Yoseva�Maria Pujirahayu Sumaji, The Calculation of�Value at Risk�Using�Variance Covariance in LQ-45 Companies 175175 The Calculation of�Value at Risk�Using�Variance Covariance in LQ-45 Companies � Yoseva�Maria Pujirahayu Sumaji Ciputra University, Surabaya, Indonesia e-mail: yoseva.maria@ciputra.ac.id Abstract: The Government of Indonesia is trying to find some solutions�to Indonesia’s economic problems.�One of the problems of Indonesia’s economic growth is the lack of capital and correct calculation of capital risks, especially in stock investments can reduce the occurrence of various capital problems in accordance with the criteria required and obtained by 9 companies analyzed.�The analytical method used in calculating market risk in stock investments in this study is variance covariance value at risk.�This method is a risk measurement through the highest estimated losses over a period of time and assumed confidence levels.�To prove the level of trust of the variance covariance value at risk method, analysis was conducted using back testing method.�The results of this study show that the method of calculating variance covariance value at risk is the right and accurate method to calculate market risk from the company’s stock. � Keywords:�VaR, variance-covariance, back testing PRELIMINARY Capital flows as a part of economic growth from the capital market, namely the Indonesia Stock Exchange. The capital market sells shares that have an economic function because the capital market provides facilities or a vehicle for meeting interests, namely those who have excess funds and those who need funds. Stocks that are known to have high risk-high return characteristics, meaning that they provide op- portunities for high profits but also have the potential to have a high risk of loss. Stock price fluctuations cause investors to gain or lose. Not only investors who have the risk of their invest- ment, but the company will also have risks that are in the company after the investor makes an investment. This risk is called speculative risk. Speculative risk, arguably includes a larger class of risk. Speculative risk is the uncertainty of events that can give rise to gain or loss. Accord- ing to Aparna Gupta (2013), speculative risk can be categorized as market risk, credit risk, strategy, business and reputation risk. Compa- nies must manage risks, especially market risks, so as not to have an impact on company earn- ings and also the profits provided to investors. This risk can occur in all sectors including the manufacturing industry sector. Company industrial sector manufacturing in Indonesia has a great influence on economic growth. The manufacturing industry is the sector most at- tractive for investors to invest. The industry ministry has been optimistic about the growth of the manufacturing industry, despite various obstacles including limited availability of infra- structure and others. According to Markowitz (1952), going public companies also have an impact on a large number of domestic and foreign investors. In investing, there are three bases that need to be calculated, namely the expected return, the level of risk, and the rela- tionship between return and risk. Investors can reduce risk by diversifying their investments. Diversified investment will provide optimal re- Business and Finance Journal, Volume 6, No. 2, October 2021 176 turns in return for investment in a portfolio. Markowitz (1952) has proven that investment risk will be reduced when combining several assets in a portfolio. Yoseva (2017) states that there are several methods of measuring risk, namely the tradi- tional method and the value at risk method. According to the traditional method of risk measurement, quantification of risk is carried out by measuring sensitivity by observing changes in one of the risk factors and their effect on the gain or loss of a portfolio. Traditional measure- ment results are the amount of loss experi- enced, but these measurements do not provide an idea of the probability of the potential amount or loss that may be experienced. In addition, the measurement is traditionally used on indi- vidual assets, so that each asset has a different risk measurement method (Sartono, 2006). Ac- cording Sartono (2006), when each of these assets are combined into one portfolio, risk measurement becomes difficult because many methods used for each calculation of the asset. In 1994, JP Morgan developed the Value at Risk (VaR) method which is then used very widely to measure various types of risk. Ac- cording to Best (1999), Value at Risk (VaR) is a statistical risk measurement method that esti- mates the maximum loss that may occur at a certain level of confidence in a portfolio. There are several models in measuring VaR, namely the Variance-Covariance model, the Historical Simulation model, and the Monte Carlo model. Previous research (Yoseva, 2017) found that calculating VaR using the Variance-Covariance model resulted in a greater undiversified VaR compared to the historical calculation model. According to Butler (1999), estimating potential losses that could arise from adverse changes in market conditions is a key element of risk management. For financial institutions and treasuries companies around the world, Value at Risk (VaR) is fast emerging as the dominant methodology for estimating exactly how much money is at risk on a daily basis in financial markets. Crouhy (2001) states that; VaR is the worst possible loss that you can expect from holding a security or portfolio over a period of time, given the specified level of probability (known as the ‘confidence level’). This research was conducted to determine the validity of risk calculations using the variance covariance method, followed by a backtesting test to see that the calculation method used is valid and accurate, or vice versa. This study uses the objects of the manufacturing industry in Indonesia which are members of the LQ-45 where the company is the most active for the last 3 years and has the highest market capitali- zation for the last 12 months, because it can represent the values of daily market trading, and to find out whether this method is used, and can be used as a reference for calculating risk, especially for companies that have a major contribution to economic growth in Indonesia. LITERATURE REVIEW Previous Research This study is a continuation of previous studies, where several researchers tested the measurement of potential losses (VaR) using the Variance-Covariance model and the Historical Simulation model. In 2005, Oom Komariyah conducted research on the risk analysis of stock market investment against Sharia in the 10 Jakarta’s Islamic Index (JII). In the study sample, 10 stock issuers representing 30 Sharia, whose shares were consistently traded in the first period from November 2002 to December 2004, Yoseva�Maria Pujirahayu Sumaji, The Calculation of�Value at Risk�Using�Variance Covariance in LQ-45 Companies 177 were taken on the Jakarta Stock Exchange. The research methodology used is the methodologi- cal value of the Risk Variance-Covariance model and the Historical Simulation model. The re- sults of the study conclude that the second model is applicable to measure a maximum of 10 losses of Sharia stocks that are included in the Jakarta Islamic Index. To test the validity of the model is to look at the failure rate (failure rate) with the Kupiec test. In 2007, a research entitled Value at Risk Method: An Application For Swedish National Pension Fund (AP1, AP2, AP3) was conducted by students of Blanka Grubjesic University of Skovde Sweden Using a Parametric Model. The study was conducted in the calculation of the Daily Earning at Risk with a parametric or Variance-Covariance model on three pension fund asset portfolios consisting of 20 types of stocks traded on the Swedish Exchange, 20 foreign stocks and 10 bonds. The period exam- ined was from January 3, 2005, to December 30, 2005, with a 95% confidence level. The resulting conclusion emphasizes that the appli- cation of a simple parametric model approach can easily be applied to the investment of the Swedish national pension fund (AP pension fund). Understanding Investment and Risk According to Bodie (2009) ordinary shares have two important characteristics as an invest- ment tool that claims the remainder (residual claim) and limited liability. Investment is a vari- ety of activities that are capable of investing a number of funds in these assets. Investment is the attachment of a number of funds or other resources to do this time, with the goal of obtaining a profit in the future (Tandelilin, 2010). This objective affects investment because of a need or need where the investment occurs spon- taneously in accordance with the development of life needs, as well as investment because of an expectation of profit and profit. Apart from motivation, there are also aspects that can arise in the investment, namely the aspect of sacri- fice. In this case, an investor must be answered resources, the aspect of hope to the investment which he did for the public welfare, the aspect of risk that each person can conduct business investment to earn a profit, but the reality is not everyone can make a profitable business, will there is a turnover or even a loss, the time aspect in which to invest requires patience in waiting for the expected return and the type aspects where each investment likes to take different forms and risks. According to Hanafi (2006) is a risk, the imbalance between the actual rate of return with the expected rate of return (ER). Risk is the prospect of an unwel- come result (operating as the standard devia- tion). With this, it can be concluded that the definition of risk is a condition that arises due to uncertainty with completely unfavorable and possible impacts. According to Fabozzi (2007) portfolio risk is not only determined by the risk-weighted average shares that make up the portfolio, but is also influenced by the correla- tion coefficient factor between the level of stock earnings. Meanwhile, a variance portfolio consisting of two or more assets depends not only on the variance of each asset but also on how close the relationship is between the two asset. Investments and Stock Returns One of the goals of investors in investing is to make a profit. If investing does not generate a profit, of course investors will not invest. So, broadly speaking, the main objective of all in- Business and Finance Journal, Volume 6, No. 2, October 2021 178 vestments is to make a profit. According to Tandelilin (2010), the expected profit from a portfolio is the weighted average of the ex- pected rate of return of each individual asset that makes up the portfolio. The presentation of the value of the portfolio that has been invested in each individual asset in the portfolio is known as portfolio weighting. If all portfolio weights are added and have a total of 100% or 1.0, then all funds have been invested with the expected portfolio return (Tandelilin, 2010). RESEARCH�METHODOLOGY Type of Research and Sampling This type of research is quantitative re- search. According to Gujarati (2001), quantita- tive research focuses on research using mea- sured data. The type of data also uses quantita- tive data to calculate returns and VaR. Sources of data in this study are secondary data sources. The calculation used in this research is the manufacturing industry in Indonesia which is registered in LQ-45, which is 45 companies registered. The sampling technique in this study was nonprobability sampling with purposive sampling type. The criteria used are based on certain reasons or rations. For the research, the criteria used are with certain considerations, namely: 1. Indonesian manufacturing companies are listed on the Indonesia Stock Exchange with active stocks and meet the criteria for the 45 most active stocks in the last 3 years. 2. Manufacturing companies have a market capitalization of more than Rp 1 trillion, because they can represent the values of daily market trading, and are even able to become an index mover in the formation of the JCI on the Indonesia Stock Exchange. Table 1 Sample Classification Source: Processed data, 2021 The number of stock data as an investment portfolio after the determination of these crite- ria is 9 shares. The daily data collected for each share is as much as 780 daily share price data. Calculation Phase In general, the calculation stages in mea- suring the risk of stock market investment poli- cies in manufacturing companies use the Value at Risk model, including: 1. Determine the type and number of shares to be used according to the sampling criteria 2. Calculate expected returns using geometry return. 3. Calculating portfolio return using a formula. 4. Calculating VaR using Matrix V, C, VC, VCV. 5. Determine the Variance of each stock and the Variance Covariance portfolio model. Testing�of�Validity The calculation of VaR in this study uses data return stock, to measure the validity of testing needs to be carried out VaR data, which includes the distribution pattern of the classical No. Criteria Number of Samples 1 Indonesian manufacturing companies are listed on the Indonesia Stock Exchange with active stocks and meet the criteria for the 45 most active stocks in the last 3 years. 30 Companies 2 Manufacturing companies have a market capitalization of more than Rp. 1 trillion, because they can represent the values of daily market trading, and are even able to become an index mover in the formation of the JCI on the Indonesia Stock Exchange. 9 Companies Yoseva�Maria Pujirahayu Sumaji, The Calculation of�Value at Risk�Using�Variance Covariance in LQ-45 Companies 179 assumptions. To determine whether this model is valid or not, then do testing Back through Test Kupiec by using the data submarines a year. In Test Kupiec is carried Test in which the level of trust Kupiec that is used is 95% and is done with a test 252 transaction data for a period of 1 year. Here’s how calculation to Kupiec Test: 1. If the failure rate (N) numbering is between 6 < N < 21, then the VaR model is consid- ered valid for measuring potential losses. 2. If N < 6 then the model is considered too conservative to measure potential losses. 3. If N > 21 then the model is considered too moderate to measure potential losses. RESEARCH RESULTS AND DISCUSSION Stock Exposure Calculation The selection of shares by the management of Indonesian manufacturing companies is based on the consideration of investment diversifica- tion in various kinds of stocks. If the case decrease in the return of an asset class, it is expected that the return on other asset classes increase, so the return on the overall portfolio relatively fluctuated. The following is a stock portfolio arrangement used in this study: Based on the exposure of stock invest- ments made by companies manufacturing Indo- nesia looks issuers that have dominated by sub automotive sector (39,49%) namely ASII (Astra), things can be understood considering the very high development of automotive companies in Indonesia due to popular demand the market will be motorized vehicles. The type of data in this research is a continuous data and time series, so as to calcu- late the result of the return day of her using the method of calculation of geometric returns are included in a logarithmic function of the ratio of the price. The use of geometric returns to avoid biased results with respect to the magni- tude of the effect is divided as a common element in calculations using arithmetic returns. Based approach to geometry return, the next is to calculate the daily for the nine selected stocks. After knowing the daily return of each stock in a predetermined period, the daily port- folio return of each stock is calculated. Then, the return t is then assessed the proportion (weighted) of each share portfolio. 100% weight- ing occurs when the overall portfolio weight is aggregate. Stock Lot Share Volume Closing Price Portfolio Value Weight ASII 932. 481 93.248. 100 6.450 601.450.245.000 39,49% CPIN 154. 889 15.488. 900 3.345 51.810.370.500 3,40% GGRM 14. 341 1.434. 100 58.350 83.679.735.000 5,49% ICBP 45. 212 4.521. 200 14.450 65.331.340.000 4,29% INDF 179. 966 17.996. 600 6.200 111.578.920.000 7,33% INTP 54. 173 5,417, 300 19.700 106.720.810.000 7,01% KLBF 1.027. 517 102.751.700 1.335 137.173.519.500 9,01% SMGR 166. 838 16.683. 800 11.050 184.355.990.000 12,11% UNVR 49. 255 4.925. 500 36.700 180.765.850.000 11,87% Total 262.467.200 1.522.866.780.000 100% Table�2�Indonesian Manufacturing Company Stock Exposures Source: Processed data, 2021 Business and Finance Journal, Volume 6, No. 2, October 2021 180 Classic Assumption Test The type of classical assumption test used is the normality test. This test is conducted to determine whether the nine stocks return dis- tribution data is normally distributed or not/ skewed. Based on the normality test showed that the overall 9 stock experienced a data abnormality in as right value Asymp. SIG (two- tailed) were smaller than at 0,05. Therefore, in calculating Variance-Covariance need to calcu- late z-score used Cornish Fisher. After her test for normality, in the know that the data is experiencing lack of normal late the data, there- fore it is necessary for the recalculation of the value of �. The � value used in the normal distribu- tion comes from the normal use of the Z-score value. While the value on the distribution of abnormal use is generated from an adjustment through the correction Z. Customization per- formed on the data form � Skewness normality to wear Expansion Cornish-Fisher. In addition to the normality test, hetero- scedasticity test is also conducted to determine homoscedasticity or heteroscedasticity data. Based on the results of the data, the return obtained is homoscedasticity because the t-sig- nificance is more than 0,05. For this reason, the calculation of return volatility using the Expo- nentially Weighted Moving Average (EWMA) approach is no longer necessary. Calculation of Variance Covariance VaR for each share The following is the stage of calculating the variance covariance of each stock:� Table�3�Matrix�Calculation�V Source: Processed data, 2021 Code ASII CPIN GGRM ICBP INDF INTP KLBF SMGR UNVR ASII 0,02148 CPIN 0,03082 GGRM 0,02093 ICBP 0,02037 INDF 0,02140 INTP 0,02434 KLBF 0,02128 SMGR 0,02332 UNVR 0,02087 Table 4�Matrix�Calculation�C Source: Processed data, 2021 Code ASII CPIN GGRM ICBP INDF INTP KLBF SMGR ASII 1 0,47436 0,32224 0,37442 0,45320 0,49842 0,42130 0,51168 CPIN 0,47436 1 0,42188 0,36999 0,39591 0,44034 0,40725 0,47591 GGRM 0,32224 0,42188 1 0,31617 0,33692 0,35293 0,33643 0,36954 ICBP 0,37442 0,36999 0,31617 1 0,36814 0,33278 0,43199 0,30018 INDF 0,45320 0,39591 0,33692 0,36814 1 0,48233 0,40005 0,40269 INTP 0,49842 0,44034 0,35293 0,33278 0,48233 1 0,43545 0,68637 KLBF 0,42130 0,40725 0,33643 0,43199 0,40005 0,43545 1 0,41835 SMGR 0,51168 0,47591 0,36954 0,30018 0,40269 0,68637 0,41835 1 Yoseva�Maria Pujirahayu Sumaji, The Calculation of�Value at Risk�Using�Variance Covariance in LQ-45 Companies 181 The VaR value shows the maximum pos- sible (potential) loss on a financial asset or portfolio in a utilization period with a certain level of confidence. In the table above is known that the value of VaR is the highest in the period of 1 day per share occurred on GGRM shares amounting to Rp 2.842,41, while the value of VaR most low occurred on KLBF Table 5�Calculation of Matrix CV Source: Processed data, 2021 Table 6 Calculation of Matrix VCV Source: Processed data, 2021 � UNVR 0,42408 0,40942 0,34128 0,34605 0,41037 0,37137 0,46918 0,38095 1 Code ASII CPIN GGRM ICBP INDF INTP KLBF SMGR UNVR ASII 0,000461 0,000314 0,000145 0,000164 0,000208 0,000261 0,000193 0,000256 0,000190 CPIN 0,000314 0,000949 0,000272 0,000232 0,000261 0,000330 0,000267 0,000342 0,000263 GGRM 0,000145 0,000272 0,000437 0,000135 0,000151 0,000180 0,000150 0,000180 0,000149 ICBP 0,000164 0,000232 0,000135 0,000414 0,000160 0,000165 0,000187 0,000143 0,000147 INDF 0,000208 0,000261 0,000151 0,000160 0,000457 0,000251 0,000182 0,000201 0,000183 INTP 0,000261 0,000330 0,000180 0,000165 0,000251 0,000592 0,000226 0,000390 0,000189 KLBF 0,000193 0,000267 0,000150 0,000187 0,000182 0,000226 0,000452 0,000208 0,000208 SMGR 0,000256 0,000342 0,000180 0,000143 0,000201 0,000390 0,000208 0,000543 0,000185 UNVR 0,000190 0,000263 0,000149 0,000147 0,000183 0,000189 0,000208 0,000185 0,000435 Code ASII CPIN GGRM ICBP INDF INTP KLBF SMGR UNVR ASII 0,000461 0,474359 0,322242 0,374418 0,453203 0,498423 0,421304 0,511683 0,424078 CPIN 0,474359 0,000949 0,421882 0,369994 0,395911 0,440341 0,407253 0,475913 0,409423 GGRM 0,322242 0,421882 0,000437 0,316169 0,336921 0,35293 0,336426 0,369543 0,341284 ICBP 0,374418 0,369994 0,316169 0,000414 0,368141 0,332778 0,431989 0,300177 0,346048 INDF 0,453203 0,395911 0,336921 0,368141 0,000457 0,482328 0,400054 0,402692 0,410373 INTP 0,498423 0,440341 0,35293 0,332778 0,482328 0,000592 0,435452 0,686373 0,371374 KLBF 0,421304 0,407253 0,336426 0,431989 0,400054 0,435452 0,000452 0,418354 0,469185 SMGR 0,511683 0,475913 0,369543 0,300177 0,402692 0,686373 0,418354 0,000543 0,380949 UNVR 0,424078 0,409423 0,341284 0,346048 0,410373 0,371374 0,469185 0,380949 0,000435 Table�7�Calculation of Variance Covariance Value at Risk�in a period of�1 day, 5 days, 10 days, and 20 days Source: Processed data, 2021 Code Price Exposure St. Deviation Z correction VaR A Day VaR 5 Days VaR 10 Days VaR 20 Days ASII 6.450,00 0,02148 2,47909216 343,38947 767,84220 1085,892853 1535,6844 CPIN 3.345,00 0,03082 2,646182746 272.80133 610,002308 862,6735373 1220,00462 GGRM 58.350,00 0,02093 2,327553661 2.842,41023 6355,8225 8988,490381 12711,645 ICBP 14.450,00 0,02037 2,577873584 758,63385 1696,35686 2399,010879 3392,71372 INDF 6.200,00 0,02140 3,109308725 412,46173 922,292466 1304,318513 1844,58493 INTP 19.700,00 0,02434 2,65294 1.272,01305 2844,30765 4022,458452 5688,6153 KLBF 1.335,00 0,02128 2,491867898 70,79996 158,31352 223,8891277 316,627041 SMGR 11.050,00 0,02332 2,844247963 732,80188 1638,59482 2317,323011 3277,18963 UNVR 36.700,00 0,02087 1,804364288 1.381,75932 3089,70778 4369,506645 6179,41556 Business and Finance Journal, Volume 6, No. 2, October 2021 182 shares amounting to Rp 70,79. For the value of VaR in the period of time 5 days ahead, the highest occurred in GGRM shares amounting to Rp 6.355,82 while the lowest occurred in s AHAM KLBF amounting to Rp 158,31. For the VaR value within the next 10 days, the highest was GGRM shares amounting to Rp 8.988,49, while the lowest occurred in KLBF shares with Rp 223,88. Finally, for the value of VaR in the period of the next 20 days per share, the highest in the shares GGRM Rp 12.711,64, while the lowest value of VaR exist on KLBF shares worth Rp 316,62. VaR Model Testing After calculating the VaR value, to deter- mine whether the value is accurate or not, a Backtesting test is performed (Jorion, 2007). One of the backtesting models is done with the Kupiec test (Kupiec, 1995), namely by compar- ing the test results between the predicted values of the actual VaR return data. Testing Back through Test Kupiec by using the data subma- rines a year. In Test Kupiec is carried Test in which the level of trust Kupiec that is used is 95% and is done with a test 252 transaction data for a period of 1 year. The following Kupiec test is evaluated: 1. If the failure rate (N) numbering is between 6 < N <21, then the VaR model is consid- ered valid for measuring potential losses. 2. If N < 6 then the model is considered too conservative to measure potential losses. 3. If N > 21 then the model is considered too moderate to measure potential losses. 4. The following is the result of VaR backtesting testing Table 8�VaR�Backtesting�Results Code Difference- Covariance Validity (<21) ASII 8 Valid CPIN 8 Valid GGRM 10 Valid ICBP 7 Valid INDF 7 Valid INTP 16 Valid KLBF 10 Valid SMGR 7 Valid UNVR 18 Valid From the results table above stated that the failure rate generated by the model Vari- ance-Covariance very small as evidenced by value 6