CHAPTER IV ANALYSIS. Table 4.1 Bisnis27 Members

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1 CHAPTER IV ANALYSIS 4.1 Data Collection In this study, adjusted close price is to represents the actual price that had been adjusted due to the stock split, dividends, and other corporate action. The 27 stocks which are the current member of Bisnis27 are represented in Table 4.1 below. Table 4.1 Bisnis27 Members AALI BNGA PGAS ADRO GGRM PNBN ANTM INCO PTBA ASII INDY SMCB BBCA INTP SMGR BBNI ITMG TINS BBRI JSMR TLKM BDMN KLBF UNTR BMRI LPKR UNVR One assumption of Markowitz Efficient Frontier Theory is that the return data of those stocks is normally distributed. Kolmogorov-Smirnov test is used in this research to found out whether the return is normally distributed or not. The test results, which conclude that the returns of the twenty seven stocks are approximately not normally distributed, could be found in the Appendix B. 4.2 Data Analysis Risk and Return of Individual Stock The quarterly risk standard deviation - and return of each stock is calculated using the geometric average approach. In this research, Matlab is used for the computation to find the optimal portfolio. Chen et al. [6] is used as the main reference in this study. However, it is noticed that the authors use arithmetic average approach to calculate the expected return as opposed to the geometric approach that used in this study. The original Matlab code is shown below. %portfolio.m load stock.txt; Portfolio = stock(185:243,:); [m n] = size(portfolio); [AvrRet]= mean(portfolio); [ExpRetVec]= (1+ AvrRet).^12-1; [CovMtx]= cov(portfolio); 19

2 The [AvrRet]= mean(portfolio);command result in mean return of each stock, then the [ExpRetVec]= (1+ AvrRet).^12-1; command result in annual expected return of each stock. By using this code, the Matlab will use arithmetic approach to find the average annual expected return. To find the geometric average return, this research use Microsoft Office Excel then it is loaded to the Matlab. The modified formula is as follows. load stock.txt; load stock1.txt ExpRet = stock1(185:243,:); Portfolio = stock(185:243,:); [m n] = size(portfolio); [ExpRetVec]= prod(expret)-1; [CovMtx]= cov(portfolio); First, the simple return of each day in particular quarter is saved into.txt format. Then this file is loaded in Matlab. After that, the [ExpRetVec]= prod(expret)-1; will result in the geometric quarterly average return of each stock. The recapitulation of geometric average return of each stock is presented in Table 4.2 below. Table 4.2 Return of Single Asset Quarter 1 Quarter 2 Quarter 3 Quarter 4 Quarter 1 Quarter 2 AALI 43.88% 20.51% 24.93% 9.19% 8.13% % ADRO 51.56% 17.53% 25.63% 22.67% 13.29% 1.53% ANTM 0.00% 95.93% 20.99% % 9.07% % ASII 35.07% 71.21% 40.13% 5.00% 20.75% 15.27% BBCA -3.40% 15.60% 31.21% 5.75% 11.97% 9.56% BBNI 3.30% % 23.55% -6.38% 14.90% 3.30% BBRI -8.20% 54.11% 19.05% 2.63% 7.84% 12.73% BDMN 0.81% 57.94% 2.59% -8.08% 14.28% 5.84% BMRI 7.41% 50.85% 48.03% 0.42% 15.96% 12.15% BNGA -5.05% 34.36% 12.90% 1.43% 25.35% 20.22% GGRM 0.00% % 22.09% 44.63% 14.85% 38.18% INCO 15.28% 86.52% 0.00% -9.50% 33.41% % INDY 43.12% 53.82% 5.38% -9.18% 4.49% 22.58% INTP 14.13% 50.85% 36.77% 29.25% 4.01% 12.40% ITMG -5.71% % 21.55% 34.90% 15.80% 0.89% JSMR -1.10% 78.11% 20.65% -3.21% -1.10% 13.13% KLBF 55.00% 62.90% 32.98% -2.26% 43.85% 12.30% LPKR 5.00% % 0.00% % 17.65% % PGAS 15.59% 46.51% 17.30% 7.12% 8.97% -8.82% PNBN -6.90% 22.22% 30.30% % 30.26% 3.03% PTBA -2.17% 77.46% 21.55% 22.84% -1.92% 1.95% SMCB % % 20.91% 16.54% 33.87% 4.82% SMGR % 31.54% 33.76% 20.81% -3.31% 19.86% TINS -1.85% % 6.17% -6.98% 18.75% -9.47% TLKM 9.42% -0.66% 23.83% 9.57% % -4.35% UNTR 53.41% 50.40% 56.78% 0.24% 18.39% 2.18% UNVR 1.92% 19.22% 15.68% 4.20% 9.95% 39.92% 20

3 From the table above, the highest return is generated by BBNI in the second quarter of 2009 which inclined %, while the biggest loss is generated by LPKR in the fourth quarter of 2009 which declined by 23.88%. Along with the return, there must be risk in the form of price volatility. The standard deviation, which measures the risk for each stock in quarterly basis, also calculated using the Microsoft Office Excel and the result could be seen Table 4.3 below. Table 4.3 Standard Deviation of Single Asset Quarter 1 Quarter 2 Quarter 3 Quarter 4 Quarter 1 Quarter 2 AALI 4.26% 3.18% 2.77% 1.67% 1.61% 2.96% ADRO 3.85% 3.75% 2.41% 2.27% 1.84% 2.85% ANTM 4.24% 5.12% 3.83% 2.66% 2.00% 3.13% ASII 4.05% 4.14% 2.86% 2.07% 1.93% 2.79% BBCA 3.46% 2.75% 2.26% 1.87% 2.60% 2.47% BBNI 2.19% 4.29% 1.97% 1.72% 1.41% 2.19% BBRI 3.67% 4.20% 3.05% 2.16% 1.68% 2.59% BDMN 4.31% 5.37% 2.57% 1.69% 2.68% 2.91% BMRI 3.70% 3.87% 2.53% 1.86% 1.96% 2.85% BNGA 3.87% 5.20% 1.95% 2.03% 2.08% 2.57% GGRM 0.00% 4.09% 2.54% 2.85% 1.97% 3.15% INCO 5.12% 5.41% 3.18% 2.42% 2.32% 3.72% INDY 3.89% 4.70% 3.06% 2.18% 2.15% 3.60% INTP 3.11% 3.58% 3.21% 2.95% 1.85% 3.04% ITMG 3.55% 5.06% 3.13% 2.75% 2.33% 2.62% JSMR 2.47% 2.72% 1.76% 1.19% 1.09% 2.45% KLBF 4.57% 3.22% 2.37% 1.61% 2.03% 2.78% LPKR 1.56% 1.20% 2.19% 1.79% 2.04% 2.98% PGAS 3.81% 3.70% 2.00% 1.80% 1.82% 2.50% PNBN 3.30% 3.16% 2.69% 1.74% 2.71% 3.58% PTBA 3.28% 3.82% 2.48% 1.83% 1.82% 2.25% SMCB 5.10% 4.27% 2.30% 2.64% 2.30% 2.58% SMGR 2.25% 2.93% 2.39% 2.02% 1.42% 3.02% TINS 3.44% 5.05% 3.18% 2.05% 2.22% 3.66% TLKM 2.87% 2.28% 2.30% 1.64% 1.51% 1.82% UNTR 4.37% 3.93% 2.57% 2.16% 2.04% 2.66% UNVR 1.98% 1.58% 2.39% 2.07% 1.75% 2.89% The table above shows that the range of price movement from each quarter is different. In the first and second quarter of 2009, many stocks have a standard deviation of 3.5% to 5.1% while in the third and fourth quarter of 2009, the standard deviation are in the range of 1% to 2% as well as the first quarter of At the second quarter of 2010, the Bisnis27 members standard deviations are on the range of 2% to 3%. 21

4 The covariance and beta is also important for the next step of the analysis. The beta and covariance matrix, which is calculated using Microsoft Office Excel, could be found in the Appendix C and Appendix D The Efficient Portfolio Using the data from previous part, the efficient portfolio of 27 stocks of Bisnis27 could be generated. To draw a smooth efficient frontier later in the next step, this research tried to construct 50 efficient portfolios. The Matlab code used to generate the return, risk, and weight proportion of assets in each portfolio is the modification of the Matlab code in Chen et al. [6] which allows short selling and margin trading, which is stated below. % COMPUTE EFFICIENT FRONTIER (SHORT SELLING ALLOWED) NumPorts = n; AssetMin = [ ]; AssetMax = [ ]; pval = 1; Constraint = portcons('portvalue',pval, NumPorts, 'AssetLims', AssetMin, AssetMax, NumPorts); [PortRisk,PortRet,PortWts] = portopt(expretvec, CovMtx, 50, [], Constraint); [OptRisk,OptRet,OptWts]=portopt(ExpRetVec, CovMtx, NumPorts, [], Constraint); The code AssetMin and AssetMax command allow the investor to have a short position and use margin to buy stock. In this research, the short selling and margin are considered as not desirable so the Matlab code will be modified to not allowing the short sell and margin action, as shown below. % COMPUTE EFFICIENT FRONTIER (NO SHORT SELLING ALLOWED) NumPorts = n; Constraint = portcons('default', NumPorts); [PortRisk,PortRet,PortWts] = portopt(expretvec, CovMtx, 50, [], Constraint); [OptRisk,OptRet,OptWts]=portopt(ExpRetVec, CovMtx, NumPorts, [], Constraint); The result is the return and risk for each 50 portfolios in each quarter which could be found in the Table 4.4 and Table

5 Table 4.4 Return of Efficient Portfolio Portfolio Number Quarter 1 Quarter 2 Quarter 3 Quarter 4 Quarter 1 Quarter % % 22.04% 2.63% 10.60% 7.05% % % 22.75% 3.48% 11.28% 7.72% % % 23.46% 4.34% 11.96% 8.39% % % 24.16% 5.20% 12.64% 9.06% % % 24.87% 6.06% 13.32% 9.73% % % 25.58% 6.91% 14.00% 10.40% % % 26.29% 7.77% 14.67% 11.07% % % 27.00% 8.63% 15.35% 11.74% % % 27.71% 9.48% 16.03% 12.42% % % 28.42% 10.34% 16.71% 13.09% % % 29.13% 11.20% 17.39% 13.76% % % 29.84% 12.06% 18.07% 14.43% % % 30.55% 12.91% 18.74% 15.10% % % 31.26% 13.77% 19.42% 15.77% % % 31.96% 14.63% 20.10% 16.44% % % 32.67% 15.48% 20.78% 17.11% % % 33.38% 16.34% 21.46% 17.78% % % 34.09% 17.20% 22.14% 18.45% % % 34.80% 18.06% 22.81% 19.12% % % 35.51% 18.91% 23.49% 19.79% % % 36.22% 19.77% 24.17% 20.46% % % 36.93% 20.63% 24.85% 21.14% % % 37.64% 21.49% 25.53% 21.81% % % 38.35% 22.34% 26.21% 22.48% % % 39.06% 23.20% 26.89% 23.15% % % 39.77% 24.06% 27.56% 23.82% % % 40.47% 24.91% 28.24% 24.49% % % 41.18% 25.77% 28.92% 25.16% % % 41.89% 26.63% 29.60% 25.83% % % 42.60% 27.49% 30.28% 26.50% % % 43.31% 28.34% 30.96% 27.17% % % 44.02% 29.20% 31.63% 27.84% % % 44.73% 30.06% 32.31% 28.51% % % 45.44% 30.92% 32.99% 29.19% % % 46.15% 31.77% 33.67% 29.86% % % 46.86% 32.63% 34.35% 30.53% % % 47.57% 33.49% 35.03% 31.20% % % 48.27% 34.34% 35.70% 31.87% % % 48.98% 35.20% 36.38% 32.54% % % 49.69% 36.06% 37.06% 33.21% % % 50.40% 36.92% 37.74% 33.88% % % 51.11% 37.77% 38.42% 34.55% % % 51.82% 38.63% 39.10% 35.22% % % 52.53% 39.49% 39.78% 35.89% % % 53.24% 40.34% 40.45% 36.56% % % 53.95% 41.20% 41.13% 37.23% % % 54.66% 42.06% 41.81% 37.91% % % 55.37% 42.92% 42.49% 38.58% % % 56.07% 43.77% 43.17% 39.25% % % 56.78% 44.63% 43.85% 39.92% 23

6 Table 4.5 Standard Deviation of Efficient Portfolio Portfolio Number Quarter 1 Quarter 2 Quarter 3 Quarter 4 Quarter 1 Quarter % 0.90% 0.96% 0.84% 0.83% 1.36% % 0.90% 0.96% 0.84% 0.83% 1.36% % 0.90% 0.96% 0.84% 0.83% 1.37% % 0.91% 0.96% 0.84% 0.83% 1.37% % 0.92% 0.97% 0.85% 0.84% 1.37% % 0.93% 0.97% 0.85% 0.84% 1.37% % 0.94% 0.98% 0.86% 0.84% 1.38% % 0.96% 0.99% 0.86% 0.85% 1.39% % 0.97% 1.00% 0.87% 0.85% 1.39% % 0.99% 1.01% 0.88% 0.85% 1.40% % 1.01% 1.03% 0.88% 0.86% 1.41% % 1.04% 1.04% 0.89% 0.87% 1.42% % 1.06% 1.06% 0.90% 0.87% 1.43% % 1.08% 1.07% 0.91% 0.88% 1.44% % 1.11% 1.09% 0.93% 0.89% 1.45% % 1.14% 1.11% 0.94% 0.90% 1.47% % 1.18% 1.13% 0.95% 0.90% 1.48% % 1.22% 1.15% 0.97% 0.91% 1.50% % 1.27% 1.18% 0.98% 0.92% 1.51% % 1.32% 1.20% 1.00% 0.93% 1.53% % 1.37% 1.23% 1.02% 0.95% 1.54% % 1.43% 1.26% 1.04% 0.96% 1.56% % 1.49% 1.29% 1.06% 0.97% 1.58% % 1.56% 1.32% 1.08% 0.98% 1.60% % 1.62% 1.35% 1.10% 1.00% 1.62% % 1.69% 1.38% 1.12% 1.01% 1.64% % 1.76% 1.41% 1.15% 1.03% 1.66% % 1.83% 1.45% 1.18% 1.04% 1.68% % 1.90% 1.49% 1.21% 1.06% 1.70% % 1.98% 1.52% 1.25% 1.08% 1.73% % 2.05% 1.56% 1.29% 1.09% 1.75% % 2.13% 1.60% 1.33% 1.11% 1.78% % 2.21% 1.65% 1.37% 1.13% 1.81% % 2.28% 1.69% 1.42% 1.15% 1.83% % 2.36% 1.73% 1.47% 1.18% 1.86% % 2.44% 1.78% 1.52% 1.20% 1.89% % 2.52% 1.83% 1.58% 1.23% 1.92% % 2.61% 1.88% 1.65% 1.26% 1.95% % 2.70% 1.93% 1.71% 1.29% 1.97% % 2.79% 1.98% 1.78% 1.32% 2.01% % 2.88% 2.03% 1.85% 1.36% 2.04% % 2.98% 2.08% 1.93% 1.40% 2.08% % 3.09% 2.14% 2.01% 1.45% 2.12% % 3.20% 2.19% 2.09% 1.51% 2.17% % 3.32% 2.25% 2.17% 1.58% 2.23% % 3.46% 2.31% 2.25% 1.65% 2.28% % 3.63% 2.37% 2.36% 1.73% 2.35% % 3.82% 2.43% 2.49% 1.83% 2.41% % 4.04% 2.49% 2.66% 1.93% 2.48% % 4.29% 2.57% 2.85% 2.03% 2.89% 24

7 Based on the Table 4.4 and Table 4.5, in the first quarter of 2009, the efficient portfolios generated expected return between 10.34% and 55%, this quite high return is accompanied by the standard deviations for each portfolio ranging from 0.94% to 4.92%. In the next quarter, the Markowitz model provides high expected returns on each portfolio. The lowest expected return is % while the highest had reached %. This high return is usually connected with high risk, but in this case, the Markowitz model succeeds to keep the risk low enough for each portfolio. The standard deviations range from 0.90% to 4.29%, lower than the previous quarter risk. In the third quarter of 2009, the efficient portfolio expected returns are spread between 22.04% and 56.78%, with standard deviations ranging from 0.96% to 2.57%. In the last quarter of 2009, the efficient portfolio generated expected returns of 2.63% to 44.63% for the portfolios. The standard deviations for those efficient portfolios are between 0.84% and 2.85% In the first quarter of 2010, the Markowitz model succeed to construct efficient portfolios which have expected returns between 10.60% and 43.85%, while its standard deviations are quite low compared to the other quarter performance, spread between 0.83% and 2.03%. In the second quarter of 2010, the efficient portfolio has the expected returns in the range of 7.05% to 39.92% with the standard deviations of 1.36% to 2.89%. This somewhat low return with moderate risk performance is suspected to be the effect of monetary crisis in Greece which affects the stock market around the globe Optimal Portfolio in the Efficient Frontier Diagram The expected returns and standard deviations of the portfolios in the previous part are used to find an optimal portfolio in each quarter. The other factor that is needed to determine the optimal portfolio and plot the efficient frontier are risk-free rate, borrowing rate, and risk aversion level. In this research, the BI Rate will be used as the risk-free rate while the loan interest from Bank Mandiri, which is 13.5%, will be used as the borrowing rate. The BI Rate data could be found in the Appendix E while below is Table 4.6 containing the BI Rate for each quarter calculated using simple average approach. Table 4.6 Risk-free Rate for Each Quarter Quarter BI Rate (average) 1/ % 2/ % 3/ % 25

8 Table 4.6 Risk-free Rate for Each Quarter (Cont.) Quarter BI Rate (average) 4/ % 1/ % 2/ % Before plotting the efficient frontier, the risk aversion level of investor should be determined first. Risk aversion level in Matlab is defined as the scalar coefficient of investor degree of risk. The higher value of risk aversion means that the investor is more averse to risk. Typical risk aversion value ranges between 2 and 4. In this study, the risk aversion level of 3 will be used to represent the moderate risk averse investors. After those factors are determined, the Matlab code below is used to determine the optimal portfolio for moderate risk averse investors and plot the efficient frontier diagram for each quarter. % OPTIMAL ASSET ALLOCATION RisklessRate = 0.065; RiskAversion = 3; BorrowRate = 0.135; [RiskyRisk, RiskyReturn, RiskyWts, RiskFraction, OverallRisk, OverallReturn] = portalloc (PortRisk, PortRet, PortWts, RisklessRate, BorrowRate, RiskAversion) % PLOT THE RESULT subplot(231) plot(portrisk, PortRet, 'm-', OptRisk, OptRet, 'x',... 0, RisklessRate, 'k:square', RiskyRisk, RiskyReturn, 'k:diamond',... [0; RiskyRisk], [RisklessRate; RiskyReturn],'r--') xlabel('portfolio Risk'); ylabel('portfolio Return '); grid on The outcome from Matlab code above is a risk-return space with an efficient frontier built out of efficient portfolio, complete with the optimal portfolio for each quarter. Below are the detailed explanation about the efficient frontier, optimal portfolio, and weight of stocks in the optimal portfolio for each quarter. 26

9 Quarter Return : 48.38% Risk : 1.7% Chart 4.1 Efficient Frontier for Quarter 1 of 2009 In the first quarter of 2009, the optimal portfolio could generate 48.38% return while it has 1.7% standard deviation. In this quarter, the optimal portfolio consists of seven stocks which are AALI, ADRO, GGRM, INDY, INTP, KLBF, and UNTR. The investment proportions for each asset could be seen in Chart 4.2 below. UNTR, 10.12% AALI, 4.48% INTP, 0.45% KLBF, 15.20% ADRO, % INDY, 25.03% GGRM, 9.91% Chart 4.2 Asset Weight in Optimal Portfolio for Quarter 1 of

10 Quarter Return : 138.4% Risk : 1.03% Chart 4.3 Efficient Frontier for Quarter 2 of 2009 In this part of 2009, the Markowitz model construct an optimal portfolio which has a quite high return, 138.4% in a quarter period, accompanied with a low standard deviation of 1.03%. This standard deviation is even lower than the previous quarter while the return is higher. The optimal portfolio in this quarter are constructed with the mix of thirteen assets which are AALI, ADRO, BBCA, BBNI, BNGA, GGRM, INTP, ITMG, JSMR, KLBF, LPKR, PNBN, and UNVR. The weights of each asset are presented in Chart 4.4 below. UNVR, 42.90% AALI, 0.65% ADRO, 10.09% BBCA, 3.91% BBNI, 0.54% BNGA, 3.06% GGRM, 5.17% INTP, 2.37% ITMG, 1.12% JSMR, 10.25% KLBF, 15.51% PNBN, 1.62% LPKR, 2.82% Chart 4.4 Asset Weight in Optimal Portfolio for Quarter 2 of

11 Quarter Return : 39.53% Risk : 1.37% Chart 4.5 Efficient Frontier for Quarter 3 of 2009 For the third quarter of 2009, the optimal portfolio had a return of 39.53% while its standard deviation is 1.37%. This time, the Markowitz portfolio selection method had construct the portfolio consists of nine stocks which are ADRO, ASII, BCA, BMRI, INTP, KLBF, SMGR, UNTR, and UNVR. The weights of each asset are shown in Chart 4.6 below. UNVR 5% UNTR 25% ADRO 21% ASII 5% BBCA 13% SMGR 4% KLBF 7% INTP 1% BMRI 19% Chart 4.6 Asset Weight in Optimal Portfolio for Quarter 3 of

12 Quarter Return : 31.76% Risk : 1.47% Chart 4.7 Efficient Frontier for Quarter 4 of 2009 In the last quarter of 2009, the optimal portfolio that could be constructed using Bisnis27 members generates a return of 31.76% while its standard deviation is 1.47%. The optimal portfolio in this quarter consists of ADRO, GGRM, INTP, ITMG, PTBA, and SMGR. The weight details are presented in the following Chart 4.8. SMGR, 6.20% PTBA, 29.47% ADRO, 18.84% GGRM, 37.37% ITMG, 7.40% INTP, 0.72% Chart 4.8 Asset Weight in Optimal Portfolio for Quarter 4 of

13 Quarter Return : 37.3% Risk : 1.33% Chart 4.9 Efficient Frontier for Quarter 1 of 2010 In the year of 2010, the optimal portfolio succeeds to gain 37.3% return with a standard deviation of 1.33%. This portfolio is constructed by five stocks which happen to be BNGA, INCO, KLBF, PNBN, and SMCB. The weight for each stock could be found in the following Chart SMCB, 11.65% BNGA, 8.23% INCO, 11.84% PNBN, 19.34% KLBF, 48.94% Chart 4.10 Asset Weight in Optimal Portfolio for Quarter 1 of

14 Quarter Return : 36.33% Risk : 2.21% Chart 4.11 Efficient Frontier for Quarter 2 of 2010 For the last quarter, the second quarter of 2010, an optimal portfolio constructed by the Markowitz model generates 37.73% return with a standard deviation of 2.33%. The current Indonesia s capital market condition affected by the monetary crisis in Greece had lead to an optimal portfolio having a quite low return with high standard deviation compared to the previous periods. The portfolio consists of only three assets which are BNGA, GGRM, and UNVR. The investment proportions for each stock are presented in Chart 4.12 below. BNGA, 15.27% UNVR, 51.51% GGRM, 33.22% Chart 4.12 Asset Weight in Optimal Portfolio for Quarter 2 of

15 From all of those optimal portfolios for each quarter, there are some stocks that survived to be in the optimal portfolio for several quarter. In the other hand, there are also some Bisnis27 stocks that never got any proportion in the optimal portfolio in any quarter analyzed. Recapitulation of proportion for each optimal portfolio is presented in Table 4.7 below. Optimal Portfolio Quarter 1 Optimal Portfolio Quarter 2 Table 4.7 Asset Weight for Each Optimal Portfolio Optimal Portfolio Quarter 3 Optimal Portfolio Quarter 4 Optimal Portfolio Quarter 1 Optimal Portfolio Quarter 2 Asset Weight Asset Weight Asset Weight Asset Weight Asset Weight Asset Weight AALI 4.48% AALI 0.65% ADRO 21.10% ADRO 18.84% BNGA 8.23% BNGA 15.27% ADRO 34.80% ADRO 10.09% ASII 4.91% GGRM 37.37% INCO 11.84% GGRM 33.22% GGRM 9.91% BBCA 3.91% BBCA 12.69% INTP 0.72% KLBF 48.94% UNVR 51.51% INDY 25.03% BBNI 0.54% BMRI 18.93% ITMG 7.40% PNBN 19.34% TOTAL 100% INTP 0.45% BNGA 3.06% INTP 1.10% PTBA 29.47% SMCB 11.65% KLBF 15.20% GGRM 5.17% KLBF 7.46% SMGR 6.20% TOTAL 100% UNTR 10.12% INTP 2.37% SMGR 3.47% TOTAL 100% TOTAL 100% ITMG 1.12% UNTR 25.08% JSMR 10.25% UNVR 5.26% KLBF 15.51% TOTAL 100% LPKR 2.82% PNBN 1.62% UNVR 42.90% TOTAL 100% 48.38% 1.7% 138.4% 1.03% 39.53% 1.37% 31.76% 1.47% 37.30% 1.33% 36.33% 2.21% As it could be seen in the table above, ADRO, GGRM, INTP, and KLBF had been selected for the optimal portfolio in four different quarters. This means that those stocks offer attractive return with acceptable risk most of the time. Moreover, stock such as ANTM, BBRI, BDMN, TINS and TLKM are never selected to be in the optimal portfolio. It means that either those stock not offering adequate return or experienced too much volatility in the price movement between 1 January 2009 and 30 June Optimal Portfolio Performance Compared to the Market To measure the performance of the optimal portfolio that has been generated in the previous section with the market, three portfolio performance measurement techniques will be used, which are the Treynor measure, Sharpe ratio, and Jensen s alpha. Those techniques measure the performance of the portfolio based on both risk and return. The result determine that either the optimal portfolio had outperformed the market or not, in terms of both risk and return. 33

16 Treynor Measure Expected return, risk-free rate, and beta is the item that is required to calculate the Treynor measure. The expected return is equivalent to the portfolio return for each quarter while the risk-free rate is the BI Rate which had been stated in the previous part. It left the beta portfolio that had not been calculated. Below is the table which explains the portfolio beta calculation for each quarter. Table 4.8 Portfolio Beta Calculation Optimal Portfolio Quarter Asset Weight Beta Weight x Beta AALI 4.48% ADRO 34.80% GGRM 9.91% INDY 25.03% INTP 0.45% KLBF 15.20% UNTR 10.12% Total (portfolio beta) 0.53 Optimal Portfolio Quarter Asset Weight Beta Weight x Beta AALI 0.65% ADRO 10.09% BBCA 3.91% BBNI 0.54% BNGA 3.06% GGRM 5.17% INTP 2.37% ITMG 1.12% JSMR 10.25% KLBF 15.51% LPKR 2.82% PNBN 1.62% UNVR 42.90% Total (portfolio beta) 0.32 Optimal Portfolio Quarter Asset Weight Beta Weight x Beta ADRO 21.10% ASII 4.91% BBCA 12.69% BMRI 18.93% INTP 1.10% KLBF 7.46% SMGR 3.47% UNTR 25.08% UNVR 5.26%

17 Table 4.8 Portfolio Beta Calculation (Cont.) Total (portfolio beta) 0.60 Optimal Portfolio Quarter Asset Weight Beta Weight x Beta ADRO 18.84% GGRM 37.37% INTP 0.72% ITMG 7.40% PTBA 29.47% SMGR 6.20% Total (portfolio beta) 0.72 Optimal Portfolio Quarter Asset Weight Beta Weight x Beta BNGA 8.23% INCO 11.84% KLBF 48.94% PNBN 19.34% SMCB 11.65% Total (portfolio beta) 0.47 Optimal Portfolio Quarter Asset Weight Beta Weight x Beta BNGA 15.27% GGRM 33.22% UNVR 51.51% Total (portfolio beta) 0.84 From the table above, it is observed that the portfolio beta is simply calculated by multiplying the weight of the asset and its beta then sum up all of it, while the beta for market (IHSG) is After the portfolio beta for each quarter had been determined, the Treynor Measure could be calculated and the result is presented in Table 4.9 below. Table 4.9 Treynor Measure Comparison Optimal Portfolio Market Quarter Quarter Quarter Quarter Quarter Quarter

18 The Treynor Measure in the table above shows that the optimal portfolio has bigger value in every quarter, compared to the market. It means that the optimal portfolio outperforms the market in every quarter, based on Treynor s assumptions Sharpe Ratio Another method to measure a portfolio performance is by using Sharpe ratio. This ratio requires some pre-defined date such as the expected return, standard deviation, and riskfree asset. Those data had been determined in the previous section so that the Sharpe ratio could be calculated directly. The result of Sharpe ratio for each quarter is presented in Table 4.10 below. Table 4.10 Sharpe Ratio Comparison Optimal Portfolio Market Quarter Quarter Quarter Quarter Quarter Quarter The table above shows that the Sharpe ratio for optimal portfolio is higher compared to the market. Moreover, the gap between the optimal portfolio s and market s Sharpe ratio is very far. It means that the optimal portfolio has a superior risk-adjusted return compared to the market Jensen s Alpha The last portfolio performance measurement is to use Jensen s alpha. The portfolio expected return, risk-free rate, portfolio beta, and market risk (represented by the standard deviation of IHSG) for each period is required to calculate the Jensen s Alpha. Since all of those data had been determined in the previous part, the calculation could be done directly. A negative alpha means that the portfolio performance is below the market while a positive alpha means that portfolio outperformed the market. The alpha result for optimal portfolio over each period is represented in Table

19 Table 4.11 Jensen s Alpha Comparison Alpha Quarter Quarter Quarter Quarter Quarter Quarter By referring to the table above, the alpha value of the optimal portfolio for each quarter is always positive. The alpha in the second quarter of 2009 is even greater than Based on those facts, refers to Jensen et al. [9], the optimal portfolio outperforms the market in every period. 37

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