Chapter 7 Investment Analysis and Portfolio Management. Frank K. Reilly & Keith C. Brown

Transkripsi

1 Chapter 7 Investment Analyss and Portfolo Management Frank K. Relly & Keth C. Brown

2 Chapter 7 - An Introducton to Portfolo Management Questons to be answered: 1. What do we mean by rsk averson and what evdence ndcates that nvestors are generally rsk averse? 2. What are the basc assumptons behnd the Markowtz portfolo theory? 3. What s meant by rsk and what are some of the alternatve measures of rsk used n nvestments? 4. How do you compute the expected rate of return for an ndvdual rsky asset or a portfolo of assets? 5. How do you compute the standard devaton of rates of return for an ndvdual rsky asset? 6. What s meant by the covarance between rates of return and how do you compute covarance? 2

3 7. What s the relatonshp between covarance and correlaton? 8. What s the formula for the standard devaton for a portfolo of rsky assets and how does t dffer from the standard devaton of an ndvdual rsky asset? 9. Gven the formula for the standard devaton of a portfolo, how and why do you dversfy a portfolo? 10. What happens to the standard devaton of a portfolo when you change the correlaton between the assets n the portfolo? 11. What s the rsk-return effcent fronter? 12. Is t reasonable for alternatve nvestors to select dfferent portfolos from the portfolos on the effcent fronter? 13. What determnes whch portfolo on the effcent fronter s selected by an ndvdual nvestor? 3

4 Background Assumptons nvestor memaksmumkan return pd tngkat rsko tertentu. Portofolo melbatkan seluruh aset dan kewajban nvestor Hubungan antara return aset dlm portofolo sangat pentng Portofolo yg bak bukanlah kumpulan sederhana nvestas yg bak secara ndvdual 4

5 Rsk Averson (Benc Rsko) Dg satu plhan antar dua aset dg return yg sama, Investor umumnya memlh aset dengan tngkat rsko lebh kecl Buktnya: Banyak nvestor membel asurans: kematan, kendaraan, kesehatan, dan ketdakpastan pendapatan. Pembel mempertukarkan baya yg past untuk rsko keugan yg tdak past Pendapatan oblgas menngkat sebandng dengan kelompok rsko dar AAA to AA to A. 5

6 Not all nvestors are rsk averse Preferens Rsko: hrs dlakukan dengan jumlah uang yg dkeluarkan-sedkt, untuk memastkan kerugan yg besar 6

7 Defnton of Rsk 1. Ketdakpastan atas hasl mendatang, atau 2. Probabltas dar hasl yg tdak dngnkan (adverse outcome) 7

8 Markowtz Portfolo Theory Mengkuanttatfkan rsko Mendervas ukuran return harapan bg portofolo aset dan rsko harapannya Menunjukkan bhw varan dar return mrp ukuran berart tentang rsko portofolo Mendervas formula untuk menghtung varan portfolo, yg menunjukkan bgm mendversfkas scr efektf suatu portofolo 8

9 Assumptons of Markowtz Portfolo Theory 1. Investor mempertmbangkan tap alternatf nvestas spt yg sdg dsajkan dg dstrbus probabltas dr return ekspektas slm beberapa perode pemlkan nvestas. 2. Investor memnmumkan utltas ekpektas satu-perode, dan kurve utltasnya menunjukkan utltas marjnal yg menurun dr kemakmuran (dmnshng margnal utlty of wealth). 3. Investor menestmas rsko portofolo atas bass varabltas return harapan. 4. Investor mendasarkan keputusan hanya pd return harapan dan rsko, sehngga kurve utltasnya mrp fungs dr return ekspektas dan varan ekspektas (atau devas standar) dr retun saja. 5. Unt level rsko tertentu, nvestor lbh memlh return lbh tngg dp return lbh rendah. Begtu juga, unt level return ekspektas tertentu, nvestor lbh memlh rsko lbh rendah dp rsko lbh besar. 9

10 Markowtz Portfolo Theory Menggunakan 5 asums, aset tunggal atau portofolo aset danggap efsen jka: Tdak ada aset/portofola aset yg menawarkan return lbh tngg dg rsko sama (atau lebh rendah), atau Rsko lebh rendah dengan return sama (lbh tngg) 10

11 Alternatve Measures of Rsk Varan atau devas standar dar return harapan Ksaran return (Range of returns) Return d bawah harapan Semvaran ukuran yg hanya mempertmbangkan devas d bawah rerata Ukuran rsko n mengasumskan scr mplst bhw nvestor ngn memnmumkan kurangnya return yg lbh rendah dp tngkat target return 11

12 Expected Rates of Return Unt aset ndvdual jumlah dr retun potensal dkalkan dg probabltas return Untuk portofolo aset rata-rata tertmbang return harapan bg nvestas ndvdual dlm portofolo 12

13 Computaton of Expected Return for an Indvdual Rsky Investment Probablty Possble Rate of Return (Percent) Exhbt 7.1 Expected Return (Percent) E(R) =

14 Computaton of the Expected Return for a Portfolo of Rsky Assets Weght (W ) (Percent of Portfolo) Expected Securty Return (R ) Expected Portfolo Return (W X R ) E(R por ) = E(R por ) W R where : W = the percent of the portfolo n asset E(R ) = the expected rate of return for asset n = = 1 Exhbt

15 Varance (Standard Devaton) of Returns for an Indvdual Investment Devas standar adl akar pangkat dua dar varan Varan adl ukuran tentang varas return yg mungkn terjad R, dr return harapan [E(R )] 15

16 Varance (Standard Devaton) of Returns for an Indvdual Investment Varance ( σ 2 ) = n = 1 [R - E(R )] 2 P Notas P = probabltas dr return yg mungkn dterma (possble rate of return), R 16

17 Varance (Standard Devaton) of Returns for an Indvdual Investment Devas Standar (σ ) = n = 1 [R - E(R )] 2 P 17

18 Varance (Standard Devaton) of Returns for an Indvdual Investment Exhbt 7.3 Possble Rate Expected of Return (R ) Return E(R ) R - E(R ) [R - E(R )] 2 P [R - E(R )] 2 P σ Varan ( 2 ) =.0050 σ Devas Standar ( ) =

19 Varance (Standard Devaton) of Returns for a Portfolo Penghtungan return bulanan: Closng Closng Date Prce Dvdend Return (%) Prce Dvdend Return (%) Dec Jan % % Feb % % Mar % % Apr % % May % % Jun % % Jul % % Aug % % Sep % % Oct % % Nov % % Dec % % E(RCoca-Cola)= -1.81% E(Rhome Depot)== 1.47% Exhbt

20 Covarance of Returns Ukuran tentang derajat dmana dua varabel berubah bersama ( move together ) retalf pada nla rerata ndvdualnya Unt dua aset, dan j, kovaran return dtentukan sbg: Cov j = E{[R - E(R )][R j - E(R j )]} 20

21 Covarance and Correlaton Koefsen korelas dhtung dg menstandarsas (membag) kovaran dg angka devas standar ndvdual Koefsen Korelas berubah2 dar -1 to +1 r r j where : j σ σ j = Cov σ σ j j = the correlato n coeffcen t of returns = the standard devaton of R = the standard devaton of R t jt 21

22 Correlaton Coeffcent Koefsen korelas berubah-ubah hanya dlm ksaran +1 s/d -1. Nla +1 akan mengndkaskan hubungan postf sempurna bhw return dua aset bergerak bersama dlm pola lner sempurna. Nla 1 akan mengndkaskan hubungan negatf sempurnal Bhw return dua aset memlk persentas perubahan sama, tetap dg arah kebalkan 22

23 Portfolo Standard Devaton Formula σ σ port where : W port j n 2 2 = w σ + w where Cov = 1 = 1 = 1 j r j σ σ j n n = the standard devaton of the portfolo w j Cov = the weghts of the ndvdual assets n the portfolo, where weghts are determned by the proporton of value n the portfolo 2 σ = the varance of rates of return for asset Cov = the covarance between the rates of return for assets and j, = j 23

24 Portfolo Standard Devaton Calculaton Beberapa aset dr portofolo bsa dgambarkan dg dua karakterstk: Return harapan Devas standar harapan dar return Korelas dukur dg kovaran, yg berpengauh pd devas standar portofolo Korelas rendah mengurang rsko portofolo namun tak mempengaruh return harapan 24

25 Combnng Stocks wth Dfferent Returns and Rsk Asset E(R Case Correlaton Coeffcent Covarance a b c d e ) W σ 2 σ 25

26 Combnng Stocks wth Dfferent Returns and Rsk Aset mungkn berbeda dlm return harapan dan devas standar ndvdual Korelas negatf menurunkan rsko portofolo Mengkombnaskan dua aset dg korelas menurunkan devas standar portofolo menjad nol hanya jka devas standar ndvdual sama 26

27 Constant Correlaton wth Changng Weghts Asset E(R 1.10 r j = ) Case W 1 W 2 E(R ) f g h j k l

28 Constant Correlaton wth Changng Weghts Case W 1 W 2 E(R ) E( port ) f g h j k l

29 Portfolo Rsk-Return Plots for Dfferent Weghts E(R) Wth two perfectly correlated assets, t s only possble to create a two asset portfolo wth rsk-return along a lne between ether sngle asset 1 2 R j = Standard Devaton of Return 29

30 Portfolo Rsk-Return Plots for Dfferent Weghts E(R) Wth uncorrelated assets t s possble to create a two asset portfolo wth lower rsk than ether sngle asset j k f g 2 h R j = R j = Standard Devaton of Return 30

31 Portfolo Rsk-Return Plots for Dfferent Weghts E(R) Wth correlated assets t s possble to create a two asset portfolo between the frst two curves j k f g 2 h R j = R j = R j = Standard Devaton of Return 31

32 Portfolo Rsk-Return Plots for Dfferent E(R) 0.20 Wth negatvely correlated assets t s possble to create a two asset portfolo wth much lower rsk than ether sngle asset Weghts R j = j k h g f 2 R j = R j = R j = Standard Devaton of Return 32

33 Portfolo Rsk-Return Plots for Dfferent Weghts Exhbt 7.13 E(R) 0.20 R j = R j = Standard Devaton of Return j k h g f 2 R j = R j = R j = 0.00 Wth perfectly negatvely correlated assets t s possble to create a two asset portfolo wth almost no rsk 33

34 Estmaton Issues Hasl alokas portofolo tergantung pd nput statstkal yg akurat Estmas dar Return harapan Devas Standar Koefsen Korelas D antara seluruh pasangan aset Dg 100 aset, 4,950 estmas korelas Rsko estmas merujuk pd kesalahan potensal 34

35 Estmaton Issues Dg asums bhw return saham dpt dgambarkan dg model pasar tunggal (sngle market model), jumlah korelas yg dperlukan mengurang jumlah aset Sngle ndex market model: b = koefsen slope yg menghubungkan return sekurtas- dg return agregrat pasar saham Rm = Return pasar saham agregat R = a + b R m + ε 35

36 Estmaton Issues Jka semua sekurtas berhubungan sama dg pasar dan a b ddervas untuk tap sekurtas (each one), dpt dtunjukkan bhw koefsen korelas antara dua sekurtas dan j dtunjukkan (gven): r j = b where aggregate b σ j 2 m σ σ = 2 m σ j the stock varance market of returns for the 36

37 The Effcent Fronter The effcent fronter menyatakan bhw set portofolo dg return maksmum unt tap level rsko tertentu, atau Isko mnmum untuk tap tngkat return Fronter lbh tepat untuk portfolo nvestas dp sekurtas ndvdual Kecual unt aset dg return tertngg dan aset rsko terendah 37

38 Effcent Fronter for Alternatve Portfolos E(R) Effcent Fronter B Exhbt 7.15 A C Standard Devaton of Return 38

39 The Effcent Fronter and Investor Utlty Kurve utltas nvestor menunjukkan salng tukar (trade-offs) yg dngnkan nvestor antara return dan rsko Slope kurve effcent fronter turun scr tetap (steadly) ketka kt bergerak nak (upward) Dua nteraks tsb akan menentukan portofolo tertentu yg dplh oleh nvestorr ndvdual Portofolo optmal memlk utltas tertngg bag nvestor tertentu Port optmal terletak pd ttk tangen antara effcent fronter dan kurve utltas dg utltas tertngg (hghest possble utlty) 39

40 Selectng an Optmal Rsky Portfolo E(R port ) U 3 U 2 U1 Exhbt 7.16 Y U 3 U2 X U 1 E( σ port ) 40

41 The Internet Investments Onlne

42 Future topcs Chapter 8 Captal Market Theory Captal Asset Prcng Model Beta Expected Return and Rsk Arbtrage Prcng Theory 42