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.
RESEARCHES & DISCUSSIONS Vietnam, as compared to many other countries in the world, has been nurturing 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 thus, questionnaires, Markowitz portfolio theory, and the capital asset pricing model (CAPM) will be employed in the research Keywords: risk tolerance, optimal portfolio, individual investor Introduction Vietnam’s stock market, after a decade of development, has attracted a lot of both foreign and domestic investors According to the State Securities 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 individual investors (i.e making up 99.6%) Due to the fact that almost individual investors 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 individual 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 analyses, Markowitz portfolio theory, and CAPM In remaining parts of the study, section will focus on theoretical guides; the data and research methodology will be presented in section 3; section discusses methods of establishing a specific portfolio; and session will assume discussions and recommendations 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 expected returns on portfolio and portfolio risks His assumptions illuminates the fact that portfolio return 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: * University of Economics - HCMC ** University of Technology - HCMC Economic Development Review - June 2011 33 RESEARCHES & DISCUSSIONS where rij is the correlation coefficient between the returns on assets i and j Not only these formulae clarify the importance of portfolio diversification in reducing investment risks, but they also figure out how to diversify efficiently (i.e the combination of perfectly 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 Investors, 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 capital asset pricing model (CAPM) in 1964 (then Lintner and Mossin respectively introduces identical 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 return and the risk premium The straight line representing the relationship between the required rate of return and the systematic 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 plotted above the SML), such the asset is underestimated 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 Rf and is the tangent of the Markowitz efficient frontier This new efficient frontier is called the capital market line (CML) No portfolio lying on the CML is superior to 34 Economic Development Review - June 2011 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 satisfaction level on a portfolio A utility function which is widely employed by financial theorists and the Association of Investment Management and Research (AIMR) is: 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 questionnaire by Dow Jones & Company carried on The Wall Street Journal in 1998 Yet, this questionnaire 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 investors 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 investors 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 economy, Vietnam’s economy, stock market and economic industries, there emerge four worth-investing industries, viz sea food, banking, natural rubber, and steel Step 3: Investment strategy and corporate RESEARCHES & DISCUSSIONS analysis After conducting basic analyses and pondering investment constraints, passive investment strategies are to be employed Based on the company factor analyses, financial criteria developed by Warrant Buffet and William O’Neil for choosing stocks, and investment constraints, the study opts for stocks whose ROE is not below the average 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 undervalued 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 management 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: (*) equivalent to its daily standard deviation within the period from July 1, 2009 to March 31, 2009 The correlation coefficient of five stocks is assumedly 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 Expected return Standard deviation ACL 0.00188 0.02964 FMC 0.00121 0.03401 TS4 0.00276 0.03836 TRC 0.00320 0.02939 VIS 0.00611 0.03714 Table 2: Correlation matrix Correlation Coefficient ACL FMC TS4 TRC ACL 1.00 FMC 0.54 1.00 TS4 0.38 0.38 1.00 TRC 0.47 0.39 0.42 1.00 VIS 0.41 0.42 0.38 0.33 VIS 1.00 In order to tackle (*), Microsoft Excel software will be employed to calculate the standard deviation and expected return of the portfolio The SOLVER function compatible with Excel will be then utilized so as to work out a lowest-risk portfolio 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 correspondence with each changed value a Accordingly, the Markowitz efficient frontier can be established due to the fact that a lowest-risk portfolio corresponding 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) 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 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- Economic Development Review - June 2011 35 RESEARCHES & DISCUSSIONS 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: Figure 2: Markowitz efficient frontier Accordingly, the weighting of capital to be invested into risk-free assets will be 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 conservative, 78.2% moderate, and 7.3% aggressive Figure 3: Capital market line Table 3: Particulars of the optimal portfolio P Expected return Standard deviation 0.0070 0.041 Weighting Riskfree TRC assets -0,38 0.44 VIS 0.94 Discussion and recommendation a Discussion: Figure 1: Allocation of risk aversion of investors in HOSE Based on the above-mentioned process of establishing 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 investors 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 moderate Conservative investors occupy 14.5%, yet their conservatism is rather low Aggressive investors make up 7.3% and their aggressiveness is kind of low Markowitz portfolio theory and CAPM are widely accepted and employed by many researchers around the world Besides, due to the fact that data utilized in the research are collated from Vietnam’s GSO and stats of securities companies, the reliability of research results are acceptable The optimal portfolio, as per the research, includes treasury bonds, TRC, and VIS The return 36 Economic Development Review - June 2011 RESEARCHES & DISCUSSIONS rate and the standard deviation of assets return are estimated by the past return and standard deviation Nonetheless, it does not have the possibilities 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 facilitates 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 accepted 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 riskfree rate When an investor has to suffer an interest 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 research 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, Vietnam’s inflation within recent years has fluctuated dizzily and unpredictably Changes in inflation will entail alternations of risk-free return, required 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 improved recently, it is still kind of low, and thereby hindering the establishment of portfolios with the same ratio as that of the Markowitz efficient frontier 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, investors will keep on buying/selling incorrectlypriced stocks until all stocks are plotted on the SML Meanwhile, in Vietnam, the stock transaction 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 pricing due to the fact that benefits of buying/selling 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 different 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 investment 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 transparent; 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 Economic Development Review - June 2011 37 RESEARCHES & DISCUSSIONS of the employment of past data, the portfolio representing 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 assumptions should be employed However, impacts of these assumptions on the model are kind of modest, 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 significance 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 not understand what they are doing” (Warrent Buffet) Individual investors in HOSE had better apply Markowitz portfolio theory and the CAPM to improve investment efficiency because they have been approved and applied internationally by both investors and researchers The three-step method (top-down approach) is used internationally by most investors and researchers for evaluating stocks; therefore, individual investors in HOSE had better consider it to estimate the profitability ratio and risk of companies, thereby improving accuracy of their estimates The first thing that individual investors should when allocating their capital is to identify objectives and obligations in their investment In addition, they should work out several market scenarios with a view to avoiding extreme optimism or pessimism, 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 38 Economic Development Review - June 2011 than 0.3) because this condition helps investors reduce remarkably the specific risk of the portfolio When transparency of information and stability 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 update 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 reaching the best decisionsn References Bodie, Z., A Kane & A.J Marcus (2003), Investments, McGraw Hill Campbell R Harvey, et al (2004), “Portfolio Selection with Higher Moments”, Working paper, Duke University Fabozzi, F.J & H.M Markowitz (Eds) (2002), The Theory and Practice of Investment Management, Wiley Markowitz, H.M (1952) “Portfolio Selection”, The Journal of Finance (1): 77–91 Reilly, Frank K & K.C Brown (2002), Investment Analysis and Portfolio Management, 7th Ed., South-Western College Pub Wei-Peng Chen, et al (2010), “Portfolio Optimization Models and Mean-Variance Spanning Tests” in Handbook of Quantitative Finance and Risk Management, Springer, Boston ... by financial theorists and the Association of Investment Management and Research (AIMR) is: Establishing an optimal portfolio for the sake of investors in HOSE The study has measured the risk. .. dizzily and unpredictably Changes in inflation will entail alternations of risk- free return, required return, and expected return, and thereby changing SML, CML, and the optimal portfolio of investors. .. Portfolio Management, 7th Ed., South-Western College Pub Wei-Peng Chen, et al (2010), Portfolio Optimization Models and Mean-Variance Spanning Tests” in Handbook of Quantitative Finance and Risk Management,