 PORTFOLIO THEORY AS ALTERNATIVE TO RISK MANAGEMENT After a set of investment opportunities (assets) has been characterized and the model of valuation under the approach of the theory of arbitration has been built, an electricity trader has the necessary elements to undertake the next task of the investment process: the risk management evaluation. This task consists of having a set of investment opportunities, finding out which and what proportion must be invested to obtain the most efficient risk/return relationship considering the investors risk condition or preferences (Elton and Gruber, 1995). Risk management through portfolio theory appears as an alternative to accomplish this task. The theory of efficient portfolios, initially introduced by Harry Markowitz in 1952, has been implemented on diverse markets and is a basic concept for risk management. This theory assumes the investors are seeking the optimal mean-variance relationship, i.e., they look for minimum variance portfolios for an expected return level. It is suggested that the return variance is an appropriate measure of risk (Elton and Gruber, 1995). The mean-variance analysis describes how the intrinsic risk of the current investment opportunities contributes to the portfolio s risk and return. Based on that information, the investor is allowed to make decisions about the portfolio allocation. Deriving the efficient frontier in the Markowitz s model, the estimation of the variance-covariance matrix becomes necessary as well as the expected mean return and variances of the investment opportunities set. In a general multi-index return model, as the one used in the arbitrage theory, the direct estimation is not necessary. The estimation of the variance-covariance matrix could be done by estimating the responsiveness of the return of each investment opportunity to the defined indexes set and the variances of those indexes. Figure 3 shows the efficient frontier for the investment set available in the Colombian energy market. Frontera Eficiente 220% 210% L-G-PD 200% 190% 180% 170% 160% 150% C-G-PC 140% 130% 120% 110% 100% 90% 80% M-G-PC 70% C-P-PD 60% 50% 40% C-P-PC M-G-PD C-G-PD M-P-PD 30% 20% L-P-PD 10% 0% -10% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 110% 120% 130% 140% 150% 160% 170% 180% 190% 200% 210% 220% 230% 240% -20% L-P-PC M-P-PC -30% -40% L-G-PC -50% Rendimiento [%] Riesgo [%] Figure 3: Efficient Frontier The distribution for the minimum variance portfolio is showed in Table 1: Table 1: Portfolio of Minimum Risk Minimum Risk 74.52% Return 28.10% C-P-PC 79.16% C-P-PD 15.40% M-P-PC 0.00% M-P-PD 0.00% L-P-PC 0.00% Allocation L-P-PD 4.11% C-G-PC 0.00% C-G-PD 0.00% M-G-PC 0.00% M-G-PD 0.00% L-G-PC 1.33% L-G-PD 0.00% Three important conclusions are derived from these results: Since the returns of the investment set are high and are positively correlated, the total risk of the portfolio is accumulative. Otherwise, as a new 37

4 opportunity of investment is included in the portfolio, the total risk increases. The opportunities set in the Colombian energy market have high returns associated with high-risk levels. That fact could be a consequence of estimating the returns based on the spot price, which has a high and positive correlation with the returns of the opportunities set and volatility near to 150 %. Given the current Colombian market structure and the characteristics of the opportunities set, it would seem that risk management through diversification is not viable, at least using it in a traditional manner. To determine the efficient frontier and the minimum variance portfolio, all historical information (Jul Sept. 99) was used. In the modern portfolio theory, in order to determine the portfolio investment term, the traders have to consider both the time basis of available historical information and the period of the opportunities in the preferred portfolio. The need of a more robust tool becomes evident. The new tool should allow portfolio performance evaluation and continuous restructuring as opportunities are exercised. In this sense, some authors have explored the use of stochastic dynamic programming. (Freight et al, 2000). 5 CONCLUSIONS AND RECOMMENDATIONS This work tries to develop a methodological approach in order to carry out the risk management process in the Colombian energy market. The approach can be summarized in three steps: Featuring investment opportunities: Information management, factor and levels of factors definition, and investment opportunities and features are carried out in this step. Determination of the return model: Economic and physical indexes definition, multi- index return model definition, and estimation of the parameters of the model are developed here. Management risk strategy: Selection and implementation of the management risk strategy are proposed in this step. Concerning the first step, it is possible to conclude: Given the great diversity of investment opportunities in the Colombian energy market, the availability of both information and tools for grouping the diverse types of investment opportunities are important. By using ANOVA, it was possible to find that the contract type, the term of investment, and the relative contract s size are key features in grouping the investment opportunities. Cluster analysis, brainstorming and fuzzy logic are other tools that can be used to address the high variability in the Colombian electricity market in order to group the investment opportunities. Concerning to the second step, it is possible to conclude: As shown in section 3, the hydrological factor has great influence on electricity prices in the Colombian energy market as well as the economic environment. The model proposed exhibits a large quantity and variety of indexes, given the novelty of the Colombian energy market; there is not enough historical information to estimate the model. The CAPM or unique index is suggested to estimate the investment opportunities return. Additionally, as shown in section 3, it is possible to state that the hydrological factor can become the index. The configuration of common market indexes, similar to the other financial markets, can be another research field. Such an index can be used to estimate the investment opportunities return. Concerning to the third step, it is possible to conclude: All of the investment opportunities are affected by physical variables (i.e. the inflow to reservoirs). This fact is introducing high levels of variability due to non-diversifiable risk and diversification risk management is not an adequate strategy. As stated in section 4, all of the investment opportunities are high and positively correlated. Moreover, the structure of variance-covariance matrix shows positive correlation between all of investment opportunities, making the risk management process using diversification difficult. Based on the shown results, in the Colombian electricity market, all investment opportunities exhibit high returns associated with high risk s levels. Concerning to the methodological approach it is possible to conclude: A methodological approach is given in order to deal with the risk management process in the Colombian energy market. The steps presented in this work could be implemented in other future utilities markets, by taking into account the specific structure of those markets. This methodological approach uses a set of proven tools, but the implementation of new tools is strongly suggested in order to deal with the three steps stated above. On the other hand, attempting to understand the risk management process in the Colombian energy market, using this approach, an educational tool can be developed. 38

5 REFERENCES Bai, J., NG, S Determining the Number of Factors in Approximate Factor Models, Boston College, Chestnut Hill, MA. Bodie, Z., A. Kane, and A. Marcus Investments, Third Edition, New York. McGraw Hill, Brealey, R A., and S. C. Myers Principles of Corporate Finance. McGraw-Hill. Cochrane, J.H Portfolio Advice for Multifactor World. National Bureau of Economic Research. Cambridge, MA. Comisión de Regulación de Energía y Gas Resoluciones No. 24 y 25. Bogotá, Colombia. Comisión de Regulación de Energía y Gas Resolución No. 97. Bogotá, Colombia. Comisión de Regulación de Energía y Gas Resolución No Bogotá, Colombia. Congreso de Colombia Ley de Servicios Públicos: Ley 142. Bogotá, Colombia. Congreso de Colombia Ley de Servicios Públicos: Ley 143. Bogotá, Colombia. Electric Power Analyst Why Electricity Prices Spike?. Elton, E., and M. Gruber Modern Portfolio Theory and Investment Analysis, Fifth Edition, New York. John Wiley and Sons. Enron Managing Energy Price Risk, First Edition, London. Fama E Multifactor Portfolio Efficiency and Multifactor Asset Pricing. Journal of Financial and Quantitative Analysis, New York 31 (4). Fleten, S.-E., S. W. Wallace, and W. T. Ziemba Hedging Electricity Portfolios Via Stochastic Programming. Norwegian University of Science and Technology, University of British Columbia. Fusaro P Energy Risk Management, First Edition, New York. McGraw Hill. Grinblatt, M., and S. Titman, S Financial Markets and Corporate Strategy, First Edition, New York. McGraw Hill. Hill, C. W. L., and G. R. Jones Strategic Management Theory: An Integrated Approach, Third Edition, Boston. Houghton Mifflin Company. Interconexión Eléctrica S.A. E.S.P Análisis del Mercado Mayorista de la Electricidad en Colombia, Primera Edición, Medellín. Colina.. Interconexión Eléctrica S.A. E.S.P Informe del Mercado de Energía Mayorista. Medellín, Colombia. Interconexión Eléctrica S.A. E.S.P Informe del Mercado de Energía Mayorista. Medellín, Colombia. Longva, P., and G. Keers Risk Management in the Electricity Industry. IAEE 17th Annual International Conference. Stavanger, Norway. Markowitz, H Portfolio Selection, Journal of Finance 7 (1). Statistical Graphics Corporation Statgraphics: Statistical Graphics System. Maryland. Pilipovic, D Energy Risk. Valuing and Managing Energy Derivatives, First Edition, New York. McGraw Hill. AUTHOR BIOGRAPHIES YANETH C. CORREA-MARTINEZ is a Ph.D. Student at Engineering Management and Systems Engineering Department of Old Dominion University. Her former university was the National University of Colombia, where she earned a degree in Engineering Management and a M.Sc. in Systems Engineering. Currently, her research interest is Systems of Systems Engineering. She can be contacted by at <ycorr001@odu.edu> LEONARDO BEDOYA-VALENCIA is a Ph.D. Student at Engineering Management and Systems Engineering Department of Old Dominion University. His former university was the National University of Colombia, where he earned a degree in Industrial Engineering and a M.Sc. in Systems Engineering. Currently, his research interests are Systems Engineering, Scheduling and Simulation. He can be contacted by at <lbedo001@odu.edu> 39

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