kuala lumpur, malaysia, march 8-10, 2016 selection of

Proceedings of the 2016 International Conference on Industrial Engineering and Operations Management Kuala Lumpur, Malaysia, March 8-10, 2016

Selection of Optimal Portfolio Model by Comparing Mock Stock Trading

Youngjoo Lee, Minsung Kim, Taeheon Kim, Hohyun Lee Date Science Lab, Paul Math School Goesan County, Republic of Korea

[email protected], [email protected], [email protected]

Abstract— There are various portfolio models and it is perplexing to judge what the most appropriate portfolio model is. This study evaluated the upper hand by comparing. This study used the Mean-Variance portfolio model, TASD (Target Absolute Semi-Deviation) model and equally weighted (1/N strategy) model. This research accomplished mock stock trading from June 25 to July 7 and evaluated portfolio models by using performance measurement.

As a result, TASD model showed the superior performance in every performance measurement expect the risk. Mean-Variance model ranked second and equally weighted model recorded the lowest. This research analyzed the reason of the result which came from the condition of stock market. The price of KOSPI rapidly decreased during this research period and all portfolio models occurred minus return. In this condition, this research realized that TASD model coped with the stock market’s fluctuation most flexibly. This research makes sure that the TASD portfolio model is the best portfolio model when we assume the stability as the most important principle. Therefore, this research proved that TASD model is most suitable model to investors who wants the stable investment.

Keywords—Portfolio selection; TASD model; performance measurement

I. INTRODUCTION

A. Research Backgroung and PurposeKorea's stock market started in 1956 March first. And now stock investors are keeping the active investment. Stock

investors are aiming for making the best profit and minimum risk by maximizing the efficiency in stock market. In other words, not continuing an investment in the light of just expected rate of return but continuing an investment in the light of investors’ expected utility. The stock investors' target profit of rate will change as per their expected utilities. So investors try to create the maximum profit and minimum risk. And to do so, investors use the portfolio many times. The reason why investors establish investment strategy with portfolio is for diversified investment in the light of investors' expected utility when they make an investment in only one stock item. Portfolio became the large foothold of investors, and now are also using that for efficient investment.

Many portfolio models have been developed to maximize the efficiency of investment for investors that started Mean-Variance model, which was suggested by Markowitz in 1952. It is difficult to make an efficient portfolio by a complete covariance model made by Sharpe in 1994 named Single index model. To make up for Mean-Variance's model's fault, Single index model considers only covariance with a single market index that shows the specific stock and move of total stock market. Portfolio model has many portfolio models such as TASD(Target Absolute Semi Deviation) model(Fish. 1997), equal weight model, minimized variance model, Three-Found model, Bayesian-Stein model as well as Single index model. Therefore, many stock investors had been confused because they did not know what portfolio model is proper to make an investment. In addition, many stock investors gave up the portfolio strategy. This research intends to compare the Mean-variance model, TASD model and equal weight model's rate of return by applying to the simulated investment. Therefore, this research set the portfolio based on 60-month long materials as the estimated period by using the data from domestic KOSPI stock market. For four portfolio models which is set as above, this research collected data for simulated investment from June 26 to July 31, and then evaluated four portfolio models’ rate of return through the Sharpe ratio and Treynor Ratio.

B. Compnents of ResearchThis paper explains the research's background and purpose in the first chapter. The first clause explains the formula and

variable that is frequently used in the second clause of this paper. Also, this paper explains the theoretical background in the first chapter and Markowitz's portfolio theory in the first clause. In addition, Mean-Variance model, TASD model and equally weighted model which are portfolio models being used in this paper can be explained with definitions and background. Also, research methodology in the third chapter shows the way to evaluate results of portfolio’s rate of return through the simulated investment program using three portfolios. This paper used Sharpe ratio, Correction Sharpe ratio and Treynor ratio to evaluate

1866© IEOM Society International


results. Furthermore, in the second clause, it discusses what measuring portfolio’s result index is, data to apply to portfolio and variables that was set in this paper. In the fourth chapter, it finds the investment proportion that obtains the price that applies to the data in portfolio. And in the second clause, it discusses the result of simulated investment. Also, in the third clause, it compares the portfolio’s rate of return by using the simulated investment. Finally, it discusses this research’s meaning and thoughts as this paper’s result in the conclusion.

This is a formula set that is frequently used in this paper.

N = The number of investing companies including portfolio

iR = Yield to average of stock

(R )iE = Expected rate of return of stock

iω = Investment proportion of stock

jω = Investment proportion of stock

iσ = Standard deviation of stock rate of return

jσ = Standard deviation of stock rate of return

ijσ = Covariance of stock and rate of return

ijρ = Correlation coefficient of stock and rate of return

itR = Yield to average of stock during period

pR = Total rate of return of portfolio

(R )pE = Expected rate of return of portfolio

pσ = Standard deviation of portfolio total rate of return

2pσ = Variance of total rate of return of portfolio

MR = Total rate of return of stock market

2Mσ = Total variance of stock market

TR = Target profit of rate of portfolio

k = Minimum expected stock returns demanded at portfolio

fR = Risk free rate of return

II. THEORETICAL BACKGROUND

A. Portfolio Selection Model 1) Mean-Variance model Mean-Variance model is a nonlinear programming model and it is the most typical portfolio model. Before Markowitz

created the portfolio theory, investors only consider the rate of return. Mean-Variance model is the model that minimizes the risk and guarantees the minimum target rate of return. The Mean-Variance model’s founder named Markowitz regarded setting a portfolio for the asset with the lowest variance as an optimal portfolio [1].



Markowitz’s paper has three implications. First, when investors invest the stock, they should not consider only stock’s rate of return. Second, even if rate of return is uniformed, variance can be reduced. Lastly, he suggested the concrete way to reduce the variance. By using these three implications he made the Mean-Variance portfolio [2]. Variance is the risk measurement tool that measures the stock’s variability forming the portfolio. Portfolio'’ variance is shown as below.

2

1 1 1 1

N N N N

p i j ij i j i j iji j i j

σ ω ω σ ω ω σ σ ρ= = = =

= =∑∑ ∑∑ (1)

Most matrix values mean the risk about other stocks and covariance after each investment proportion and covariance of two stocks is multiplied. Meanwhile, the matrix value of diagonal is i j= and means its own risk of each stock after its identical investment proportion and its own variance are multiplied. Variance can be divided into i j= and i j≠

2 2 2

1 1 1

N N N

p i j ij i ii j i

w

i j i j

σ ω ω σ σ= = =

= +

= ≠

∑∑ ∑ (2)

2) TASD model Discussion about whether variance of portfolio’s return is apposite or not to measure a risk in the optimal portfolio was

held. This made another method to measure a risk. The stock investors realize the risk in the case of not achieving the target level and want to avoid it. Therefore, many researches were conducted to minimize the risk that can be reduced, which investors desire. Minimizing the risk is a measure of risk only considering return that does not meet the target level [3].

Markowitz [4] studied that Semi-Variance is the most relevant thing to measure the return in ‘Portfolio Selection.’ Semi-variance means variance only in case of considering of a lower return than a target level. TASD model is the most typical portfolio model to use the concept of minimizing a risk [5]. TASD model is defined as following [6].

1

N

ii

i

R TRTASD for all R TR

N=

−= <∑

(3)

3) Equally weighted model

Equally weighted portfolio model provides the same weight which weighs stock N amount like 1EQ

i Nω = . This strategy

does not need the past data because it does not need the measurement of parameter. However, it is not an effective portfolio strategy because it omitted the optimized process. When this characteristic is figured out, equally weighted portfolio strategy does not have hazard estimation, but only has the risk about the model [7]. This equally weighted portfolio does not have any specific formula.

First, equally weighted portfolio academically drew the example [8]. [9] assert that equally weighted portfolio can be superior to Markowitz's Mean-Variance portfolio. After this, [10], [11], [12] analyzed the various portfolio model about equally weighted portfolio. Consequently, equally weighted portfolio shows that this portfolio gets abreast of other portfolios [13].

III. RESEARCH METHODOLOGY

A. First Clause Simulated investment result evaluation method This research finds out the superiority about portfolio characters by the simulated investment on portfolio models with each

different character and analyzed the results through comparative analysis. This research is supposed to be a comparative analysis portfolio model by Mean-Variance model, TASD model, and Equally weighted portfolio model. The purpose of this research is to select the best one in the three models.

The portfolio model was compared by using the particular standard. Performance measure is the standard to compare the portfolio model. But comparing the portfolio model result can be changed by performance measure, and then this research used many performance measures to compare the strategies with portfolios. This research used four performance evaluation



methods to evaluate the portfolio results. This research compared the portfolio results and found out superiority from the standard of results by using portfolio rate of return and risk, Sharpe ratio, Treynor ratio and Jensen’s Alpha.

1) Sharpe ratioToday, Sharpe ratio is a typical index to measure stock results. And then Sharpe ratio indicates how much excess profit can

be made when bearing risks as stock by using measurement for standard deviation. Excess profit appeared as non-risk profit rate deducted from actual profit ratio. Sharpe ratio considers the risk and stock market return case at the same time. The higher investment Sharpe ratio is, the more successful output is. Sharpe ratio used standard deviation to consider an overall risk of investment [14].

(sharpe ratio) p fp

p

R RSR

σ−

= (4)

2) Modified Sharpe RatioSometimes the case of excess profit rate has a negative quantity. In case Sharpe ratio and excess profit rate of stock have a

negative quantity, they do not have any meaning and interpretation. In other words, instances under every condition are the same without rate of return and risk, and then the higher rate of return is or the lower risk is. When excess profit rate has a negative quantity, the result turns the opposite. Modified Sharpe Ratio is to settle this problem by using Sharpe ratio formula [14].

, 0

(R R ) ,

p fp p f

p

p f p

R RMSR If R R

Elsewhereσ

σ

−= ⋅⋅⋅ − ≥

= − × ⋅⋅⋅ (5)

3) Treynor ratioTreynor ratio is the index to measure the result compared with non-risk profit rate. The higher the Treynor ratio is, the

higher the efficiency of selection strategy is. Treynor ratio uses beta coefficient to show the market risk. Beta coefficient means sensitiveness of rate of return on an individual asset about fluctuation in stock price. Beta coefficient shows how many systematic risks relatively of a particular category rather than other average categories. If beta coefficient has a negative quantity, it can be explained to respond to the other ways by market risks. Beta coefficient is divided into stock rate of return and covariance of stock market by standard deviation of the stock market.

2

(R , R )M

p mp

Covσ

β = (6)

In the formal, beta index of average assets is one. Beta coefficient is a relative value so it has a datum point. Treynor ratio index indicates non-risk excess rate of return of unit beta coefficient. It is called variability ratio and is used to assess a portfolio. The higher the Treynor ratio is, the higher rate of return about beta coefficient is.

(Treynor ratio) p fp

p

R RT

β−

= (7)

4) Jensen’s AlphaJensen’s Alpha is an index to measure the portfolio result rather than rate of return on stock market in scale. Jensen’s Alpha

measures expected difference rate for return in portfolio rate for return and risk. At this time, the higher excessive rate of return is, the higher investment result is. Jensen’s Alpha is defined as following below.

(R R )Mp p f p M fR Rα β= − − − (8)

pR = Whole rate of return of portfolio

fR = Non-risk rate of return



MR = Whole rate of return of stock market

pβ = Beta coefficient

B. Experiment Environment 1) Variable setting Optimal solution of Mean-Variance model, TASD model, and Equally weighted model deduction uses mathematical

programming methods. Mathematical programming methods are used to deduct variable value on the condition. Optimal solution is an investment proportion. In order to figure out the investment proportion, the first figures out the estimation of data rate of return, covariance, dispersion and deducts optimum investment proportion on the condition of each selection model.

2) Simulated investment In this research, investment proportion was used to practice investment in Kiwoom Securities. In this research, five

hundred million won was used with the portfolio model in three IDs. 0.35% of sale commission was applied. Simulated investments were on operation from June 25 to July 7 inclusive.

3) Data collection Data of each model is composed of the top 20 KOSPI total market values. Stock information of Cheil Industries Inc. and

Samsung Electronics Co. Ltd registered in a stock market exists respectively in December 18, 2014 and November 14, 2014. AmorePacific Corp. and AmorePacific Group Inc. were excluded for data collection because they affected to split the stock , and then it was hard to select an investment category. TABLE I. is the Investment category of the top 20 KOSPI total market values on the basis of June 19th, 2015. Sign(*) excluded in portfolio constitution.

TABLE I. KOSPI TOP 20

Rank Name code Company name Rank Name code Company name

1 005930 Samsung Electronics Co. Ltd 13 055550 Shinhan Financial Group Ltd

2 000660 SK Hynix Inc 14 005490 POSCO

3 005380 Hyundai Motor Co. Ltd 15 051910 LG Chem Ltd

4 015760 KEPCO 16 000270 Kia Motors Corp

5 028260 Cheil Industries Inc* 17 002790 AmorePacific Group Inc*

6 090430 AmorePacific Corp* 18 105560 KB Financial Group Inc

7 005935 Samsung Electronics Co. Ltd 19 000810 Samsung Fire & Marine Insurance Co Ltd

8 032830 Samsung Life Insurance Co. Ltd 20 033780 KT&G Corp

9 035420 NAVER Corp 21 034730 SK C&C Co. Ltd

10 017670 SK Telecom Co. Ltd 22 051900 LG Household & Healthcare Ltd

11 018260 Samsung SDS Co. Ltd* 23 096770 SK Innovation Co Ltd

12 012330 Hyundai Mobis Co. Ltd 24 003550 LG Corp

• Data on the top 20 KOSPI total market value composed in from May 31, 2015 to May 31, 2015 inclusively.

4) Measure result index Measuring result index of result portfolio selection model needs the entire rate of return of stock market. The entire rate of

return of stock market was composed to consider a daily price. Daily rate of return consists of data from June 25, 2015 to July 7, 2015 inclusive.

IV. RESULT ANALYSIS AND RESEARCH RESULT This chapter shows a mock stock trading differing in variables by portfolio composition. As a result, this research

compared and analyzed the result values.

A. Application of portfolio selection model This clause applies to top 20 KOSPI total market values to three portfolio selection models.

1) Top 20 KOSPI total market value



a) Mean-Variance portfolio model Mean-Variance portfolio model of Markowitz considers variance as a risk and selects optimal portfolio proportion to

minimize variance. The formula of portfolio selection model of Markowitz is shown as below [15].

2

1 1

N N

p i j iji j

Minimizeσ ω ω σ= =

=∑∑ (9)

,1

1 T

i i tt

subject to R RT =

= ∑ (10)

1(R )

N

p i ii

E R kω=

= ≥∑ (11)

11

N

ii

ω=

=∑ (12)

0 1,2, , Ni for iω ≥ = (13)

Equation (9) shows the purpose to minimize variance of rate of return of investment target consisting of portfolio. This research presents it through covariance matrix to find the optimal value that fulfills appropriate function. As the value that adds

the rate of return of i for t period and is divided into the period under observation, the (10) presents the rate of return of j .

This research sets up t on a daily basis. Therefore, the rate of return of j adds the rate of return on a daily basis and is divided by the period under data sample. Equation (11) presents that the average return of portfolio demands more than k . It constricts portfolio to meet minimum required rate of return. To meet the minimum required rate of return more than risk-free rate of return, this research sets up k as corporate bond yield rate during 3 years. Therefore, this research fixes k to 3.31433% that is average of corporate bond yield rate for three years in the Bank of Korea Economic Statistics System. (12) presents that the sum of proportion of investment has to be 1. (13) presents that each proportion of investment has to be more than 0. The proportion of investment that not only meets the all constraints but also minimums the fitness function is shown as TABLE Ⅱ.

TABLE II. INVESTMENT PROPORTION OF MEAN-VARIANCE MODEL

Company Investment proportion

Samsung Electronics Co. Ltd 0.0576194

SK Hynix Inc 0.0236349

Hyundai Motor Co. Ltd 0.0542928

KEPCO 0.0474977


Samsung Life Insurance Co. Ltd 0.1019522

NAVER Corp 0.0037153

SK Telecom Co. Ltd 0.0408616

Hyundai Mobis Co. Ltd 0.0472699

Shinhan Financial Group Ltd 0.0509298

POSCO 0.1494745

LG Chem Ltd 0.0322907

Kia Motors Corp 0.0314231




KB Financial Group Inc 0.0532017 Samsung Fire & Marine Insurance Co Ltd 0.0395496

KT&G Corp 0.0805375

SK C&C Co. Ltd 0.0176865

LG Household & Healthcare Ltd 0.0574742

SK Innovation Co Ltd 0.0336180

LG Corp 0.0398245

b) TASD portfolio model

TASD portfolio model applies to Downside risk that only considers the security of not achieving the target level. The formula of model is shown as below [6].

1

N

ii

i

R TRMinimize TASD for all R TR

N=

−= <∑

(14)

1

1 T

i itt

subject to R RT =

= ∑ (15)

1(R )

N

p i ii

E R kω=

= ≥∑ (16)

11

N

ii

ω=

=∑ (17)

0 1,2, ,i for i Nω ≥ = (18)

The fitness function has the purpose to minimize Downside risk and does not consider the security that achieves the target level by processing them 0. Equation (15)~(18) are the same as Mean-Variance portfolio model. This research sets up the target level to 0.2. The proportion of investment that not also satisfies constraints but also minimize the fitness function is shown as TABLE III.

TABLE III. INVESTMENT PROPORTION OF TASD MODEL


Samsung Electronics Co. Ltd -

SK Hynix Inc -

Hyundai Motor Co. Ltd -

KEPCO -

Samsung Electronics Co. Ltd -

Samsung Life Insurance Co. Ltd -

NAVER Corp 0.0165542

SK Telecom Co. Ltd -

Hyundai Mobis Co. Ltd -




Shinhan Financial Group Ltd -

POSCO -

LG Chem Ltd 0.3598871

Kia Motors Corp -

KB Financial Group Inc - Samsung Fire & Marine Insurance Co Ltd -

KT&G Corp -

SK C&C Co. Ltd 0.4641206


SK Innovation Co Ltd -

LG Corp -

c) Equally weighted portfolio model The equally weighted portfolio model disperses the investment risk by investing an equal proportion in each fund. The

equally weighted portfolio model can disperse the investment risk, simply contrary to another portfolio model, based on estimation or data. Each proportion of investment is the value that divides the whole into 20 securities. The proportion of equally weighted portfolio model is shown as TABLE IV.

TABLE IV. INVESTMENT PROPORTION OF EQUALLY WEIGHTED MODEL



SK Hynix Inc 0.05

Hyundai Motor Co. Ltd 0.05

KEPCO 0.05


Samsung Life Insurance Co. Ltd 0.05

NAVER Corp 0.05

SK Telecom Co. Ltd 0.05

Hyundai Mobis Co. Ltd 0.05

Shinhan Financial Group Ltd 0.05

POSCO 0.05

LG Chem Ltd 0.05

Kia Motors Corp 0.05

KB Financial Group Inc 0.05 Samsung Fire & Marine Insurance Co Ltd 0.05

KT&G Corp 0.05

SK C&C Co. Ltd 0.05


SK Innovation Co Ltd 0.05

LG Corp 0.05



B. Result evaluation of portfolio selection modelThis clause evaluates a result of portfolio selection model. This research compares a result in various methods to have

validity. To measure a performance of portfolio selection, this research uses return, variance, Sharpe ratio, Treynor ratio and Jensen’s alpha of portfolio.

1) The return and risk of portfolioAs a result of performance measurement, the rate of return of all portfolios presents in negative number and TASD model,

Mean-Variance model and equally weighted model are shown highly in an order. Especially the rate of return of equally weighted model appears to –230% that is the lowest return rather than the other portfolio. The standard deviation of portfolio shows similar value generally. Above all, TASD model display the highest standard deviation that means the highest return. On the other hand, equally weighted model shows the lowest standard deviation that means the lowest return. To compare the return and risk with stock market this research seeks the return and standard deviation of KOSPI. The rate of return of KOSPI appears to –0.021692328 that shows decrease of return of stock market.

TABLE V. RATE OF RETURN AND STANDARD DEVIATION OF EACH MODEL

Portfolio model return Standard deviation

Mean-Variance model -0.6309725 0.0288507

TASD model -0.1305807 0.0322649

Equally Weighted model -2.2995198 0.0287787

2) Sharpe ratioThe Sharpe ratio is the index that presents excess rate of return per risk. The portfolio that has high excess rate of return and

low risk has an excellent quality so it has the highest Sharpe ratio. TABLE VI. shows the Sharpe ratio from the mock stock trading for 10 days. As shown in the table, the Sharpe ratio has a negative value. The case that has a negative value does not have a meaning. Therefore, this research used Modified Sharpe ratio, the supplement of Sharpe ratio.

TABLE VI. SHAPE RATIO OF EACH MODEL

Portfolio model return Risk-free rate of return Standard deviation Sharpe ratio

Mean-Variance model -0.6309725 0.0331433 0.0288507 -23.0190589

TASD model -0.1305807 0.0331433 0.0322649 -5.07437118

Equally Weighted model -2.2995198 0.0331433 0.0287787 -81.0553057

TASD model, Mean-Variance model and equally weighted model are shown highly in an order in the Modified Sharpe ratio. It indicates that the TASD model which gets the highest return shows the highest excess return also. On the other hand, it indicates that the equally weighted model which gets the lowest return shows the lowest excess return also. The Sharpe ratio of KOSPI verifies to –0.0006073 that means decrease of return in stock market generally.

TABLE VII. MODIFIED SHARPE RATIO OF EACH MODEL

Portfolio model return Risk-free rate of return Standard deviation Modified Sharpe ratio


TASD model -0.1305807 0.0331433 0.0322649 -0.0052825


3) Treynor ratioThis table shows Treynor ratio on the basis of beta coefficient and the return of portfolio. As Sharpe ratio regards the

factors affecting excess return of portfolio as the risk of portfolio, Treynor regards the factor affecting excess return of portfolio as the systematic risk, the risk of stock market. Therefore, Treynor ratio quantifies the value to divide excess return into beta coefficient meaning the systematic risk. The beta coefficient was shown in Mean-Variance as 14.6122837, TASD model as 5.6998298, the equally weighted model as 16.9720640 that all portfolio models present high beta coefficient, especially equally weighted model and Mean-Variance model. The return of KOSPI showed to –0.0216923 during the research period. It means if the return of stock market decreases by 1% the equally weighted model and Mean-Variance model each decrease by 16.9% and 14.6%. The value of beta coefficient is predictable that two aforementioned portfolios present the



negative rate of return more than TASD model does. Therefore, TASD model indicates the lowest beta coefficient that is less sensitive to the stock market. In addition, TASD model shows superior return per risk of stock market relatively. Whereas equally weighted model indicates the highest beta coefficient that is sensitive to the stock market. In addition, equally weighted model shows poor return per risk of stock market.

TABLE VIII. TREYNOR RATIO OF EACH MODEL

Portfolio model return Risk-free rate of return Beta coefficient Treynor ratio


TASD model -0.1305807 0.0331433 5.6998298 -0.0287244


4) Jensen’s Alpha Jensen’s Alpha presents the difference of expected return and real return under the risk of stock. It means successful

investment when it comes to result high Jensen’s Alpha that shows higher real return than expected return. As shown in the table, Jensen’s Alpha of TASD model and Mean-Variance model indicates in positive number that shows real return is higher than expected return under the risk of stock. Especially TASD model shows the highest value of Jensen’s Alpha. On the other hand in equally weighted model real return is lower than expected return even though expected model has the high risk.

TABLE IX. JENSEN’S ALPHA OF EACH MODEL

Portfolio model return Risk-free rate of return Standard deviation Return of KOSPI Jensen’s Alpha

Mean-Variance model -0.6309725 0.0331433 0.0288507 -0.0191602 0.1371584

TASD model -0.1305807 0.0331433 0.0322649 0.0052825 0.1488299

Equally Weighted model -2.2995198 0.0331433 0.0287787 -0.0671309 -1.4019888

V. CONCLUSION AND DISCUSSION This research compared and analyzed which portfolio model gains the upper hand by selecting the portfolio model with a

range of properties. This research selected Mean-Variance model which considers risks as a variance. TASD model considered investment of not achieving the target level and equally weighted model made an investment in equal weight. This research established an optimal solution of portfolio models for the top 20 KOSPI total market values based on June 19 and executed the mock stock trading. The research period was two weeks from June 24 to July 7. Finally, this research evaluated portfolio model performance by using performance measurements such as return, portfolio risk, Sharpe ratio, Treynor ratio and Jensen’s ratio. The result of portfolio model’s performance was shown as below.

First, TASD model showed the highest result not only in return but also in portfolio risk. On the other hand, equally weighted model indicated relatively lowest on both return and portfolio risk. When return rate of equally weighted model was compared with comparison target models, it showed that its return rate was significantly low and its standard deviation was similar.

Second, in case of considering standard deviation of portfolio in regard to a risk, TASD model showed the highest Modified Sharpe ratio suggested that TASD model has the highest excess return per portfolio risk. Whereas the Modified Sharpe ratio of equally weighted model recorded the lowest suggested that equally weighted model has lowest excess return per portfolio risk. It is assumed that this result has a marked difference between models in the portfolio and similar risks.

Third, all portfolio models showed great sensitivity about the stock market that recorded minus return. Above all, TASD model relatively indicated the lowest sensitivity about the stock market rather than another portfolio models. On the contrary the equally weighted model recorded the highest sensitivity. Also, in case of considering standard deviation of stock market in regard to risk, TASD model ranked the highest excess return per stock market risk. On the other hand, the equally weighted model ranked the lowest excess return per stock market risk.

Fourth, the return of TASD model and Mean-Variance model was higher than the expected return considering the risk. In particular, TASD model showed the highest return than expected return considering the risk. Whereas, equally weighted model indicated the lowest return.

Therefore, TASD model showed the superior performance in every performance measurement expect the risk rather than other comparable portfolio models. Mean-Variance model ranked the second and equally weighted model recorded the lowest. This research forecasted the reason of the result came on this wise. The price of KOSPI was the sharpest decline in nearly two years during the research period and all portfolio models had minus return. The decrease of stock market appears to be influenced by plebiscite about bailout loan in Greece. Also as the stock market of China plummeted, this circumstance affected



the stock market of Korea. The prospect about company performance is negative in the aftermath of Middle East respiratory syndrome coronavirus(MERS). As the TASD model considers only the Downside risk and reduce it, TASD model coped with fluctuation of stock market most flexibly. Therefore, this research makes sure that TASD model is the best portfolio model when investors assume the stability as the most important principle. It minimizes the minus return when the people do not know the future in the stock market. Therefore, this research proved that TASD model is most suitable model to investors who wants the stable investment. On the contrary, the equally weighted model did not handle the circumstance of crisis because it did not seek estimate systematically.

This research has a limit point on this wise. The research period of mock stock trading was a short period from June 25th to July 7th. Portfolio is usually a long-term investment so the research could not bring the stable data. Also, the comparison could be meant only in the case of depreciate of stock market. It is hard to generalize the result of the research in the generic case. However, investment should be able to cope with any variance. So this research is relevant. As the variables about stock’s situation in this research needs to be considered, this research is significant.

The future research is needed to support the plausibility by long-term investment. If there is possible for optimal portfolio models to be compared in this research, the future research is supposed to extend in stock market not only in Korea stock market but also America and China.

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thesis, Seoul National University, R.O. Korea, 2013.[15] H. Kim. “Performance of the Markowitz' portfolio selection model over the accuracy of the estimated values of expected returns,

standard deviation, and correlation,” Master thesis, Yonsei University, R.O. Korea, 2012.

Youngjoo Lee is a student in Paul Math International School in Korea. Her research interests include financial management, operation research, risk management and time series data analysis.

Minsung Kim is a student in Paul Math International School. His research interests include marketing management and decision analysis and company management.

Taeheon Kim is a student in Paul Math International School. His research interests include statistics and economy.


kuala lumpur, malaysia, march 8-10, 2016 selection of

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