1

FOREIGN TRADE UNIVERSITY

FACULTY OF BUSINESS ADMINISTRATION---------***--------

GRADUATION THESISMajor: International Business

Administration

THE APPLICATION OF CUMULATIVE PROSPECT

THEORY IN BUILDING OPTIMAL PORTFOLIO IN

VIETNAMESE STOCK MAKRKET

Student name: Nguyễn Thị Thu

Hằng

Student code: 1001020040

Class: A8

Intake: 49

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Supervisor: M.Sc. Le Thi Thu

Ha Noi, May 2014

ACKNOWLEDGEMENTS

Firstly, I express my deep sense of gratitude to M.Sc.

Le Thi Thu for her inspiring guidance, scholarly

interpretations and valuable criticisms throughout the

course of my thesis. I am gratefully obliged to the

faculty of Business Administration at Foreign Trade

University, for approving the title and supporting me to

conduct the study. I extend my sincere thanks to Ms Pham

Mai Phuong Linh, Hoang Xuan Huy, Nguyen Viet Phuong, for

their support.

Especially, I also thank my close friends Ngo Bach Thien

Huong, Le Ngoc Hai, Nguyen Tung Minh, Ngo Thi Thu Huong,

Nguyen Lan Anh, Pham Hai Yen and Nguyen Phuong Thanh for

all their encouragement throughout the completion of the

work.

Above all, many thanks to mom, dad, and my younger

brother and sisters who always stimulate and spend all

love for me.

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Nguyen Thi Thu Hang

Class: A8, Faculty of Business Administration, Intake: 49, Foreign Trade

University

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CONTENT

CHAPTER 1: INTRODUCTION................................1

1.1.The rationale of the research....................1

1.2.Objectives of the research.......................3

1.3.Scope of the research............................3

1.4.Research methodology.............................3

1.5.Research structure...............................4

CHAPTER 2: CUMULATIVE PROSPECT THEORY..................5

2.1.Introduction to Cumulative Prospect Theory.......5

2.2.Hypotheses of Cumulative Prospect Theory.........6

2.2.1. Three basic hypotheses.............................6

2.2.2. Mathematic form.................................8

2.2.3. Stochastic Dominance approach to test hypotheses........11

2.3.Typical biases explaining for Cumulative Prospect

Theory..............................................18

2.3.1. Loss Aversion...................................19

2.3.2. Anchoring and Adjustment..........................19

2.3.3. Herding Bias....................................20

CHAPTER 3: BUILDING OPTIMAL PORTFOLIO FOR INDIVIDUAL

INVESTORS.............................................22

3.1.Individual investors............................22

3.2.Optimal portfolio...............................23

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3.2.1. Introduction....................................23

3.2.2. Approaches of portfolio optimization..................24

3.2.3. Processes of portfolio management...................26

3.2.4. Optimization constraints...........................28

3.3.Designing optimal portfolio for individual

investors...........................................29

CHAPTER 4: MODEL OF STATIC PORTFOLIO OPTIMIZATION UNDER

CUMULATIVE PROSPECT THEORY............................31

4.1.Introduction....................................31

4.2.Static Portfolio Choice under Cumulative Prospect

Theory..............................................32

4.2.1. Background....................................32

4.2.2. Content of Static Portfolio Optimization model...........33

4.3.Evaluation of Static Portfolio Optimization Model

36

4.3.1. Advantages.....................................36

4.3.2. Disadvantages..................................37

CHAPTER 5: INTRODUCTION TO VIETNAMESE INDIVIDUAL

INVESTORS.............................................39

5.1.Overview of Vietnamese stock market.............39

5.1.1. A brief history of Vietnamese stock market..............39

5.1.2. Overall movements of Vietnamese stock market during the

period of 2007-2013....................................41

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5.2.Overview of individual investors................44

5.3.Typical features of individual investor in

designing portfolios................................44

5.3.1. Lack of knowledge................................44

5.3.2. Lack of technological investment tools.................46

5.3.3. Affected by behavioral biases........................47

CHAPTER 6: DATA AND METHODOLOGY.......................52

6.1.Data collection.................................52

6.2.Overview of methodology.........................52

6.3.Research design.................................53

6.3.1. Stochastic Dominance approach.....................53

6.3.2. Questionnaire survey..............................55

6.4.Limitations of the study........................56

CHAPTER 7: EMPIRICAL RESULTS..........................57

7.1.Shape of the value function.....................57

7.2.Shape of the probability weighting function.....58

7.3.Empirical result................................59

CHAPTER 8 – RECOMMENDATION............................61

8.1.Individual investors............................61

8.1.1. Improve knowledge and skills.......................61

8.1.2. Build up plausible investment strategy.................62

8.1.3. Filter information and experts’ opinions................65

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8.1.4. Apply models in practical investments..................66

8.1.5. Notations......................................67

8.2.Financial institutions and investment service

suppliers...........................................70

8.2.1. Provide instruments for constituting and managing portfolio.70

8.2.2. Provide biases defense for private clients...............72

CONCLUSION............................................73

REFERENCE.............................................75

APPENDIX A: SURVEY....................................79

APPENDIX B: MATHEMATICAL BACKGROUND...................81

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LIST OF ABBREVIATIONS

BFT

CPT

EMH

EU

GDP

PT

SD

VN-Index

Behavioral Finance Theory

Cumulative Prospect Theory

Efficient Market Hypothesis

Expected Utility Theory

Gross Domestic Product

Prospect Theory

Stochastic Dominance

Vietnamese Index of Stock Price

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LIST OF TABLES

Table

5.1

HOSE’s listing summary recorded in April

201440

Table

5.2

HNX’s listing summary recorded in April

201441

Table

5.3

Level of knowledge of individual investors in

2000-2007 in Viet Nam45

Table

6.1c and d 54

Table

7.1

List of joint hypotheses in testing the

curvature of value function57

Table

7.2Result of Tasks I, II and III 58

Table

7.3

List of joint hypotheses in testing the

curvature of probability weighting function59

Table

7.4Result of Tasks IV and V 59

LIST OF EXHIBITS

Exhibit

2.1

The value function assumed by Prospect

Theory7

Exhibit The value function u (x) for different values 9

10

2.2 of α,β∧μ

Exhibit

2.3The probabilities distortion functions,γ=0.61 and δ=0.69

10

Exhibit

2.4

Prospect Theory S-shape function and

Reverse S-shape function15

Exhibit

2.5Schematic depiction of the Wc

dclass of

probability weighting function18

Exhibit

3.1The process of portfolio management 26

Exhibit

5.1VN-index in the period of 2004 to 2014 42

Exhibit

5.2HNX-index in the period of 2004 to 2014 42

Exhibit

5.3

Dow Jones and VN-index from the end of 2008

to the end of 201049

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CHAPTER 1: INTRODUCTION1.1. The rationale of the research

Individual wealth management, especially individual

optimal portfolio has been relatively new but expanding

field that attract more and more the concern of

financial researchers. Numerous studies regarding this

domain are carried out over the world, including

standard finance models and behavioral finance model.

The major characteristics of private investors are small

capital size, lack of technology support and affected by

behavioral biases. Small scale of investments prevents

individual investors from selecting many securities for

their portfolio. The shortage of supporting high-tech

tools poses the problem of how individual practioners

apply optimal portfolio models. Lastly, behavioral

biases are the in-depth reason for investors’ wrong

decisions and mistakes while constituting portfolio. In

three above features, individual behaviors is considered

as the most typical difference, which divides optimal

portfolio models into two approaches: one based on

Standard Finance paradigm, and one based on Behavioral

Finance paradigm.

Standard Finance paradigm proposes Markowitz Portfolio

Theory, which is considered as the best mathematical

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model for optimizing portfolio. This model of portfolio

optimization bases on the assumption that individual

investors are analytically sophisticated and

knowledgeable about markets. By assumption, private

investors in such these constituted models make optimal

decision in a rational manner. However, MPT is strongly

criticized by behavioral finance scholars. According to

Bernstein (1998), “evidence reveals repeated patterns of

irrationality, inconsistency and incompetency in the

ways human being arrive at decisions and choices when

faced with uncertainty”. Nofsinger (2001) asserts that

assumption of rationality and unbiasedness of economic

participants has been drubbed by psychologist for a long

time.

As the mandatory requirement of financial research,

behavioral finance researchers advance substitute models

of individual portfolio management. The major studies

specializing in portfolio optimization emphasize that

(i) investors are normal (Statman, 2005); (ii) they use

S-shape utility function (Kahneman and Tversky, 1979)

that reflects their attitudes toward risk; (iii)

investors are also affected by their emotions (Lopes,

1987). Derived from these realistic assumptions, a vast

number of researches regarding individual portfolio have

conducted in over the world. The principal contribution

of individual optimal portfolio is with no doubt

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Cumulative Prospect Theory initiated by Kahneman and

Tversky (1992) – the keystone of Behavioral Finance

Theory.

Moving focus on Vietnamese stock market, due to the

great number of private investors to the financial

market, individual wealth management is still a pivotal

domain. According to the interview result of Tran Dac

Sinh – chairman of HOSE, by the end of the year 2013,

there were 1.3 million trading accounts comprise

1,282,071 accounts of domestic individual investors

compared with 5,081 accounts of domestic institutional

investors, 13,950 accounts of foreign individual

investors and the 1,631 remaining of foreign

institutional investors. In addition, during the

development of the Vietnamese stock market, there is an

increasing number of private investors picking stock and

allocating their portfolio instead of short-term

trading.

Nevertheless, in reality, Vietnamese individual

investors are not equipped by strategic models helping

them to overcome their emotional and cognitive biases.

Many of them simplify portfolio selection process by

using heuristics approach because they find models of

optimal portfolio sophisticate and difficult to apply.

Other individual investors designing portfolio based on

available models are still unable to optimize their

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wealth because of models’ implausible assumption of

rationality. This status is one of the reasons causing

the speculative bubble crash in 2007, even maybe

threatening the sustainability of Vietnamese stock

market.

Thus, the matter of wrong individual portfolio

investment decisions affecting on the sustainability and

the enhancement of Vietnamese stock market is the

rationale of my thesis “The application of Cumulative

Prospect Theory in building optimal portfolio for

individual investors in Vietnamese stock market”.

1.2. Objectives of the research

Behavioral Finance paradigm is a theoretical and

empirical system that includes numerous sub-theories

such as Heuristics, Prospect Theory, Cumulative Prospect

Theory, behavioral biases, disposition effect, etc. Each

relative theory, which has its mathematic forms, can be

a base constructing models of portfolio optimization.

Due to limited time and a lack of research capacity, my

thesis will only concentrate on Cumulative Prospect

Theory – the keystone of Behavioral Finance Theory, and

the most simple model, which is so-called “Static

Portfolio Optimization model”, with one risky asset and

one free-risk asset in one-period economy.

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My thesis aims to answer two key research questions. Are

hypotheses of Cumulative Prospect Theory compatible with

Vietnamese individual investors’ characteristics? If the

model is suitable for privately applying, are there any

recommendations to realize the models in practical

investments?

1.3. Scope of the research

Individual investors were picked up for the survey since

they were more likely to have limited knowledge about

application of the Behavioral Finance or Cumulative

Prospect Theory in portfolio construction, hence prone

to make psychological mistakes. The influence has

primarily analyzed in term of whether behavioral factors

affect the portfolio management behavior of individual

investors.

1.4. Research methodology

This study follows the methodology of survey research

design of which data processing was supported by

quantitative approach.

As Holme and Solvang (1996), a quantitative method is

formalized, structured and is characterized by

selectivity as well as a distance from the source of

information. The approach concentrates on numerical

observations and attempts to generalize a phenomenon

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through formalized analysis of observed data where

statistic indicators are indispensable parts. On the

other hand, a qualitative approach is formalized to a

lesser extent is directed at testing whether the

information is valid. The typical feature of this method

is the use of verbal description instead of purely

numerical data and aims at creating a common

understanding of the subject in research.

In my thesis, by using descriptive survey, primary data

is collected for quantitative and qualitative analyses.

Stochastic Dominance is used to interpret individual

decisions between two options.

1.5. Research structure

Except Introduction, Conclusion and Appendices, the

thesis is structured as follows:

Chapter 2: Cumulative Prospect Theory

Chapter 3: Building Optimal Portfolio for individual

investors

Chapter 4: Static Portfolio Optimization Model Under

Cumulative Prospect Theory

Chapter 5: Introduction to Vietnamese individual

investors in the stock market

Chapter 6: Data and Methodology

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Chapter 7: Empirical results

Chapter 8: Recommendations

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CHAPTER 2: CUMULATIVE PROSPECT THEORY 2.1. Introduction to Cumulative Prospect Theory

Cumulative Prospect Theory (Kahneman and Tversky, 1992)

is one of the most important theories of Behavioral

Finance Paradigm. CPT has assistance for behavioral

researchers to understand and explain individual

decision-making process under uncertainty. Hence, CPT

has many important implications in constructing

portfolio.

Cumulative Prospect Theory is the second version of

Prospect Theory (Kahneman and Tversky, 1979). Both of

them are considered as two of the best theories to

explain individual decision under risk. In essence,

there are many such relative theories as Expected Value,

Expected Utility having great contribution to the

financial decision-making process under conditions of

risk, but each of them has its own limitations. Expected

value is calculated by multiplying its payoff with its

probability. This model fails in predicting the final

choice because the value was not always directly related

to its precise monetary worth, but rather dependent on

other psychological factors. Daniel Bernoulli (1738)

releases works discovering this contradiction and

advancing an alternative to the expected value notion.

Throughout his experiments, Bernoulli recognizes that

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the value a person attaches to an outcome can be

influenced by such factors as the likelihood of winning,

or probability, etc. Expected Utility, however, the

notion of Expected Utility also fails in predicting all-

loss choices.

In 1979, Kahneman and Tversky provided an alternative,

empirically supported theory of choice, so-called

Prospect Theory, one that accurately describes how

people actually go about making their decision. In

short, the theory predicts that individuals tend to be

risk averse in a domain of gains and relatively risk-

seeking in a domain of losses. However, there are some

theoretical problems in PT. The main problem is that the

functional form of PT violates “stochastic dominance”

(Kahneman and Tversky, 1979, pp. 283±284). Stochastic

dominance requires that a shift of probability mass from

bad outcomes to better outcomes leading to an improved

prospect. The theoretical problems have recently been

resolved in a new version of PT, called Cumulative

Prospect Theory (CPT) that was introduced by Tversky and

Kahneman (1992); in particular, CPT satisfies stochastic

dominance.

2.2. Hypotheses of Cumulative Prospect Theory

2.2.1. Three basic hypotheses

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According to Kahneman and Tversky in their work in 1992,

there are three elements forming the decision making

process of CPT. CPT-investor is defined as an investor

who behaves consistently with Cumulative Prospect

Theory.

Firstly, a CPT –investor will be concerned with the

deviation of his final wealth from a reference level

instead of final value under EU hypothesis. Secondly,

CPT-investor is more sensitive with losses than gains.

Lastly, investors do not evaluate random outcomes using

reasonable probabilities, but base upon distortion by

overestimating low probabilities.

For the first hypothesis, Kahneman and Tversky presented

in their study in 1979 the following experimental

evidence to illustrate that the evaluation of decision

outcomes has to be reference-dependent (“reference” in

this context refers to the current state of wealth), a

principle that is incompatible with Expected Utility. In

this empirical work, experimental participants were

asked to choose between a lottery offering a 25% chance

of winning 3000 and a lottery offering a 20% chance of

4000, 65% of their participants chose the second option

(20%; 4000). On the contrary, when they were asked to

choose between a 100% chance of winning 3000 and an 80%

chance of winning 4000, 80% of them chose the former

(100%, 3000). On contrary to reality, EU predicts that

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they should not choose different option in both

circumstances as the expected utility in the second

choice is always better than the first one.

To understand this certain situation, consider a gamble:

(x−m,p−m;x−m+1,p−m+1;…;x0,p0;…;xn−1,pn−1;xn,pn )

Where the notation should be understand as “gain xi with

probabilitypi with i=−m,n; where the outcomes are

organized in increasing order, so that xi<xj for i<j, and

where x0 = 0. For instance, a lottery offering a 50%

chance of winning $333 or losing $111 would be

formulated as (−111,12 ;333,12 ). Under EU, a rational

investor valuates the above gamble as:

∑i=−m

npiu(W+xi)

Where: W is the current asset and u(x) is the utility

function that is increasing and concave.

This formulation demonstrates the four key components of

prospect theory: 1) reference – dependence, 2) loss

aversion, 3) diminishing sensitivity, and 4) probability

weighting.

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Exhibit 2.1: The value function

(Source: Kahneman and Tversky (1979))

According to Miyamoto (1987) and Kahneman and Tversky

(1979), they advance a value function with a reference

point at the outcome, located at zero (see Exhibit 1.1).

Their findings emphasize on the graphic function of u(x)

is S-shape, reflecting the principal of “diminishing

sensitivity” for the outcome evaluation. For example,

the subject strongly discriminates between 0 and 20

rather than between 80 and 100 even though both where

these figures regarding gains and losses. In other

words, a dollar is always appreciated less as an

investor becomes wealthier.

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Secondly, it is also found that u(x) is more sensitive to

losses than for gains (loss aversion). Empirical tests

conducted by Kahneman and Tversky (1991) indicate that

losses are weighted about twice as heavily as gains –

losing $1 is about twice as painful as the pleasure of

gaining $1.

Last but not least, Kahneman and Tversky find that

preferences of subjects can be modeled by probability

weighting that amplifies small probabilities and reduces

higher probabilities. Therefore, the weighting function

is definitely sensitive to changes in probability near

the final points 0 and 1 but obviously insensitive to

changes in probability in middle region. As Kahneman and

Tversky (1979), weighting function is an important

hypothesis in supporting explanation for investors’

decision.

2.2.2. Mathematic form

Let W and Wref be the wealth and the reference level at

the end of the period.

Define the deviation D from the reference level as

follows:

D=W−Wref

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D is the random variable that alters and motivates all

decision because each investor has different reference

level, hence different deviation D.

Let FXand SXbe the cumulative distribution function and

the complementary distribution function, respectively.

FX (x)=P (X≤x ) and SX (x)=1−FX (x)

2.2.2.1. The value function

According to Kahneman and Tversky (1992), the value

functionu (x)is defined as follows:

u (x)=¿

Where: x is random variable D, 0<∝<1,α≤β<1∧μ>1

It can be referred from definition of the value function

that the function g (x)and l (x) are positively homogenous,

increasing, invertible, and twice differentiable.

Parameter ∝ and β demonstrate risk aversion, parameter μ

illustrate loss-aversion. Moreover investors show the

tendency to risk-averse for gains and risk-seeking for

losses, hence it is clear to find that α≤β<1. Kahneman

and Tversky (1979) suggest that ∝=0.8, β=0.88 and μ=2.25

. See Exhibit 2.2

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Exhibit 2.2: The value function u (x) for different values

of α,β∧μ

(Source: Kahneman and Tversky, 1979)

2.2.2.2. The probability weighting function

The third element forming CPT decision-making process

lies in the systematic distortion of physical

probability measure. The probabilities distortion may be

slightly different in case of gains (D>0) and losses (D<0).

The probability distortions (or probability weighting

functions) are denoted by Pgand Pl. For a random variable

D with cumulative distribution function FX and

decumulative distribution SX, Tversky and Kahneman

(1992) suggest the following two probabilities weighting

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functions with Pg: [0;1 ]→ [0;1 ] for gains andPl: [0;1 ]→ [0;1 ]for

losses:

Pg (p )= pγ

[pγ+(1−p)γ ]1 /γ with0.28<γ<1

Pl (p )= pδ

[pδ+(1−p)δ ]1 /δ with0.28<δ<1

Where:p=FX(D), γ and δ are both less than 1 as if γ=1or

δ=1, there is no distortion in gain domain or loss

domain, respectively.

It is can be referred from the definition of the

probability weighting function Pgand Plthat they are

differentiable. Remember that investors show the

tendency to risk-averse for gains and risk-seeking for

losses, hence it is clear to find that γ<δ.

Kahneman and Tversky (1992) estimated γ=0.61 and δ=0.69

for a typical investor. (See the Exhibit 2.3)

Exhibit 2.3: The probabilities distortion functions,γ=0.61 and δ=0.69

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(Source: Kahneman and Tversky, 1992)

Ingersoll (2008) shows that the condition of ( γ,δ>0.28)

ensures that Pgand Pl are increasing. Rieger and Wang

(2004) indicate that the probability weighting function

is not monotone for γ≤0.278.

Prelec (1998) proposes an alternative specification for

the weighting function: P (p )=e−(−lnp)γ, where parameter γis

similar to the one in the function proposed by Kahneman

and Tversky.

2.2.2.3. Objective function (Prospect function)

Bernard and Ghossoub (2009) define the objective

function of the CPT-investor, denoted byO (D), as:

O (D)=∫0

+∞

Pg (SX (x ))dg (x)+∫−∞

0

Pl(FX (x ))dl (x )

Or, the CPT-objective function O (D)also rewrite as:

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O (D)=∫0

+∞

Pg (SX (x ))dg (x)−∫0

+∞

Pl (FX (x ))dl (x)

Where: FX (x) and SX (x) are cumulative distribution function

and decumulative distribution function, respectively

(see page 8), Pland Pgare probability weighting functions

(see page 10)

In order to ensure that both integrals are finite and

computable, the objective function requires thatα<2min (γ;δ) and β<2min (γ;δ), where αandβ is parameter in

the value function (see page 9), γ∧δ are parameters in

the probability weighting function (see page 10)

2.2.3. Stochastic Dominance approach to test hypotheses

2.2.3.1. Overview of approaches

In order to test features of Prospect Theory, Kahneman

and Tversky (1979) employ the Certainty Effect approach

that also supports for Cumulative Prospect Theory. In

their experiments in 1979 and 1992, they rely upon

comparison of two outcomes, one certain, one uncertain;

hence, probabilities distortion function can be

explainable for their results. Wu and Gonalez (1996)

also apply the Certainty Effect approach on their study

supporting Tversky and Kahneman’s probability weighting

function.

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Even though Certainty Effect approach has many

applications and implications in decision theory under

uncertainty, it has the well-known drawback, recognized

by Levy and Levy (2001). Many experiments show that the

approach is ineffective in case of more than two

outcomes and each outcome has the same probability (for

instance, gain $1000 with probability of 25%; loss -$200

with probability of 25%; gain $0 with probability of

25%; gain -$300 with probability of 25%). The problem of

Certainty Effect poses the need of alternative

approaches.

In their work, Levy and Levy (2001, 2002a) propose to

employ Stochastic Dominance (SD) criteria to analyze

decisions and implied preference in experimental

research. The prominent advantages of SD approach over

Certainty Effect approach are that SD can compare two

uncertain choices with many outcomes, which can be all

positive, all negative or mixed. According to Levy and

Levy (2002b), Certainty Effect approach is not

explainable for the curvature of the preference with

mixed prospects while SD approach can provide

conclusion. Furthermore, based on SD condition, recent

studies suggest experimental designs that can isolate

elements of CPT without having to estimate all

parameters of functions.

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In my thesis, the experiment, testing whether investors’

decisions are consistent to CPT, is conducted with the

support of SD approach. Firstly, we consider theoretical

framework of Stochastic Dominance Approach.

2.2.3.2. Stochastic Dominance approach

a. Background

In this section, consider an individual investor who has

investor has investment chances in one of the n

portfolios, where return (per unit invested) in a single

period on portfolio i is Xi (non-negative random

variable). Hence, wealth at the end of the period iswXiwith i=1;n.

Let w and v(x)be the current wealth and utility function

respectively. According to expected utility criterion,

the investor will choose portfolio k if:

E [v (wXk )]=max1≤i≤n

E[v (wXi)]

It is clear that if you determine the distribution of

each wXi(i=1;n) and value function of each option, you

can predict and explain the portfolio preferred to

others.

Notation:

The cumulative distribution function of X: FX (x)=P(X≤x)

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The complementary or tail distribution function of X:SX (x)=FX (x)=1−FX (x)

Density function: fX (x )=F'X (x )

b. Absolute and First-order Stochastic Dominance

Absolute dominance/ almost-sure dominance: Y is

absolutely dominant over X ifP (X≤Y)=1 and there is at

least one y such that FY (y)<FX (y )

First-order stochastic dominance/ simple stochastic

dominance: Y is first-order stochastically dominant over

X if FY (y)≤FX (y )for all y, and there is at least one y such

thatFY (y)<FX (y ). It can be understood that Y has more

chance than X of being bigger than any given value y.

When Y is first order stochastic dominant over X, this

relationship is defined as Y≥fsdX

And,P (Y≤y )=FY (y )≤P (X≤y )=FX (y ), thus, if Y is absolutely

dominant over X, then Y is also first-order

stochastically dominant over X.

Theorem: Supposeu' (x )>0, then portfolio i is preferred to

portfolioj if either wXi is absolutely dominant over wXj

or wXi≥fsdwXj (See the proof in Appendix B)

c. Second-Order Stochastic Dominance

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Second-order stochastic dominance: Y is second-order

stochastically dominant over X if ∫−∞

x

FY (y )dy≤∫−∞

x

FX (y )dy for

all x, and there is at least one x, for which the above

inequality is strict. When Y is second-order stochastic

dominant over X, this relationship is defined as Y≥ssdX

Theorem: Suppose thatv' (x )>0 (implying that investors

prefer more to less) and v'' (x )<0(implying that investor

is risk averse), WXi is preferred to wXj if wXi is second

- order stochastically dominant overwXj, or:

∫−∞

x

Fi (y )dy≤∫−∞

x

Fj (y )dy

(See the proof in Appendix B)

d. Prospect Stochastic Dominance

Prospect stochastic dominance: Y is prospect

stochastically dominant over X (v'>0,v''>0for x<0 , and

u''<0forx>0) if and only if

{∫y0

FY (x )−FX (x )dx≥0forallx≤0

∫0

x

FY (x )−FX (x )dx≥0forallx≥0

With at least one strict inequality.

2.2.3.3. Applying Stochastic Dominance approach to test

hypotheses of CPT

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Investors are assumed to abide by the framework of CPT.

It implies that investors are compatible with three

basic hypotheses of CPT (See page 6)

The value function is u (x) where x is defined as the

deviation of wealth in comparison with a determined

reference point) (See page 9)

u (x)=¿

The probability function is Pg(FX (x )) for non-negative

outcomes and Pl (FX (x )) for negative outcomes, with

P (0 )=0,P (1)=1, where FX (x) is the cumulative distribution

function of X. (See page 10)

Pg (p )= pγ

[pγ+(1−p)γ ]1 /γ with0.28<γ<1

Pl (p )= pδ

[pδ+(1−p)δ ]1 /δ with0.28<δ<1

Exhibit 2.4: Prospect Theory S-shape function and

Reverse S-shape function

24

(Source: Levy and Levy (2002a))

Denote UP the set of prospect value functions containingu (x) that are convex for x<0 and concave for x≥0

Denote UP∗¿¿ the set of inverse prospect value functions

containing u (x) that are convex for x<0 and concave forx≥0

Denote Uconvex the set of prospect value functions

containing u (x) that convex for all x

Denote Uconcave the set of inverse prospect value functions

containing u (x) that are concave for all x

In essence, to test the value function or the

probability weighting function, it is advised that

researchers will test the curvature of graphic curves of

both functions. If u (x) that convex for x<0 and concave

25

for x≥0, then u (x) is an element of the set of prospect

value functions. Similarly, if the probability functionP(p) has the reserve S-shape, then P(p) is also a

probability weighting function of Cumulative Prospect

Theory.

Stochastic Dominance Approach relies on comparison of

two outcomes. By analyzing choice results, scholars are

able to predict the shape of the value function and

probability weighting function.

1.3.3.1. Applying Stochastic Dominance to test the value

function

Consider two prospects X and Y:

E [u (X ) ]−E [u (Y )]

¿∫a

b

u (x ) [fX (x )−fY (x) ]dx

¿ [u (x ) [FX (x )−FY (x )] ]b

a−∫a

bu' (x ) [FX (x )−FY (x )]dx

¿−∫a

b

u' (x ) [FX (x)−FY (x) ]dx=∫a

b

u' (x) [FY (x )−FX (x )]dx

Consider the function: h (x)=∫a

x

[FY (y )−FX (y )]dy

26

Let A=[a0,a1 ] and B=[b0,b1 ] be intervals such that

A∪B=[a,b ]. Given prospects X and Y, h (x)=∫a

x

[FY (y )−FX (y )]dy.

Then,

h (x)≤h (a1)fora0≤x<a1, and

h (x)≥h (b0)forb0≤x<b1

Both inequalities hold if and only if X is preferred to

Y for all function u (x), that are convex in A and concave

in B

X dominates Y according to Prospect theory (See page

14), denoted byX≥PY, if and only ifh (x)≤h (0)fora≤x<0, andh (x)≥h (0)for0≤x<b. Remember that X≥PY if and only if X is

preferred to Y according to Prospect Theory or u∈UP

Denote X≥P∗¿ Y ¿ when X dominates Y according to Inverse

Prospect Theory, if and only ifh (x)≥h (a)fora≤x≤0, andh (x)≤h (b)for0≤x≤b. And, X≥P∗¿Y¿ if and only if X is

preferred to Y according to Inverse Prospect Theory for

all u∈UP∗¿ ¿

Denote X≥ssdY when X dominates Y according to second-

order stochastic dominance (see page 18), if and only ifh (x)≥h (a)fora≤x≤b. And, X≥ssdY if and only if X is

preferred to Y according to second-order stochastic

dominance for all u∈Uconvex

27

Denote X≥s∗sdY when X dominates Y according to inverse

second-order stochastic dominance, if and only ifh (x)≤h (b)fora≤x≤b. And, X≥convexY if and only if X is

preferred to Y for all u∈Uconvex

1.3.3.2. Test the probability weighting function

We assume that the decision maker abides by Cumulative

Prospect Theory, we have:

Pg (FX (x ))= Fγ (x)

[Fγ (x)+Sγ (x )]1γ

with0.28<γ<1

Pl (FX (x ))= Fδ (x)

[Fδ (x)+Sδ (x )]1δ

with0.28<δ<1

The empirical researches show that probability weighting

function is “shallow in the open interval and changes

abruptly near the end-points where P (0 )=0,P (1)=1” (Tversky

and Kahneman, 1992). More specifically, an inverse S-

shape probability weighting function will be concave

first, then convex.

Consider the probability distortion functions that are

concave in ¿ and convex in ¿, for given values of d, c

in [0,1]. Denote this class by Wcd (See Exhibit 2.5)

If c<d, then the segment between c and d is nearly

linear, then the probability weighting function is

28

inverse S-shaped and continuous in (0,1) (as

desired)

If c=d, thus c will be the inflection of these

inverse S-shaped function

Ifc>d, the probability weighting function is

unrestricted between d and c. It is hard to

conclude the shape of the probability weighting

function.

Exhibit 2.5: Schematic depiction of the Wcdclass of

probability weighting function

(Source: Manel and Franz (2007))

2.3. Typical biases explaining for Cumulative Prospect

Theory

This thesis focuses on three typical biases explaining

for Cumulative Prospect Theory, namely loss aversion,

29

anchoring - adjustment and herding. Loss aversion is a

pivotal part of risk attitude influencing investment

choices. Analyzed cognitive bias is anchoring –

adjustment, which forms the reference lever, stemming

from faulty reasoning. In addition, emotional biases

such as herding originating from impulsive feelings or

intuition, rather than conscious reasoning and are

hardly possible to be adjusted to traditional

rationality.

2.3.1. Loss Aversion

Kahneman and Tversky (1979, 1992) advanced Prospect

Theory and Cumulative Prospect Theory that describe how

decision-makers actually behave when confronted with

choice under uncertainty. The value function shows the

asymmetry between the values people treat between gains

and losses. This theory hypothesizes that prior losses

increase risk-seeking, while prior gains reduce it. This

asymmetry is called loss aversion.

Empirical tests conducted by Kahneman and Tversky (1991)

indicate that losses are weighted about twice as heavily

as gains – losing $1 is about twice as painful as the

pleasure of gaining $1. In other words, people tend to

hold on losses in the hope that prices will eventually

go back up. It can be explained on the basis of the

Cumulative Prospect Theory, that value function is

30

upward sloping for wealth levers under each individual’s

reference point. In additional, investors are predicted

to be risk averse in gains. Shefrin and Statman (1985)

called this occurrence, stemmed from loss aversion, of

“selling winners too early and riding losers too long”

as disposition effect.

Loss aversion is one of three components of risk

attitude under the lenses of behavioral finance.

Numerous studies resolving the problem of portfolio

optimization derive from the base assumption of risk,

particularly, loss aversion, there can be Static

portfolio optimization model and Multi-stock portfolio

optimization under Prospect Theory for instances.

2.3.2. Anchoring and Adjustment

As proposed by Tversky and Kahneman (1974), Anchoring

and Adjustment heuristic is one strategy for estimating

unknown magnitude by starting from information that is

adjusted to yield the acceptable value. A vast number of

studies demonstrate that regardless of how the initial

anchors were selected, people have the tendency to

adjust their anchors inefficiently, leaving final

estimates too close to the original anchor,

consequently, irrationally. In other words, people are

generally better at relative comparison than absolute

numbers.

31

In his survey carried out in 2006, Pompian require

participants to estimate a good buy price for a share.

Investors are likely to start by using an initial value

as an anchor which can be the 52-week price of stock for

instance. People, then adjust their information by using

their analysis and interpretation which are indicated as

inefficient approach. It is undeniable that investors

anchor their thoughts to a logically irrelevant

reference point while making portfolio investment

decision.

Andersen (2010) presents the involvement of anchoring in

investment decision of market participants by using an

existing arbitraging algorithm. He applies the algorithm

for practical date of Dow Jones Industrial average,

providing evidence that anchoring plays an indispensable

part in the weekly price fixing of the Dow Jones

Industrial Index.

Anchoring and Adjustment bias shapes a reference point

in investors’ mind when they designing portfolios.

People, basing on their experience with their own

anchors, select securities for their portfolio.

Furthermore, reference level of price is also forming in

their invisible cognition. The reference point is the

central point of the S-shape function of the Cumulative

Prospect Theory.

32

2.3.3. Herding Bias

“Herding behavior is an alternative explanation of the

way that investment choices are made by investors”

(Demirer and Kutan, 2006, Ferruz at al., 2008).

Hirshleifer and Teoh (2003) define herding in financial

markets as mutual imitation leading to a convergence of

action. In other words, herding is a fundamental

tendency of human society that people follow the

investment decisions taken by majority. That is why

people tend to alter their “wrong” answer when they are

confronted with the judgment of large group of people.

Popular analysts have considerable influence on private

investors‘ decisions. However, even completely rational

professionals can deal with herding bias when they take

into account other’s viewpoints, even if they know

people react in a herd like manner. One reason is

originating from the past when our ancestors used to

live sociably and generally tend to seek the allowance

from the crowd rather than being a stand-out.

Furthermore, they believe when a large number of people

are unanimous in its judgments, they are certainly right

due to their illusion that the crowd may know something

they do not.

Word of mouth is a pivotal importance of herding.

Investors generally trust their relatives, colleagues,

33

friends instead of credible institutions or media

(printed newspaper, television, radio). Talking to

others seems rapid and effective information - spreading

approach that no means of communication can surpass. In

their study, Shiller and Pound (1986b) with their

intensive survey in investor’s behavior, only six

percent of the respondents specified newspapers and

periodicals.

The existence of herding may have implications for

asset-pricing models because its behavioral affects on

stock price movement. The assumption of EMH is totally

incorrect because in the real world, people, instead be

rationally valuate the stock price, they react in herd-

like manner.

In spite of the fact that herding bias is not a

component of CPT-investor, this important bias provides

a proof that it is not plausible to apply models of

portfolio optimization of which assumption is investors’

rationality and independence.

34

CHAPTER 3: BUILDING OPTIMAL PORTFOLIO FOR INDIVIDUAL

INVESTORS 3.1. Individual investors

An individual investor is a person who buys and sells

securities for their personal account, and not for

another company or organization. Private investors play

an indispensable part in stock market from the developed

stock markets such as USA’s to the emerging financial

market such as Viet Nam’s.

Standard Finance Paradigm assumes that individual

investors are analytically sophisticated and

knowledgeable about markets. By assumption, private

investors in such these constituted models make optimal

decision in a rational manner. However, numerous studies

criticizing the notion of rationality, pointing out that

individual investors are affected by irrational nature

of buying and selling behaviors. According to Bernstein

(1998), “evidence reveals repeated patterns of

irrationality, inconsistency and incompetency in the

ways human being arrive at decisions and choices when

faced with uncertainty”. Nofsinger (2001) asserts that

assumption of rationality and unbiasedness of economic

participants has been drubbed by psychologist for a long

time.

35

The irrationality of individual investors is discovered

during the decision-making process because this process

is a cognitive process resulting in the choice of a

course of action among several alternatives. In this

process, the emphasis is on thinking based on weighting

the outcomes and alternative prior to the last decision.

During this process, individual investors are under the

influence of numerous biases that drive them to wrong

decisions and mistakes.

Regularly, individual investors are irrational while

they have to make buying and selling decisions in the

stock market. In reality, private investors are under

the lack of abilities, knowledge and technology,

therefore, they decide to manage their asset through

investing in an investment trust. The investment trust

is just cognized inside, not the rational entity in the

market. Pompian (2006) lists more than twenty biases

appearing in the decision-making process, which alter

and motivate all decisions of individual investors.

In light of the above discussion, individual investors

are irrational and biased during the process of making

decision or process of buying and selling. Private

investors manage their assets on the basis of investment

trusts instead of investment analyses. Thus, it is

advisable that individual investors should have

36

different investment instruments from institutional

investors.

3.2. Optimal portfolio

3.2.1. Introduction

Wealth management and especially the portfolio choice,

one important bloc of the financial literature, have

developed substantially over several decades, utilizing

the enormous advancement under power of mathematics and

calculus science.

For the start, my thesis provides definitions of

portfolio and optimal portfolio. A portfolio is defined

as a grouping of financial assets such as stocks, bonds

and cash equivalents, as well as their mutual, exchange

– traded and closed-fund counterparts. Optimal portfolio

is a set of portfolios that offers the highest expected

return rate for a particular investor’s acceptable level

of risk or the lowest risk for a given level of expected

return.

Portfolio construction is designed based on underlying

principle of the notion that risk can be diversified by

adding other assets that allow the portfolio to achieve

a better outcome per each risk unit. From an investor’s

perspective, portfolios are to be constructed taking

into account risk return preference of investors with

optimal portfolios lying on the efficient frontier. With

37

each intensive objective either minimizing risk or

maximizing return, more models of portfolio choice are

proposed.

The optimal portfolio literature can be reviewed as

being in two major parts according to the approaches.

The first is Markowitz mean – variance model which is

well-known as “Modern portfolio theory”, which developed

on the premise of expected utility theory by Markowitz

(1952b, 1959) and Tobin (1958, 1965). Each security is

modeled by two parameters: mean and variance of its

return rate. Parameter “mean” is representative for

expected return concept, while “variance” is

representative for risk concept. The key insight of the

model is the expected return is combination weighted

average return of each individual security, but variance

of portfolio is not. Thus, rational investors focus on

the subset of portfolios lying on “efficient frontier”

which achieve the maximum value for a given variance or

the minimum risk for each expected return rate. The

investor’s ultimate decision is on the basis of their

preference along the efficient frontier.

Although the mean-variance model seems attractive and

useful, there is a variety of problems for

practitioners. As Michaud (1989), the principal problems

are stemming from optimization procedure that leads to

concentrated portfolios, corner solutions, the shortage

38

of robustness and especially requirement of much input

data, hence it is unsuitable for private investors. The

model is also strongly criticized by psychologists

because it is built in terms of investors’ rationality.

The underlying assumption of Modern portfolio theory

prevents MPT from applying in reality.

The second approach is developed under the advancement

of behavioral finance that proposes better understanding

of portfolio management behavior as well as decision-

making process. When people confront with risk and gain,

they are affected of invisible biases deriving from

psychology (Kahneman and Tversky, 1979, 1991) and

emotions (Lopes 1987). Furthermore, investors have more

accurate security assessment in long-time rather than

within one year.

Portfolio construction based on behavioral finance

assumes that investors are irrational. Each behavioral

model introduced in this domain concentrates on several

major psychological concepts such as risk asymmetry,

emotions, behavioral biases, the prospect theory, mental

accounting etc. Within this thesis, my concentration is

on the model designed on Cumulative Prospect Theory

base.

3.2.2. Approaches of portfolio optimization

39

The expected utility theory, developed by Von Neumann

and Morgenstern (1947), originates from early working

paper of Bernoulli (1738), providing an idealized,

normative economic model of rational decision under

uncertainty. Complying with the theory, investors

maximize their utility through aggregating the weighted

outcomes. Utilities, formulated in a utility function,

are graphed nonlinearly related to monetary amounts.

In their study in 2005, Copeland, Weston and Shastri

witness that expected utility rests on a set of axioms,

such as comparability or completeness, transitivity and

invariance. Comparability means that agents know exactly

their preference, hence can select the most desired

outcomes. Transitivity implies that people have

consistent preferences that are unable to be altered.

Invariance can be understood that preferences are framed

independently. Based on these assumptions, models of

portfolio optimization, asset allocation and valuation

are constructed. The expected utility model, as with all

theoretical models, is not without its limitations. One

is that the theory considers uncertainty as objective

risk. It is obviously unacceptable to plan for

probabilities of events.

Despite its limitations, EU assumption is irreplaceable

until the occurrence of psychological concept in

finance. Each behavioral concept, such as risk

40

asymmetry, emotions, behavioral biases, prospect theory,

mental accounting, can be added into a model of

portfolio optimization. Nevertheless, Prospect Theory

and Cumulative Prospect Theory are two most popular

approaches to resolve the problem of optimization under

lenses of behavioral finance.

The Prospect Theory is similar in character to that of

utility function, but the major difference between two

theories is the reference point. While EU is the key

background for construction of mean-variance portfolio

theory, PT is an essential premise for models of

portfolio choice in behavioral finance. However, many

researches show the limitation of PT that the theory can

be only applied to gambles with at most two nonzero

outcomes; it predicts that people sometimes choose

dominated gambles.

In modified version published in 1992, the theory known

as “Cumulative Prospect Theory” is popularly accepted

and typically used in both academic and practical

worlds. Empirical research has been testing CPT and

providing evidence of its relevance for models of

investment decision than original version. The

theoretical and empirical studies, proposed by Tversky

and Kahneman (1979), are a striking proof in support of

the CPT when CPT is accessible to resolve some

limitations of Prospect Theory.

41

To conclude, different assumptions shape different

models of portfolio optimization. The Expected Utility

Theory is the key motivation for traditional

mathematical model while PT and CPT are indispensable

parts of the enhancement of optimal portfolio models

accounting for behavioral biases.

3.2.3. Processes of portfolio management

Exhibit 3.1: The process of portfolio management

(Source: CFA Institute, 2014, CFA Level1Book 1, Portfolio

management)

3.2.3.1. Create a policy statement

Policy statement is a commitment of investors about

goals and constraints as it relates to their investment.

This step is judged as the most important of all stages

in portfolio management process.

Create a policy statementDevelop an investment strategyPortfolio selectionAsset allocationMonitor and update portfolios

42

It is requisite for an investor to understand his true

financial needs both in short-run and long-run. Based on

this good understanding, the investor will manage his

portfolio to meet his needs. When there is market

volatility or a change in his private needs, the policy

statement will guide him to make necessary adjustments

in a disciplined manner.

Prior to design a policy statement plan, it is of

pivotal importance for an investor to express his

investment objectives in terms of risk and return.

It is undeniable that return objectives play great roles

in investment decision-making process as they help to

focus investors on reaching financial goal. However,

level of risk tolerance are far more important than

expected return rate. With each risk level, the

requirement of return rate is distinct. Furthermore,

despite the need for a high return, an investor may be

uncomfortable with the risk that is attached to that

higher return portfolio. As such, it is important to

consider not only return, but the risk of the investor

in a policy statement.

3.2.3.2. Develop an investment strategy

Strategic investment plan is the strategy combining

investors’ goals and objectives with current financial

market and economic conditions.

43

Before investment decision, investors should spend time

on researching and analyzing the macroeconomic

situation. There is no one denying the dependence

between the development of stock market upon the

sustainability of national economy and the stability of

manufacturing environment.

Actual experiences show that stock and other asset

prices are important parts of the driving forces to

economic growth. For example, the rise of stock prices

has positive effects to the increased investment of

enterprises (excluding too high speculation and

imperfect information). Stock prices also have effects

to the wealth of the households and their spending.

3.2.3.3. Select securities

Portfolio selection is the process that investors decide

to pick securities for their portfolio. In this stage,

the investor will choose securities including foreign

exchange, gold, stocks, bonds, etc. Portfolio selection

is an indispensable step in portfolio management

process. Based on policy statement, investment strategy

and private screening systems, assets are add in to list

of portfolio.

There are many approaches to pick stock or securities.

Many fundamental investors prefer huge companies that

generate more profit with sustainable growth rates.

44

While some individual investors select technical tools

to pick growing stocks based on market performance

rather than the company’s fundamental factors. Types of

preference lead to the different selection of stocks,

bond or cash.

3.2.3.4. Allocate assets

After having a list of securities, investors jump into

the next stage, allocation. The major objective of this

step is to distribute total original monetary wealth

into different investments. In other words, they have to

answer the following questions: how proportion of cash

should an investor maintain? How much proportion of

asset X should be purchased? In my thesis, the model

Static Portfolio Optimization model, designed on the

basis of Cumulative Prospect Theory, aims to help

investors to answer these questions in real world.

In reality, with the support of such models as Capital

Asset Pricing Model, Fama French Three Factors,

Discounted Cash Flow model, Dividend Discounted Model,

etc, investors are equipped with many screening system

allowing to shorten choosing process.

3.2.3.5. Monitor and update portfolios

The last stage of portfolio management process requires

investors to adjust when both markets and investors’

45

needs change. It is necessary for investors to monitor

for these changes as they occur and update the plan as

soon as the market changes has big influence on

portfolio performance in the foreseeable future.

3.2.4. Optimization constraints

3.2.4.1. Regulation and taxes

Regulation and taxes are constraints imposed on the

optimization process. Investors may be forbidden by law

to hold some assets because in some cases, unconstrained

portfolio optimization would lead to short-selling of

some assets while short-selling can be forbidden in

several countries. Additionally, it is impractical to

hold an asset due to too high associated tax cost.

3.2.4.2. Transaction costs

Transaction costs are the costs of trading in order to

change the portfolio weights. Since the optimal

portfolio changes with time, there is a financial

incentive to optimize again frequently. However, too

frequent trading will lead to too-frequent transactions

costs; hence, the optimal strategy is to find the

frequency of re-optimization and trading that balance

between transaction costs and up-to-date optimal

portfolios.

46

3.3. Designing optimal portfolio for individual

investors

Each individual investor is affected by different types

of cognitive and emotional biases. These biases

influence on purchasing and selling decisions, hence

have great impacts on selection and allocation stages

(See Exhibit 3.1).

Selection stage is the stage when individual investors

choose stocks, bonds and cash for their portfolio. The

choices can deviate from the initial investment policy

and strategy due to herding and anchoring for instances.

Therefore, investors should take advantage of screening

system to isolate them from the craziness of the stock

market.

Allocation is the process of optimization, thus it is of

critical importance to apply suitable models to allocate

portfolios. For example, if one of the most obvious

biases is loss aversion, the investor should apply the

model of portfolio optimization based on loss aversion

index or loss aversion function. Another examples, when

an investor abide by Cumulative Prospect Theory, he

should use models based on theoretical framework of CPT.

To summarize, designing individual portfolio is

different from financial institutions because of

investors’ irrationality. Each investor requires a

47

private model benefiting them in order to optimize their

portfolio. These models should be based on the most

clear biases affecting on them.

48

CHAPTER 4: MODEL OF STATIC PORTFOLIO OPTIMIZATION

UNDER CUMULATIVE PROSPECT THEORY4.1. Introduction

Cumulative Prospect Theory has been emerging as the best

financial premises for constructing optimal portfolio in

comparison with Expected Utility Hypothesis and Prospect

Theory; hence, some theoretical optimization models have

been designed under CPT.

Pirvu and Schulze (2012), in their working paper No.

742, propose advance model of multi-stock portfolio

optimization under CPT. The model is developed on the

basis of Static portfolio optimization of Bernard and

Ghossoub (2009). They consider a CPT-investor in one-

period economy with one riskless bond and multiple risky

stocks, which follow a multivariate elliptical

distribution. The key contribution of their work is a a

two-separation between the riskless bond and a mean-

variance-portfolio. Based on their finding, they resolve

the optimization problem by imposing a regulatory risk

constraint.

He and Zhou (2011) resolve the static problem in the

presence of n risky choices, corresponding to a multi-

stock financial market. They introduce a new measure of

loss aversion for large payoffs, known as large-loss

49

aversion degree (the LLAD), which is proved to be a

pivotal determinant of the model. The problem of

maximizing the prospect value is explicitly demonstrated

for the cases when the reference level is the risk-free

return and when it is not. They compose the LLAD, the

reference point and the curvature of of the probability

distortion within their statics of optimal risky

portfolio.

Gomes (2003) in “Portfolio Choice and Trading Volume

with Loss-Averse Investors” presents a model of

portfolio selection and security trading volume in case

of loss aversion bias. The demand function of model is

discontinuous and non-monotonic risky assets. Loss-

averse investors complying with disposition effect will

not hold stocks unless the equity return rate is quite

high. Gomes provides the cogent proof of that elasticity

of the aggregate demand curve fluctuate considerably,

depending upon the distribution of wealth.

Within the thesis, my principal objective is to

introduce Static portfolio optimization model holding in

a risky asset and a risk- free asset under Cumulative

prospect Theory, in a one-period economy. This model

valid in case of the assumption of CPT-investor is

reasonable.

50

4.2. Static Portfolio Choice under Cumulative Prospect

Theory

4.2.1. Background

Consider the portfolio choice problem in case of one-

period economy with one risk-free asset (return rate p

over the period) and one risky asset (return rate q over

period).

Denote W0 to be the investor’s initial wealth. An amountK (withK>0) is invested in the risky asset and the

remaining (W¿¿0−K)¿ is invested in the risk-free asset.

Assume that short-selling is forbidden.

The final wealth at the end of the period is given by:

W=(W0−K ) (1+p)+K (1+q)=W0 (1+p)+K(q−p)

Define y as the excess return rate on the risky asset

over the risk-free rate:

y=q−p

Define Wref, the reference level of wealth at the end of

period as:

Wref=W0 (1+r )

Wrefis the amount the individual would have receive at

the end of period if he invested all his initial W0 in

the risk-free asset (for example: bank account or

Treasury bills).

51

It is clear to see that:

W=Wref+Ky

The deviation from the reference level is defined as:

D (K)=W−Wref=Ky

4.2.2. Content of Static Portfolio Optimization model

The objective function of the CPT – investor, O(x), is

given by:

O (D)=∫0

+∞

Pg (S (x ))dg (x )−∫0

+∞

Pl (F (−x ))dl(x) (See page 11)

F and S is the cumulative distribution functions and

decumulative distribution functions of risky asset and

risk-free asset, respectively.

Lettingy=xK, in order to x=Ky anddx=Kdy.

Thus, S (x)=S (Ky ) andF (x)=F (Ky ). Then, obtain:

O (D (K ))=∫0

+∞

Pg (S (Ky) )dg(Ky)−∫0

+∞

Pl (F (−Ky ))dl (Ky)

¿∫0

+∞

∝(Ky)∝−1Pg (S (y ))Kdy−∫0

+∞

μβ (Ky )β−1Pl (F (−y ))Kd(y)

¿K∝∫0

+∞

Pg (S (y ))dg (y )−Kβ∫0

+∞

Pl (F (−y))dl(y)

To simplify, rewrite the formulation as follows:

O (D (K ))=G (y )−L (y ) (¿)

52

Where { G (x )=∫0

+∞

Pg (S (y))dg(y )

L (x )=∫0

+∞

Pl (F (−y) )dl(y )

Thus, portfolio optimization holds ifO (D (K ))=max

K>0(K∝G (y )−KβL (y ))

Let denote by R (y ) the ratio of G (y) to L (y). We have:

R (y )=G (y)L (y)

=∫0

+∞

Pg (S (y ))dg (y )

∫0

+∞Pl (F (−y ))dl (y )

CASE 1: Firstly, consider the situation where only

borrowing is allowed, so K>0

Problem 1: Given 0<∝≤β<min {1;2min (δ;γ )} where αandβ is

parameter in the value function (see page 9), γ∧δ are

parameters in the probability weighting function (see

page 10), suppose that short-selling is prohibited and

investors are allowed to borrow in order to invest in

the risky asset. We resolve the optimization problem of

maximizing the prospect value of (¿) (See page 31)

maxK>0

(K∝G (y)−KβL (y) )

Proof:

53

If ∝=β, then we can write O (D)=K∝O (y ), then we consider 3

cases as follows:

- If O (y)=0, any holding in the risky asset is

optimal. The prospect value is constant and equal

to 0

- If O (y)>0, the borrowing finite amount to invest in

the risky asset optimize the portfolio. The

prospect value is equal to +∞.

- If O (y)<0, the optimal amount K to invest in the

risky asset is equal to 0.

If ∝≠β, the maximum prospect value holds when:

d (K∝G (y )−KβL (y ))dK

=0

According to Bernard and Ghossoub (2009), the equality

yields the only root:

K'=(βL (y )αG (y ))

1α−β=(∝β )

1β−α R (y)

1β−α

In order to K' is the optimal point for the equality, it

leads to the requirement as follows:

d2 (K∝G (y)−KβL (y) )d2K

<0

↔ (α−1 )Kα−2<K'α−β (β−1)Kβ−2

54

When K=K', then (α−1)K'∝−2<K'α−2 (β−1 )↔α<β (as desired).

Thus, K' is the optimal allocation when borrowing is

allowed.

CASE 2: Consider the condition where both short-selling

and borrowing constraints are imposed. This leads toK∈ [0;W0 ]

Problem 2: Given 0<∝≤β<min {1;2min (δ;γ )}, where αandβ is

parameter in the value function (see page 9), γ∧δ are

parameters in the probability weighting function (see

page 10), suppose that both short-selling and borrowing

are not allowed, we resolve the optimization problem of

maximizing the prospect value of ( ¿ ) (See page 31)

maxK>0

(K∝G (y)−KβL (y) )

Proof:

If ∝=β, then we can write O (D)=K∝O (y ), then we consider 3

cases as follows:

- If O (y)=0, any holding in the risky asset is

optimal. The prospect value is constant and equal

to 0

- If O (y)>0, It is optimal to invest W0in the risky

asset optimize the portfolio.

- If O (y)<0, the optimal amount K to invest in the

risky asset is equal to 0.

55

If ∝<β, the maximum prospect value holds when:

K'=min(W0;(∝β )1

β−α R (y)1

β−α)Thus, in this section we have just indicate the optimal

portfolio allocation rate K'. Clearly, the optimal

holding is dependent upon R (y ). As pointed out by Bernard

and Ghossoub, R (y ) is the key to resolve the problem of

portfolio allocation.

As you can see the result of both cases, R(y) has key

contribution to the final allocation K. Thus, to find

the optimal allocation rate K, it is essential to find

the optimal value of R(y).

The higherR (y ), the higher the optimal allocation K in

the risky asset:

R (y1 )≥R (y2 )→K' (y1 )≥K' (y2 )

R (y ) is also called CPT-ratio. This ratio quantifies the

risky asset‘s upside and downside measured by G (y) andL (y), respectively.

In their work, Bernard and Ghossoub include their

finding of the maximum value of R (y ) as follows:

R (y )≤Rmax=(βα )W0β−α

56

To summarize: ∝<β (See the detailed proof in page 32, 33

when ∝=β)

Case 1: consider the situation where only borrowing is

allowed, so K>0

Koptimal=(∝β )1

β−αR (y )1

β−α

Case 2: Consider the condition where both short-selling

and borrowing constraints are imposed. This leads toK∈ [0;W0 ]

Koptimal=min(W0;(∝β )1

β−αR (y )1

β−α)Where:

R (y )≤Rmax=(βα )W0β−α

4.3. Evaluation of Static Portfolio Optimization Model

4.3.1. Advantages

Static Portfolio Optimization model is the simplest

model resolving the problem of maximizing the prospect

value in one period economy with one risky asset and one

risk-free asset for CPT-investor. The model is

constructed on the basis of Cumulative Prospect Theory,

hence it is applicable for investors who are loss-

averse, anchoring in the reference level and

overweighting small probabilities. Furthermore, this

57

model is easy to understand and apply in practical

world.

To academics, Bernard and Ghossoub introduce a new

approach to resolve the problem of optimization under

the lens of CPT. Based on their working paper, more

researches are conducted with more complex and

sophisticated scenarios.

4.3.2. Disadvantages

4.3.2.1. Violate Loss Aversion Index

Risk attitude consists of three components: (i) the

basis utility; (ii) probability distortion, and (iii)

loss aversion known as “behavioral concept” measured

through LA index. Numerous academics point out that

there are many different alternative measures of

behavioral criterion of loss aversion in the literature

with their own advantages and disadvantages. As

Kobberling and Wakker, loss aversion is illustrated by

an index defined as follows:

LAkw= limx→0−¿l'(x)

limx→0+¿g' (x )

¿ ¿

¿¿

The gist of the formulation is to consider foundations

of risk attitude outside marginal utility by using a

“probabilistic risk attitude” resulting from model of

rank-dependent utility. As Schmidt and Zank (2007), this

58

idea is inherited from Prospect Theory introduced by

Kahneman and Tversky (1979), and Expected Utility

Theory, but is inaccessible to apply under Cumulative

Prospect Theory because it ignore rank dependence. In

their work, Schmidt and Zank (2005) propose an

alternative quantitative approach to define loss

aversion in terms of both the value function and

probabilities distortion.

Consider the Objective function:

For x>0 is a fixed real number, then

Og (d )=∫0

+∞

Pg (S (x))dg(x)=∫0

+∞

Pg¿¿¿

¿∫0

+∞

Pg ¿¿

Similarly, Ol (x)=l (x ) withx>0. Hence, for any x>0, we have

O (x)=g (x)=xα and |O (−x )|=|−l (x)|=μxβ. Consequently, loss

aversion holds when xα<μxβ or μ>xα−β

Obviously, when ∝=βand μ>1, loss aversion holds.

When ∝<β, the model violates the accepted measure of

loss aversion proposed by Kobberling and Wakker in a

neighborhood of the reference point, namely for:

0<x<ε=μ1

α−β

59

However, the violation with loss aversion index

suggested by Kobberling and Wakker is not a serious

matter as some recent experimental studies show that

individuals’ decision sometime violate loss aversion,

Bleichrodt and Pinto’s work of “An Experimental Test of

Loss Aversion and Scale Compatibility” in 1995 is a

typical example.

Thus, in their model of Static portfolio optimization,

Bernard and Mario (2009) consider loss aversion as the

behavioral phenomenon that “losses loom larger than

gains” (Kahneman and Tversky) that do not concern where

loss aversion deriving from, the utility function or

from the probability weighting function or from both.

4.3.2.2. Ignore diversification benefits

It is undeniable that the model is too simple with only

one risky asset and one risk-free asset, which cannot

reach the portfolio diversification. Investors who

desire to invest more types of asset do not take

advantage of the Static portfolio optimization model.

However, this difficulty is surmountable with the

evolutionary model of Pirvu and Schulze (2012) with

multi-stock portfolio optimization under CPT.

60

CHAPTER 5: INTRODUCTION TO VIETNAMESE INDIVIDUAL

INVESTORS5.1. Overview of Vietnamese stock market

5.1.1. A brief history of Vietnamese stock market

On July 2000, Viet Nam took a major step towards

establishing a more robust market and forming a new

channel of capital mobilization for enterprises by

opening Securities Trading Centre in Ho Chi Minh. On the

first day of trading, only two individual stocks with

total market capitalization of VND 444,000 million

(about USD 27.95 million) were transacted on the market.

After four years of preparation and a vast number of

delays, the Government of Viet Nam ultimately fulfilled

its commitment to the opening of Vietnamese stock

market. After 13 years of the enhancement, Vietnamese

stock market has been evolving with significant

contribution to the national economy sustainable

development.

5.1.1.1. HOSE

Due to the rapid growth of the securities market, the

economic innovation and the business restructure, Prime

Minister approved Decision No.599/QĐ-TTg to transform Ho

Chi Minh Trading Centre into Ho Chi Minh Stock Exchange

61

(HOSE), which is current accounting for about 89% of

aggressive capitalization.

Thirteen years after the foundation of the Vietnamese

stock market, at the end of June 2013, the market had

309 listed companies in Ho Chi Minh with capitalization

worth almost USD 40 billion, an increase of 480% in

comparison with year 2000. Especially, the average

trading volume per day during June 2013 reached about

65.69 million shares, equivalent to about USD 51 million

per a trading session. The amazing turnover rate was

42.05% during the first six-month period in 2013.

The products traded on HOSE consist of stock, corporate

bonds, municipal bonds and fund certificates. There are

currently also two types of fund certificates, 38 bonds

listed on HOSE with the volumes of about 30.3 billion

shares, 70 million bonds and 45 million fund

certificates, respectively.

Table 5.1: HOSE’s listing summary recorded in April 2014

ALL STOCK

INVESTMENT

FUND

CERTIFICATE

BOND

Total listed

shares (1

share)

342 302 2 38,00

Percent (%) 100,00 88.30 0.58 11.11

62

Listed

Volume (1000

shares)

30,314,902

.9

30,199,292

.145,417.53 70,092.3

Percentage

(%)100,00 99.62 0.15 0.23

Listed Value

(VND

million)

309,457,33

4.2

301,993,93

0.9454,175.30

7,009,22

8.0

Percentage

(%)100,00 97.59 0.15 2.27

(Source: www.hsx.vn, the official website of Ho Chi Minh Stock

Exchange)

5.1.1.2. HNX

Ha Noi Stock Exchange was established in accordance with

Decision No.01/2009/QDD-TTg by Prime Minister on the

basis of transforming and restructuring Ha Noi

Securities Trading Center.

By the end of June 2013, HNX had 387 listed companies in

Ho Chi Minh with capitalization worth almost USD 4.65

billion compared to USD 40 billion recorded at HOSE,

which implies the considerably small scale of HNX.

Despite the scale of market capitalization, the average

trading volume per day during June 2013 still reached

about 54.03 million shares, equivalent to about USD

19.80 million per a trading session.

63

The products traded on HNX consist of stock, corporate

bonds, municipal bonds and Government underwritten bonds

with the volumes of about 8.89 billion shares, 5.72

billion bonds in total, respectively.

Table 5.2: HNX’s listing summary recorded in April 2014

ALL STOCK BOND UPCOME

Total listed

shares (1

share)

1052 377 532 143

Percent (%) 100 35.84 50.57 13.59Listed

Volume (1000

shares)

16,606,128

.32

8,895,613.5

7

5,720,220.8

3

1,990,293.9

2

Percentage

(%)100 53.57 34.45 11.99

Listed Value

(VND

million)

680,801,16

2.7

88,956,135.

68572,022,088 19,902,939

Percentage

(%)100 13.06 84.01 2.92

(Source: www.hnx.vn, the official website of Ha Noi Stock Exchange)

5.1.2. Overall movements of Vietnamese stock market during the period of

2007-2013

64

In essence, the cyclical movement of the growth rate of

Gross Domestic Product (GDP) accompanying with the

integration of financial and merchandise markets into

the global marketplace (as 2006 marks the milestone of

Vietnam’s entry to the World Trade Organization) are the

two key motivation for the stock market performance and

enlargement from 2007-2013.

Year 2007 is considered as the heyday of Vietnamese

stock market where VN-index had peaked an all time

closing of 1170.67 points, an increase of more than 55%

in comparison with the last trading day in 2006 despite

every low market base (Figure 1). HOSE had completed 248

trading sessions with a total transaction volume of more

than 2.3billion shares, equivalent to market transaction

value of VND 224,000, an increase of 200% in volume and

an increase of 280% in value. On average, HOSE recorded

9.2 million shares transferring each session, about VND

980 billion. HASTC performed 248 successful sessions

with the volume of 616.3 million and the total value of

VND 63859 billion, up 6 times on the volume and 15.8

times on the amount of transaction value (Figure 2).

Trading scale rocketed to VND 255 billion per day in

2007 in comparison with VND 19 billion per day in 2006.

Exhibit 5.1: VN-index in the period of 2004 to 2014

65

(Source: http://www.fpts.com.vn)

Exhibit 5.2: HNX-index in the period of 2004 to 2014

(Source: http://www.fpts.com.vn )

In 2008, Vietnamese stock market was crippled by the

financial crisis originated from USA and the crash of

speculative bubbles inside the securities market

overheated and overestimated. It was the years of the

index decline, the fall of market price of shares, the

illiquidity, the divestments of foreign investors and,

especially, the intervention of Government. Within 2008,

66

there were four times altering the price vibration

amplitude of a share on both stock exchanges. In support

of the securities demand and the market recovery, the

Government proposed and implemented the 19 solutions

group preventing Vietnamese stock market from serious

ruin.

The stock market in 2009 could be divided into two major

periods based on the recovery signals. The first quarter

is known as the stock market bottom when VN-index

declined to 235.50 points (24 February 2009). Investors’

pessimism covered almost sessions from January to March.

The stock market, nevertheless, recovered due to

Government’s painstaking effort by supporting stimulus

package for the remaining period. A large number of

financial incentives were transferred directly to

commercial banks in order to unfreeze capital flow in

enterprises. The stock market indices made a strong

bullish reversal. VN-index reached more than 600 points

– an incredible achievement under global crisis

pressure. By the end of 2009, the absolute market

capitalization was worth of VND 620,000 billion compared

with VND 225,000 billion in 2008, an increase of nearly

300%. The figure of listed companies was up to 447

companies attracting investors for opening about 739,000

new trading accounts. Foreign portfolio investment value

was nearly USD 6.6 billion at the end of December 2009.

67

It can be understood that the period of 2010 to 2013

witnessed no obvious trend. The market volatility was

lying on the range of 400 and 500 with average level of

liquidity. The gist of this condition was indicated by

economic experts because of the caution of investors and

the scarcity of cash-flow. During this period,

Government continued to implement resolutions to

orientate money-flow to manufacturing and limit inflows

to the stock market and the real estate market.

The recovery of stock market in 2013 was the most

predominant signal to illustrate the improvement of

investors’ confidence index. By the end of 2013, VN-

Index gained by 21.97% with close price at 504.63

points, HNX-Index increase 18.83% to 67.84 points.

Average trading volume and transaction worth on both

exchanges were about 108 million shares and VND 1,381

billion per day, equivalently to an increase of 3.14%

and 5.27% respectively compared to that of 2012. The

market size reached to 31% GDP with market

capitalization worth VND 964,000 billion on the rise of

26% compared to the previous years. All major indices

assist Vietnam to be one of countries that has the best

recover rate in the world.

5.2. Overview of individual investors

68

The figure and the quality of individual have been

increasing throughout several years. More and more

people owning idle cash have been participating in the

stock market for profitable investments. For a start,

individual might be untrained and uninformed, however,

after the crash of speculative bubbles in 2007, they

have token awareness of knowledgeable equipment.

According to the interview result of Tran Dac Sinh –

chairman of HOSE, by the end of the year 2013, there

were 1.3 million trading accounts comprise 1,282,071

accounts of domestic individual investors in comparison

with 5,081 accounts of domestic institutional investors,

13,950 accounts of foreign individual investors and the

1,631 remaining of foreign institutional investors.

Furthermore, according to a statistic of www.cafef.vn,

the average daily trading value of individual investors

accounts for 85% of total value trading in a session.

Due to the character of the securities market is a high

risk and affected strongly by the expectation factor of

the investors; it can be seen that the investors can

push the stock prices beyond the long-term trend. The

investors’ expectation is decided by psychological

factor leading to the over reflection in the securities

market; therefore the overoptimistic attitude can make

the prices go up or pessimist spirit can make the prices

go down too much. Thus, it is undeniable that domestic

69

individual investors contribute a critical importance to

the enhancement and movement of the Vietnamese stock

market.

5.3. Typical features of individual investor in

designing portfolios

5.3.1. Lack of knowledge

Despite having great contribution to trading value in

Vietnamese stock market, the quality of individual

investors, has been poor.

In the period of 2000-2005 or establishment phase, with

nearly 2000 accounts, stock market transactions

attracted almost professional investors specializing in

finance. The majority of investors in the first

generation have been successful and influential experts

in financial institutions, security companies. According

to www.laodong.com.vn , based on some criteria, they

showed the table assessing the capacity of individual

investors in the period of 2000-2007 as follows:

Table 5.3: Level of knowledge of individual investors in

2000-2007 in Viet Nam

No CriterionPoint (/10)

2000-2005 2006-20071 Knowledge of finance 4 22 Connections/relationships in 5 1

70

financial market

3Knowledge of Vietnamese stock

market5 2

4Knowledge of Global stock

markets3 1

5 Individual financial resource 4 16 Level of influence 4 17 Level of being affected 4 1

Total 27 10(Source: www.laodong.com.vn (2007), Trinh do nha dau tu ca nhan den

dau?)

In full flourish of the Vietnamese stock market in the

period of 2006-2007, a vast number of investors from

every social level were induced to participate the

securities market even they had had no idea of

securities, fundamental analysis or technical analysis.

The number of accounts rocketed to 300,000 accounts

served by about 70 security companies. According to

www.laodong.com.vn , based on some criteria, they showed

the table assessing the capacity of individual investors

in the period of 2006-2007 (See Exhibit 5.5)

It is clear to find that all criteria are less than ones

in the period prior to 2006. It can be explained by a

vast number of accounts opened from 2005. Numerous

investors came from different jobs, different social

level and educational standard. Many of them have no

71

idea of knowledge base of finance. Level of knowledge of

individual investors in 2006-2007 was calculated to be

about 10/70 points. With about 250,000 accounts, the

average point for individual investors in this period is

about 11.2 point/an investor. In contrast, level of

knowledge of individual investors in 2000-2005 is

calculated to be about 27/70 points. With about 2000

accounts, the average point for individual investors in

this period is about 17.5 point/an investor in

comparison with 11.2 point/an investor in the period of

2000-2005.

After the speculative bubble crash, domestic individual

investors have been aware of the improvement of

knowledge and skills, but they are judged as

unprofessional and risk-taking.

Due to the low quality, almost investors have no

awareness of applying models of optimization into

practical investments. They often invest in short-term

instead of one period economy. Instead of selecting

securities based on fundamental or technical elements,

domestic individuals make decision based on insider

information or rumors. Due to small amounts of money,

they often select shares with high liquidity and high

volume, then conduct as many transactions as they want,

ignoring brokerage and trading costs corroding their

returns. Moreover, they are inaccessible to credible and

72

sufficient data sources that are required for models of

portfolio optimization. Thus, numerous individual

investors do not desire or have ability to apply models

of optimal portfolio in real-world.

5.3.2. Lack of technological investment tools

Without the support of technological investment tools as

well as modern financial services, individual investors

in Vietnam have little opportunities for improve their

portfolio performance. It is common knowledge that

technology has marvelous power in simplifying

mathematical complex function. Hence, if investors are

assisted with models coded in computers then it is no

doubt about the more return rate and less risk level.

Furthermore, technological tools help investors to

shorten the time of making decision as well as to

eliminate behavioral biases such as herding, cognitive

or anchoring, etc.

Due to 13 years of the stock market, a number of

financial investment tools are currently limited. There

are many popular investment tools in big stock markets

such as stock screener, option screener, earning

calendar, IPO calendar, prospectus library, etc., but in

Vietnam, these supporting tools have been a green field.

It is unbelievable that software Excel, provided in

every computer labeled Microsoft, seem be strange to

73

Vietnamese investors. This problem poses many

difficulties for individual investors to be

knowledgeable and rational.

5.3.3. Affected by behavioral biases

5.3.3.1. Loss aversion bias

Majority of experts and brokers confirms the presence of

loss aversion (known as disposition effect) among

investors, including themselves. Clearly, investors have

the propensity to hold on their losing stocks to avoid

realizing loss, then averse the regret of making bad

investment decision. Besides, they sell winning stocks

quickly to avoid the regret of falling price later.

In their empirical study of individual investors’ biases

in Vietnamese stock market, Vuong Duc Hoang Quan and Dao

Quy Phuc (2012), throughout conducting a survey of

behavioral biases, describe loss aversion as one of

biases appearing with high percentage with 47.7%. The

figure presents the fact that a huge number of investors

are influenced by disposition effect. Stemming from this

bias, many evidences are shown for the existence of loss

aversion bias, we would take a shot of the Vietnamese

stock market in 2008 for instance of the presence of

loss aversion.

74

Let us pick the period of 2008 – the time of stock

market bubble crash for instance. Major investors, who

were interviewed, affirmed to keep losers stocks in

their accounts even though loss rate exceeded the figure

of 80%. It would be understood that the more stocks they

kept, the more losses they suffered. 90% of losing

investors had scruples about cutting losses or selling

losers stocks which might assist them to get out of

stock market bubble crashes. Despite cutting loss when

loss rate exceeds a certain level (usually 10%) is of

pivotal importance for rational investors to maintain

their wealth, they continue illusory thought that

holding on losses is a form of long-term investments.

Unfortunately, the price level kept falling down until

their wealth value was impoverished.

According to statistics of the credible financial

website www.cafef.vn, from January 2007 to June 2008,

there were about 40 winning sessions and 80 losing

sessions. Assuming investors bought securities at the

beginning of 2008 and the price reduced 10% after 2

weeks of transaction. Because of high rate of liquidity

in winning session, thus, investors could sell all of

their loser stocks in these trading days, but they did

not. The principal reason of their hesitation to sell

losers was deep-rooted from their prosperity that price

would go back up.

75

Loss aversion is a major part of risk attitude

influencing to how investors constitute their portfolio

and optimize their investments. This bias is a critical

characteristic of CPT-investor, which is tested in this

thesis.

5.3.3.2. Anchoring and Adjustment

Anchoring and Adjustment bias is a popular bias

accounting of wrong portfolio investment decision made

by individual investors. By anchoring in US stock

market, experts’ analyses and predictions and other

information sources, investors adjust information,

deviating reasonable approach to pick profitable

securities.

The bias is considered as significant heuristic having

economic consequences for decision-makers as well as the

efficiency of the Vietnamese stock market. In their

empirical study, Anchoring and Adjustment accounts for

43% of responses for the survey carried out by Vuong Duc

Hoang Quan and Dao Quy Phuc (2012). Furthermore, Nguyen

Duc Hien, Trinh Quang Hung and Bui Huong Giang (2013),

through investigating 661 analysts’ reports forecasting

price in Vietnam from 2009-2012, provide the proof of

the existence of anchoring and adjustment bias among

economic experts when they try to forecast stock

returns. Additionally, they present that anchoring and

76

adjustment have a considerable effect on genders and

different groups of experts as well as the time horizon

through a multi-variable regression model.

Let me take the anchoring in US stock market for

instance.

In the report published by the Wall Street Securities

company, by using correlation function, analysts show

the relationship between VN-index and Dow Jones with

correlation coefficient up to 81%. The correlation

coefficients between VN-index with Nasdaq index and S&P

500 is 92% and 85% respectively.

Anchoring in US stock market is one of many anchors in

financial markets when they make decision for long-term

portfolio investments, namely: economic experts’

viewpoints, previous price, insiders’ information, etc.

According to Luu Thi Bich Ngoc (2013), in terms of

anchoring, there are two groups of forecasting stock

prices for investment decision making. One depends on

previous price while the other is influenced by other

information rather price.

Exhibit 5.3: Dow Jones and VN-index from the end of 2008

to the end of 2010

77

(Source: Report of Wall Street Securities JSC)

Anchoring and Adjustment bias shapes a reference point

in investors’ mind when they designing portfolios.

People, basing on their experience with their own

anchors, select securities for their portfolio.

Furthermore, reference level of price is also forming in

their invisible cognition. The reference point is the

central point of the S-shape function of CPT.

78

5.3.3.3. Crowd mentality or Herding bias

During the process of formation and development of the

Vietnamese stock market, herding is a prominent and

tendency in the market. A vast number of investors

entering the securities market with limited knowledge

about the market, neglecting fundamental bases of

stocks. Because of their level of society and

occupations, investors are diversified. Furthermore,

joining with huge expectations is a key driver to push

stock price rocket and be overvalued, then forming

speculative bubbles. The bigger price bubble was; the

more new investors were induced to participate in the

stock market.

A typical example of herd-like manner was highlighted in

speculative bubble crash in 2007. On 29 August 2007,

Hong Kong and Shanghai banking Corporation (HSBC) in

Viet Nam released a report that stock price were

undervalued after adjustment. In support of this

announce, Citigroup Bank confirmed that the Vietnamese

stock market would overcome the global financial crisis,

which is spreading into every aspect of Vietnamese

components. As soon as the optimistic predictions of two

prestige international financial companies were

published, VN-index boosted from about 900 points to

1100 points in mid October 2007.

79

Another example of herd behavior in Vietnamese stock

market is 20 August 2013 when Nguyen Duc Kien, former

vice chairman of the founding council of the Asia

Commercial Bank (listed stock code: ACB), was arrested.

Immediately, pessimistic information spread out, which

made investors sold off ACB stocks as well as bank

securities, VN-index dropped 20.72 points (equivalent to

a decrease of 4.74%). HNX-Index closed at 66.89 points,

a decrease of 5.32% compared to the previous trading

day. ACB’s price went down 6.9% compared to the

reference price at the beginning of the session.

According to Tran Ngo My and Huy Huynh Truong (2011) and

Ngo Thi Diem Huong (2013), they provide empirical

evidences of the presence of herd behavior among

investors. Tran Ngo My and Huy Huynh Truong (2011)

examine the existence of herding in the Vietnamese stock

market and the asymmetric effects of herding which

depends on market movements. Their study indicate that

herding behavior in immature stock market could be

explained by a set of characteristics typical of the

Vietnamese stock market such as a lack of transparency

in information disclosure, small transaction and high

magnitude of market volatility. Ngo Thi Diem Huong

continues to complete the methodology to ensure the

existence of crow mentality in both upward and downward

market condition in the Vietnamese stock market. Based

80

on the research of Gelos and Wei (2002), she uses solid

evidences to show that Vietnamese stock market creates

favorable conditions for herding bias. The major reasons

of herding are derived from incomplete and ineffective

legal framework accompanying with market manipulation,

individuals’ limited abilities, limited financial

commodities and problems regarding of trading session

T+3.

In spite of the fact that herding bias is not a

component of CPT-investor, this important bias provides

a proof that it is not plausible to apply models of

portfolio optimization of which assumption is investors’

rationality and independence.

81

CHAPTER 6: DATA AND METHODOLOGY6.1. Data collection

Primary data, collected for a specific purpose and

required in order to complement secondary data

(Wiedersheim –Paul and Eriksson, 1997), has been

gathered using a questionnaire survey distributed to

investors trading at a brokerage floor and as an online

survey to access investors who prefer to trade via

internet.

The major purpose of the study was to focus on

individual investors, as they were more likely to have

limited knowledge about the application of Behavioral

Finance Theories as well as Cumulative Prospect Theory’s

models of portfolio optimization in practical

investments, hence leading to poor portfolio performance

and wrong investment strategies.

Due to experimental research of decision-making under

Cumulative Prospect Theory, it can be imply that every

individual investor can make the same mistakes and be

affected by biases regardless of the age, gender,

experience, etc. Thus, my thesis only emphasizes on the

considerable samples, does not take care of background

information.

82

The valid number of responses collected by the

questionnaire survey was 204. All of them are investors

having at least one-year experience and trading

currently on HOSE or HNX.

6.2. Overview of methodology

The Static Portfolio Optimization with one risky-asset

and one risk-free asset in one period of time is the

model designed for CPT-investors abide by three

elements. Firstly, they will be concerned with the

deviation of their final wealth from a reference point.

Secondly, they are more sensitive with losses than

gains. In other words, “Losses losses loom larger than

gains”. Lastly, decision-making process is based on

probability distortion function. So, in order to ensure

the possibility of the application of this model, we

have check whether Vietnamese investors comply with

assumptions of CPT. As the model is constructed based on

three fundamental functions developing from CPT

hypotheses excepting for loss aversion function, hence,

we have to conduct an experiment to isolate two

different elements of CPT-investors.

The analytical stochastic dominance conditions

introduced above suggest experimental designs of

prospects to test the value function and probability

weighting function. By using questionnaire with four

83

tasks, each task comprises two prospects with more than

two outcomes, we distribute the survey online, through

trading floors and clients of brokerages, gathering data

for further analysis.

6.3. Research design

6.3.1. Stochastic Dominance approach

After considering the possibility of holding

experimental research and realizing that it could be

implemented, the stochastic dominance method was chosen

for this study. The approach was applied for three major

reasons:

(i) The efficient way to compare pairs of prospects

(ii) Investors were likely to provide credible

information as the nature of survey was anonymous

(iii) The Stochastic Dominance Approach outperforms

other methods in testing Cumulative Prospect

Theory

Stochastic Dominance conditions are sufficient to

characterize combinations of classes of value function

and probability weighting function. We can use the

approach to test joint hypotheses on the curvature of

the utility function and the probability deformation

function.

84

Parameters c and d are the key for the application of

the stochastic dominance (See page 18). Thus, we need to

design tasks to choose c and d such that c is

sufficiently big and d is sufficient small in order to

the probability weighting function concaves up to d and

convex from c. Between c and d, the probability

weighting function is nearly linear. The higher the c

and and the lower the d, the less we assume about the

probability distortion function, but the more

restrictive is the set of portfolios we can design.

Hence, to increase the freedom in choosing the

prospects, we need to understand the minimum of c and

the maximum of d.

As the calculation of Manel and Franz (2007), we receive

the following results as follows:

Table 6.1: c and d

γ c d

1 0.00 1.000.9 0.02 0.980.8 0.05 0.900.7 0.07 0.840.6 0.09 0.790.5 0.1 0.76

(Source: Manel and Franz, 2007)

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The experimental research can be done in two ways.

Firstly, if we assume that the probability weighting

function is inverse S-shaped, stochastic dominance

conditions provide solid basis of testing the curvature

of the value function. Secondly, if we suppose that the

specifications of CPT for the curvature of the utility

function hold, then the corresponding stochastic

dominance conditions serve the purpose of testing

assumption on the shape of the probability weighting

function.

The content of these tasks is based on the design of

Manel and Franz (2007). Firstly, three tasks are

designed to test the curvature of the value function

with the assumption of inverse S-shaped probability

weighting function. Task I presents an all-gains choice,

task II presents all-losses choice and task III uses a

mixed choice (See table 7.2). All of them are designed

so thatX≥PSDY. The probability weighting function is

assumed to to be inWcd, so it is unnecessary to question

about the shape of the probability weighting function,

which is assumed. Hence, the key is to test whether u (x)

is in UPfor X≥PSDY and whether u (x) is in UP∗¿¿for Y≥P∗SDX.

Secondly, two tasks are designed to focus on the

probability weighting function. The value function is

assumed to follow the specifications of CPT, and then,

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prospect stochastic dominance is used to test the

convexity of the probability weighting function.

6.3.2. Questionnaire survey

The questionnaire survey was the most convenient

approach for empirical researches, especially for

behavioral experiments. Taylor et al. (2006) show that

questionnaires are sensible option when information is

needed from a large group of people, and is a powerful

method to capture their opinion and attitude.

Three principal points emphasized by Taylor at al.

(2006) orientate me while designing the questionnaire

survey for the purpose of the thesis:

(i) Assuring the participants of confidentiality

(ii) Keeping questionnaire compact and using questions

which focus on core of the research work

(iii) Gathering respondents’ interest and retaining

it

The questionnaire consists of four tasks, each task

includes two uncertainty prospects X and Y, where X

dominates Y by prospect stochastic dominance with CPT’ s

weighting probability weighting function. Investors can

select unique preferred option. Then, software Microsoft

Excel was used for statistical analysis.

87

The survey is demonstrated in the Appendix A. In actual

experiments, the orders of tasks were randomized. The

tasks were introduced with the written question:

“Suppose you decide to invest $10000 in below

portfolios. Which portfolios do you choose, X or Y? when

it is given that the dollar gain or loss one month from

now will be as follows”.

The experimental survey is divided into two sections,

one part to test the value function and the remaining

part to test the probability weighting function. In the

first section, we assume that the probability is inverse

S-shaped and the goal is to investigate the curvature of

the value function. In contrast, in the second section,

we assume that the value function is S-shaped; we have

to test the hypothesis of probability distortion

function.

6.4. Limitations of the study

The major weakness of my thesis is that my thesis aims

to study domestic individual investors’ decisions using

questionnaires. Making financial decisions require a set

of complicated information and elements that differs

from the nature of the questionnaire. However,

individual investors find the questionnaire easy to

understand, relax and novelty, hence they are eager to

finish all tasks without a complaint or discomfort.

88

A second limitation arises out of the number of

responses. Currently, Vietnam has more 1.3 million

individual accounts in the stock market with about 1.23

million active accounts conducting transactions. While

the number of samples collected is 204 responses.

Furthermore, the investors mainly come from Ha Noi,

which accounts for a mere 7,3% of the Vietnamese

population. It remains to further researches whether

investors in other regions of Vietnam would have the

same attitude to choices under uncertainty.

89

CHAPTER 7: EMPIRICAL RESULTS7.1. Shape of the value function

The result of Tasks I, II and III are exhibited in the

rightmost column of Table 7.2. For each task, the number

of responses is provided as well as the percentage of

individuals that chose the respective prospect.

Table 7.1: List of joint hypotheses in testing the

curvature of value function

Task

SD

conditio

ns

Joint hypotheses

Result

Not

question

ed

ConclusionValue

function

Probability

weighting

function

IX≥SSDY

Y≥S∗SDX

u∈UPu∈UP∗¿ ¿

Pg∈W0.1

Pg∈W0.9

Not

rejected

RejectedP

Consistent with u S-

shaped

u is not a element ofUP∗¿¿

IIX≥S∗SDY

Y≥S∗SDX

u∈UPu∈UP∗¿ ¿

Pl∈W0.1

Pl∈W0.9

Not

rejected

RejectedP

Consistent with u S-

shaped

u is not a element ofUP∗¿¿

IIIX≥PSDY

Y≥P∗SDX

u∈UPu∈UP∗¿ ¿

P∈W1 /1

P∈W2 /3

Not

rejected

RejectedP

Consistent with u S-

shaped

u is not a element ofUP∗¿¿

In all three tasks, prospect X is preferred over

prospect Y (See Table 7.2). In task I, the value

function is assumed to convex for gains, but Y is not

90

preferred according to inverse second-order stochastic,

hence, u¿x) cannot be in UP∗¿¿.

Similarly, in the Task II, the value function is assumed

to concave for losses, concluding that u is not in UP∗¿¿.

The result of task III completes the picture for mixed

outcomes. Under the assumption that the probability

weighting function is concave in[0, 23 ], and given that Yis not preferred, the value function cannot be in UP∗¿¿.

In all the three tasks, the majority of individuals

prefer the prospect stochastic dominance X. Based on the

rejected shapes of the value function, the value

function is consistent with the result.

Table 7.2: Result of Tasks I, II and III

X Y CHOICETASK I GAIN/LOSS PROB. GAIN/LOSS PROB. N X[%] Y[%]

X≥SSDY,c=0.1

Y≥S∗SDX,d=0.9

0 10% 0 50% 204 79.41 20.591000 40%2000 40%3000 10% 3000 50%

TASK II GAIN/LOSS PROB. GAIN/LOSS PROB. N X[%] Y[%]

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X≥S∗SDY,c=0.1

Y≥S∗SDX,d=0.9

-3000 50% -3000 10% 204 86.76 13.24-2000 40%-1000 40%

0 50% 0 10%TASK III GAIN/LOSS PROB. GAIN/LOSS PROB. N X[%] Y[%]

X≥PSDY,c=1 /6

Y≥P∗SDX,d=2 /3

-6000 1/3 -6000 1/6 204 71.07 28.933000 ½ -3000 1/34500 1/6 4500 1/2

(Source: Data collected from the survey in Appendix A)

7.2. Shape of the probability weighting function

The results of Tasks IV and V are presented in the

rightmost columns of Table 7.4 (See page 63).

In Task IV, X is preferred by most subjects. Hence, the

hypothesis that the probability weighting function is

convex from 0.02 cannot be rejected. In other words, P

is a element of W0.02. In Task V, however, the majority of

subjects prefers prospect Y. It can be referred from

this situation that both Pl and Pg are convex in the

corresponding intervals. Together with the results of

Task IV, the reasonable conclusion is that the

probability weighting function is not convex near the

origin. Notice that Task IV is a slight modification of

Task V. In Task IV the extreme outcomes are set equal;

in X the maximum outcome has been added and in Y the

minimum outcome has been added, both with a probability

of 2%. This change is sufficient to reverse the

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preference of the majority of subjects. The difference

between the result of two tasks suggests that decision

makers use the range of outcomes as a decision

criterion.

Table 7.3: List of joint hypotheses in testing the

curvature of probability weighting function

Task

SD

conditio

ns

Joint hypotheses

Result

Not

question

ed

ConclusionValue

function

Probability

weighting

function

IV X≥PSDY u∈UP P∈W0.02Not

rejectedu Cannot rejectP∈W0.02

V X≥PSDY u∈UP P∈W0 Rejected uu is not a element of

W0

Table 7.4: Result of Tasks IV and V

X Y CHOICETASK IV GAIN/LOSS PROB. GAIN/LOSS PROB. N X[%] Y[%]

X≥PSDY,c=0.02

Y≥P∗SDX,d=00.74

0 10% 0 50% 204 80.8819.1

2

1000 40%

2000 40%

3000 10% 3000 50%TASK V GAIN/LOSS PROB. GAIN/LOSS PROB. N X[%] Y[%]

X≥PSDY,c=0

Y≥P∗SDX,d=1

-3000 50% -3000 10% 204 36.7663.2

4

-2000 40%

-1000 40%

0 50% 0 10%

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(Source: Data collected from the survey in Appendix A)

7.3. Empirical result

The empirical test is based on the experiments suggested

by Manel and Franz (2007) to test whether individual

investors are compatible with specifications of

Cumulative Prospect Theory including the value function

and the probability weighting function. My experiment is

carried out through brokerage floors and online survey,

attracting 204 investors with at least one-year

experience in HOSE or HNX.

My survey is designed with five tasks, in each task, an

individual investor has to decide to choose prospect X

or prospect Y. In Task I, II, III, IV, the numbers of

responses choosing X are 162, 177, 145, 165 subjects,

respectively. In Task V, prospect Y is preferred with

129 participants. All primary data is processed and

analyzed as above.

By using stochastic dominance, in order to test the

curvature of the value function, the probability

weighting function is assumed to inverse S-shape, which

is inWcd. The results of Task I, II and III are used to

conclude that the value function is consistent to

prospect stochastic dominance, or u(x) is a element of

the set of prospect functions.

94

In order to test the shape of the probability weighting

function, it is advised that the value function is

assumed to be S-shape. In Task IV, the hypothesis that

the weighting function is an element of W0.02 cannot be

rejected. In Task V, the event that 63.24% of

participants prefers prospect Y over prospect X shows

the effect of the range of outcomes upon individual

decisions. In this section, the empirical result proves

the meaningfulness of the probability weighting function

in Vietnamese stock market.

As the result presented and analyzed in the chapter 7,

we conclude that Vietnamese investors’ characteristics

are compatible with Cumulative Prospect Theory. Thus, it

is possible and plausible to apply the Static Portfolio

Optimization model in Vietnamese stock market.

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CHAPTER 8 – RECOMMENDATION 8.1. Individual investors

8.1.1. Improve knowledge and skills

It is of critical importance to enlarge your knowledge

and skills in securities investment, if not, your

temporary gain will only be on the basis of luck which

cannot bring usual and sustainable return. Take a look

into the investment history, almost investors without

experience and underlying cognition became losers in the

security market. Stock understanding of stock market

consists of fundamental elements, technical analysis,

macroeconomics cycle and especially behavioral biases

including herding, cognitive biases, emotional biases,

PT and CPT. And, skills, which comprise information

processing, decision-making, stock selecting and

portfolio allocating, can be daily exercised. With

sagacity, your active portfolio can beat the market,

which is unable in standard finance, but accessible with

behavioral finance and strategic investors.

There are numerous sources for investors to ameliorate

their understanding of the Vietnamese stock market.

Firstly, textbooks, syllabuses, reference books majoring

in securities investment, which are written by credible

authors or released by famous publishers, are available

source for investors to access. Besides, investors can

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look for specialized studies of finance domain, or

convincing data source from securities service

companies. Taking advantage of close connection with

your friends, your instructors or investors, you can

study more and earn experience from other’s mistakes.

Last but not least, starting with small-amount

investments, you can avoid losing much money and prevent

you big losses in the future.

90% of loser investors are caused by herding bias which

drives them to out of the game in short-time. Just 10%

of mature, consistent and educated investors can be

succeed and accompany with Vietnamese stock market as

investors owning these characteristics are able to

select right stock in right time with reasonable price.

Thus, the deep-rooted factors contributing to achievers

can be nothing, but knowledgeability and decisiveness.

8.1.2. Build up plausible investment strategy

The first mission of an investor is to have awareness of

himself. It is common knowledge that if you have no idea

about who you are, what you desire, how you reach your

ambitions; you cannot take any action to be the peak. In

the investment world, the basic philosophy is the same.

In order to design an efficient strategy for ourselves,

there are six principal points emphasized for individual

investors, namely:

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First of all, the age has great influence on investment

period and accepted risk level because each period of

your life requires different financial plans and

investment vectors. For example, when a man in the age

of twenty-five to thirty, has to settle his family,

earns his own house and stable income with his dream

occupation. In the period of constructing, the

acceptable risk levels should be higher than the one in

the age of more than thirty. In addition, the number of

dependents who maybe his wife, children, parents,

reduces the level of risk leading the investor to become

more defensive.

Income plays necessary role in investment decision-

making process, especially portfolio creating in long-

term. The more money you earn; the higher risk level and

the longer investment time you approve. In evidence,

when your income exceed expenditures which can be known

as budget surplus, your financial surplus can support

you to venture upon pennies or conserve a portfolio as

long as you desire.

Large-scale accumulated assets (cash, securities, real

estates, businesses) have significant effect on the

level of risk and expected returns of investors.

Obviously, for a student paying attention at a

university with small amount of money, 30-40% is

desirable return rates which are considered as

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outstanding portfolio performance for unprofessional

investors. However, for a businessman of wealth, his

investment portfolio should yield at least 100% and

outperform in comparison with other projects having the

same initial investment capital requirement.

Additionally, cash reserve is an important key need to

be weighted. The reserve rate of cash has direct

relationship with investors’ level of confidence. Prior

to project a new portfolio, ensuring the source of cash

is mandatory requirement for each investor. According to

experts’ recommendation, normally, you should reserve

amount of cash equivalent to six-fold the average

monthly spending.

Next, insurance contracts protect investors against

danger of complete losses. The participation of

insurance contracts such as life insurance, non-life

insurance creates the adequate preparation which is

essential for professional investors. Especially, if you

have great mind of long-term investment, insurance

contracts, which reduce the variance, can be added into

your portfolio.

Last but not least, experience and knowledge not only

have assistance to portfolio choice, but also to manage

and allocate wealth. If you experience harsh trials in

period of 2007 and 2009, capture important rules of the

99

movement of Vietnamese stock market or shares, you will

be more equanimous even when your portfolio are

seriously going down.

The second mission of individual investors is to design

an investment strategy suitable for themselves after

preparation. There are four steps creating a reasonable

investment approach, namely, selecting, position

acceptance, position supervision, position close.

Stock choice issues a challenge to every long-term

investor who decides to design and allocate portfolio.

The model proposed in my thesis guide people an

allocating approach on the basis of investors’ behavior

under Cumulative Prospect Theory, hence, individual

investors had better contrive a new screening system

supporting the process of picking securities for their

own portfolio. We first observe the movements of stock

by listing notable securities into your watch lists,

which ensure you to pay more attention. If you are a

fundamental analyst, a watch list requires up-to-date

events and business plans. And, if you are a technical

expert, it is irrefutable that checking daily price

performance is the key for winning. To choose a good

stock to add into the watch list, you should gather both

fundamental analysis and technical predictions. Luckily,

you only get two to three per a group of ten stocks,

thus, it is not a surprise to the majority of loser

100

stocks in your watch list, from which we transfer the

best securities into your official portfolio.

Prior to consider different contexts of position, we

clarify the definition of it. In financial trading,

position is a binding commitment to buy or sell a given

amount of financial instruments such as securities,

currencies or commodities, for a given price. There are

two basic types of position: long and short. Short

position is defined as the sale of a borrowed security,

commodity or currency with the expectation that the

asset will fall in value. For example, an investor who

borrows shares of stock from a broker and sells them on

the open market is said to have a short position in the

stock. The investor eventually returns the borrowed

stock by buying back from the open market. If the stock

price is falling, the investors will earn a profit,

called short position. Long position is the buying of a

security with the expectation that stock price will rise

in value. For example, dealers often take long in

specific securities to maintain inventories and allow

for quick and easy trading, then the trader closed his

position and locked in a profit of 10%.

Position acceptance is an important part of the game.

For a start, you set out to determine which position is

your preference: long or short. Even thou the overall

market trend is upward, investors suffering losses in

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the past admit the fact that almost stocks go down in

the foreseeable future. Hence, investors are recommended

for avoiding short position in order to prevent them

from being time-consuming and costly. Investors need to

take notice of broker selection. If you are a private

investor, all you need is a discount broker who provides

the most basic services and help you order.

Position supervision is the most critical role of the

investment process because information and

investigations are inputted into trading making-

decisions process. In this step, you alter their

investment decisions if there are changes in the

tendency of securities in your portfolio. If your stock

is a winner stock, continue buying, unless, cut losses

immediately.

An investor close a position when stock price reaches

the target price or its performance cannot meet his

expectation. However, many of us do not determine

exactly when to take profits or cut losses. Normally, it

is recommended that selling in case of significantly

decreasing in underlying fundamental factors such yearly

net income, broad unity and intensive competition.

8.1.3. Filter information and experts’ opinions

In the era of information technology, customers are

supported to access to information system and data

102

resource. Fundamental and technical analysts are able to

get an advantage of daily reports, articles provided by

securities joint stock companies as well as SSC and

other service institutions on the internet and

newspapers. However, availably high-quality sources are

really rare. Moreover, unreliable information source can

lead investors to make investment decisions wrong,

bearing some biases such as herding, anchoring and

adjustment, loss aversion, etc.

Official information sources include financial

statements, formal recommendation of experts and

economists in journals and credible institution. In

particular, given company’s financial statements are one

of the most important documents that investors should

conduct research prior to make investment decision as

these documents capture the financial situation and the

business plan of a company at a point of time. It is

widely known that thorough understanding of the company

reduces the level of risk you suffer. Besides, numerous

sources of expert assessments and reports published each

day are valuable for investment decisions. You had

better subscribe two to three reliable firms or

organization to avoid overloading information. Notice

that financial statements can be manipulated, experts’

opinion can be prejudice investors in favor of some

inferior companies, thus, be intelligent and unbiased.

103

Strategy and tactic plan of foreign investors caught

individual investors’ central attention. Nonetheless,

foreign domestic or institutional investors have

distinct approaches and plans, hence sometimes their

decisions are proved to be wrong to Vietnamese

investors. In addition, foreign transactions may lead to

rumors affecting on Vietnamese stock market. In order

for winners, you ought to isolate you from others,

especially foreign cash flow.

Regarding the advice of family, friends and the crowd,

be careful. Word of mouth is the passing of information

by oral communication that is the easiest way to alter

your decisions and emotional status. Thus, keeping

emotionless and impassive are my advices for you. You

should remember that everyone is engulfed in the herding

if they always listen to others.

8.1.4. Apply models in practical investments

If above recommendations are made for the selecting

process, here is my advice for individual investors

while allocating portfolio under a chosen list of stock.

Static portfolio optimization is one of the most world-

class model of maximizing portfolio with one risky asset

and one risk-free asset in a period of time. The model

is effective against investors who behave under

Cumulative Prospect Theory including three

104

characteristics: using reference point instead of the

final outcomes to compare and decide, loss averse and

overweighting small probabilities. As designed on the

basis of behavioral biases, the model is extremely

appropriate for private investors.

The outstanding features of the model in comparison with

available models are the applicability and simplicity,

especially exclusivity.

Firstly, we consider the applicability of the model.

Though the model is demonstrated sophisticatedly in

chapter three, individual investors should take

advantage of the eventual results. The investors only

need to determine their own functions for themselves.

Furthermore, the model is strongly supported by the vast

number of behavioral researchers in this emerging field.

Besides, in my thesis, chapter four has provided a solid

proof for the possibility of applying the model in

Vietnamese stock market due to the meaningful of two

root functions of the model: the value function and

weighting probability function. Thus, investors, with

some assistant of software excel equipped in private

computers, laptops or tabs, are easily accessible to use

the model.

Secondly, because the model is used for individual

investors, so many unnecessary hypotheses are

105

eliminated. With only three hypotheses, Static model is

easy to understand and apply in real world.

Last but not least, it is undeniable that about 90%

investors behave under financial biases which can be

controlled by institutional investors. Therefore, the

models specializing in overcoming the difficulties of

private clients differ from the models for institutions

like Markowitz portfolio model. In support of this

argument, it is clear that each investor has his

distinct value function and probability weighting

function, thus, he will be self-served for themselves,

which ensure the exclusivity.

8.1.5. Notations

Diversifying your portfolio or “Don’t put all your eggs

in one basket” is the classic advice of the greatest

ever investor Warren Buffet. There are many types of

portfolio diversification: systematic diversification

and idiosyncratic diversification. Idiosyncratic

diversification is simple to achieve by holding more

investments, while systematic diversification is the

obverse of systematic risk, thus, typically harder to

conduct. However, both of them can reduce level of risk

by investing in a variety of asset. For example, in

Static model, Bernard and Ghossoub constitute a

portfolio with one risky asset and one risk free asset.

106

This type of portfolio is also considered as a

diversification. In the evolvement of Static portfolio

optimization, Pirvu and Schulze (2012), in their working

paper No. 742, propose advance model of multi-stock

portfolio optimization under Cumulative Prospect Theory

which is a radical resolution for problem of maximizing

portfolio under CPT. Therefore, investors are

recommended to diversify their portfolios with the

support of Static model and its evolvement models. If

your problem is credit limit, you are advised to invest

into a Mutual Fund or an Exchange-Traded Fund.

In order for successful portfolio choice, my thesis

suggests a famous model known as CAN SLIM (Current

quarterly earnings per share – Annual earnings –New

products – Small supply and large demand – Leader or

Laggard – Institutions’ sponsorship – Market direction).

CAN SLIM, developed by William O’Neil – the co-founder

of Investor’s Business Daily, is a philosophy of

screening, purchasing and selling common stocks. This

investment method is describe in his highly recommended

book “How to make money in stock”.

O’Neil emphasizes the importance of choosing stocks of

which earnings per share ratio (EPS) in in the most

recent quarters have grown on throughout the last year.

The growth rate of a company‘s EPS is heated

controversial debate, but the CAN SLIM system proposes

107

no less than 18-20%. By using statistic analysis method,

O’Neil found that in the period of 1953 to 1993, three-

quarters of the 500 top-performing securities in the US

stock market showed a 70% increase in quarterly EPS

prior to a major price rise. O’Neil also says that: “18-

20% growth is just a rule of thumb, the truly

spectacular earners usually demonstrate growth of 50% or

more.” Nonetheless, some cautions must be mentioned –

for example: shenanigans or red flags. The system

strongly asserts that investors should know how to

recognize the manipulation of company performance, thus,

investors must have underlying understanding about the

company.

CAN SLIM also thanks to the importance of annual

earnings growth. The system indicates that a growing

company should present high annual earnings growth rates

(annual EPS) in each of the last five years. It is

pivotal for fundamental investors who adopt the mindset

that investing of buying a piece of a business, becoming

an owner of it. Annual earnings growth within the 25-50%

range is plausible for value investors in their long-

term investment.

O'Neil's third criterion for a good company is that it

has recently undergone a change, which is often

necessary for a company to become successful. Whether it

is a new management team, a new product, a new market,

108

or a new high in stock price, O'Neil found that 95% of

the companies he studied had experienced something new.

The S in CAN SLIM stands for supply and demand, which

refers to the laws that govern all market activities.

The analysis of supply and demand in the CAN SLIM method

maintains that, all other things being equal, it is

easier for a smaller firm, with a smaller number

of share outstanding, to show outstanding gains. The

reasoning behind this is that a large cap company

requires much more demand than a smaller cap one to

demonstrate the same gains. Besides, O'Neil explores

this further and explains how the lack of liquidity of

large institutional investors restricts them to buying

only large-cap, blue-chip companies, leaving these large

investors at a serious disadvantage that small private

investors can capitalize on. Because of supply and

demand, the large transactions that institutional

investors make can inadvertently affect share price,

especially if the stock's market capitalization is

smaller. Because individual investors invest a

relatively small amount, they can get in or out of a

smaller company without pushing share price in an

unfavorable direction. In support of that, in his study,

O'Neil found that 95% of the companies displaying the

largest gains in share price had fewer than 25 million

shares outstanding when the gains were realized. 

109

In this part of CAN SLIM analysis, distinguishing

between market leaders and market laggards is of key

importance. In each industry, there are always those

that lead, providing great gains to shareholders, and

those that lag behind, providing return that are

mediocre at best. The idea is to separate the contenders

from the pretenders. Firstly, The relative price

strength of a stock can range from 1 to 99, where a rank

of 75 means the company, over a given period of time,

has outperformed 75% of the stocks in its market group.

CAN SLIM requires a stock to have a relative price

strength of at least 70. However, O'Neil states that

stocks with relative price strength in the 80–90 range

are more likely to be the major gainers. O’Neil’s system

strongly reminds that Do not let your emotions pick

stock. A company may seem to have the same product and

business model as others in its industry, but do not

invest in that company simply because it appears cheap

or evokes your sympathy. Cheap stocks are cheap for a

reason, usually because they are market laggards. You

may pay more now for a market leader, but it will be

worth it in the end. 

Next, CAN SLIM recognizes the importance of companies

having some institutional sponsorship. Basically, this

criterion is based on the idea that if a company has no

institutional sponsorship, all of the thousands of

110

institutional money managers have passed over the

company. CAN SLIM suggests that a stock worth investing

in has at least three to 10 institutional owners.

However, be wary if a very large portion of the

company's stock is owned by institutions. CAN SLIM

acknowledges that a company can be institutionally over-

owned and, when this happens, it is too late to buy into

the company. If a stock has too much institutional

ownership, any kind of bad news could spark a

spiraling sell-off. O'Neil also explores all the factors

that should be considered when determining whether a

company's institutional ownership is of high quality.

Even though institutions are labeled "smart money", some

are a lot smarter than others. 

Last but not least, the final CAN SLIM criterion is

market direction. When picking stocks, it is important

to recognize what kind of a market you are in, whether

it is bear or bull. Although O'Neil is not a market

timer, he argues that if investors don't understand

market direction, they may end up investing against the

trend and thus compromise gains or even lose

significantly. Moreover, CAN SLIM maintains that the

best way to keep track of market conditions is to watch

the daily volumes and movements of the markets. This

component of CAN SLIM may require the use of some

111

technical analysis tools, which are designed to help

investors/traders discern trends.

8.2. Financial institutions and investment service

suppliers

8.2.1. Provide instruments for constituting and managing portfolio

Even though the Static portfolio optimization model is

easy to use and understand, individual investors need

more investment services to support their long-term

decision and portfolio allocation.

The major securities screening is carried out on several

investment service websites such as cophieu68.com,

bloomberg.vn, mms.com.vn, etc, but the inefficiency of

tools is clearly proved. My thesis will offer an

adequate explanation for this phenomenon. Firstly,

individual investors with the low degree of awareness

and knowledge cannot design a criterion system to

filter. Furthermore, even when investors are

professional experts and economists, there is no system

providing stock screening to defend their emotional and

cognitive biases. Eventually, after picking stock, they

have no awareness of applying model of asset allocating

for their portfolio. Thus, in light of the above

reasons, investment tools deal with seemingly distorted

and crippled enhancement.

112

These difficulties are not insurmountable, even opening

more opportunities for investment service suppliers.

More training courses of stock market and investment

should be introduced to attract investors’ attention for

knowledge improvement. The content of lectures should be

brief, concise and well-rounded. Especially, behavioral

finance theory needs focusing in these courses with

useful advices to avoid behavioral biases such as

herding, anchoring, loss aversion, regret aversion, etc.

Furthermore, instructors can introduce some models of

picking stock (the implication of CAPM and Fama Three

Factors model), or portfolio optimization.

The second obstacle can be overcome with investment

instruments assisting investors to detect behavior

mistake and provide recommendations. Based on studies of

behavioral biases and their remedies introduced by

Pompian (2006) for instance, financial institutions

supplying investment tools are able to design modern

screening systems that incorporate biases. These new

systems will open a new era of technological tools

controlling emotions and cognitions.

Finally, financial support tool suppliers can design a

system allowing people to remove complicated

calculations when constituting portfolios. For example,

an investor, by answering a questionnaire, can be

determined his principal biases. On the basis of main

113

biases, several model of portfolio optimization

recommended to him, and Static portfolio optimization

for instance.

To summarize, the development of behavioral finance

branch has creates more and more opportunities for

financial service organizations to assist investors in

constituting portfolios in one period.

8.2.2. Provide biases defense for private clients

Psychological factors are still green in financial

academic and practical fields, hence, even though the

behavioral finance domain induces more and more scholars

with a vast of studies and empirical researches, there

is few security companies having awareness of the

importance of designing a defense protecting customers

from wrong and regret decisions.

As Pompian (2006), there are more than twenty biases

affecting investment decision of private investors. The

figure shows the big problem that everyone has to face

to daily trading session. In order for better clients’

performance, service suppliers should construct biases

defense system for their customers. By using this

defense system, customers have capacity at avoiding

unexpected mistakes.

114

CONCLUSIONIndividual domestic investors have important

contribution to the enhancement of Vietnamese stock

market. However, there is seemingly no effective

portfolio optimization model benefiting Vietnamese

investors. This status leads to many serious consequence

on the enhancement of the stock market, that is major

reason for implementing my thesis.

The main body of this thesis consists of four chapters

dealing with selected topic in the field of behavioral

portfolio allocation. A detailed summary of the results

and concluding remarks are presented as follows:

Chapter ONE illustrates the theoretical framework and

literature of one instrument of Behavioral finance

paradigm - Cumulative Prospect Theory, which is the key

base for Static portfolio optimization. This section

also provides general approaches to test hypotheses of

Cumulative Prospect Theory, particularly Stochastic

Dominance conditions.

Chapter TWO deals with a theoretical issue of the

portfolio optimization models. In this chapter, by

comparing several approaches to resolve the problem of

portfolio maximum, my thesis shows the outstanding

features of Cumulative Prospect Theory approach over

115

other approaches. The central objective of this chapter

is to demonstrate the Static portfolio optimization

model which also criticized with some limitations.

In chapter THREE, my thesis summarizes the overall

viewpoint about the Vietnamese stock market with great

movements throughout years from 2007. Then,

characteristics of investors in constituting portfolio

are named such as lack of knowledge, lack of

technological investment tools and affected by such

behavioral biases as loss aversion, anchoring –

adjustment and herding bias.

Chapter FOUR studies the main question whether the model

is possible to be applied in Vietnamese stock market.

The major aim is the test of assumptions of Cumulative

Prospect Theory in Vietnamese stock market. The result

implies the plausibility of applying this model in

Vietnam.

Based on these finding and analysis, the last chapter

provides recommendations for both individual investors

and investment service suppliers in order for applying

and effectively using the Static model in practical

world. The main advices for private investors are to

improve knowledge and skills, design plausible strategy,

filter information, apply the models of optimization in

reality and use CAN SLIM system for portfolio choice.

116

And, service suppliers are recommended to provide more

investment tools such as biases defense system, training

courses, portfolio systems in order for better client’s

performances.

This research determines that the assumptions of CPT

cannot be rejected in Vietnamese stock market.

Additionally, my thesis introduce a new model of asset

allocation of Bernard and Ghossoub (2009) for biased

investors as well as the theoretical framework of

stochastic dominance approach. Moreover, my

recommendations in designing and managing portfolio are

useful for about 85% of domestic investors in HOSE.

Research result can be considered as empirical basis for

the next deep research in behavioral finance in Vietnam,

especially for portfolio issues.

Due to the lack of time and research capacity, my thesis

is not without its limitations, I express my deep

appreciation for contributions to complete my work.

Finally, I would like to acknowledge again my tutor

M.Sc. Le Thi Thu, my family and my friends for their

encouragements during the completion of the thesis.

Ha Noi, 20 May, 2014

Nguyen Thi Thu Hang

117

Class: A8, faculty of Business Administration, Intake: 49, Foreign Trade

University

118

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124

APPENDIX A: SURVEY

Suppose you decide to invest $10000 in below portfolios.

Which portfolios do you choose, X or Y? when it is given

that the dollar gain or loss one month from now will be

as follows”

TASK I: X Y

GAIN/LOSS PROB. GAIN/LOSS PROB.

0 10% 0 50%1000 40%2000 40%3000 10% 3000 50%

TASK II: X Y

GAIN/LOSS PROB. GAIN/LOSS PROB.

-3000 50% -3000 10%-2000 40%-1000 40%

0 50% 0 10%

TASK III: X Y

GAIN/LOSS PROB. GAIN/LOSS PROB.

-6000 1/3 -6000 1/63000 ½ -3000 1/34500 1/6 4500 1/2

125

TASK IV: X Y

GAIN/LOSS PROB. GAIN/LOSS PROB.

0 10% 0 50%

1000 40%

2000 40%

3000 10% 3000 50%

TASK V: X Y

GAIN/LOSS PROB. GAIN/LOSS PROB.

-3000 50% -3000 10%

-2000 40%

-1000 40%

0 50% 0 10%

126

APPENDIX B: MATHEMATICAL BACKGROUND

Theorem: Supposeu' (x )>0, then portfolio i is preferred to

portfolioj if either wXi is absolutely dominant over wXj

or wXi≥fsdwXj (see the proof in Appendix B)

Proof of theorem:

Because if either wXi is absolutely dominant overwXj,

then wXi≥fsdwXj (as), it is necessary to prove only that

if wXi≥fsdwXj then portfolio i is preferred to portfolioj

E [v (wXi ) ]−E[v (wXj )]

¿∫−∞

+∞

v (y) [fi (y )−fj (y) ]dy

¿ [v (y ) [Fi (y)−Fj (y) ]]+∞

−∞−∫−∞

+∞v' (y )[Fi (y )−Fj (y )]dy

¿0−∫−∞

+∞

v' (y )[Fi (y )−Fj (y )]dy

Thus, if Fi (y )−Fj (y )<0 (or Fi (y )≤Fj (y )forally¿, then:

E [v (wXi ) ]−E [v (wXj) ]>0, or wXi is preferred to wXj

Theorem: Suppose thatv' (x )>0 (implying that investors

prefer more to less) and v'' (x )<0(implying that investor

127

is risk averse), WXi is preferred to wXj if wXi is second

- order stochastically dominant overwXj, or:

∫−∞

x

Fi (y )dy≤∫−∞

x

Fj (y )dy

Proof of the theorem:

Because v' (x )>0 and v'' (x )<0, v' (x ) is a positive strictly

decreasing function, therefore, the limit limx→+∞

u' (x) exists

E [v (wXi ) ]−E[v (wXj )]

¿∫−∞

+∞

v (y) [fi (y )−fj (y) ]dy

¿ [v (y ) [Fi (y)−Fj (y) ]]+∞

−∞−∫−∞

+∞v' (y )[Fi (y )−Fj (y )]dy

¿−∫−∞

+∞

v' (y ) [Fi (y)−Fj (y ) ]dy

¿−[v' (x)∫−∞

xFi (y )−Fj (y )dy] +∞

−∞+∫−∞

+∞v''

(x )∫−∞

xFi (y )−Fj (y )dydx

¿−v' (+∞ )∫−∞

+∞Fi (y)−Fj (y )dy+∫

−∞

+∞ [v'' (x )∫−∞

xFi (y )−Fj (y )dy]

Becausev' (+∞ )>0; ∫−∞

+∞

Fi (y )−Fj (y)dy<0; v'' (x )<0 so, it implies

that :

128

∫−∞

x

Fi (y )−Fj (y)dy<0 , then E [v (wXi ) ]−E [v (wXj) ]>0(as desired)