OPTIMAL PORTFOLIO RISK AND RETURN ANALYSIS OF BISNIS27 INDEX MEMBERS IN 2009 – 2010 USING MARKOWITZ EFFICIENT THEORY FINAL PROJECT
By Radhiyan 19007087
Undergraduate Program School of Business and Management Institut Teknologi Bandung
VALIDATION PAGE
OPTIMAL PORTFOLIO RISK AND RETURN ANALYSIS OF BISNIS27 INDEX MEMBERS IN 2009 – 2010 USING MARKOWITZ EFFICIENT THEORY
By RADHIYAN ID No: 19007087
A Final Project in Partial Fulfillment of the Requirement for the Degree of Bachelor of Management
Undergraduate Program of Management Study School of Business and Management Institut Teknologi Bandung July 23, 2010
Approved By
______________________________ Dr. Ir. Budhi Arta Surya, MSc
OPTIMAL PORTFOLIO RISK AND RETURN ANALYSIS OF BISNIS27 INDEX MEMBERS IN 2009 – 2010 USING MARKOWITZ EFFICIENT THEORY RADHIYAN 19007087 Examination Date: August 4th, 2010 Graduation Date: October 23rd, 2010 Undergraduate of Business and Management Program, Institut Teknologi Bandung 2010 Final Project Advisor: Dr. Ir. Budhi Arta Surya, MSc
ABSTRACT Stock, as one of investment instruments, is becoming many people choice to put their money in. Some of them gain and become rich, while the other struggling to make money. In the old days, investor focuses on return of their assets, and risk is often put behind. Nowadays, risk is getting more and more attention as people realize that investment always has two sides, risk and return. Investing in portfolio proven to be effective to maximize risk and maintaining the return. Diversification is the main factor to construct a well-diversified portfolio Harry M. Markowitz, a Nobel Prize winner, comes with a theory on how to select an optimal portfolio. His study stated that in a given asset universe, the efficient portfolio combination – which has highest return for certain level of risk, vice versa – will display a curve called efficient frontier. Optimal portfolio for an investor lies somewhere within this curve. Optimal portfolio for each investor may differ, depends on the current risk-free rate and risk aversion level of those investor. This paper studies about how to select an optimal portfolio from twenty seven members of Bisnis27 stocks. Bisnis27 is chosen as the asset universe because it consists of highly liquid stocks and the universe is relatively small compared to other indices such as Kompas100 and LQ45. The analysis is done in quarterly basis to represent the portfolio adjustment to meet current condition. Time horizon of the study is limited to 1 January 2009 to 30 June 2010 because ADRO and INDY, as the member of Bisnis27, held their Initial Public Offering (IPO) in the last quarter of 2008. Objectives of this study is to identify how are the risk and return of the optimal portfolio, what are the stocks that constructed it, and how is the performance of the optimal portfolio regarding its risk-adjusted return compared to the market. The first step will be constructing several efficient portfolios to draw the efficient frontier curve. The computation is done using Microsoft Office Excel and Matlab. Then, the efficient portfolios are plotted in a risk-return space to form an efficient frontier. The efficient frontier is useful to determine an optimal portfolio for an investor. This optimal portfolio will differ from one investor to another due to the risk-free rate and risk aversion level. The risk-free rate is calculated by using simple average method to the BI rate at a certain 3 months time (a quarter), while the risk aversion level is set to represents a moderate risk averse investor. After an optimal portfolio is determined for each quarter, the risk, return, and weight of asset for those optimal portfolios is analyzed. The last step will be comparing the portfolio performance with the market. This step is important to give investor a big picture on how the optimal portfolio performs compared to the market. IHSG is used to represents the whole Indonesia’s stock market. This section is done by analyzing three portfolio performance measurements, which are Treynor measure, Sharpe ratio, and Jensen’s alpha. Keywords: stock, portfolio risk and return, Markowitz Efficient Theory, efficient frontier, portfolio performance measurement. v
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OPTIMAL PORTFOLIO RISK AND RETURN ANALYSIS OF BISNIS27 INDEX MEMBERS IN 2009 – 2010 USING MARKOWITZ EFFICIENT THEORY RADHIYAN 19007087 Tanggal Sidang: 4 Agustus 2010 Tanggal Kelulusan: 23 Oktober 2010 Program Sarjana Sekolah Bisnis dan Manajemen, Institut Teknologi Bandung 2010 Pembimbing Tugas Akhir: Dr. Ir. Budhi Arta Surya, MSc
ABSTRAKSI Saham, sebagai salah satu instrumen investasi, akhir-akhir ini menjadi pilihan banyak orang untuk memutar uang mereka. Banyak orang mendapatkan keuntungan dan dengan sekejap menjadi kaya, namun banyak juga yang harus berjuang keras, bahkan merugi dalam investasinya. Di masa lalu, investor terfokus pada keuntungan dari asset yang mereka pegang, dan risiko sering diacuhkan. Sangat berbeda dengan saat ini dimana risiko mendapat porsi perhatian lebih seirining dengan meningkatnya kesadaran para investor bahwa dibalik keuntungan yang menjanjikan dalam investasi, terdapat resiko. Investasi dalam bentuk portofolio telah terbukti efektif untuk memaksimalkan tingkat pengembalian dengan tetap mejaga risiko yang ada. Diversifikasi merupakan faktor kunci untuk membangun sebuah portofolio baik. Harry M. Markowitz, seorang pemenang Nobel, datang dengan teori tentang bagaimana memilih portofolio yang optimal. Studinya menyatakan bahwa dari sekumpulan aset tertentu, kombinasi portofolio yang efisien - yang memberikan keuntungan tertinggi pada tingkat risiko tertentu, maupun sebaliknya – dapat menampilkan sebuah perbatasan yang disebut efficient frontier curve. Portofolio yang optimal untuk seorang investor terletak di suatu titik pada kurva tersebut. Portofolio optimal untuk setiap investor dapat berbeda, tergantung pada tingkat riskfree saat itu dan tingkat keberanian mengambil resiko dari investor itu sendiri. Dalam studi ini dibahas tentang bagaimana untuk memilih portofolio yang optimal dari 27 saham anggota index Bisnis27. Bisnis27 dipilih sebagai kumpulan asset karena terdiri dari saham - saham berlikuiditas tinggi dan anggotanya relative sedikit bila dibandingkan dengan indeks lain seperti Kompas100 dan LQ45, sehingga untuk berinvestasi didalamnya dibutuhkan dana yang tidak terlalu banyak. Analisis dilakukan di setiap kuartal untuk menggambarkan proses penyesuaian portofolio yang biasa dilakukan untuk mengikuti kondisi saat ini. Tenggang waktu dari data penelitian ini dibatasi dari 1 Januari 2009 sampai 30 Juni 2010 karena ADRO dan INDY, sebagai anggota Bisnis27 termuda, baru mengadakan Penawaran Umum Perdana (IPO) pada kuartal terakhir tahun 2008. Tujuan penelitian ini adalah untuk mengidentifikasi bagaimana tingkat resiko dan keuntungan dari sebuah portofolio optimal, apa saja saham yang terdapat dalam portofolio tersebut, dan bagaimana kinerja dari portofolio optimal itu dengan melihat tingkat keuntungan yang telah disesuaikan dengan resiko terhadap pasar secara keseluruhan. Langkah pertama pertama adalah membangun beberapa portfolio efisien untuk kemudian menggambar kurva efficient frontier. Perhitungan dalam tahap ini menggunakan Microsoft Office Excel dan Matlab. Kemudian, portofolio efisien tersebut digambarkan dalam diagram risk-return untuk membentuk sebuah kurva efficient frontier dan kemudian mementukan portfolio optimal. Portofolio optimal ini akan berbeda dari satu investor yang lain karena perbedaan tingkat risk-free dan tingkat keberanian mengambil resiko antara seorang investor dengan investor lainnya. Tingkat risk-free dihitung dengan menggunakan metode rata-rata sederhana pada BI rate (suku bunga Bank Indonesia) pada setiap kuartal. Sedangkan tingkat keberanian investor akan resiko diatur untuk mewakili investor yang memiliki tingkat keberanian vii
menengah. Setelah portofolio optimal ditentukan untuk setiap kuartal, risiko, keuntungan, dan proporsi dari setiap aset dalam portofolio optimal tersebut dianalisa. Pada tahap terakhir, akan dibandingkan kinerja portofolio optimal dengan pasar secara keseluruhan. Langkah ini penting untuk memberikan investor gambaran besar tentang bagaimana kinerja portofolio optimal tersebut dibandingkan dengan pasar. IHSG digunakan untuk mewakili pasar saham Indonesia secara keseluruhan. Studi komparasi ini dilakukan dengan menganalisa tiga metode pengukuran kinerja portofolio, yaitu Treynor measure, Sharpe ratio, dan Jensen’s alpha. Kata kunci: saham, resiko dan keuntungan portofolio, Markowitz Efficient Theory, efficient frontier, pengukuran kinerja portofolio.
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FOREWORD
The writers deliver the deepest thankfulness to the God generous because this final project can finish punctually. The final project discusses about optimal portfolio risk and return analysis of Bisnis27 index members in 2009 – 2010 using Markowitz Efficient Theory. This final project was made in order to fulfill the requirement to be graduated from SBM ITB In the process of deepen this report; the writers get some direction, correction, and suggestion that are why the writers deliver a lot of thankfulness to: Dr. Ir. Budhi Arta Surya, MSc, as the academic counselor for the kindness and guidance throughout the composition of this paper. Mantapski, sir. My parents, Irwansyah and Kostia Erawati, for their understanding and support until the Final Presentation. Mr. Arief Ressa as my mentor in internship program at Mandiri Sekuritas Bandung for the guidance about technical analysis in stock market. Gita Ayuwigati, my lovely girlfriend, who always being patience and supportive during this final project. Thank you to always make me believe that I can do this, dear. Everything about you is God’s gift to me. Mrs. Dina, Ms. Mira, and Ms. Ria, the three rempong girls as the colleague at Mandiri Sekuritas Bandung for the joyful time during work hour. Emyr Giovanni, Gautama Prawira, Julian Kamil, Dorojatun Prakoso, Sandy Nandhiwardhana, and other companion in arms of SBM 2010 batch which could not be mention one by one.
The writer hopes this report will be useful for all of people that need it or for further studies on portfolio risk and return.
Bandung, July 2010 Radhiyan
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TABLE OF CONTENTS APPROVAL PAGE ......................................................................................................iii ABSTRACT..................................................................................................................v ABSTRAKSI ................................................................................................................vii FOREWORD ................................................................................................................ix TABLE OF CONTENTS..............................................................................................xi LIST OF CHARTS .......................................................................................................xiii LIST OF FIGURES ......................................................................................................xv LIST OF TABLES ........................................................................................................xvii LIST OF APPENDICES ...............................................................................................xix CHAPTER I INTRODUCTION ...................................................................................1 1.1 Background .................................................................................................1 1.2 Problem Identification ................................................................................2 1.3 Research Objectives ....................................................................................2 1.4 Research Scope and Limitations .................................................................3 CHAPTER II THEORETICAL FOUNDATIONS.......................................................5 2.1 Investment .................................................................................................5 2.2 Stock ..........................................................................................................6 2.3 Markowitz Efficient Frontier Theory ........................................................6 2.4 Risk and Return .........................................................................................8 2.4.1
Rate of Return .......................................................................................8
2.4.2
Average Return .....................................................................................8
2.4.3
Standard Deviation ...............................................................................9
2.4.4
Beta .......................................................................................................10
2.5 Risk and Return of Portfolio .....................................................................10 2.5.1
Portfolio Return ....................................................................................10
2.5.2
Portfolio Risk ........................................................................................11
2.6 Measuring Portfolio Performance ..............................................................13 2.6.1
Jensen’s Alpha ......................................................................................13
2.6.2
Sharpe Ratio ..........................................................................................13
2.6.3
Treynor Measure ...................................................................................14
CHAPTER III METHODOLOGY ...............................................................................15 3.1 Problem Identification ...............................................................................15 xi
3.2 Research Objectives .................................................................................. 16 3.3 Literature Study ........................................................................................ 16 3.4 Data Collection ......................................................................................... 16 3.5 Data Analysis ............................................................................................ 16 3.5.1
Risk and Return of Individual Stock .................................................... 16
3.5.2
The Efficient Portfolio ......................................................................... 16
3.5.3
Optimal Portfolio in the Efficient Frontier Diagram ............................ 17
3.5.4
Measuring Portfolio Performance ........................................................ 17
3.6 Conclusion ................................................................................................ 17 CHAPTER IV ANALYSIS .......................................................................................... 19 4.1 Data Collection ........................................................................................... 19 4.2 4.3 Data Analysis ............................................................................................. 19 4.3.1
Risk and Return of Individual Stock .................................................... 19
4.3.2
The Efficient Portfolio ......................................................................... 22
4.3.3
Optimal Portfolio in the Efficient Frontier Diagram ............................ 25
4.3.4
Optimal Portfolio Performance Compared to the Market ................... 33
4.3.4.1 Treynor Measure .................................................................................. 34 4.3.4.2 Sharpe Ratio ......................................................................................... 36 4.3.4.3 Jensen’s Alpha...................................................................................... 36 CHAPTER V CONCLUSION AND RECOMMENDATION .................................... 39 5.1 Conclusion .................................................................................................. 39 5.2 Recommendation for Investor .................................................................... 42 5.3 Recommendation for Further Studies ........................................................ 42 REFERENCES ............................................................................................................. 45 APPENDIX .................................................................................................................. 47
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LIST OF CHARTS Chart 1.1 Efficient Frontier for Quarter 1 of 2009 .......................................................27 Chart 2.2 Asset Weight in Optimal Portfolio for Quarter 1 of 2009 ............................27 Chart 3.3 Efficient Frontier for Quarter 2 of 2009 .......................................................28 Chart 4.4 Asset Weight in Optimal Portfolio for Quarter 2 of 2009 ............................28 Chart 5.5 Efficient Frontier for Quarter 3 of 2009 .......................................................29 Chart 6.6 Asset Weight in Optimal Portfolio for Quarter 3 of 2009 ............................29 Chart 7.7 Efficient Frontier for Quarter 4 of 2009 .......................................................30 Chart 8.8 Asset Weight in Optimal Portfolio for Quarter 4 of 2009 ............................30 Chart 9.9 Efficient Frontier for Quarter 1 of 2010 .......................................................31 Chart 10.10 Asset Weight in Optimal Portfolio for Quarter 1 of 2010 ........................31 Chart 11.11 Efficient Frontier for Quarter 2 of 2010 ...................................................32 Chart 12.12 Asset Weight in Optimal Portfolio for Quarter 2 of 2010 ........................32
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LIST OF FIGURES Figure 1.1 IHSG Movement in 2009 ............................................................................1 Figure 2.1 Example of Efficient Frontier......................................................................7 Figure 3.1 Flow of the Research ...................................................................................15
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LIST OF TABLES Table 4.1 Bisnis27 Members ........................................................................................19 Table 4.2 Return of Single Asset ..................................................................................20 Table 4.3 Standard Deviation of Single Asset ..............................................................21 Table 4.4 Return of Efficient Portfolio .........................................................................23 Table 4.5 Standard Deviation of Efficient Portfolio .....................................................24 Table 4.6 Risk-free Rate for Each Quarter ...................................................................25 Table 4.7 Asset Weight for Each Optimal Portfolio .....................................................33 Table 4.8 Portfolio Beta Calculation ............................................................................34 Table 4.9 Treynor Measure Comparison ......................................................................35 Table 4.10 Sharpe Ratio Comparison ...........................................................................36 Table 4.11 Jensen’s Alpha Comparison .......................................................................37 Table 5.1 Asset Weight for Each Optimal Portfolio .....................................................40 Table 5.2 Performance Comparison between the Optimal Portfolio and Overall Market .......................................................................................41
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LIST OF APPENDICES APPENDIX A : Matlab Code .......................................................................................48 APPENDIX B : Normal Probability Plot Result ..........................................................49 APPENDIX C : Beta for each Bisnis27 Members .......................................................56 APPENDIX D : Covariance Matrix..............................................................................57 APPENDIX E : BI Rate Data .......................................................................................58
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