Measuring risk toleranve and establishing an optimal portfolio for individual investors in HOSE

This study is to estimate risk tolerance of investors in HCMC Stock Exchange (HOSE) and then work out a portfolio optimization model on the basis of risk tolerance known. To do thus, questionnaires, Markowitz portfolio theory, and the capital asset pricing model (CAPM) will be employed in the research.

1 Introduction

Vietnam’s stock market, after a decade of

de-velopment, has attracted a lot of both foreign and

domestic investors According to the State

Securi-ties Commission of Vietnam (SSC), this market

until late October 2009, has had 766,725 accounts

in total, wherein around 3,147 accounts are

opened by organizations and 763,578 ones by

in-dividual investors (i.e making up 99.6%) Due to

the fact that almost individual investors do not

have sufficient knowledge of investment theories,

they cannot make the best use of diversification

so as to minimize investment risks However,

much as some individual investors also attend to

diversification, they mainly base their decisions

on sentiments instead of sensible investment

strategies to undertake diversification; and thus

the efficiency of diversification is not high enough

This paper is to measure the risk tolerance of

in-dividual investors in HOSE and then work out a

portfolio optimization model on the ground of available data related stocks quoted in HOSE until April 1, 2009 and with the support of basic analy-ses, Markowitz portfolio theory, and CAPM In re-maining parts of the study, section 2 will focus on theoretical guides; the data and research method-ology will be presented in section 3; section 4 dis-cusses methods of establishing a specific portfolio;

and session 5 will assume discussions and recom-mendations

2 Theoretical guides

a Markowitz portfolio theory:

In early 1950s, investors in the world tried in vain to establish an optimal portfolio due to the fact that they could not find out an appropriate scale to measure the risk of assets or portfolios

In 1952-1959, Markowitz developed a portfolio model wherein he enlisted two scales, viz ex-pected returns on portfolio and portfolio risks His assumptions illuminates the fact that portfolio re-turn variance is a significant measurement of portfolio risks The expected return, according to Markowitz, is the average weighting of constituent assets’ return, and can be calculated as follows:

where Rp is the return on the portfolio, Ri is the return on asset i, and wi is the weighting of constituent asset i (that is, the share of asset i in the portfolio)

The portfolio return variance can be written

as follows:

Vietnam, as compared to many other

countries in the world, has been

nurtur-ing an infant stock market This study is

to estimate risk tolerance of investors in

HCMC Stock Exchange (HOSE) and then

work out a portfolio optimization model

on the basis of risk tolerance known To

do thus, questionnaires, Markowitz

port-folio theory, and the capital asset pricing

model (CAPM) will be employed in the

re-search.

Keywords: risk tolerance, optimal portfolio,

indi-vidual investor

where rijis the correlation coefficient between

the returns on assets i and j

Not only do these formulae clarify the

impor-tance of portfolio diversification in reducing

in-vestment risks, but they also figure out how to

diversify efficiently (i.e the combination of

per-fectly uncorrelated assets not only influences the

expected portfolio return but also reduces portfolio

risks) This is also the focus of Markowitz portfolio

theory

This theory allows us to establish an efficient

frontier from risky assets; and along the efficient

frontier, no portfolio is superior to others

In-vestors, for their own sake, will opt for portfolios

with the highest utility on the frontier Yet, if a

risk-free asset is added to the efficient portfolio,

it is possible to identify portfolios which are more

superior to others on the efficient frontier The

study will establish an efficient frontier with the

presence of risk-free assets

b Capital asset pricing model (CAPM):

Based on Markowitz portfolio theory and some

assumptions, William Sharpe developed the

capi-tal asset pricing model (CAPM) in 1964 (then

Lintner and Mossin respectively introduces

iden-tical models in 1965 and 1966) CAPM is used to

determine a theoretically appropriate required

rate of return of a risky asset or portfolio

In CAPM, the required rate of return of a risky

asset or portfolio equals the sum of risk-free

re-turn and the risk premium

The straight line representing the relationship

between the required rate of return and the

sys-tematic risk is called security market line (SML)

If the expected return of an asset is larger than

its required return (i.e the expected return in

plot-ted above the SML), such the asset is

underesti-mated and investors should hold it; and vice versa

In sum, based on the CAPM, it is possible to

tailor a new efficient frontier which is different

from that of Markowitz in that it is a straight line

that goes through the point Rfand is the tangent

of the Markowitz efficient frontier This new

effi-cient frontier is called the capital market line

(CML)

No portfolio lying on the CML is superior to

others and investors must determine their own utility curve so as to find out an optimal portfolio

on the CML Such the optimal portfolio must be the tangent of both the CML and the utility curve

c Investors’ utility function:

As per the portfolio theory, each investor will have their own utility function and he/she will just invest in portfolios with the highest utility It is assumed that an investor can base on the expected return and portfolio risks to impose his/her satis-faction level on a portfolio A utility function which is widely employed by financial theorists and the Association of Investment Management and Research (AIMR) is:

3 Establishing an optimal portfolio for the sake

of investors in HOSE The study has measured the risk tolerance of

55 individual investors in HOSE via a question-naire by Dow Jones & Company carried on The Wall Street Journal in 1998 Yet, this question-naire has been preliminarily adjusted to the case

of Vietnam, that is, the total mark representing the risk tolerance of investors is compared with the risk of securities invested

The optimal portfolio is established according

to the following steps

Step 1: Measuring the risk tolerance of

in-vestors and define their constraints and goals

In this study, investors are supposed to seek portfolios of the last three quarters of 2010 and with the holding period return rate of some 15% Investment constraints include: (1) the investment capital of VND100 to VND150 million, (2) stock investment is the subordinate occupation and in-vestors have a monthly stable source of income, and (3) investors are risk-averse and the A value

of the utility equation is four

Step 2: Basic analyses

After analyzing the performance of world econ-omy, Vietnam’s econecon-omy, stock market and eco-nomic industries, there emerge four worth-investing industries, viz sea food, banking, natural rubber, and steel

Step  3:  Investment strategy and corporate

After conducting basic analyses and pondering

investment constraints, passive investment

strategies are to be employed Based on the

com-pany factor analyses, financial criteria developed

by Warrant Buffet and William O’Neil for

choos-ing stocks, and investment constraints, the study

opts for stocks whose ROE is not below the

aver-age of each industry and less volatile And thus,

there are 15 types stock to be invested namely

ACL, FMC, MPC, TS4, CHV, CTG, VCB, STB,

DPR, DRC, HRC, TRC, HSG, SMC, and VIS

Step 4: Application of CAPM

The CAPM is employed so as to sort out

un-dervalued stocks out of the 15 above-mentioned

ones The expected return (Ri) of each type of stock

will be determined by its daily average return rate

within the first quarter of 2010, and the required

return will be calculated by CAPM

Step 5: Choosing stocks which have the low

correlation with each other

There are eight out of fifteen stocks which are

undervalued Due to the fact that eight stocks, as

compared to the investment capital and

manage-ment competence of investors, are quite enormous,

just five stocks with low correlation with each

other namely ACL, FMC, TS4, TRC, and VIS are

chosen

Step 6: Establishing the Markowitz efficient

frontier

In order to establish a Markowitz efficient

frontier for the case of Vietnam, it is necessary to

tackle the simultaneous equations below:

Where, the daily expected return of each stock

is assumedly equal to its daily return within the

period from Jan 4, 2010 to March 31, 2010 The

standard deviation of return is also assumed to be

equivalent to its daily standard deviation within the period from July 1, 2009 to March 31, 2009

The correlation coefficient of five stocks is as-sumedly equal to the coefficient within the period from April 2, 2009 to March 31, 2010

Table 1: The expected return and standard deviation

of chosen stocks

Table 2: Correlation matrix

In order to tackle (*), Microsoft Excel software will be employed to calculate the standard devia-tion and expected return of the portfolio The SOLVER function compatible with Excel will be then utilized so as to work out a lowest-risk port-folio corresponding to an expected return (a) This

is to say, if the value a is changed, it is probable

to find out a lowest-risk portfolio in correspon-dence with each changed value a Accordingly, the Markowitz efficient frontier can be established due to the fact that a lowest-risk portfolio corre-sponding to a given return rate has already been found

Step 7: Establishing the capital market line

(CML) CML is a straight line originated from Rf and touching the Markowitz efficient frontier at the portfolio i, and together with CAL creates an angle with the maximum angle coefficient (i.e

max)

The Microsoft Excel software will be employed

to calculate the angle coefficient of CAL; and the SOLVER function compatible with Excel will be then utilized so as to work out CML and the port-(*)

Correlation

folio i.

Step 8: Defining the optimal portfolio

The optimal portfolio, as assumed in CAPM,

must be the point where CML touches the utility

curve At that point, the angle coefficients of CML

and the utility curve are equal

With the standard deviation of the optimal

portfolio which has been worked out, it is possible

to calculate the weighting of capital to be invested

into risky assets as per the following formula:

Accordingly, the weighting of capital to be

in-vested into risk-free assets will be

4 Research results

Via what has been presented thus far, the risk

tolerance of individual investors can be summed

up that around 14.5% surveyed investors are

con-servative, 78.2% moderate, and 7.3% aggressive

Figure 1: Allocation of risk aversion of investors in

HOSE

Based on the above-mentioned process of

es-tablishing an optimal portfolio, it is probable to

tailor the Markowitz efficient frontier and CML

as illustrated below, and simultaneously define the

optimal portfolio for the sake of surveyed

in-vestors

Figure 2: Markowitz efficient frontier

Figure 3: Capital market line Table 3: Particulars of the optimal portfolio P

5 Discussion and recommendation

a Discussion:

Overall, the allocation of dots (which express the risk tolerance of investors in HOSE within the survey period) is seemingly identical to the normal distribution; and almost all investors are the mod-erate Conservative investors occupy 14.5%, yet their conservatism is rather low Aggressive in-vestors make up 7.3% and their aggressiveness is kind of low

Markowitz portfolio theory and CAPM are widely accepted and employed by many re-searchers around the world Besides, due to the fact that data utilized in the research are collated from Vietnam’s GSO and stats of securities com-panies, the reliability of research results are ac-ceptable

The optimal portfolio, as per the research, in-cludes treasury bonds, TRC, and VIS The return

Expected return

Standard deviation

Weighting

Risk-free assets

rate and the standard deviation of assets return

are estimated by the past return and standard

de-viation Nonetheless, it does not have the

possi-bilities that the past will reappear in the future;

and consequently the practical efficient frontier

may be different from the theoretical one

To evaluate stocks as per three-step method is

reliable Yet, it is also dependent on the amount

of information, the way of data processing, and

subjective opinions of investors that stocks are to

be distributed to different stock baskets; and

thereby the efficient portfolio of each investor is

also various

At present, there are a lot of software that

fa-cilitates the establishment of Markowitz efficient

frontier and CML In the research, just the Excel

software is employed due to the fact that it is easy

to use and popular among individual Vietnamese

investors

In order to define the optimal portfolio, CAPM

has been utilized Much as CAPM theory is

ac-cepted worldwide, it still possesses some fictional

assumptions For example, this theory assumes

that an investor can lend and borrow unlimited

amounts under the risk-free rate of interest (by

buying treasury bonds for instance) Yet in fact, of

course, investors cannot borrow under the

risk-free rate When an investor has to suffer an

inter-est rate (Rb) which is larger than the risk-free rate

(RFR), the straight line CML, will be broken into

the RFR-F-K-G zigzag And thus, for those who

utilize their own money to invest in stocks, the

re-search results will not be altered; vice versa, the

research results will definitely be changed if the

investors borrow money to invest in stocks

Besides, CAPM assumes that neither inflation

nor any changes of inflation (interest rate) are

predicted accurately and adequately Yet,

Viet-nam’s inflation within recent years has fluctuated

dizzily and unpredictably Changes in inflation

will entail alternations of risk-free return,

re-quired return, and expected return, and thereby

changing SML, CML, and the optimal portfolio of

investors

As per the CAPM, securities investments are

all highly divisible into small parcels Much as the

liquidity of Vietnam’s stock exchange has been

im-proved recently, it is still kind of low, and thereby

hindering the establishment of portfolios with the

same ratio as that of the Markowitz efficient fron-tier Therefore, the actual ratio of stocks within a portfolio may be a bit different from the defined optimal one

Another assumption of CAPM is that there is

no transaction or taxation costs Accordingly, in-vestors will keep on buying/selling incorrectly-priced stocks until all stocks are plotted on the SML Meanwhile, in Vietnam, the stock transac-tion cost covered by individual investors accounts for 0.15 to 0.4 percent; the tax rate per transfer is 0.1% of the transfer value (or the fixed tax rate of 20% for all transfers) Since there are transaction costs and transfer taxes, investors will not adjust all differences generated from the incorrect pric-ing due to the fact that benefits of buypric-ing/sellpric-ing incorrectly-priced stocks, in many cases, will make up for transaction costs and taxes At this time, the straight line SML will be turned into a set of parallel lines Once SML is changed, the identification of incorrectly-priced stocks will be altered, and thereby changing constituent stocks

of the stock basket Consequently, the optimal portfolio is changed as well Additionally, when the amount of stock within the portfolio rises, the nonsystematic risk will be reduced Yet, if the transaction cost exists, investors are advised to weight up added benefits from diversification and transaction costs

The CAPM also assumes that all investors have the same expectation In practice, different investors possess different information and differ-ent ways of processing information; and thus their expectations are also various Besides, investors are assumed to have the same investment period

Hence, if they have different expectations or in-vestment periods, their SML and CML must be different as well

Moreover, the capital market, as in the CAPM,

is assumed to balance When the capital market balances, assets will be priced on the SML Yet, due to the fact that Vietnam’s securities law has not been tightened, disclosures on the Vietnam’s stock market are neither adequate nor transpar-ent; and thereby creating disparity in information amongst investors and causing wrong estimates of return rate of listed stocks

In addition, the measurement of systematic risk (beta) of stocks also needs revisiting in terms

of the employment of past data, the portfolio

rep-resenting the market portfolio, the period of data

collation, etc

After discussing some assumptions of CAPM,

it is apparent that these assumptions are fictional;

and the point is whether or not such the theory

which is developed with such fictional

assump-tions should be employed However, impacts of

these assumptions on the model are kind of

mod-est, and perhaps impossibly change the research

results This is to say, when evaluating a theory,

it is advised not to base on its assumptions but on

the extent to which it can explain problems in the

real world Visibly, the fact that such the theories

have been employed by investors and economists

for 50 years has proven their great practical

sig-nificance

b Recommendations:

Individual investors should not “put all their

eggs into one basket,” that is, investing only in a

company or certain field However, they should

also avoid scattering their investments carelessly

because “wide diversification is only required

when investors do not understand what they are

doing” (Warrent Buffet) Individual investors in

HOSE had better apply Markowitz portfolio

the-ory and the CAPM to improve investment

effi-ciency because they have been approved and

applied internationally by both investors and

re-searchers

The three-step method (top-down approach) is

used internationally by most investors and

re-searchers for evaluating stocks; therefore,

individ-ual investors in HOSE had better consider it to

estimate the profitability ratio and risk of

compa-nies, thereby improving accuracy of their

esti-mates

The first thing that individual investors should

do when allocating their capital is to identify

ob-jectives and obligations in their investment In

ad-dition, they should work out several market

scenarios with a view to avoiding extreme

opti-mism or pessiopti-mism, thereby making estimated

data more exact

Next, investors had better analyze stocks from

industries considered as potential opportunities

Stocks to be included in the portfolio should have

negative or low correlation coefficients (smaller

than 0.3) because this condition helps investors reduce remarkably the specific risk of the portfo-lio When transparency of information and stabil-ity of market price in Vietnam are still poor, individual investors should check information and data from all sources, and try to “understand and interpret rationally” numerical data publicized by companies Moreover, they should regularly up-date information in order to adjust or alter their portfolios accordingly

Due to the fact that all theories and methods have their own shortcomings, investors should employ different methods and compare outcomes produced by these methods with a view to reach-ing the best decisionsn

References

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3 Fabozzi, F.J & H.M Markowitz (Eds) (2002), The Theory and Practice of Investment Management, Wiley.

4 Markowitz, H.M (1952) “Portfolio Selection”, The Journal of Finance 7 (1): 77–91.

5 Reilly, Frank K & K.C Brown (2002), Investment Analysis and Portfolio Management, 7th Ed.,

South-West-ern College Pub.

6 Wei-Peng Chen, et al (2010), “Portfolio Optimiza-tion Models and Mean-Variance Spanning Tests” in

Handbook of Quantitative Finance and Risk Management,

Springer, Boston.