Download 1.4. creating securities investment portfolios

THE STATE BANK OF VIETNAM
MINISTRY OF EDUCATION AND TRAINING
BANKING ACADEMY OF VIETNAM
**********
TRAN VAN TRI
CONSTRUCTION AND MANAGEMENT OF
THE STOCK PORTFOLIO IN VIETNAM
MAJOR
: FINANCE - BANKING
CODE
: 62.34.02.01
SUMMARY OF PH.D DISSERTATION ON
ECONOMICS
HANOI – 2015
The dissertation is completed at:
………………………………………………………………………
…………….…………………………………………………………
Scientific supervisor:
Supervisor 1: Prof.Dr. Nguyen Khac Minh
Supervisor 2: Assoc.Prof., Dr. Truong Quoc Cuong
Commentator 1:
Commentator 2:
Commentator 3:
The dissertation shall be defended in front of the Board of
Examination of……
In ……………….. At: ……… , ……../……./……..
The dissertation can be found at the libraries as follows:
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INTRODUCTION
1. The necessity of the topic
For the stable and sustainable development of the stock market of
Vietnam, it is necessary to work out technical solutions for investors
to analyze stock investment.
The positive effect of portfolio investment has been proved both in
studies and in reality. In Vietnam, the studies that are applied
practically in the market are limited; the scope of examining the
application is also limited within a small group of certain securities.
The application of portfolio theory in creating and managing
investment items in the stock market of Vietnam needs to be studied,
developed, and applied. Therefore, the researcher chose “Creating
and managing stock portfolio investment in Vietnam” as the topic
of the thesis.
2. Overview of the study
2.1. Studies on theories and experiments in the world
2.1.1. Mean – variance portfolio theory
Markowitz is the father of “Modern portfolio theory” with two
studies: Portfolio Selection [76] and Portfolio Diversification [77].
After Markowitz, some studies attempt to improve the effectiveness
or replace Mean – variance portfolio theory including Tobin, Lee
[71], Kraus and Litzenberger [70], Fama [61] Fama [60], Hakanssan
[65], [66], Meton [79], Mossin [81], Li and Ng [72], Zhou and Li
[73] Bielecki and colleagues [53], Xia and Yan [90]. However, Mean
– variance portfolio theory has been remaining its significant role in
modern portfolio theory.
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2.1.2. Stock pricing models
There are a considerable number of studies on input for mean –
variance portfolio theory. Single-index model and multi-index model
were developed. Some typical studies were those of Roll, R. và S.
Ross [84]; Dhrymes, Friend and Gultekin [57], Brown, Weinstein
[54], Cho, Elton, Gruber [56], Ross [86], Ingersoll [67].
The Capital Asset Pricing Model (CAPM) was developed in the early
years of 1960s by William Sharpe [87], John Lintner [69] and Jan
Mossin [81]. This model can quickly quantify the relation between
income and risks of assets, and has still been the main standard in asset
pricing. Some experiments applying Capital Asset Pricing Model
(CAPM) are those of Ming-Hsiang Chen [80], Puneet Handa,
S.P.Kothari, and Charles Wasley [83], Gabriel A.Hawawini [62],
Grigoris Michailidis [63].
2.1.3. Investment portfolio evaluation
Studies on Investment Portfolio Performance Evaluation consider
both incomes and risks including Sharpe Ratio, Treynor Ratio,
Jensen Ratio; Friend, Blume and Crockett’s.
The theories and models mentioned above are helpful for creating
and managing investment portfolio of the thesis.
2.2. Studies on theories and experiments in Vietnam
Researchers and experimentalists in Vietnam have accessed to
modern investment portfolio theory in creating and managing stock
investment portfolios. However, no study has fully applied modern
investment portfolio theory in creating and managing investment
portfolios in the stock market of Vietnam. On the other hand,
applying Capital – Asset Pricing Model (CAPM) in portfolio
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selection still has certain shortcomings which will be studied and
remedied in this thesis.
3. Aims of the study
The study aims to applying the Capital – Asset Pricing Model (CAPM)
and Portfolio Theory by Markowitz to experimenting on creating and
managing investment portfolios in the stock market of Vietnam.
4. Object and scope of the study
a. Object of the study:
Creating and managing investment portfolios in the stock market
of Vietnam.
b. Scope of the theory:
- Theory and experiment for creating and managing stock
investment portfolios are based on theoretical framework of the
Capital – Asset Pricing Model (CAPM) and Portfolio Theory by
Harry Markowitz.
- Indexes of VNINDEX, HNXINDEX, rate of Government bonds,
and rates of bonds listed on Ho Chi Minh Stock Exchange and Hanoi
Stock Exchange are from 2008 to 2013.
5. Methodology
- Applying Quantitative method with secondary source of
statistics.
- Using Eviews software for regression to find out the value of
systematic risk (β) of securities based on the Capital – Asset Pricing
Model (CAPM) and to identify the value of α of the stock as the basis
for pricing and selecting investment portfolio.
- Applying mathematical model and Solve tool to identify
proportion of investment of securities and form investment portfolio.
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- Applying methods of Sharpe, Treynor, and Jensen to evaluate
performance of investment portfolios and manage investment portfolios.
6. Expected contributions of the thesis
- Systematize and clarify investment portfolio theory, Capital – Asset
Pricing Model (CAPM), and some effective methods for investment
portfolio performance evaluation by Sharpe, Treynor, and Jensen.
- Analyze benefits of portfolio investment.
- Point out the factors determining the increase in benefits of
portfolio investment.
- Point out time for observation and frequency of data observation
to apply Capital – Asset Pricing Model (CAPM) for highest
effectiveness.
- Propose solutions to increasing reliability of effectiveness
assessment of investment portfolios when applying methods for
investment portfolio performance evaluation by Sharpe, Treynor,
and Jensen.
- Analyze and point out factors needed to be created and adjusted to
improve the ability to apply in creating portfolios and propose solutions.
7. Contents and organization of the thesis
Introduction, Conclusion, and 3 chapters:
Chapter 1: Basic problems with creating and managing stock
investment portfolios.
Chapter 2: Conducting experiments on creating and managing stock
investment portfolios in Vietnam.
Chapter 3: Solutions to complete application of investment portfolio
theory in creating and managing stock investment
portfolios in Vietnam.
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CHAPTER 1
BASIC PROBLEMS WITH CREATING AND MANAGING
SECURITY INVESTMENT PORTFOLIOS
1.1. SECURITY INVESTMENT PORTFOLIO
1.1.1. Definition of security investment portfolios
1.1.2. Income and risks of security investment portfolios
1.1.2.1. Income of security investment portfolio
𝒏
𝐄(𝑹𝑷 ) = ∑ 𝒘𝒊 . 𝑬(𝒓𝐢 )
𝒊=𝟏
1.1.2.2. Risks of security investment portfolios
𝑛
𝝈2𝑃
=
𝑛
∑ 𝑤𝑖2 𝝈2𝑖
𝑖=1
+ ∑ ∑ 𝑤𝑖 𝑤𝑗 𝐶𝑜𝑣 ( 𝑖, 𝑗 )
𝒏
𝝈𝑷 =
𝑛
√∑ 𝒘𝟐𝒊 𝝈𝟐𝒊
𝒊=𝟏
𝑖=1 𝑗=1
𝒏
𝒏
+ ∑ ∑ 𝒘𝒊 𝒘𝒋 𝑪𝒐𝒗 ( 𝒊, 𝒋 )
𝒊=𝟏 𝒋=𝟏
( i # j)
1.1.3. Investment portfolio diversification
1.1.3.1. Systematic and unsystematic risks
Unsystematic risks are particular risks or specific risks of separate
assets which can be got rid of by diversification. Systematic risks are
the rest of overall risks after excluding unsystematic risks. These
risks cannot be excluded by diversification of investment portfolios.
1.1.3.2. Investment portfolio diversification and coefficient β
As portfolios are fully diversified – market portfolios, the level of
risks of each security contributed to portfolio is
𝜷𝒊 = 𝝈𝒊𝑴 /𝝈𝟐𝑴
Coefficient β of a security measures its income sensitivity in
comparison with income of market portfolio.
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1.1.4. Overview of some Capital – Asset Pricing Models
1.1.4.1. Capital – Asset Pricing Model (CAPM)
𝑬(𝒓𝒊 ) = 𝒓𝒇 + 𝜷𝒊 [ 𝑬(𝑹𝑴 ) − 𝒓𝒇 ]
1.1.4.2. Single – index model
𝒓𝒊 − 𝒓𝒇 = 𝜶𝒊 + 𝜷𝒊 [ 𝑬(𝒓𝑴 ) − 𝒓𝒇 ] + 𝒆𝒊
1.1.4.3. Model of Arbitrage Pricing Theory (APT)
𝒏
𝑬(𝒓𝒊 ) = ∑ 𝜷𝒊,𝒌 × [𝑬(𝒓𝒌 ) − 𝒓𝒇 ] + 𝒖𝒊
𝒌=𝟏
1.1.5. Strategies in managing security investment portfolios
Active management strategy of investment portfolios, passive
management strategy of investment portfolios, mixed management
strategy of investment portfolios.
1.2. PROCEDURE OF CREATING AND MANAGING INVESTMENT
PORTFOLIOS
Procedure of creating and managing investment portfolios consists of
following steps: identifying investment aims and policies, selection of
security for investment, creating investment portfolios (asset
distribution), and managing investment portfolios (evaluating and
adjusting investment portfolios)
1.3. SELECTION OF STOCK FOR INVESTMENT WITH
CAPITAL – ASSET PRICING MODEL (CAPM)
The model is built based on the offset level of risks of investment
or maximizing the usefulness of investment portfolios with result: in
the equilibrium of the capital market, expected income of a random
security is higher than risk-free rate by an amount that offsets risks
by the composition of systematic risks of the security (β of the
security) and level of risk offset of market portfolio.
𝑬(𝒓𝒊 ) = 𝒓𝒇 + 𝜷𝒊 [ 𝑬(𝑹𝑴 ) − 𝒓𝒇 ]
The diagram is called Security Market Line (SML). In the
equilibrium, the securities that are properly priced are laid on the
Security Market Line (SML). Underpriced securities with positive value
of α (α: variance between actual return rate and return rate based on
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Capital Asset Pricing Model (CAPM)) will lie on the upper side of the
Security Market Line (SML) and they are recommended to be kept in
the portfolio. Vice versa, overpriced securities with negative value of α
will lie under the Security Market Line (SML) and they are
recommended to be removed from the investment portfolio.
1.4. CREATING SECURITIES INVESTMENT PORTFOLIOS
1.4.1. Creating effective investment portfolios of risk securities
Problem 1: Objective function:
𝒏
𝑬(𝑹𝒑 ) = ∑ 𝒘𝒊 𝑬(𝒓𝒊 ) → 𝒎𝒂𝒙
𝒊=𝟏
With the restrictions as follows:
∑𝒏𝒊=𝟏 𝒘𝒊 = 𝟏
𝟎 ≤wi ≤ 1
𝝈𝟐𝒑 ≤ 𝝈𝟐𝒙
Problem 2: Objective function:
𝒏
𝝈𝟐𝒑
=
∑ 𝒘𝟐𝒊 𝝈𝟐𝒊
𝒊=𝟏
𝒏
+ ∑ 𝒘𝒊 𝒘𝒋 𝑪𝒐𝒗(𝒓𝒊 𝒓𝒋 ) → 𝐦𝐢𝐧
𝒊=𝟏
𝒋=𝟏
With the restrictions as follows:
𝒏
∑ 𝒘𝒊 = 𝟏
𝒊=𝟏
𝟎 ≤wi ≤ 1
𝒏
𝑬(𝑹𝒑 ) ≥ 𝐫𝒚 , 𝒗ớ𝒊 𝑬(𝑹𝒑 ) = ∑ 𝒘𝒊 𝑬(𝒓𝒊 )
𝒊=𝟏
(𝒊 ≠ 𝒋)
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The other restrictions are based on investment objectives and legal
regulations.
1.4.2. Creating optimal securities investment portfolios
Combining the risk-free securities with efficient portfolio C to
create optimal portfolio P
𝑬(𝑹𝑷 )= 𝒓𝒇 + [
𝑬(𝒓𝒄 )−𝒓𝒇
𝝈𝒄
] 𝝈𝑷
This chart shows the capital allocation curve - CAL-curve;
effective investment portfolio C is chosen as the maximum of slope
of capital allocation curve.
Problem 3:
Objective function:
𝑬(𝒓𝒄 ) − 𝒓𝒇
→ 𝑴𝒂𝒙
𝝈𝒄
With the restrictions as follows
𝒏
∑ 𝒘𝒊 = 𝟏
𝒊=𝟏
𝟎 ≤ 𝐰𝐢 ≤ 𝟏
1.4.3. DEFINING OPTIMAL SECURITIES INVESTMENT
PORTFOLIOS FOR INVESTORS
Utility function and indifference curve of investors
U = E (Rp) – 0,5A𝝈𝟐𝒑
The chart shows the utility curve (indifference curve) of investors.
Defining optimal portfolios for each investor
The investors will choose an investment portfolio on the optimal
capital allocation curve for themselves based on the coefficient of
risk aversion and their utility functions. Specifically, investors
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allocate capital between risk-free securities rf and securities portfolio
C so that the utility functions of investors achieve maximum utility
value. Then, the investment proportion in C portfolio:
𝑬(𝒓𝒄 ) − 𝒓𝒇
𝒘∗𝒄 =
𝑨𝝈𝟐𝒄
With the achieved proportion, it is easy to calculate investment
proportion in each securities and risk-free securities.
1.5. INVESTMENT PORTFOLIOS MANAGEMENT
1.5.1. Assess effectiveness of investment portfolios
Shape method:
𝑬(𝑹𝑷 ) − 𝒓𝒇
𝐒=
𝝈𝑷
Treynor method:
𝑬(𝑹𝑷 ) − 𝒓𝒇
𝐓=
𝜷𝑷
Jensen method:
𝜶𝑷 = 𝑬(𝑹𝒑 ) − 𝒓𝒇 − 𝜷𝑷 [𝑬(𝑹𝑴 ) − 𝒓𝒇 ]
Evaluation rate:
𝐄𝐯𝐚𝐥𝐮𝐚𝐭𝐢𝐨𝐧 𝐫𝐚𝐭𝐞 =
𝜶𝒑
𝜷𝒑
General income components of portfolios:
Analyzing the income components of the portfolios to consider
whether the extra income generated by the portfolios is
commensurate with the risk increased to the portfolios.
1.5.2. Adjust investment portfolios
In the case that the portfolios are no longer effective, investors
adjust their portfolios by selling existing securities that are no longer
fit and purchasing better securities.
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CHAPTER 2
EXPERIENCE OF CONSTRUCTING AND MANAGING
SECURITIES INVESTMENT PORTFOLIOS IN VIETNAM
Overview of Vietnam stock market shows that portfolio theory
can be applied in analyzing and investing securities for a number of
conditions and assumptions about the capital market satisfied. The
first condition is sufficient historical data of securities and market to
perform regression for predictions. Market size is relatively large; the
number of investors participating in the market are growing;
commodities on the market begin to meet the needs of portfolio
construction and investment.
Investment funds mostly use basic analysis techniques to select
investment securities in which two methods of top-down analysis and
bottom-up analysis are combined in the process of constructing and
managing investment portfolios.
2.2. SELECTING INVESTMENT STOCKS
2.2.1. Econometric problem of the capital asset pricing model
𝑬(𝒓𝒊 ) − 𝒓𝒇 = 𝜷𝒊 [ 𝑬(𝑹𝑴 ) − 𝒓𝒇 ] + 𝒖𝒊 (**)
Estimate [E(Ri) - rf] according to [E(RM) - rf] with the function
(**), we will have beta coefficient of each securities.
2.2.2. Selecting data
- Daily data within the five-year period from 2008 to 2013.
- Weekly data within the five-year period from 2008 to 2013.
Within a week, select Wednesday to avoid pricing effect at the
beginning and the ending of a week.
- Daily data within the two-year period from 2011 to 2013.
The test results of the data strings are stopping strings. Estimate
[E(ri) - rf] according to [E(RM) - rf] to find out beta value of securities.
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Comparing the results of R-squared adjusted from the regression using
observational data with different observational time and frequency shows
that the model is fit with the data of 5 years, the weekly observational
frequency.
2.2.3. Estimate beta coefficient of securities
Using the data source of stocks, the securities price index on two
securities exchanges with five-year-observation period and weekly
frequency, interest rates of government bonds of the same
observation period; applying equation (**) to estimate the beta of
the selected stocks; the estimated result is given by Appendix 2.
Based on these data, investors may consider selecting stocks to
build their own investment portfolios.
2.2.4. Alpha coefficient of stocks, selecting stocks
Expected income of securities according to capital pricing model
is calculated and shown in column 6 of Appendix 3.
Extra income (alpha) of stocks is the difference between the actual
income and income on demand of capital pricing model.
𝜶 = 𝒓𝒊 − 𝑬(𝒓𝒊 )
Calculate the real profitability of stocks; then, calculate the alphas
of stocks on both securities exchanges of Ho Chi Minh City and
Hanoi City shown in column 8 of Appendix 3.
From the results of calculating the alphas of stocks on both
securities exchanges of Ho Chi Minh City and Hanoi City, we choose
the stocks that have the highest positive alpha values to build
portfolios. At each department, we select 10 stocks in descending order
from high to low numeric values of experimental alphas. The results of
stock portfolio are shown on the Table 2.1a and 2.1b.
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2.3. CREATING OPTIMAL INVESTMENT PORTFOLIOS
2.3.1. Creating effective border
Using the problem 2 - minimize the risk to develop effective
border. In particular, wi (i = 1,20) are variables respectively
measuring the proportion of stocks in the portfolio: KBC, PAN,
KDC, LGC, LBM, PET, PAC, DRC, MPC, VNM, PGS , NPS, CAN,
PLC, STP, VDL, HCC, SD6, SAP, S55. Solve the mathematical
models to find the proportion invested in each stock. We have the
effective investment portfolios of risky securities shown in Table 2.4.
2.3.2. Selecting effective investment portfolios
Apply problem 3 of choosing effective investment portfolios Portfolio C to incorporate with risk-free securities to generate
optimal investment portfolios.
Solving the above problem on the risk-free interest rate:
0.2045%/week, we have the slope of the capital allocation curve with
the maximum value: 0.17793; efficient investment portfolio C is set
with parameters given by Table 2.5.
2.3.3. Creating optimal investment portfolios
2.3.3.1. Optimal investment portfolios with borrowing interest
rate equal to lending interest rate
Combine investment portfolio C identified above with risk-free
securities, we will create optimal investment portfolios. Changing the
investment ratio between the risk-free securities and investment
portfolio C can create a set of optimal investment portfolios shown
on the optimal capital distribution curve:
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𝑬(𝑹𝑷 )= 𝒓𝒇 + [
𝑬(𝒓𝒄 )−𝒓𝒇
𝝈𝒄
] 𝝈𝑷 = 0,002045 + 0,17793 𝜎𝑃
With the established optimal capital allocation curve, investors select
their portfolios on the basis of acceptable risk level. With the level of
risk aversion corresponds to the value A, respectively 1, 2,3,4,5, we have
the optimal portfolio shown in Table 2.6.
The levels of risk aversion of investors are determined through the
questionnaire that is described in Appendix 5.
2.3.3.2. Optimal investment portfolios having the difference
between borrowing interest rate and risk-free lending one
The equation of optimal capital allocation curve with borrowing
interest rate greater than the risk-free interest rate is:
𝑬(𝑹𝑷 )= 𝒓𝒃 + [
𝑬(𝒓𝒄 )−𝒓𝒃
] 𝝈𝑷
𝝈𝒄
The optimal capital allocation curve with risk-free lending interest
rate is CAL1 curve; the optimal capital allocation curve with
borrowing interest rate (rb) is CAL2 curve. Similar to the way of
identifying the CAL1 curve, the CAL2 curve was chosen as the capital
allocation one with the highest slope. By replacing the interest rate rb
for interest rate in problem 3, we have the optimal problem of
determining the investment portfolio D assuming that the borrowing
interest rate to invest is 20% / year, or 0.3846% / week, equation of
CAL2 curve as follows:
𝐸(𝑅𝑃 )= 0.003846 + 0.140149𝜎𝑃
The achieved effective investment portfolio D is shown on the
table 2.7.
2.4. MANAGING INVESTMENT PORTFOLIOS
2.4.1. Evaluate the effectiveness of investment portfolios at
creating time
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The VN INDEX is used to represent the market portfolio, the
average income of the market portfolio is 0.142%/week; the standard
deviation of the market portfolio income is 4.45%; Government bond
yield on average during this period is 0.2045%/week.
2.4.1.1. Evaluate the effectiveness of portfolio C
All three Jensen, Treynor, and Sharpe methods evaluate that C
portfolio is a well-constructed and effective investment portfolio. The
results are shown in Table 2.9.
2.4.1.2. Evaluate the effectiveness of portfolio D
The measure indicates that the investment portfolio D is effective.
The results are shown in Table 2.10.
2.4.1.3. Evaluate the effectiveness of optimal investment
portfolios
All optimal portfolios are optimal and effective when comparing
to the market portfolio. The results are shown in Table 2.11.
2.4.2. Reassess the effectiveness level and adjust investment portfolios
2.4.2.1. Reassess the effectiveness level of investment portfolios
The reevaluation of the efficiency level and investment portfolio
adjustment are made on the basis of data from January 01,2010 until
December 31, 2014; risk-free interest rate is 0.18%/week; VNINDEX
index is selected to represent the market portfolio.
Based on the calculated results until the end of 2014 in Table
2.13, the optimal investment portfolios constructed for investors with
specific risk acceptance level are still effective.
2.4.2.2. Adjust investment portfolios
The degree of effectiveness of the portfolios can be raised through
the adjustment of the portfolios. The process of adjusting the
portfolio is performed in sequential steps: revaluate securities, adjust
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stock portfolios, adjust collections of effective investment portfolios,
adjust investment portfolios C, and adjust the optimal investment
portfolios. The results are given in the table from 2:14 to 2:17.
The degrees of effectiveness of the investment portfolios have
increased after adjustment shown in Table 2:18.
2.5.
ADVANTAGES
AND
RESTRICTIONS
IN
THE
CONSTRUCTION AND MANAGEMENT OF INVESTMENT
PORTFOLIOS ON SECURITIES MARKET IN VIETNAM
2.5.1. Advantages in the construction and management of
investment portfolios on securities market in Vietnam
The market is being completed and efficient; stock data is built and
provided quite sufficient; asset pricing model is quite suitable when e
being applied to select investment stocks.
The experiment shows that:
- Building and managing investment portfolios on Vietnam stock
market in accordance with the system of theory in chapter one can
absolutely be conducted.
- Asset pricing models can be applied to choose which stocks to
invest; Harry Markowitz theory of investment portfolios can be
applied to determine the proportion of investment and capital
allocation for each stock.
- The most appropriate data in using the capital asset pricing
model is observed in 5 years, the frequency observed in the week and
use data on Wednesday.
- Vietnam's stock market has responded initially in compliance
with several hypotheses on the capital market.
2.5.2. Restrictions in the construction and management of
investment portfolios on securities market in Vietnam
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Some problems continue to be proposed solutions in the third
chapter:
- Need solutions to make the market more effective.
- Increase the supply on the stock market.
- The assessment of the effectiveness of short-term investment
portfolios must be associated with the reliability or certain statistical
significance.
- How short selling of securities transactions will impact the
construction and management of the investment portfolios?
- Develop and manage the investment portfolios in real
conditions: investors must pay the transaction costs to borrow with
interest rate greater than risk-free interest rate for the investment.
- The steps and methods of building investment portfolios in the
absence of financial leverage.
In addition, a number of issues that the thesis addressed in chapter
2 will be further processed in solutions in Chapter 3, but due to
subjective conditions or scope of the thesis they should not be
resolved thoroughly. These problems may be suggestive directions
for further research on the issue of building and managing investment
portfolios on Vietnam stock market.
CHAPTER 3
SOLUTIONS TO FINISH THE APPLICATION OF
INVESTMENT PORTFOLIOS THEORY IN CONSTRUCTING
AND MANAGING SECURITIES INVESTMENT
PORTFOLIOS IN VIETNAM
3.1.
SOLUTIONS
TO
IMPROVE
SECURITIES MARKET IN VIETNAM
EFFICIENCY
FOR
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The solutions focus primarily on improving the quality of
information disclosure and enhancing surveillance activities on the
stock market.
3.2. SOLUTION TO INCREASE THE SUPPLY ON SECURITIES
MARKET
Increasing the number and types of goods on the stock market
helps the market more exciting, investors have more choice to
diversify portfolios and reduce risks, thereby building and managing
investment portfolios are more efficiently. This group of solutions
include:
- Strengthening the equitization of state enterprises.
- Encouraging public companies to list their stocks on the stock
exchanges.
- Developing securities investment funds.
- Accelerating the implementation of development schemes for
derivatives market.
- Developing corporate bond market.
3.3. TECHNICAL SOLUTION GROUP
3.3.1. Solution to create investment portfolios
The solution group supports the construction of the portfolios
in some cases when the investment conditions in the market
change: there is no risk-free stock; markets allow short selling of
securities, etc.
3.3.1.1. Build optimal investment portfolios without risk-free
securities
Optimal investment portfolio is one of the investment portfolios
on the effective frontier. The investment portfolio is selected as a
utility-maximizing investment.
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Objective function:
U = E(Rp) – 0,5A𝝈𝟐𝒑 → 𝑴𝒂𝒙
The restrictions:
𝑛
∑ 𝑤𝑖 = 1
𝑖=1
𝟎 ≤ 𝐰𝐢 ≤ 1
Give A a turn for the values 1; 2; 3; 4; 5 and the problem is the
investment proportion of the risky securities in optimal portfolios. Based
on this proportion, we can calculate the values of the expected return, the
standard deviation, and the utility of the investment. The calculation
results are given in Table 3.1.
3.3.1.2. Optimal investment portfolios in the condition that
market allows short selling of securities
In the problem developed above, we removed the non-negative
constraints and constraints exceeded 100% for the investment
proportion of the securities in the portfolio: the problem of 2 – risk
minimizing portfolio and the problem of 3 – select effective
investment portfolios.
The results of efficient portfolios, investment portfolios and D in
condition that short sales of stocks are permitted are presented in
table 3.2, 3.3 and 3.4 respectively.
The equation of CAL1 curve is
𝑬(𝑹𝒑 ) = 𝟎, 𝟎𝟎𝟐𝟎𝟒𝟓 + 𝟎, 𝟐𝟔𝟒𝟏𝟑𝝈𝒑
The equation of CAL2 curve is
𝑬(𝑹𝒑 ) = 𝟎, 𝟎𝟎𝟑𝟖𝟒𝟔 + 𝟎, 𝟐𝟑𝟗𝟕𝟕𝝈𝒑
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3.3.1.3. Consider the transaction cost when applying capital
asset pricing model
In terms of transaction fees that are payable, SML curve is not a
single one but a strip which includes the extensions on both sides of
the SML curve when there is no transaction fee. Whether the width of
the strip is large or small depends on the transaction fee payable
under the regulations. Investors should pay attention to this problem
in the process of building and managing investment portfolios.
3.3.2. Solutions to manage investment portfolios
3.3.2.1. Use methods of assessing effectiveness of portfolios
suitable with each type of risk
Treynor method should be used for the well-diversified portfolios
such as the investment portfolios according to the index; Sharpe
method should be used to assess the portfolios which are not welldiverfied and still contain non-systematic risks.
Treynor and Jensen methods are uniform in evaluating portfolio
performance. When one investment portfolio is effective with Jensen
method, it will be effective by means of Treynor.
3.3.2.2. Adjust investment portfolios in the condition that
market allows short selling of securities
Securities selected to perform in the list short sales are
expected to have lower prices in future. The stock is overvalued,
with the expected price of the stock falls faster in the future.
Then, investors will purchase for refund.
Choose 30% of the stock in each transaction centers included
in the list with the aim of shorting the stocks. The constraints of
the problem are adjusted: as for the stocks selected for short
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sales, their weights in the portfolio are constrained as being not
positive. The remaining share in the portfolio must be nonnegative.
3.3.2.3. Assess the effectiveness of investment portfolios associated
with statistical significance
Assuming that the price of the stock and the market index in the
past will repeat in the future, historical data of stock and index
VNINDEX, HNXINDEX can be used. Apply regression to estimate
factors in the assessment method of effective investment portfolios.
Estimating equations: Equations of Jensen assessment method and
equation of the capital market line (CML). On this basis, analyze and
evaluate the effectiveness of the portfolio with the Jensen and Sharpe
methods. We did not assess the effectiveness of the portfolio with
Treynor measure because, as discussed above, the effective portfolios
with a Jensen measure are also effective with Treynor measure. The
estimates of factors and evaluate the effective portfolio are given in
the table from 3.5 to 3.9.
3.3.2.4. Estimating a suitable period of time for adjusting the
portfolio
It is necessary for estimating a suitable period of time for
evaluating and adjusting the portfolio that would be flexible
depending on the stage of the stock market development. In addition,
we need to identify an optimal trading band of expected return (or
threshold of expected return) for the portfolio in general, and for each
stock in particular. If target returns exceed the threshold, the portfolio
should be adjusted.
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3.4. OTHER SOLUTIONS
3.4.1. Select suitable data
Under some kinds of conditions, it is necessary to carry out more
experiments with multiple data sources. On the basis, draw more
accurate conclusions about how to choose the time and the frequency
of observations to ensure more accurate estimates.
3.4.2. Investigate market portfolios
Market portfolios in asset pricing model are effective portfolios.
Meanwhile the HNXINDEX and VNINDEX index do not meet this
requirement. So, in order to apply capital pricing model effectively
on the stock market in Vietnam in the present context:
- A common market portfolio needs to be built for the
overall market to ensure greater representation by the
consolidated shares portfolio on the Stock Exchanges of
Hanoi, Ho Chi Minh and Upcom.
- In the case that the developed market portfolio as describe above
is not available, we can still use VNINDEX, HNXINDEX being
representatives of the market portfolio but should recalculate the
proportion of each stock in the portfolio so that the standard
deviation of the portfolio is the smallest.
- Increase market properties for Vietnam's stock market
3.4.3. Use suitable risk-free interest rate
Deviation in extra income when selecting unsuitable risk-free
interest rate is
where:
is Risk-free interest rate selected to calculate
is Suitable risk-free interest rate
22
The investment process takes place in a certain period, in which
the risk-free interest rate fluctuates, directly affecting the selection
and investment results. Hence, we have to take into account the
fluctuation level of the risk-free interest rate; use information about
announced yield curve to determine the risk-free interest rate.
3.4.4. Reduce the effects of investment according to group
psychology
The disclosure of new information of public companies is only
the necessary condition so that effective market and stock prices can
reflect market information. If investors make decisions to buy or sell
securities based on the use of effective information, it will be a
sufficient condition for market information to convert into stock
prices. To reduce the group psychological effects of the large number
of investors in the purchase and sale of securities, it is essential to:
Disclose information on the market accurately, timely, and
transparently in accordance with regulations on the rights to disclose
information on securities and securities markets.
There should be programs of popularizing, improving and training
knowledge of the stock and securities market for investors.
Encourage investors to use the announced and collected information
effectively, to analyze information, and to identify market conditions
and fluctuations in stock prices in order to make investment
decisions.
In the case that information cannot be collected or analyzed or the
scale of investment is small, investors should invest through securities
investment funds or through the investment fund management
companies.
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3.4.5. Reduce administrative intervention towards building
synchronous financial markets
- Stock market has close ties with the money market, gold market,
and foreign exchange market, etc. The stability of these markets
helps the stock market more efficient, facilitating and creating good
environment to apply modern portfolio theories.
- Reduce administrative intervention into the supply and demand
on the stock market by easing price fluctuation band, increasing the
percentage of shares held in companies with foreign investors, and
then eliminating holding percentage limit of foreign investors as well
as the amplitude of the transaction price.
CONCLUSION
The thesis has solved several fundamental contents as follows:
Firstly, systematize
the basic theories concerning
the
construction and management of optimal portfolios in securities
investment.
Secondly, create and manage optimal securities investment
portfolios for 220 securities on the market.
Thirdly, from experiment, propose solutions to improve the
application of modern investment portfolios theory in creating and
managing securities investment portfolios in Vietnam.
Fourthly, assign the capital pricing model by using econometric
models to estimate the systematic risk of stocks.
Fifthly, apply the capital pricing model in pricing and selecting
investment stocks in different databases.
Sixthly, indicate the compatibility level between model and market
data in several stocks that are not high. It is recommended to adjust
24
models or have measures to promote market development to improve
efficiency of the model.
Seventhly, estimate Sharpe, Treynor and Jensen coefficients and
evaluation ratios of several investment portfolios and market portfolios.
Subsequently, analyze to evaluate efficiency level of the portfolios.
Eighthly, propose solutions to overcome and improve the
reliability of conclusions about the effectiveness of the
investment portfolios.
Although there have been a lot of efforts in the implementation of
the thesis, certain limitations may not be avoided. I look forward to
receiving the sincere comments from scientists, teachers, friends, and
colleagues. Sincere thanks!
LIST OF RELATED SCIENTIFIC PUBLICATIONS
1. Tran Van Tri (2012), “Application of Capital Asset Pricing
Model (CAPM) for stock options to invest”, Banking Technology
Review, (No. 76), Page 50-55
2. Tran Van Tri (2014), “Application of Capital Asset Pricing
Model for stock options to invest”, Journal of Science and Education,
(No. 144), Page 23-32.
3. Tran Van Tri (2014), “Construction of the optimal stock
portfolio by Markowitz model”, Banking Technology Review, (No.
103), Page 55-62.
4. Tran Van Tri (2014), “Evaluation of the effectiveness of
the optimal portfolio - Theory and Reality”, Journal of FinanceMarketing Research, Page 39-44.