MM 6055

CAPITAL MARKET ANALYSIS

Portfolio Management

For Final Exam

Ferdinand Throedu (29111343)

MASTER OF BUSINESS ADMINISTRATION

SCHOOL OF BUSINESS AND MANAGEMENT

INSTITUT TEKNOLOGI BANDUNG

2012

Executive Summary

The Objective of this paper is to make optimum risky mutual funds equity portfolio. The

writer act as a treasury manager and have to sell and convince investors to buy his portfolio.

The portfolio per unit is set IDR 100.000.000 which should be consisted of 5 stocks as

given.And as a treasury manager, writer should found and calculate the optimum weight for

each stock in this portfolio that would satisfy investors demand and attract more customers to

buy this portfolio.

Before making the calculations, assumed that investors are mostly risk averse, means that

he/she will buy portfolio with the same return but lower risk. So the writer should recommend

the best combinations or proportions of each stock in this portfolio that will make optimum

risky portfolio (maksimum sharpe ratio) based on historical data on each stock within 5 years

(2007-2012).

In forming optimum risky portfolio, there are some steps are needed to follow :

- Collect Historical Data from Yahoo finance and Measure Average of SBI rate

- Measure Holding Period Return, Expected Return (AAR), Geometric Return and

Standard Deviation of each stock and also IHSG

- Build Covariance Matrix and Correlation Matrix then Calculate Beta of Each stock

- Measure past performance of each stock

- Determine contraints

- Forming Optimum Risky Portfolio using Add Solver

After calculations, writer recommend the optimum risk portfolio : PGAS (52,69%),

ITMG(21,34%), ASRI (18,66%), TLKM (7,31%), and BUMI (0%). This results considered

as efficient (diversified) portfolio that can be offered to risk averse investors (quite high

return 28,02% with lower volatility compare to each individual stock in this portfolio).

Considered on Master Plan Acceleration and expansion of Indonesia Economic Development

2011-2025 (MP3EI), Gas, coal Mining and ICT are included in 22 main economic activities

that will be expanded rapidly in several next years.

I. OBJECTIVE

The Objective of this paper is to make optimum risky mutual funds equity portfolio.

The writer act as a treasury manager and have to sell and convince investors to buy his

portfolio. The portfolio per unit is set IDR 100.000.000 which should be consisted of 5 stocks

as given.And as a treasury manager, writer should found and calculate the optimum weight

for each stock in this portfolio that would satisfy investors demand and attract more

customers to buy this portfolio.

Before making the calculations, assumed that investors are mostly risk averse, means

that he/she will buy portfolio with the same return but lower risk. So the writer should

recommend the best combinations or proportions of each stock in this portfolio that will make

optimum risky portfolio (maksimum sharpe ratio) based on historical data on each stock

within 5 years (2007-2012).

There are 2 questions that writer should answer :

1. How much do you have to invest for each stock in which the total investment of 5

stocks will not exceed the budget of portfolio setting per unit? How much is the

return of your portfolio and the net assets value (NAV)?

2. How is the risk of your portfolio that you will be proposed ?

II. ANALYSIS

A. Theory of Efficient Diversification and Performance of Stocks

As we know that diversifying our portfolio means we try to reduce or eliminate non-

systematic risk or diversiable risk. By doing diversification into many more stocks,

portfolio volatility should continue to fall.

There are two kind of investors : risk seeker and risk averse. Risk seeker investors usually

prefer to get higher risk to achieve higher return while risk averse investors usually prefer

to minimize risk to achieve some level target of return. Thats why to attract more

investors who has characteristic as risk averse, we should provide the optimum risky

portfolio. The optimum risky portfolio means that portfolio have a maksimum reward to

volatility (risk) ratio.

In order to form optimum risky portfolio based on hisorical data on each stock, there are

some steps that needed to follow :

1. Measure annual expected return and standard deviation of each stock .

There are several techniques to measure return of stock :

- Holding Period Returns : rate of return over a given investment period

- Arithmetic Average : sum of returns in each period divided by number of periods

=

=n

1T

Tavg

n

HPRHPR

- Geometric Average : single per period return that give the same cumulative

performance as the sequence of actual returns

1 )HPR(1HPR

/1n

1T

Tavg

+=

=

n

- Dollar weighted of Returns : internal rate of return (IRR) of cash flows

2. Build Covariance and Correlation Matrix of each stock in portfolio and also market

We need these matrix to calculate Beta of each stock (to calculate Beta portfolio also)

and also standard deviation of portfolio.

Covariance Matrix :

Correlation Matrix :

3. Measure Past Performances of each stock in portfolio

In order to measure past performance of each stock in a portfolio, we can use 3 type

of measurements :

- Sharpe Measure : ratio of stock excess return to standard deviation. This ratio

measures the reward to volatility trade off.

- Treynor Measure : ratio of stock excess return to beta. This ratio gives average

excess return per unit risk (systematic risk) incurred

- Jensen Measure : the alpha of an investment. If alpha is positive means that this

stock is undervalued while alpha is negative means that this stock is overvalued

Before we calculate 3 ratios above, we need to define expected return of risk free asset

(average of SBI rate) and calculate Expected return of market and also Beta of each stock.

4. Measure Expected Return of Portfolio, Standard Deviation of Portfolio, Beta of

Portfolio and Reward to Volatility Ratio of Portfolio

Expected Return of Portfolio :

Standard Deviation of Portfolio :

Beta of Portfolio :

=

=n

1i

ip iW

Reward to Volatility Ratio of Portfolio

B. Forming Optimum Risky Portfolio

As Given, five stocks that should be include at portfolio are ITMG, TLKM, ASRI, BUMI

and PGAS. These are some datas about these five stocks from reuters (accessed at 9 Nov

2012) :

ITMG TLKM ASRI BUMI PGAS

Company Name

Indoraya

Tambang Megah

PT Telkom

Indonesia

Alam Sutra

Realty

Bumi

Resources

Perusahaan Gas

Negara

Main Business Coal Mining

Telecommunication

Infrastructure Property Coal Mining Gas Mining

Current Price Rp41.600 Rp9.400 Rp570 Rp640 Rp4.575

= ==

+=n

i

n

j

n

i

i

1 1

2

1

))()( jijii2

p

2 k ,Cov(kwwkwk

Beta 1,62 0,6 1,49 1,86 0,88

Market Cap

(Mil.): Rp46.496.408 Rp188.496.000 Rp11.003.670 Rp13.502.710 Rp113.935.104

Shares

Outstanding

(Mil.):

1.129,93

20.160,00

19.649,41

20.773,40

24.241,51

a. Collect Historical Data from Yahoo finance and Measure Average of SBI rate

First step to form an optimal portfolio is to collect monthly historical data on each stock and

also IHSG (JKSE) from Yahoo Finance between Dec 2007 until October 2012 (because

ITMG listed from Dec 2007). Writer choose Monthly Data because dates between each

stock data is match (better than weekly data). IHSG historical data also downloaded because

it reflects market movements.

Average (annual) of SBI rate between 2007-2012 is used to determine expected return of risk

free asset. From calculation we got average SBI rate as much as 7,03%

b. Measure Holding Period Return, Expected Return (AAR), Geometric Return and Standard

Deviation of each stock and also IHSG

Annualized ITMG TLKM ASRI BUMI PGAS IHSG

Expected Return (arithmatic) 44,28% 7,33% 38,48% -11,21% 20,59% 13,36%

Geometric Return 25,08% 3,26% 25,84% -35,18% 13,75% 9,99%

Standard Deviation 63,25% 29,03% 56,99% 79,99% 38,52% 26,91%

Based on data above, it can be seen that within 5 years, rank of stock based on expected

return (from highest to smallest) : ITMG, ASRI, PGAS, TLKM, BUMI. And rank of stock

based on volatility (from highest to smallest) : BUMI, ITMG, ASRI, PGAS, TLKM.

c. Build Covariance Matrix and Correlation Matrix then Calculate Beta of Each stock

We can build Covariance Matrix and Correlation Matrix between each stock (and also IHSG)

using Data Analysis add-ins at Excel

Covariance Matrix

ITMG TLKM ASRI BUMI PGAS IHSG

ITMG 0,03276

TLKM 0,00385 0,00690

ASRI 0,01571 0,00152 0,02660

BUMI 0,02154 0,00252 0,02005 0,05240

PGAS 0,01070 0,00294 0,00807 0,00406 0,01215

IHSG 0,00955 0,00366 0,00883 0,01111 0,00526 0,00593

Correlation

Matrix

ITMG TLKM ASRI BUMI PGAS IHSG

ITMG 1,00000

TLKM 0,25617 1,00000

ASRI 0,53230 0,11230 1,00000

BUMI 0,51988 0,13271 0,53694 1,00000

PGAS 0,53622 0,32143 0,44865 0,16107 1,00000

IHSG 0,68560 0,57234 0,70343 0,63051 0,61988 1,00000

Using equation : , Beta of each stock could be calculated :

Stock Beta

ITMG 1,611607

TLKM 0,617421

ASRI 1,489921

BUMI 1,874488

PGAS 0,887426

These beta results already looks suitable from beta provided by reuters.

d. Measure past performance of each stock

After we calculate beta of each stock, market return, average SBI rate, return and volatility of

each stock, now we can Measure past performance of each stock : Sharpe Measure, Treynor

Measure and Jensen Measure.

Stocks Sharpe Treynor Jensen

ITMG 0,589 0,063 0,270

TLKM 0,010 0,005 -0,036

ASRI 0,552 0,211 0,220

BUMI -0,228 -0,097 -0,301

PGAS 0,352 0,153 0,079

IHSG 0,235 0,063 0,000

From Calculation Results above, it can be seen that only 3 stocks that had better past

performance than IHSG : ITMG, ASRI and PGAS. While PGAS and BUMI past

performances are worse than IHSG. It is noticed also that PGAS and BUMI are overvalued.

e. Determine contraints

Before we use add solver to construct optimum risky portfolio, we should determine the

constraints. There are 4 constraints that writer used :

- Total of investments should be 100 Million Rupiah

- For Stock which have return more than 20% annualy (ITMG,ASRI,PGAS), total

investments for that three stocks should at least 75 Million Rupiah

- For Stock which have high risk (volatility more than 51% and Beta above 1,45 :

ITMG, ASRI,BUMI), total investments for that three stocks should at most 40

Million Rupiah.

- For stock which have negative alpha/overvalued (TLKM,BUMI), total

investments for that two stocks should at most 10 Million Rupiah

f. Forming Optimum Risky Portfolio using Add Solver

And last step we will use add solver to find best proportions of each stock on portfolio to

achieve optimum risky portfolio (maksimum sharpe ratio) and also fulfill constraints. And

after running the add solver, we got the optimum risky portfolio as described below :

Stock Amount Invested Weight Expected Return Standard Deviation

ITMG Rp21.342.594 21,34% 44,28% 63,25%

TLKM Rp7.312.663 7,31% 7,33% 29,03%

ASRI Rp18.657.406 18,66% 38,48% 56,99%

BUMI Rp0 0,00% -11,21% 79,99%

PGAS Rp52.687.337 52,69% 20,59% 38,52%

Total Rp100.000.000

Required Rp100.000.000

Total Return (rupiah) Rp28.015.847

Portfolio Expected Return (%) 28,02%

Variance 13,99%

Stdev Portfolio 37,41%

Average risk free return 7,03%

Reward to Risk Volatility Ratio 0,5610

Beta 1,1347

VAR -59,01%

-Rp59.005.711

For BUMI dont get any weight because of contraints that already decided and because of bad

pas performance in the past (negative Sharpe, Treynor and Jensen Ratio; also below market)

and has a very high volatility (79,99%)

Based on Analysis above, now we can answer question no 1 and 2 :

1. In order to achieve Optimum Risky (Max Reward to Volatility Ratio) Portfolio, i have to

invest :

Stock Amount Invested Weight in Portfolio

ITMG Rp21.342.594 21,34%

TLKM Rp7.312.663 7,31%

ASRI Rp18.657.406 18,66%

BUMI Rp0 0,00%

PGAS Rp52.687.337 52,69%

The return of writer portfolio is 28,02% per annum or Rp28.015.847 for first year. This rate

of return already bigger than return of BUMI, TLKM and PGAS but below return of ITMG

and ASRI.

Calculation for Net Asset Value :

Stock Amount Invested Weight in Portfolio Current Price Shares Outstanding

ITMG Rp21.342.594 21,34% 41.600 513

TLKM Rp7.312.663 7,31%

9.400 778

ASRI Rp18.657.406 18,66% 570 32732

BUMI Rp0 0,00%

640 0

PGAS Rp52.687.337 52,69%

4.575 11516

Total Rp100.000.000 Total 45540

assumed no fee charged

Return 28,02% Initial NAV Years Rp2.196

1st Year NAV 1 Rp2.811

2nd Year NAV 2 Rp3.599

3rd Year NAV 3 Rp4.607

4thYear NAV 4 Rp5.897

5th Year NAV 5 Rp7.550

assumed there is 5% back end load (until 5 year);reduces 1 %next year

Return 28,02% Initial NAV Years Rp2.196

Back end load 5,00% 1st Year NAV 1 Rp2.699

2nd Year NAV 2 Rp3.351

3rd Year NAV 3 Rp4.204

4thYear NAV 4 Rp5.328

5th Year NAV 5 Rp6.821

2. About Risk of portfolio that writer proposed :

- Standard Deviation of Portfolio is 37,41% , smaller than ITMG, ASRI, BUMI,

PGAS .

- Beta of Portfolio is 1,13 , closer to 1 than ITMG, TLKM, ASRI, BUMI.

Based on data above it can be seen that by diversification, volatility of portfolio become smaller than

volatility of individual stock. And because most of investors are risk averse, the optimum risky (max

reward to volatility ratio) portfolio (include some constraints) is the best portfolio that can be offered

to them. Maksimum risk aversion that an investor should choose to invest in this portfolio is :

C. Macroeconomy analysis and prospectus

Within Current GDP growth of 6,4% , interest rate of 5,75% (SBI rate), and inflation

rate of 4,5% in second quarter 2012, Indonesia economy has sustainable growth of 6,5%

.This growth will cause demand for energy (oil, gas and coal) increase. Demand for

energy not only come frome domestic market but also from foreign market such as China.

Thats why energy industry such as Gas and Coal Mining should have good prospect for

few next years. The property industri also will be stronger because of low mortgage rate

(KPR), increment of GDP per capita and increment of house and property needs. For

Telecommunication Industry, growth become slower in last 3 years but sentiment and

prospect in the future still positive because telecommunication technology in Indonesia

not mature enough. IHSG index also increase by 10,37% from 3141,69 in January 2012 to

4350,29 in October 2012 and have target price of 4400 at the end of 2012.

Considered on Master Plan Acceleration and expansion of Indonesia Economic

Development 2011-2025 (MP3EI), Gas, coal Mining and ICT are included in 22 main

economic activities that will be expanded rapidly in several next years.

Name of Portfolio : Secure Fund Portfolio

Total investments per unit : Rp 100 Million

Shares outstanding in each unit : 45.540 shares

NAV per unit : Rp 2.196

Indoraya

Tambang

Megah,

21.34%PT

Telekomunika

si Indonesia,

7.31%

Alam Sutra

Realty,

18.66%

Bumi

Resources,

0.00%

Perusahaan

Gas Negara,

52.69%

Secure Fund Portfolio

9995,2.50

)(2

=

=

rrEA

p

fp

Return & NAV per unit

Period Return NAV per unit

1 months 0,26% Rp2.202

3 months 3,14% Rp2.265

6 months 13,14% Rp2.485

1 years 28,02% Rp2.811

3 years 109,79% Rp4.607

5 years 243,81% Rp7.550

Another statistic measurements :

Stdev Portfolio 37,41%

Reward to Risk Volatility Ratio (Sharpe Ratio) 0,5610

Beta 1,1347

VAR (max loss per annum) -59,01%

or -Rp59.005.711

Return Volatility

ITMG 44,28% 63,25%

TLKM 7,33% 29,03%

ASRI 38,48% 56,99%

BUMI -11,21% 79,99%

PGAS 20,59% 38,52%

Secure Fund Portfolio 28,02% 37,41%

III. CONCLUSION and RECOMMENDATION

3.1 Conclusion

1. The optimum risky portfolio means that portfolio that have maksimum reward to volatility

ratio (sharpe ratio). This kind of portfolio is considered as efficient (diversified) portfolio

because it has lower volatility to achieve good return. And because most of investors are risk

averse, this efficient portfolio should be the best portfolio that can be offered to them.

2. In forming optimum risky portfolio, there are some steps are needed to follow :

- Collect Historical Data from Yahoo finance and Measure Average of SBI rate

- Measure Holding Period Return, Expected Return (AAR), Geometric Return and Standard

Deviation of each stock and also IHSG

- Build Covariance Matrix and Correlation Matrix then Calculate Beta of Each stock

- Measure past performance of each stock

- Determine contraints

- Forming Optimum Risky Portfolio using Add Solver

3. To Support the analysis in forming optimum risky portfolio, we should consider

macroeconomic analysis and prospect of this portfolio (return, NAV, volatility and

maximum loss)

3.2 Recommendation

Optimum Risky Portfolio that i recommend to invest :

Stock Amount Invested Weight in Portfolio Expected Return Standard Deviation

ITMG Rp21.342.594 21,34% 44,28% 63,25%

TLKM Rp7.312.663 7,31% 7,33% 29,03%

ASRI Rp18.657.406 18,66% 38,48% 56,99%

BUMI Rp0 0,00% -11,21% 79,99%

PGAS Rp52.687.337 52,69% 20,59% 38,52%

And statistic analysis of this kind of portfolio :

Portfolio Expected Return (%) 28,02%

Variance 13,99%

Stdev Portfolio 37,41%

Average risk free return 7,03%

Reward to Risk Volatility Ratio 0,5610

Beta 1,1347

VAR per annum -59,01%

or -Rp59.005.711

I choose PGAS as the biggest investment proportion(52,69%) in this portfolio because of it

has return (>20%) but has lower volatility (38,52%) compare to ITMG (63,25%) and ASRI

(56,99%). The second biggest proportion (21,34%) goes to ITMG because it has biggest

annual return but also bear highest risk too. For BUMI dont get any weight because of

contraints that already decided and because of bad pas performance in the past (negative

Sharpe, Treynor and Jensen Ratio; also below market) and has a very high volatility (79,99%)

Considered on Master Plan Acceleration and expansion of Indonesia Economic Development

2011-2025 (MP3EI), Oil and Gas, coal Mining and ICT are included in 22 main economic

activities that will be expanded rapidly in several next years.

\

APPENDIX I Charts of 5 years Movement Price of Each Stocks versus IHSG

- ITMG versus IHSG

- TLKM versus IHSG

- ASRI versus IHSG

- BUMI versus IHSG

- PGAS versus IHSG