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

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

Chapter 7 - An Introduction to Portfolio Management Questions to be answered: 1. What do we mean by risk aversion and what evidence indicates that investors are generally risk averse? 2. What are the basic assumptions behind the Markowitz portfolio theory? 3. What is meant by risk and what are some of the alternative measures of risk used in investments? 4. How do you compute the expected rate of return for an individual risky asset or a portfolio of assets? 5. How do you compute the standard deviation of rates of return for an individual risky asset? 6. What is meant by the covariance between rates of return and how do you compute covariance? 2 Bandi, 2010

Chpt 7-Reilly & Brown UNS

Maksi

7. 8. 9. 10. 11. 12. 13.

What is the relationship between covariance and correlation? What is the formula for the standard deviation for a portfolio of risky assets and how does it differ from the standard deviation of an individual risky asset? Given the formula for the standard deviation of a portfolio, how and why do you diversify a portfolio? What happens to the standard deviation of a portfolio when you change the correlation between the assets in the portfolio? What is the risk-return efficient frontier? Is it reasonable for alternative investors to select different portfolios from the portfolios on the efficient frontier? What determines which portfolio on the efficient frontier is selected by an individual investor?

3 Bandi, 2010


Maksi

Background Assumptions • investor memaksimumkan return pd tingkat risiko tertentu. • Portofolio melibatkan seluruh aset dan kewajiban investor • Hubungan antara return aset dlm portofolio sangat penting • Portofolio yg baik bukanlah kumpulan sederhana investasi yg baik secara individual 4 Bandi, 2010


Maksi

Risk Aversion (Benci Risiko) • Dg satu pilihan antar dua aset dg return yg sama, Investor umumnya memilih aset dengan tingkat risiko lebih kecil • Buktinya: – Banyak investor membeli asuransi: kematian, kendaraan, kesehatan, dan ketidakpastian pendapatan. • Pembeli mempertukarkan biaya yg pasti untuk risiko keugian yg tidak pasti

– Pendapatan obligasi meningkat sebanding dengan kelompok risiko dari AAA to AA to A…. 5 Bandi, 2010


Maksi

Not all investors are risk averse

• Preferensi Risiko: hrs dilakukan dengan jumlah uang yg dikeluarkan-sedikit, untuk memastikan kerugian yg besar

6 Bandi, 2010


Maksi

Definition of Risk 1. Ketidakpastian atas hasil mendatang, atau 2. Probabilitas dari hasil yg tidak diinginkan (adverse outcome)

7 Bandi, 2010


Maksi

Markowitz Portfolio Theory • Mengkuantitatifkan risiko • Menderivasi ukuran return harapan bg portofolio aset dan risiko harapannya • Menunjukkan bhw varian dari return mrp ukuran berarti tentang risiko portofolio • Menderivasi formula untuk menghitung varian portfolio, yg menunjukkan bgm mendiversifikasi scr efektif suatu portofolio

8 Bandi, 2010


Maksi

Assumptions of Markowitz Portfolio Theory 1. 2. 3. 4. 5.

Investor mempertimbangkan tiap alternatif investasi spt yg sdg disajikan dg distribusi probabilitas dr return ekspektasi slm beberapa periode pemilikan investasi. Investor meminimumkan utilitas ekpektasi satu-periode, dan kurve utilitasnya menunjukkan utilitas marjinal yg menurun dr kemakmuran (diminishing marginal utility of wealth). Investor menestimasi risiko portofolio atas basis variabilitas return harapan. Investor mendasarkan keputusan hanya pd return harapan dan risiko, sehingga kurve utilitasnya mrp fungsi dr return ekspektasi dan varian ekspektasi (atau deviasi standar) dr retun saja. Unt level risiko tertentu, investor lbh memilih return lbh tinggi dp return lbh rendah. Begitu juga, unt level return ekspektasi tertentu, investor lbh memilih risiko lbh rendah dp risko lbh besar. 9 Bandi, 2010


Maksi

Markowitz Portfolio Theory • Menggunakan 5 asumsi, aset tunggal atau portofolio aset dianggap efisien jika: – Tidak ada aset/portofolia aset yg menawarkan return lbh tinggi dg risiko sama (atau lebih rendah), atau – Risiko lebih rendah dengan return sama (lbh tinggi) 10 Bandi, 2010


Maksi

Alternative Measures of Risk • Varian atau deviasi standar dari return harapan • Kisaran return (Range of returns) • Return di bawah harapan – Semivarian – ukuran yg hanya mempertimbangkan deviasi di bawah rerata – Ukuran risiko ini mengasumsikan scr implisit bhw investor ingin meminimumkan kurangnya return yg lbh rendah dp tingkat target return 11 Bandi, 2010


Maksi

Expected Rates of Return • Unt aset individual – jumlah dr retun potensial dikalikan dg probabilitas return • Untuk portofolio aset – rata-rata tertimbang return harapan bg investasi individual dlm portofolio

12 Bandi, 2010


Maksi

Computation of Expected Return for an Individual Risky Investment Exhibit 7.1

Probability 0.25 0.25 0.25 0.25

Expected Return (Percent)

Possible Rate of Return (Percent) 0.08 0.10 0.12 0.14

0.0200 0.0250 0.0300 0.0350 E(R) = 0.1100 13

Bandi, 2010


Maksi

Computation of the Expected Return for a Portfolio of Risky Assets Weight (Wi ) (Percent of Portfolio) 0.20 0.30 0.30 0.20

Expected Portfolio Return (Wi X Ri )

Expected Security Return (Ri ) 0.10 0.11 0.12 0.13

0.0200 0.0330 0.0360 0.0260 E(Rpor i) = 0.1150

Exhibit 7.2

n

E(R

por i

)=

∑WR i

i

i =1

where : W i = the percent of the portfolio in asset i E(R i ) = the expected rate of return for asset i 14 Bandi, 2010


Maksi

Variance (Standard Deviation) of Returns for an Individual Investment • Deviasi standar adl akar pangkat dua dari varian • Varian adl ukuran tentang variasi return yg mungkin terjadi Ri, dr return harapan [E(Ri)]

15 Bandi, 2010


Maksi

Variance (Standard Deviation) of Returns for an Individual Investment n

Variance (σ ) = ∑ [R i - E(R i )] Pi 2

2

i =1

Notasi Pi = probabilitas dr return yg mungkin diterima (possible rate of return), Ri 16 Bandi, 2010


Maksi

Variance (Standard Deviation) of Returns for an Individual Investment Deviasi Standar n

(σ ) =

∑ [R

2

i

- E(R i )] Pi

i =1

17 Bandi, 2010


Maksi

Variance (Standard Deviation) of Returns for an Individual Investment Exhibit 7.3 Possible Rate

Expected

of Return (R i )

Return E(R i )

R i - E(R i )

[R i - E(R i )]

0.08 0.10 0.12 0.14

0.11 0.11 0.11 0.11

0.03 0.01 0.01 0.03

0.0009 0.0001 0.0001 0.0009

2

Pi 0.25 0.25 0.25 0.25

2

[R i - E(R i )] Pi 0.000225 0.000025 0.000025 0.000225 0.000500

Varian ( σ 2) = .0050 Deviasi Standar ( σ ) = .02236

18 Bandi, 2010


Maksi

Variance (Standard Deviation) of Returns for a Portfolio Exhibit 7.4

Penghitungan return bulanan: Date Dec.00 Jan.01 Feb.01 Mar.01 Apr.01 May.01 Jun.01 Jul.01 Aug.01 Sep.01 Oct.01 Nov.01 Dec.01

Closing Price

Dividend

Return (%)

60.938 58.000 -4.82% 53.030 -8.57% 45.160 0.18 -14.50% 46.190 2.28% 47.400 2.62% 45.000 0.18 -4.68% 44.600 -0.89% 48.670 9.13% 46.850 0.18 -3.37% 47.880 2.20% 46.960 0.18 -1.55% 47.150 0.40% E(RCoca-Cola)= -1.81%

Closing Price

Dividend

Return (%)

45.688 48.200 5.50% 42.500 -11.83% 43.100 0.04 1.51% 47.100 9.28% 49.290 4.65% 47.240 0.04 -4.08% 50.370 6.63% 45.950 0.04 -8.70% 38.370 -16.50% 38.230 -0.36% 46.650 0.05 22.16% 51.010 9.35% E(Rhome E(RExxon)= Depot)= 1.47% 19

Bandi, 2010


Maksi

Covariance of Returns • Ukuran tentang derajat dimana dua variabel berubah bersama (“move together”) retalif pada nilai rerata individualnya • Unt dua aset, i dan j, kovarian return ditentukan sbg: Covij = E{[Ri - E(Ri)][Rj - E(Rj)]}

20 Bandi, 2010


Maksi

Covariance and Correlation • Koefisien korelasi dihitung dg menstandarisasi (membagi) kovarian dg angka deviasi standar individual • Koefisien Korelasi berubah2 dari -1 to +1

rij =

Cov ij

σ iσ

j

where : rij = the correlatio n coefficien t of returns

σ i = the standard deviation of R it σ j = the standard deviation of R jt 21 Bandi, 2010


Maksi

Correlation Coefficient • Koefisien korelasi berubah-ubah hanya dlm kisaran +1 s/d -1. • Nilai +1 akan mengindikasikan hubungan positif sempurna – bhw return dua aset bergerak bersama dlm pola linier sempurna.

• Nilai –1 akan mengindikasikan hubungan negatif sempurnal – Bhw return dua aset memiliki persentasi perubahan sama, tetap dg arah kebalikan 22 Bandi, 2010


Maksi

Portfolio Standard Deviation Formula n

σ port =

n

∑w σ 2 i

2 i

n

+ ∑∑ w i w j Cov ij

i =1

i =1 i =1

where :

σ port = the standard deviation of the portfolio Wi = the weights of the individual assets in the portfolio, where weights are determined by the proportion of value in the portfolio

σ i2 = the variance of rates of return for asset i Cov ij = the covariance between the rates of return for assets i and j, where Cov ij = rijσ iσ j 23 Bandi, 2010


Maksi

Portfolio Standard Deviation Calculation • Beberapa aset dr portofolio bisa digambarkan dg dua karakteristik: – Return harapan – Deviasi standar harapan dari return

• Korelasi diukur dg kovarian, yg berpengauh pd deviasi standar portofolio • Korelasi rendah mengurangi risiko portofolio namun tak mempengaruhi return harapan 24 Bandi, 2010


Maksi

Combining Stocks with Different Returns and Risk Asset 1

Case a b c d e

E(R i )

Wi

σ

.50

.0049

.07

.20

.50

.0100

.10

.10

2

Correlation Coefficient +1.00 +0.50 0.00 -0.50 -1.00 Bandi, 2010

2


σi

i

Covariance .0070 .0035 .0000 -.0035 -.0070 Maksi

25

Combining Stocks with Different Returns and Risk • Aset mungkin berbeda dlm return harapan dan deviasi standar individual • Korelasi negatif menurunkan risiko portofolio • Mengkombinasikan dua aset dg korelasi 1.0 menurunkan deviasi standar portofolio menjadi nol hanya jika deviasi standar individual sama 26 Bandi, 2010


Maksi

Constant Correlation with Changing Weights Asset

E(R i )

1

.10

2

.20

rij = 0.00

2

Case

W1

W

f g h i j k l

0.00 0.20 0.40 0.50 0.60 0.80 1.00

1.00 0.80 0.60 0.50 0.40 0.20 0.00

Bandi, 2010


E(R i ) 0.20 0.18 0.16 0.15 0.14 0.12 0.10 27 Maksi

Constant Correlation with Changing Weights

Case

W1

W2

E(Ri )

E(port)

f g h i j k l

0.00 0.20 0.40 0.50 0.60 0.80 1.00

1.00 0.80 0.60 0.50 0.40 0.20 0.00

0.20 0.18 0.16 0.15 0.14 0.12 0.10

0.1000 0.0812 0.0662 0.0610 0.0580 0.0595 0.0700 28

Bandi, 2010


Maksi

Portfolio Risk-Return Plots for Different Weights E(R) 0.20 0.15 0.10

With two perfectly correlated assets, it is only possible to create a two asset portfolio with risk-return along a line between either single asset

2

Rij = +1.00 1

0.05 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12

Standard Deviation of Return 29 Bandi, 2010


Maksi

Portfolio Risk-Return Plots for Different Weights E(R) 0.20 0.15

f With uncorrelated assets it is possible to create a two asset i portfolio with lower risk j than either single asset

k

0.10

2

g h

Rij = +1.00 1 Rij = 0.00

0.05 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12



Maksi

Portfolio Risk-Return Plots for Different Weights E(R) 0.20 0.15 0.10

f With correlated assets it is possible to create a i two asset portfolio j between the first two curves k

2

g h

Rij = +1.00 Rij = +0.50

1 Rij = 0.00

0.05 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12



Maksi

Portfolio Risk-Return Plots for Different Weights E(R) 0.20 0.15

With negatively correlated assets it is possible to create a two asset portfolio with much lower risk than either single asset

Rij = -0.50

2

g h j k

0.10

f

i Rij = +1.00 Rij = +0.50

1 Rij = 0.00

0.05 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12



Maksi

Portfolio Risk-Return Plots for Exhibit 7.13 Different Weights E(R) 0.20

f

Rij = -0.50 Rij = -1.00

2

g h

0.15

j

0.10

k

0.05

i Rij = +1.00 Rij = +0.50

1 Rij = 0.00

With perfectly negatively correlated assets it is possible to create a two asset portfolio with almost no risk

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12



Maksi

Estimation Issues • Hasil alokasi portofolio tergantung pd input statistikal yg akurat • Estimasi dari – Return harapan – Deviasi Standar – Koefisien Korelasi • Di antara seluruh pasangan aset • Dg 100 aset, 4,950 estimasi korelasi

• Risiko estimasi merujuk pd kesalahan potensial 34 Bandi, 2010


Maksi

Estimation Issues • Dg asumsi bhw return saham dpt digambarkan dg model pasar tunggal (single market model), jumlah korelasi yg diperlukan mengurangi jumlah aset • Single index market model:

R i = a i + bi R m + ε i • bi = koefisien slope yg menghubungkan return sekuritas-i dg return agregrat pasar saham • Rm = Return pasar saham agregat 35 Bandi, 2010


Maksi

Estimation Issues • Jika semua sekuritas berhubungan sama dg pasar dan a bi diderivasi untuk tiap sekuritas (each one), dpt ditunjukkan bhw koefisien korelasi antara dua sekuritas i dan j ditunjukkan (given): σ m2 rij = b i b j σ iσ j where σ m2 = the variance of returns for the aggregate stock market 36 Bandi, 2010


Maksi

The Efficient Frontier • The efficient frontier menyatakan bhw – set portofolio dg return maksimum unt tiap level risiko tertentu, atau – Isiko minimum untuk tiap tingkat return

• Frontier lbh tepat untuk portfolio investasi dp sekuritas individual – Kecual unt aset dg return tertinggi dan aset risiko terendah 37 Bandi, 2010


Maksi

Efficient Frontier for Alternative Portfolios Exhibit 7.15

E(R)

Efficient Frontier

A

B

C

Standard Deviation of Return 38

Bandi, 2010


Maksi

The Efficient Frontier and Investor Utility • Kurve utilitas investor menunjukkan saling tukar (trade-offs) yg diinginkan investor antara return dan risiko • Slope kurve efficient frontier turun scr tetap (steadily) ketika kit bergerak naik (upward) • Dua interaksi tsb akan menentukan portofolio tertentu yg dipilih oleh investorr individual • Portofolio optimal memiliki utilitas tertinggi bag investor tertentu • Port optimal terletak pd titik tangen antara efficient frontier dan kurve utilitas dg utilitas tertinggi (highest possible utility)

39 Bandi, 2010


Maksi

Selecting an Optimal Risky Portfolio Exhibit 7.16

E(R port )

U3’ U2’

U1’

Y U3

X

U2 U1

E(σ port ) Bandi, 2010


Maksi

40

The Internet Investments Online www.pionlie.com www.investmentnews.com www.micropal.com www.riskview.com www.altivest.com

41 Bandi, 2010


Maksi

Future topics Chapter 8 • • • • •

Capital Market Theory Capital Asset Pricing Model Beta Expected Return and Risk Arbitrage Pricing Theory 42 Bandi, 2010


Maksi

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

Recommend Documents