Upload
ferdinand-troedu-p-gultom
View
21
Download
0
Embed Size (px)
DESCRIPTION
Capital Market final exam
Citation preview
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