Is There Any Sectoral Cointegration in Indonesia Equity Market?

S A R I P A T I Vol. 10 | No. 3 ISSN: 2089-6271 | e-ISSN: 2338-4565 | https://doi.org/10.21632/irjbs


INTRODUCTION
Investment is the purchase of an asset with the hope that it will generate revenue or will appreciate before being sold for a profit in the future. Investors can invest in the capital market where they can optimize risk and return on the investments.
To successfully undertake the optimized result, investors must build an efficient portfolio of assets that can generate the highest return with the least risk through diversification.
In managing a portfolio, diversification is a risk management technique that reduces risk by allocating investments into various financial instruments without affecting the portfolio return notably. If the assets in a portfolio have different reaction in regard to the current market condition, it can be an opportunity for the investor to gain their investment from minimizing the volatility.
For the past decades, fund managers have commonly used style (growth or value stock) and market capitalization (large-cap, middle-cap, or small-cap) to build their stock portfolios that can capture the greatest potential opportunities in the market. According to Fitriana (2009), the most common methods used by fund managers in Indonesia are Markowitz, single index, and CAPM.
However, these classifications of equities can change over time due to company's performance and market condition.
Another way to minimize portfolio risk is to create an equity sector allocation method that will divide equities into some sub-groups or sectors that has some similar responses given a particular market condition. Vardharaj and Fabozzi (2007)  The research objective is to analyze whether there is any cointegration among sectors in Indonesia equity market. This study will test the cointegration among 9 sectors to find the relationships among the sectors. Cointegration test is deemed to be more appropriate than another method for its result will provide direct answer whether diversification using sectoral allocation is applicable. After that, causality test is also performed to find out whether there is any causal relationship among the sector indices. The results can provide insights for investors and fund managers for applying sectoral diversified portfolio and asset allocation strategy in the complexity of Indonesian capital market.

Literature Review
There are several past works of literature about constructing efficient portfolio through diversification. In order to build an optimum portfolio, investors must consider the risk and the return. Success in minimizing the portfolio risk will result in an efficient portfolio. Gupta & Basu (2011) stated the indifference between sector integration in developed and emerging equity market. They also found that a portfolio constructed using conditional correlations performs better, in the term of higher risk-adjusted return, than each country's benchmark index.
Gupta & Basu also found that the correlations between asset returns change over time so an accurate estimation is needed to understand the changes and help investor in choosing a portfolio that performs better in term of its risk-return. Jayasuriya (2008) also carried out a study which aimed to construct efficient portfolio frontier for China's and India's equity market. By using market capitalization as the weight and sector closing prices from January 1993 to November 2004 to make up portfolios for each country, the study found out that the investment portfolios constructed from all sectors are more efficient than those constructed from only three sectors with the largest capitalization as it is apparent that all sectors portfolio dominates in terms of risk minimization for a given portfolio return. Another study by Vardar et al (2012), which aimed to investigate the short run and long-run relationship in the Istanbul Stock Exchange over the period 1997-2011, shows that all sectors show evidence of a long-run relationship, limited short-term causal relationship because most of the sectors are likely to be influenced by macroeconomic condition and political events for long-term period. However, a study by Law & Ibrahim (2014) found that different sector reacts differently to a market condition, although they have an identical temporal result. To that extent, this study would like to know if there is any cointegration between the sector indices in Indonesia Stock Exchange. This research took into account the possibility that different time period, short run and medium run, may result in different outcomes. In the end, this study aims to know whether sectoral diversification is applicable in Indonesia's equity market.

Data
In order to find out if there is any cointegration in Indonesia equity market, this research conduct a descriptive study using data from weekly closing indices prices during the short-term period (2016) and medium-term period (2012-2016) Table 1 below.
This study examines two different periods of time in order to find the relationship among sectors in short term and middle term period, which may give different results. Five-year period of 2012-2016 is chosen to avoid economic crisis that occurred back in 2008 and to conform the nation's economic cycle which happened to be recovery phase.

METHODS
where a = r -1. The null hypothesis is that a, the coefficient of y t-1 is zero. The alternative hypothesis is: a < 0 and evaluated using the t conventionalratio for a: where a is the estimate of a, and se (a) is the coefficient standard error.
where l is the log value of the likelihood function having k parameters estimated using T observations.
Third, Johansen developed cointegration test based on VAR (vector autoregressive) using a Group object. The method estimates the maximum probability, whilst allows multiple cointegrating vectors in the multivariate system. VAR of order p is written as follows: where y t is a k vector of stationary I(1) variables, c t is a vector of deterministic variables and e t is a vector of innovations. The VAR could also be written as: If the coefficient matrix has reduced rank r <k, then there exists k x r matrices a and b each with rank r such that P = ab' and b'Y t is I(0). r is the number of cointegrating relations (the cointegrating rank) and each column of b is the cointegrating vector.
The elements of a are known as the adjustment parameters in the vector error correction model.
In this method, the estimated P matrix is from an unrestricted VAR and the test whether to reject the restrictions implied by the reduced rank of P.
The next step is to test the direction of both short and medium term relationship should there is any cointegration is found in the series by using where the first equation is testing causality of x to y, the second equation is testing causality of y to x and l represents the chosen lag length. The joint hypothesis for each of the equations will be: H 1 = not all of the bs are equal to 0 For instance, the null hypothesis for the first equation about Granger causality model above states that x does not Granger-cause y and if F-statistic is less than F-critical, the decision will reject the null hypothesis meaning that x does Granger-cause y.     Table 6 and 7. The VECM models were then tested using Least Square estimator to make sure that the sum of the squares of the residuals is minimized.  The Vector Error Correction models above (Table   6 and Table 7) are not the final equation because a good estimator has to be the one with highest adjusted R-squared. Therefore, the models are then estimated using least square estimator (LSE) to ensure that they represent the prediction correctly. In Table 8 and Table 9