Performance Evaluation of Stock Price Indexes in the Indonesia Stock Exchange

This study evaluates the performance of stock price indexes in the Indonesia Stock Exchange by using Sharpe Index, Treynor Ratio, Jensen Alpha, Adjusted Sharpe Index, Adjusted Jensen Index and Sortino Ratio. The stock price indexes evaluated are the Jakarta Composite Index (JCI), Sectoral Index consisting of 10 sectoral stock price indexes, LQ45 Index, Jakarta Islamic Index (JII), Kompas100 Index, BISNIS-27 Index, PEFINDO25 Index, SRI-KEHATI Index, Main Board Index (MBX), Developed Board Index (DBX). Data used in this research is daily closing data of stock price indexes studied and riskfree interest rate represented by BI rate during period January 3, 2011, until July 17, 2017. Data were obtained from Bloomberg. The results of this study indicate that only three stock price indexes perform better than risk-free and stock-market instruments when calculated by using Sharpe Index, Treynor Ratio, Jensen Alpha, Adjusted Sharpe Index, and Adjusted Jensen Alpha Index. Meanwhile, when calculated by using the Sortino Ratio, the stock price index of miscellaneous industry sector has the best performance.


Research Background
Before Markowitz (1952) introduced his famous Portfolio Theory, the success of investment was often only seen from the return generated, so the return became the main consideration for investors in investing (Zulkafli, Ahmad, & M., 2017).Markowitz (1952) through his theory states that the purpose of investors is to increase their prosperity and to achieve it, they need to hold diversifications to reduce risks by not sacrificing the return.
One indicator of stock portfolio is the stock price index especially the composite.This type of stock price index can become a benchmark whether a stock portfolio that includes into the stock price index calculation shows increasing values.
In any stock market, a stock price index is often formed to become a benchmark for stock market movement and the Indonesia Stock Exchange is no exception.Based on the official website of Indonesia Stock Exchange (www.idx.co.id), until the end of 016, there have been 11 stock price indexes in Indonesia Stock Exchange.The stock price indexes are Composite Stock Price Index (CSPI), Sectoral Index consisting of 10 sectoral stock price indexes, LQ45 Index, Jakarta Islamic Index (JII), Kompas 100 Index, BISNIS-27 Index, PERFINDO25 Index, SRI-KEHATI Index, Main Board Index (MBX), Developed Board Index (DBX), and Individual Stock Price Index.The indexes, except the Individual Stock Price Index, may be used to represent the performance of share portfolios included into the index calculations.
For instance is JII, it can be utilized to see the performance of sharia stock portfolios included in the JII calculation.
To see the performance of the portfolios, two measurement instruments can be used; they are Sharpe Index introduced by Sharpe (1966) and Treynor Ratio introduced by Treynor (1965).
The instruments have been widely used by practitioners and academicians in investment management (Bednarek, Patel, & Ramezani, 2014;Low & Chin, 2013).Sharpe Index and Treynor Ratio even become standards in industry in measuring risk-adjusted returns (Deborah Kidd, 2011;Scholz & Wilkens, 2005) and the most widely cited measurement instruments by researchers in portfolio management (Lo, 2002).Nevertheless, these two portfolio performance measurement instruments are not free from criticisms.Cvitanic, Lazrak, and Wang (2007) mention that the utilization of Sharpe Index may cause problems due to time differences.So, the effort to maximize the Sharpe Index is different for short and long term.Deborah Kidd (2011) states that Sharpe Index has a weakness because it only measures one dimension of risk that is variance.Further, Sharpe Index is designed to apply to an investment strategy expecting a normal distribution of return that is different with the actual conditions.To overcome bias on the estimated standard deviation which may occur in the Sharpe Index, Jobson and Korkie (1981) developed Adjusted Sharpe Index (ASI).
Meanwhile, unlike Sharpe (1966)  As for return of stock price indexes studied here was calculated by the following formula : Where : Index t = Stock Price Index Closing in the Indonesia Stock Exchange at day t Index t -1 = Stock Price Index Closing in the Indonesia Stock Exchange at day t -1 To measure the portfolio performance, Sharpe Index, Treynor Ratio, Jensen Alpha, Adjusted Sharpe Index (ASI), Adjusted Jensen Alpha Index (AJI) and Sortino Ratio were used.
Sharpe Index is calculated with the following formula : Treynor Ratio is calculated with the following formula : (2) Ratio Beta Portfolio

Treynor = Average Portfolio Return -RFR
While beta of portfolio were calculated by using the following: Where :

Table 1 .
Descriptive Statistics of Stock Prices Indexes in the Indonesia Stock Exchange

Table 2 .
Performance of Stock Price Indexes in the Indonesia Stock ExchangeSimilar to the Sharpe Index, by using the Treynor Ratio to rank the performance of stock price indexes in the Indonesia Stock Exchange as illustrated in Table3, it can be seen that the stock

Table 3 .
Performance Ranking Summary of Stock Price Indexes in the Indonesia Stock Exchange