Journal - Is Taiwan First ETF Efficient

8/3/2019 Journal - Is Taiwan First ETF Efficient

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Journalof Financial StudiesVol.12 No.3 December 2004 107

Is Taiwans First Exchange Traded Fund Efficient?

byAndy Lin

andFan-Ju (Christina) Meng

Malaspina University-College, Canada

** Please address correspondence to: Andy Lin, Ph.D. Professor of Finance, Faculty of SocialSciences & Management, Malaspina University College, 900 Fifth Street, Nanaimo, BC Canada

V9R 5S5 Tel: 250-753-3245 Ext. 2446 Fax: 250-740-6551 E-mail: [email protected]

** We are grateful to anonymous reviewers for their valuable comments and suggestions. Errors remaining aredefinitely our responsibility.

Abstract

Taiwans first ETF, TTT, was launched in June 2003. In addition to the characteristics andperformance of TTT, this research examined whether ETF is a better choice for Taiwans investorsby applying the mean-variance analysis and portfolio evaluation techniques. In the mean-varianceanalysis, the empirical result shows that TTT has a smaller standard deviation as compared to itsfifty underlying stocks, which makes TTT an attractive investment tool for Taiwans conservative

investors. However, further examination shows that the performance of TTT is relativelyunsatisfactory in comparison with the market benchmark portfolio and a hypothetical portfolio.Evidently, TTT, based on the market capitalization in determining the allocation weights, does notyield the most appealing portfolio while the hypothetical portfolio, which applies the Markowitzstheoretical framework, is showing more attraction during the sample period. In an attempt to furthervalidate the results, the examination was applied to an extended period. Statistical results prove thatthe hypothetical portfolio still outperforms TTT in two of three performance measures. Afterincorporating various costs of portfolio construction and rebalancing as well as transaction taxes, thehypothetical portfolio retains its dominance, suggesting another dimension for future ETFformation.

Key words: exchange traded fund, portfolio theory, efficient portfolio, Sharpe ratio, Treynor ratio,Jensen Index.


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Journalof Financial StudiesVol.12 No.3 December 2004108

Is Taiwans First Exchange Traded Fund Efficient?

I. Introduction

Although exchange traded funds (ETFs) have a brief history, this market

segment offers excitement because of its remarkable growth rate. According to

Morgan Stanley Research, as of December 31, 2002, the size of ETFs increased

35% to US$131.56 billion and the number of ETFs grew 39% to 280, traded in 26

stock exchanges around the world as compared with the previous year. In 2002,

there were 47 new ETFs issued in Europe, 15 new ETFs in the United States and

10 new ETFs in Japan (Cheng and Chang, 2003). In 2004, two new Chinese ETFs,

one representing major stocks in Shanghai Stock Exchange and one incorporating

ADRs, were launched in the U.S. markets. Currently, the United States, Japan and

Europe are the three major ETF markets in the world. In terms of asset size and

daily turnover, the United States represents the largest ETF market share at

72.25%, followed by Japans 14.83% and Europes 7.55% (Cheng and Chang,

2003). Financial Research Corporation of Boston also forecasted that ETFs

would enjoy an average annual growth rate between 30% and 50% over the nextfive years. Moreover, the popularity of ETFs has increased so rapidly that ETFs

account for over two-thirds of the daily trading volume on the American Stock

Exchange (Fuhr, 2001).

Taiwans economy has been growing dramatically over the past years. An

incredible demand has been seen in the financial markets for good financing and

investment products. After becoming a member of World Trade Organization, it

is essential for Taiwan government to provide more financial products and expand

the depth and breadth of equity and financial markets to cope with global

challenges. Since equity investments are popular in Taiwan and individuals are

the major investors in Taiwans stock market (Yang, 2003). Considering the

feasibility of various financial products and the characteristics of Taiwans stock

markets, the ETF concept was introduced to Taiwan in 2003, ranking Taiwan the

28th ETF trading market in the world (SFC, 2003).


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Polaris Taiwan Top 50 Tracker Fund (TTT), the first ETF in Taiwan, was

launched by Polaris International Securities Investment Trust Co., Ltd. (PISIT)

and began trading in Taiwan Stock Exchange on June 30, 2003. To increase

liquidity for arbitraging and hedging traders, Taiwan Futures Exchange

simultaneously launched a new futures contract, TX50 futures. TTT and TX50

futures represent the same underlying stocks. As of April 27, 2004, the total asset

of TTT reached NT$46.8 billion and 9.16 million units, rocketing from NT$4.28

billion with 1.16 million units at its inception.

Since ETFs have become one of the fast-growing investment classes in the

global market recently, there are growing literatures on ETFs. Numerous scholars

debated about advantages and disadvantages of ETFs by comparing ETFs with

other investment tools. For instance, Papmehl (2001) and Zigler (2002) proposed

ETF is a good investment tool for everyone, while Damato and Lucchetti (2000)

argued that ETF is only good for specific investors. In addition, previous works

also focused on comparing ETF returns to changes in their net asset value (Elton

et al., 2002), analyzing the tax consequences of holding ETFs (Poterba and

Shoven, 2002), studying the dynamics of price deviations from the underlying

portfolios (Engle & Sarkar, 2002), comparing price discovery in the ETF cash

market and index futures markets (Hasbrouck, 2003), and discussing the cost and

the market structure of ETF trading (Boehmer & Boehmer, 2003).

Acting in response to the apparent importance of this market and

development, this research concerns primarily the portfolio formation and

capital allocation of ETFs and its suitability to individual investors in

Taiwan. What are the characteristics of ETFs that have made them a

popular investment product in the global financial market? Are ETFs

really so advantageous as opposed to other portfolio type of investment

tools currently available in the Taiwan market? Is ETF popular andacceptable in Taiwan too? Can new ETFs be designed to expand the

investment spectrum in Taiwan? These are the questions that motivate this

research.

Therefore, the logical sequencing of this research falls in four steps. First


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of all, after the introduction, the development history and characteristics ofETFs, including TTT, will be discussed. Secondly, a quantitative method

will be applied to examine whether Taiwans first ETF fits the investment

needs in Taiwan. Markowitzs portfolio theory and the most common

performance evaluation techniques, including Sharpe Ratio, Treynor Ratio

and Jensen Index, will be employed to compare TTT to its underlying

stocks, the general stock market as well as a hypothesized portfolio

calculated based on the theory. Thirdly, if TTT is not an efficient portfolio,

an optimal one will be proposed on the ground of the traditional portfolio

theory. And finally, based on the findings, some regulatory and practicalimplications regarding new ETF innovations and future developments will

be recommended.

II. Literature

1. Development and Types of ETFs

The concept of ETF stems from the growth of index-linked investmentproducts in the 1970s. Toronto Index Participation Shares (TIPS) and Toronto

100 Index Participation Units (HIPS) were launched in 1990 in Canada, and

investors were impressive with the expense structure of these products (Wiandt &

McClatchy, 2002). The real emergence of the ETF market was in the United

States where the first successful ETF, the Standard & Poors Depository Receipts

(SPDRs), debuted in AMEX in January 1993. The product can trace its roots to

exemptions from the Investment Company Act of 1940 that were granted by the

SEC to several other failed ETF introductions. SPDRs dominated the ETF market

until the Nasdaq-100 Index Tracking Stock entered the market in 1999

(Freyre-Sanders et al., 2001).1

ETFs are structured as either unit trusts or mutual funds, and several differences

between the two formats exist. Wiandt and McClatchy (2002) further divided

ETFs into three major types: the management investment company, the unit


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investment trust and the grantor or basket trust. Management investment

company type of ETFs is the major category in the market and is almost

indistinguishable to a mutual fund. While it requires a board of directors, it can

reinvest dividends back into the portfolio, thereby reducing the cash drag. In

addition, it is allowed to lend securities, which is a possible source of additional

income, to maximize performance and is allowed to optimize its portfolio,

permitting mangers flexibility in tracking its benchmark by employing futures,

options, or highly correlated substitute securities (Wiandt & McClatchy, 2002).

The appeal of a unit trust structure is its low operation costs since a board of

directors and its associated cost are not required. The target index must be

followed rigidly through a full replication. However, dividends are kept in

non-interest bearing accounts until those dividends are paid to investors quarterly.

This will cause a slight cash drag, or tracking error to the index because cash is not

fully invested. In addition, it is not allowed to lend holdings and to use derivatives

when managing the portfolio (Wiandt & McClatchy, 2002). The last type of ETFs,

grantor trusts, also called Holding Company Depository Receipts (HOLDRS),

creates a static basket to provide thematic exposure to different market segments.

It does not track a benchmark and will never be rebalanced (Wiandt & McClatchy,

2002).

2. Unique Features of ETF

The ETF with the same underlying shares as the index is divided into smaller

trading units. Investors can follow the trend of the index by trading beneficiary

certificates, which represent the index funds, on the stock exchange (TSEC, 2004).

Therefore, an ETF has the following unique features:

2.1 Passive management

The purpose of ETFs is to target the profit of the trading index, so each ETF

is designed to generally track broad-based, industry sector or country indexes.

Under the concept of passive management, the only scenario for adjusting the

constituents and weights of the portfolio is based on the changes of the

constituents and weights of the underlying index.


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2.2 Combining features of both stock and index fund

An ETF comprises both the features of stocks and open-end index funds;

meanwhile, an ETF can be traded in both primary and secondary markets. The

similarity between an ETF and a stock is that an ETF can be listed on the stock

exchange and traded in margin throughout the day. The process of creation and

redemption of ETFs is similar to that of the open-end funds and thus new shares

can be continuously offered.

2.3 Creation and redemption mechanism

The creation and redemptions mechanism is the process where authorized

participants transact directly with the fund. It is on an in kind basis. An

authorized participant is usually an institutional investor, specialist or market

maker who has signed a participant agreement with a particular ETF sponsor or

distributor (AMEX, 2004). Namely, in this mechanism underlying securities canbe swapped for the ETF shares and vice versa. Since an ETF is of securitized

index, the physical assets of an ETF are the index basket, which tracks the index.

Creations and redemptions occur in creation unit aggregations or multiples

thereof and involve delivering a specified basket of securities to the fund in

exchange for shares and vice versa (AMEX, 2004). The in-kind creation of ETF

is given to the index basket in exchange for a specific amount of ETF, while the

in-kind redemption of ETF is given a specific amount of ETF in exchange for the

index basket. To avoid dilution of existing fund shares, creations and redemptions

occur after the market closing, or at the-end-of NAV of the fund (Ou, 2003a).

3. Advantages and Disadvantages of ETFs

ETFs offer three main benefits: low fees and expenses, trading flexibility and

deferred taxes (Wiandt & McClatchy, 2002).

3.1 Trading flexibility

Exchange listing results in greater trading flexibility for ETFs. For example,

ETFs in the United States can be shorted, purchased on margin, purchased by way

of stop or limit orders, and not limited to the up-tick rule. Options can be written


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or bought on some ETFs, and, in most of cases, as few as one ETF share can be

purchased. In addition, there are less short-term trading restrictions for ETFs.

They can be used to equitize cash, providing a way for investors to put cash to

work in the market or maintain allocation targets while determining where to

invest for the longer term. A wide variety of ETFs also exists, such as fixed

income, industry sector and international diversification. The considerable

breadth of ETF alternatives provides investors with the ability to invest in indexes

that were previously unobtainable.

3.2 Tax implications

With the ETF redemption process, lower cost basis securities are exchanged

out of the fund first, leaving higher cost basis securities in the portfolio. Poterba

and Shoven (2002) analyzed the tax consequences of holding ETFsand concluded

that the ETF redemption process substantially reduces distributions of realized

capital gains. In addition, since ETFs are passively managed, typically provides

tax advantages versus actively managed funds. ETFs are not required to sell

securities to meet investor cash redemptions, and thus will not potentially

generate capital gains tax liability for remaining investors (Perrier, 1993).

3.3 Lower costs

Three major costs are applicable to ETFs, including operating costs, the bid/ask

spreads variances and royalties. Most of ETFs have extremely low operating

costs because they are passively managed. The creation and redemption

mechanism used by arbitrageurs has minimized variances, meaning lower

discounts or premiums between the NAV and the market price.

However, one area of weakness is claimed. Transaction costs, both visible

and hidden, can be unacceptable high for the unwary investor to pay while buying

and selling the actual ETF. Hidden costs are the most subtle to analyze and have

produced the strongest debate in literature (Wiandt & McClatchy, 2002). For

instance, ETFs can not be purchased for free from their issuers the way mutual

funds operate. Moreover, an ETF, as with any stocks, also has a bid-ask spread.


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4. New Applications of ETFs

There are many applications where ETFs can serve as an efficient vehicle.

Fuhr (2001) listed several applications, including equitizing cash flows,

implementing a US sector allocation or sector rotation models, executing

US-style investment strategies, building an international portfolio, adjusting and

hedging a sector, broad US market or international exposure. As well, the ETF

has begun to put more sophisticated investment techniques at the hands of

investors that were previously inaccessible due to cost or complication.

Dresdner Kleinwort Wasserstein Research (2001) found that during the periodSeptember 10 to 17, 2001 when the global economic outlook was further

weakened and investors were inclined to sell technology stocks further, the

average volatility of large individual stocks was far greater than the whole index.

If ETFs exist on every index or every style, investors can gain an array of risk

controlled investment building blocks to any strategy (Freyre-Sanders et al.,

2001).

Core-satellite investment framework is now the foundation for institutional

managed money, especially pension funds. They hold ETFs as core investments,

which provide a broad market exposure for long-term holding that is easy to

establish, easy to track, inexpensive, and efficient in tax planning. On the other

hand, they actively manage some specific assets as satellite investments to

increase performance. This strategy will reduce risks, but investors also can enjoy

the opportunity of higher returns (Freyre-Sanders et al., 2001).

5. Polaris Taiwan Top 50 Tracker Fund (TTT)

Taiwan Stock Exchange launched its first ETF on June 30, 2003. In the first

three months of TTT listing, TTT assets soared from NT$4.3 billion at its IPO in

the end of June 2003 to NT$29.23 billion by the end of September 2003, and the

number of stock baskets increased from 116 to 654.2 The main contributor of the

growth is Taiwans National Financial Stabilization Funds that released their

holdings to TTT in late August 2003 (Sun, 2003). In the same period, the average

daily turnover of TTT was 6,916 lots.3 And the average daily turnover rate was


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5.6%, lower than those of top 20 ETFs in the world of 11.9%. The major TTT

players during this period were propriety dealers, accounting for about 50% of

total trading volume, and institutional investors, representing local and foreign,

taking another 20% (Sun, 2003).

In collaboration with the FTSE Group, the Taiwan Stock Exchange compiled

a new Taiwan 50 Index in October 2002 to replace the traditional Taiwan index.

TTT is the first product linked to the Taiwan 50 Index. However, the Index is not

compiled solely for the ETF, but also for other derivative products such as the

Taiwan 50 Index (TX50) futures and options (TSEC, 2004). Currently, TX 50

futures contracts initiate trading with a value of NT$500 per point on the same day

as TTT. The value of TX50 futures per contract is the largest among all futures

with the underlying shares in Taiwans stock market.

The 50 stocks in TTT are mainly selected based on the market capitalization.

These constituent stocks are readjusted by a standard calculation procedure every

quarter to closely monitor and exactly track the pulse of the market. Although

more than five hundred stocks were eliminated during the selection process, it

does not decrease the importance of the Index. In fact, it adequately reflects the

essence of the market, accounting for 70% of the total market value, with acorrelation coefficient of 98.9% to the benchmark weighted stock price index

(TSEC. 2004).

Though TTT grew very fast, the TX50 futures market performed dreadfully with

the daily trading volume below ten contracts and relatively bigger spreads

between the bid/ask prices of nearly 1% (TAIEX, 2004). Increasing TTT size

from creation and trading volume show more institutional investors have

gradually accepted this product, while individual investors and the secondary

market need to be promoted further. In addition, the failure of TX50 futures

mainly results from big contract values, which is not appealing and lacks

suitability in Taiwans stock market where individual investors dominate.

6. Characteristics and performance of TTT

Table 1 sets forth the characteristics of TTT. Like the ETFs in the United States,


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TTT encompasses the same characteristics, including passive management, the

creation and redemption mechanism and the combination of merits of stocks and

mutual funds. Since TTT has its base value determined by the Taiwan 50 Index,

the return on TTT with the return on Taiwan 50 Index will be compared and the

return differences will be decomposed and analyzed. In what follows, the TTT

return is divided into two components: the return due to changes in the NAV of

TTT and the return due to deviations of NAV from price.

Table 1: Major Characteristics and Trading Regulations of TTT

Benchmark Index Taiwan 50 IndexStock Code 0050Listing Taiwan Stock ExchangeIssuer/Manager Polaris International Securities and Investment Trust Company Ltd.Technical Advisor State Street Global Advisors Asia Limited (SSGA Asia)Custodian Chinatrust Commercial BankIssue of Units Scripless, units held in the Depository and not available for withdrawal in physical formDepository Taiwan Securities Central Depository Co. LimitedNet Asset Value (NAV) NAV will be calculated based on the market value of the assets of the Fund after income and

expenses accrual and announced after 4:00 pm on each dealing day.Total Expense Ratio (TER) TER includes Management fee, custodian fees, index license fees, etc. Such expenses will

be accrued daily and subtracted from the NAV. Based on an estimated fund size of NTD 5billion, TER will be approximately 40 basis points.

Voting rights The Manager will act in the unit holders interest and exercise voting rights for the sharesheld in the Fund.

Distribution When the Funds investment performance exceeds that of the Benchmark Index by 5% ormore, the Fund will make a distribution.

Commission Same as for ordinary stocks varies by broker but no higher than 0.1425% of theconsideration

Board lot 1,000 units, no odd lot tradingTax 0.1% levied on the sale of the units, lower than 0.3% levied on the sale of regular stocksBid/ask spread NT$0.01 if the price of the unit is below NT$50

NT$0.05 if the price of the unit is above NT$50Limit up and down 7%, same as that for stocksTSEC Information Disclosure 1. Estimated NAV per unit every 15 seconds

2. Index level very 15 seconds3. Transacted price of TTT and the 5 best bid/ask prices and volume

Margin Trading 1. Available on listing2. Short selling under margin trading is exempted from the tick rule (which requires short

sales to take place at no lower than the previous days closing price)Creation and redemption Creation to subscribe for units of the Fund using index baskets and cash component

Redemption to redeem units of the Fund for index baskets and cash componentPortfolio Composite File(PCF)

Details of index baskets for creation and redemption will be disclosed through the TSECwebsite to all market participants

Tax No tax is levied on creation or redemptionCreation / Redemption Unit 1,000,000 unitsIssue / Redemption Price NAV per unit on the day of creation or redemptionCreation consideration /Redemption consideration

NAV per unit * number of units applied for in the creation or redemption order

Types of creation 1. Creation2. Team creation3. 90% rule creation4. Creation and sale of ETF on the same day5. 90% rule creation and sale of ETF on the same day

Types of redemption 1. Redemption2. Redemption and sale of stocks on the same day

Creation and redemption fee Varies by participating dealers but subject to the limit:1. Creation fee cannot exceed 2% of the creation consideration2. Redemption fee cannot exceed 1% of the redemption consideration

Source: Taiwan Stock Exchange Corporation


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It is important to note that the NAV of TTT per share is equal to the total market

value of the securities that substantiate the TTT plus an accumulation value that is

equal to accumulated cash dividends on the underlying shares minus accumulated

management fees. As shown in Table 2, the mean daily return of the TTT NAV is

0.001813 from June 30, 2003 to April 14, 2004, or equivalent to 66.17% per

annum. The result is better than the other two, but the differences among the three

are very small and less than 1 basis point. The differences of accumulated return

between them are larger between the NAV of TTT and market price of TTT. The

difference between Taiwan 50 Index and the NAV of TTT is mainly by tracking

errors and operating costs. The difference between the NAV of TTT and themarket price of TTT, called deviation, results from expectations of investors.

Table 2: Performance of Taiwan 50 Index, NAV and Market Price of TTT (Mean

Daily Return: June 30, 2003 to April 14, 2004)

Taiwan 50 Index NAV of TTT Market Price of TTT

Mean 0.001753 0.001813 0.001738

Standard Deviation 0.013980 0.014001 0.013230

Accumulated Return 0.347118 0.358972 0.344066

The difference in performance due to the tracking error is easy to estimate by

directly comparing the NAV return of TTT and the price return on the Taiwan 50

Index. However, the NAV of TTT used here is from Polaris International

Securities Investment Trust, which has subtracted the relevant expenses, such as

custodian fees, management fees, index license fees and etc., from the NAV by a

daily basis. Therefore, the real NAV should be theoretically higher than the NAV

used here. Even though operating costs have been incorporated, on average, the

TTT NAV daily return still outperformed the return on Taiwan 50 Index by

1.4037% over the examined period.

What could account for the differences? The major contributor is the method

of calculating the Taiwan 50 Index. Since the Taiwan 50 Index is weighted by

market capitalization of underlying shares, only stock dividends are considered

and cash dividends are not included in the Index (TSEC, 2004). In other words, if


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investors invest in the index futures, they will not receive cash dividends, while

investors who invest in the index securities will receive cash dividends. Figure 1

shows the tracking errors of TTT. Evidently, the tracking errors increased

significantly in June and July, the peak season of dividend distributions.

Figure 1: Tracking Errors of TTT

0

0.003

0.006

0.009

0.012

0.015

0.018

6/30/03

7/30/03

8/30/03

9/30/03

10/30/03

11/30/03

12/30/03

1/30/04

2/29/04

3/30/04

Above discussion assumes that all purchases and sales occurred at NAV.

However, the TTT price can deviate from NAV, representing a cost and anopportunity to the investor. Figure 2 shows the pattern of premiums or discounts

between daily NAVs and closing prices. This is expressed as the dollar difference

divided by the NAV. According to empirical literatures, over a long period the

difference between the price and NAV is insignificant because, through the

creation and redemption mechanism, arbitrage limits deviations (Elton at al.,

2002). This happened in Taiwan as well. On average, TTT prices lie above NAV

by 0.000451. The range is between 0.016086 and -0.012110 during the studied

period. In most cases, the difference doesnt yield any worthwhile arbitraging

opportunity.


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Figure 2: Premium or Discount of TTT

-0.018

-0.012

-0.006

0

0.006

0.012

0.018

6/30/03

7/30/03

8/30/03

9/30/03

10/30/03

11/30/03

12/30/03

1/30/04

2/29/04

3/30/04

III. Portfolio Selection

Prior to Markowitzs pioneering work on mean-variance efficient portfolios,

investment strategies were decided by maximizing the discounted value of future

returns without considering investment risks. Markowitz (1959) proposed that an

investor can reduce risks by portfolio diversification; namely, an investor can

remove unsystematic risks by the mean-variance analysis for securities. Based on

his proposition, an efficient portfolio is defined as the one providing the largest

return for a given level of risk or the smallest standard deviation of return for a

same level of return.

1. The mean-variance model

There are three major factors in the mean-variance analysis: expected return on

individual securities, variance on individual securities and covariance or

correlation between individual securities. The expected return and variance of a

portfolio are represented by the following formulas:

E(Rp) = =

n

i 1

WiE(Ri) (1)

p2 =

=

n

i 1

Wi2i

2 + =

n

i 1

=

n

j 1

WiWjij , i j (2)


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where E(Rp) : the expected return of portfolio

E(Ri) : the expected return of security i

Wi: the proportion invested in security i and =

n

i 1

Wi =1

p2: the variance of the return on the portfolio

i2 the variance of the return on security i

ij: the covariance between the returns of securities i and j

n: the number of securities in the portfolio

The expected return of the portfolio is the weighted average of the expectedreturns on individual securities included in the portfolio. The portfolio risk is a

function of each individual securitys risk and the covariances between the returns

of the individual securities. As n becomes larger and approaches infinity, the first

item, average variance, becomes smaller and approaches zero. However, when

the number of securities increases, the costs of diversification increase too.

Statman (1987) proposed that investors should increase the number of securities

for their portfolios as much as possible only if the marginal benefits are higher

than the marginal costs.

In the mean-variance framework, the portfolio with the smallest variance for

a given level of expected return can be calculated. Given the minimum variance

portfolios, the minimum variance frontier can be further obtained. The basic

Markowitz model is solved by quadratic programming. Furthermore, the

expected return-risk combination for a risk-averse investor is located at the

tangent point by combining an individual investors personal preferences and the

efficient set of portfolios. The efficient portfolio set can be further expanded by

including a risk-free asset.

2. Critiques of Markowitzs portfolio theory

Though the portfolio theory has a long history over 50 years, now numerous

researches are still based on it because of its appeals (Change, 2002). However,

the model is seen with some deficiencies. First, the model emphasizes greatly on

statistics. It is known widely that the efficient frontier is very sensitive to


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expected returns, variances and covariances of securities. Black and Litterman

(1990) also affirmed this view by studying the Germany bonds. Second, the

procedure of calculating the optimal portfolio is complicated, but this problem has

been solved by computer softwares. Third, the single-period analysis is not

appropriate in the modern complicated economic environment. Koskrosidis and

Duarte (1997) and Chopra and Ziemba (1993) concluded that the inputs selected

from different periods will cause different empirical results. Finally, the model is

built on the assumption that returns of securities are normally distributed, so it is

not applied to those financial assets with asymmetric distribution (Change, 2002).

Other researchers such as Elton et al (2003) provide alternative criteria for

portfolio selection. The list includes the geometric mean return, safety first,

stochastic dominance, and analysis in terms of characteristics of the return

distribution. The first two criteria do not utilize the idea of expected utility, while

the other two criteria, like the mean-variance analysis, make use of this scheme.

The geometric mean criterion is to select optimum portfolios with the highest

expected geometric mean return without considering the form of investors utility

functions or the distribution of security returns. The safety first criterion stems

from a belief that investors will employ a simpler decision model that

concentrates on avoidance of bad outcomes, rather than complicated mathematics

calculations. Stochastic dominance defines efficient sets of investments based on

the assumptions about investor behavior of utility functions. The final criterion

for selecting portfolios is proposed on the basis of three moments of return

distributions, called skewness.

3. Evaluation of Portfolio Performance

Over the last two decades portfolio evaluation has evolved dramatically. The

modern portfolio theory has changed the evaluation process from crude return

calculations to rather detailed explorations of risk and return (Elton at al. 2003).

These measures seek to relate the return on a portfolio to its risk, but differ in their

definitions of risk and the risk-adjusted performance. Recognizing the necessity

of incorporating both return and risk into analysis, Treynor (1965), Sharpe (1966)

and Jensen (1968) developed measures of portfolio performance in 1960s. These


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techniques are based on the concepts of capital asset pricing model (CAPM) and

often referred to as the composite (risk-adjusted) measures of portfolio

performance.

3.1 Reward-to-volatility measure Treynor Index

Treynor (1965) introduced a risk-adjusted measure of portfolio performance

called the reward-to-volatility ratio, or Treynor ratio. Treynor ratio assumes that

portfolios are well diversified, so the undiversifiable risk is ignored and total risk

can be represented by the systematic risk. Based on CAPM, Treynor ratio is the

slope of the security market line. Therefore, the higher the slope, the better the

portfolio performs. The ratio is defined as:

Treynor ratio = (Rp Rf) /p

where Rp : the return of portfolio during some period of time

Rf: the risk-free rate of return during the period

p : the beta of the portfolio

(Rp Rf): the excess return or risk premium of portfolio

3.2 Reward-to-variability measure Sharpe Index

Sharpe (1966) argued that Treynor ignored the unsystematic risk of portfolio

and thus introduced a risk-adjusted measure of portfolio performance called the

reward-to-variability ratio (RVAR). Furthermore, Sharpe (1966) pointed out that

Treynor Ratio is a better measure for the future evaluation due to the fact that the

capital asset pricing model is ex ante, not ex post. The rationale is similar to

Treynors ratio; that is, the higher the Sharpe ratio, the better the portfolio

performs. The measure can be presented as:

Sharpe Ratio = (Rp Rf)/p

where (Rp Rf) is the excess return or risk premium of portfolio and p is the

standard deviation of return for portfolio during the period.


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3.3 Differential return measure Jensen Index

Like Treynor Index, Jenson measure is based on CAPM, while Jensen (1968)

argued that Sharpe Index and Treynor Index only can be used for the performance

comparison because they are not absolute indicators. Therefore, Jensen

calculated the difference between the actual excess return on portfolio during

some period and the risk premium on that portfolio that should have been earned

based on CAPM, given its level of systematic risk. If the difference is positive, it

means the portfolio performance is better than the market performance. The

equation is given as:

p= (RpRf) p(Rm Rf)

IV. Methodology

1. Design

To formulate the research model and process, Markowitzs portfolio theory,

Sharpe ratio, Treynor measure and Jensen index will be employed to examine

whether TTT is an efficient investment tool for Taiwans investors. Though these

methods have their own deficiencies, they are still the most commonly used ones

in practice. This investigation involves three major steps. First, the

mean-variance analysis is applied to examine the return and risk of Taiwans first

ETF and its underlying 50 stocks in the sample period. Secondly, the portfolio

theory is employed to construct an efficient portfolio which comprises the same

underlying shares based on the outcomes of the mean-variance analysis. Finally,based on the portfolio performance evaluation criteria, the new hypothetical

portfolio is compared to TTT and the market portfolio, represented by Taiwan

Stock Exchange Capitalization Weighted Index (TAIEX). Three performance

measures will be computed again in an out-of-sample period to further verify the

examined hypothesis. It is expected that the hypothetical portfolio built on the


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ground of modern portfolio theory should be more efficient than its counterparts

before taking into consideration of transaction costs.

2. Data

The sample period extends from June 30, 2003, the first listing day of TTT, to

April 14, 2004 with a total of 198 observations. Additionally, an out-of-sample

test runs from April 15, 2004 to May 12, 2004, consisting of 20 observations.

Since the data period is short, all of measurements used in this research are

transformed to a daily basis.4 TTTs constituent list is adjusted every quarter to

reflect new developments in the financial market, so the constituent list has been

adjusted twice during the sample period.5

The closing prices of TAIEX, TTT and its underlying shares are obtained from

Bloomberg database. All closing prices of securities have been adjusted for

dividend payments. The risk-free rate adopted here is the yield rate of ten-year

Taiwan government bond. The rate stood at 2.29% on March 31, 2004 (Allianz

President Insurance, 2004). Since all returns in this research are based on a daily

ground, the risk-free rate is also converted to a daily return.

3. Mean-Variance Analysis

Pertaining to the assumptions of the portfolio theory, an investor will choose

among investment alternatives by complying with the efficient portfolio principle.

The means and variances of TTT and 50 stocks are computed and compared. The

major results of portfolio theory follow directly from the assumption that

investors like return and dislike risk (risk-averse attitude). Therefore, if TTT is an

efficient investment tool for investors, it should possess a relatively high return

and low risk as compared to other alternatives.

4. Establishment of the Optimal Portfolio

With the initial return and risk results of TTT and its underlying shares, the next

step is to identify the optimal portfolio based on the portfolio theory and then

compare this new portfolio to TTT. Following Markowitzs theoretical


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framework, return maximization is the solution objective. The constraints include

minimization of standard deviations, the capital allocation for each security is

zero or positive, and the sum of these allocations is equal to one.6

Objective: maximizing E(Rp) = =

n

i 1

WiE(Ri)

Constraints: minimizingp2 =

= =

n

i

n

j1 1

WiWjij , ij ; 0Wi1; and=

n

i 1

Wi = 1

The procedure of comparing TTT and the new portfolio has the following stepsand calculations are entirely based on a daily basis.

(1) Covariances (ij) are computed for every two individual securities.(2) Means and variances, obtained from the mean-variance analysis, are inputted

for each security.

(3) Covariances are entered for every pair of securities.(4) The risk-free rate is supplied.(5) Let the computer generate four thousand combinations.(6) The weights corresponding to the optimal capital allocation for each security

is generated by the program.

(7) The mean, standard deviation and beta are computed for portfolios.(8) The Sharpe ratio, Treynor ratio, Jensen Index are computed for portfolios.

Comparing with other inferior portfolios, an efficient portfolio should

characterize with relatively higher values in all three performance measures.

Theoretically speaking, the new portfolio derived based on the portfolio theory is

optimal and locates on the efficient frontier. As a result, the outcome should be

that the new portfolio performs better than TTT and the market portfolio, TAIEX,

which are constructed on the basis of market capitalization.

5. Out-Of-Sample Test

The evaluation methodology employed in the previous section will be applied

again to evaluate these portfolios during an extension period. Furthermore, the


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constituent list was adjusted during this second period based on new additions and

deletions. To ensure that the calculation and portfolios are done at the same

standards, these newly added stocks are applied same allocation weights as the old

replaced stocks. There are three replacements; however, no specific match of the

three pairs was announced. As a result, there will be six possible pairing matches.

To make certain none of the matches is missing from investigation, all six matches

will be studied and they are shown as six scenarios in Table 3.7

Table 3: List of the Scenario Analysis

Possible replacement Matches(New additions to TTT: 1605, 2888 and 3012)OldStocks(Code) Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5 Scenario 6

2105 1605 2888 3012 1605 2888 3012

2349 2888 3012 1605 3012 1605 2888

2356 3012 1605 2888 2888 3012 1605

V. Empirical Results

1. The mean-variance analysis

The means and standard deviations for TTT and its underlying shares are set

forth in Table 4. The graphical relationship of mean and variance is shown in

Figure 3. The point labeled TTT in Figure 3 illustrates the mean-variance position

for TTT. Based on the portfolio theory, investors are risk averters when making

investment decisions; as a result, a rational investor will prefer the portfolio with a

lower risk. From the graph, it is evident that TTT significantly reduces the risk

with the smallest standard deviations of 0.01323 among all. At the same return

level of near 0.001738, TTT has the smallest variance. In addition, according tothe portfolio theory, an efficient portfolio is the one locating toward the upper-left

corner of the graph. It is obvious that TTT is relatively lying at the theoretically

correct location as opposed to its underlying shares, confirming that TTT indeed

achieves portfolio efficiency.

Table 4: Statistics for TTT and Its Underlying Shares


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Security Standard Deviation Mean Security Standard Deviation Mean

0050 TT 0.01323 0.001738 2388 TT 0.02452 -0.00037

1216 TT 0.02558 0.00320 2401 TT 0.02144 0.00362

1301 TT 0.01568 0.00104 2408 TT 0.02672 0.00152

1303 TT 0.01607 0.00181 2409 TT 0.02834 0.00628

1326 TT 0.01815 0.00232 2412 TT 0.01408 0.00066

1402 TT 0.02652 0.00342 2454 TT 0.02147 0.00173

2002 TT 0.01629 0.00207 2475 TT 0.03017 0.00430

2105 TT 0.01864 0.00134 2603 TT 0.02487 0.00178

2201 TT 0.01838 0.00062 2609 TT 0.02238 0.00267

2204 TT 0.01977 0.00032 2610 TT 0.02316 0.00283

2301 TT 0.01889 0.00098 2801 TT 0.02387 0.00233

2303 TT 0.02372 0.00255 2880 TT 0.02079 0.00181

2308 TT 0.01715 0.00039 2881 TT 0.01907 0.00125

2311 TT 0.02623 0.00344 2882 TT 0.02341 0.00225

2317 TT 0.02035 0.00194 2883 TT 0.02167 0.00235

2323 TT 0.02399 0.00098 2886 TT 0.02040 0.00226

2324 TT 0.02135 0.00051 2887 TT 0.02262 0.00321

2325 TT 0.02952 0.00298 2890 TT 0.02150 0.00220

2330 TT 0.02055 0.00110 2891 TT 0.01817 0.00241

2344 TT 0.02719 0.00152 2892 TT 0.02143 0.00155

2349 TT 0.02420 0.00004 2912 TT 0.01983 0.00238

2352 TT 0.02079 0.00120 3009 TT 0.02819 0.00596

2353 TT 0.02191 0.00154 3045 TT 0.01725 0.00181

2356 TT 0.01850 0.00113 6505 TT 0.02211 0.00326

2357 TT 0.02259 0.00043 9904 TT 0.01956 0.00117

2382 TT 0.02070 0.00126

Figure 3: Means and Variances of TTT and Its Underlying Shares

-0.00100

0.00000

0.00100

0.00200

0.00300

0.00400

0.00500

0.00600

0.00700

0.00000 0.00500 0.01000 0.01500 0.02000 0.02500 0.03000 0.03500

2. Portfolio Selection

TTT

Variance

Return


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After the risk-free rate, mean, variance and covariance for each security are

supplied to the Excel program, the new allocation for each security in the new

hypothetical TTT is calculated based on the modern portfolio theory, while the

proportion for each security in current TTT is obtained by weighting the market

capitalization. The weights column dated as March 31, 2004 for securities in TTT

are presented in parallel with those in the new hypothetical portfolio in Table 5.

Significant discrepancies are seen across the table, showing the obvious results

based on different approaches. A close examination reveals that a significant

weights rebalance is required for almost all underlying shares if a different

portfolio construction approach is to be adopted.

Table 5: Weights Comparisons in TTT and the New Portfolio

TSE CodeWeights in TTT

(March 31, 2004)

Weights inHypothetical

PortfolioTSE Code

Weights in TTT(March 31, 2004)

Weights inHypothetical

Portfolio

1216 0.006911 0.028266 2388 0.005416 0.007852

1301 0.026896 0.010256 2401 0.006463 0.030717

1303 0.032646 0.017515 2408 0.010470 0.006656

1326 0.025263 0.041258 2409 0.030927 0.045780

1402 0.007781 0.025927 2412 0.058095 0.001733

2002 0.034188 0.016253 2454 0.023179 0.037416

2105 0.004835 0.014078 2475 0.014892 0.033024

2201 0.006635 0.019400 2603 0.007619 0.022612

2204 0.009474 0.015661 2609 0.008091 0.006841

2301 0.008720 0.010300 2610 0.006073 0.042929

2303 0.050776 0.015788 2801 0.010559 0.011425

2308 0.006563

0.028238

2880 0.014665

0.022159

2311 0.013393 0.004688 2881 0.030575 0.031595

2317 0.041874 0.008088 2882 0.052681 0.001892

2323 0.009627 0.001431 2883 0.023139 0.000390

2324 0.014309 0.007901 2886 0.027677 0.009584

2325 0.006670 0.037612 2887 0.013250 0.034009

2330 0.128613 0.005063 2890 0.007071 0.020155

2344 0.008254 0.010517 2891 0.023138 0.018459

2349 0.004873 0.038060 2892 0.015324 0.024060

2352 0.009650 0.016176 2912 0.005627 0.025823

2353 0.011271 0.011619 3009 0.020130 0.042390

2356 0.004642 0.037719 3045 0.016020 0.016172

2357 0.019211 0.011178 6506 0.045956 0.032996

2382 0.022945 0.036061 9904 0.006943 0.004280

Table 6, on the other hand, compares the risk-adjusted performance measures

of these two portfolios and the market benchmark index. Evidently, the new

portfolio based on the modern portfolio theory outperforms TTT and TAIEX in all

three performance measures. During the sample period, TAIEX was in the

uptrend with the positive average return of 0.001824. Among the three, the

hypothetical portfolio has the largest mean of 0.002369 and the highest risk with

the standard deviation of 0.013594 and the beta of 1.024509. After comparing the


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risk-adjusted measures of performance, the new portfolio still performs better

than the other two with the largest Sharp Ratio of 0.166183, Treynor Ratio of

0.002205 and Jensen Index of 0.000502. According to the evaluation criteria of

these techniques, the theoretical portfolio appears to be better than the other two.

Table 6: Performance Evaluation in the Sample Period

PortfoliosMeasures

TAIEX TTT Hypothetical

Mean 0.001824 0.001738 0.002369

Standard Deviation 0.012652 0.013230 0.013594

Coeff. of Variance 6.9364 7.61220 5.73829

Beta 1 0.970680 1.024509

Sharp Ratio 0.135521 0.123085 0.166183

Treynor Ratio 0.001715 0.001678 0.002205

Jenson Index 0 -0.000036 0.000502

However, this preferential performance will be losing part of its shine if the

transaction costs of establishing a portfolio, transaction taxes and portfolio

rebalancing costs are to be factored in.8 After incorporating various costs, the

daily mean return reduces to 0.002194 which is still higher than those offered by

TTT and the market benchmark. In other words, investors will still be better off

by forming the theoretically optimized portfolio and rebalancing the portfolio by

themselves if practically applicable.

Based on the coefficient of variation (CV), the hypothetical portfolio also shows

a smallest value, suggesting that relatively the portfolio is more appealing.

Unfortunately, TTT has the smallest return of 0.001738 though the second largest

standard deviation of 0.013230 and the smallest beta of 0.970680 among the three

portfolios. In addition, based on the comparison of the risk-adjusted measures,TTT has the smallest Sharpe Ratio, Treynor Ratio and Jensen Index at 0.123085,

0.001678 and -0.000036, respectively. In other words, TTT is showing the least

attraction among the three.

3. Out-Of-Sample Test


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The results of out-of-sample runs for TTT, TAIEX and the six scenarios are

presented in Table 7 when an extended period is applied. Chen Shin (2105), Ritek

(2349) and Inventec (2356) account for 1.41%, 3.81% and 3.77% of the new

portfolio, respectively. These weights are assigned to Walsin Lihwa (1605), Shin

Kong Financial Holding (2888) and Quanta Display (3012), alternatively based

on the six scenarios. The results for the scenario analysis post very small

discrepancies. The means are in the range between -0.007224 and -0.007263,

standard deviations between 0.02263 and 0.02269 and betas between 1.0478 and

1.0544. Taking a conservative approach, the worst scenario will be employed as

the representative and to be compared with TTT and the market benchmark. Inthis case, Scenario Two with the worst performance (see Table 7) will be used as

the comparison target.

Table 7: Portfolio Performance Evaluation in Out Of Sample Period

TAIEX TTT Scenario 1 2 3 4 5 6

Mean -0.006944 -0.005905 -0.007229 -0.007263 -0.007240 -0.007229 -0.007238 -0.007263

Std. Dev. 0.021296 0.018975 0.0226279 0.022688 0.022690 0.0226282 0.0226841 0.022688

Beta 1 0.824976 1.0478599 1.051334 1.054380 1.0478172 1.0543295 1.051428

Sharpe -0.331238 -0.316956 -0.324321 -0.324950 -0.323913 -0.324333 -0.323905 -0.324945

Treynor -0.007054 -0.007290 -0.007004 -0.007012 -0.006969 -0.007004 -0.006969 -0.007012

Jenson 0 -0.000195 0.000053 0.000044 0.000090 0.000052 0.000090 0.000044

During the extended period, TAIEX has a negative mean, showing a downtrend

market. As well, TTT and the new portfolio all have negative means, but TTT

demonstrates the best performance with the smallest negative mean of the three.

Meanwhile, TTT has the smallest standard deviation and beta among them.

However, very different results are present in risk-adjusted performance measures

and there is no consistent result for the three measure techniques. Generally, thenew portfolio is the best in two of the three criteria with Treynor ratio standing at

-0.007012 and Jensen Index at 0.000044, but the worst in Sharpe ratio of -0.32495.

TTT only demonstrates a better performance in Sharpe ratio. To conclude, two of

three indicators show that TTT is not the optimal alternative.


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VI. Conclusions and Recommendations

In this research, whether the ETF is an efficient investment instrument for

Taiwans investors is examined. ETFs characteristics and performance of ETF

are first addressed. It is obvious that ETFs have become an overwhelming

investment product in the United States with an average daily volume exceeding

half of AMEXs total trading and its fast-growing asset size reached US$102.14

billion in 2003. The success of ETFs suggests that ETFs are a feasible and

convenient investment vehicle.

Taiwans first ETF, Polaris Taiwan Top 50 Tracker Fund, was launched in June

2003. The creation and redemption mechanism sustains a small deviation of NAV

from market price and the design of TTT combines the merits of traditional

securities and mutual funds. When examining differences in return based on the

price of the TTT and its NAV during the first ten months of listing, it is found that

the average difference in return is less than 0.000451 per day. The principal tool

that restricts the deviation of price from NAV is the ability of investors to create or

delete ETFs at the end of every trading day by turning in or receiving the physical

bundle of securities that back up the ETF. In addition,the differences between the

TTT NAV and the Taiwan 50 Index averaged at 0.014037 because cash dividends

receiving from holding underlying shares were excluded from the Index while

included in the TTT NAV.

In addition to the characteristics and performance of TTT, this research further

examined whether ETF is a better alternative for Taiwans investors by applying

the mean-variance analysis, the portfolio theory and portfolio evaluation

techniques. In the mean-variance analysis, the empirical result shows that TTT

has a smaller standard deviation as compared to its fifty underlying stocks, whichmakes TTT an attractive investment vehicle.

However, when the study explored further, it is found that the portfolio

performance of TTT was worse than the market portfolio and the theoretical

optimal portfolio. The empirical results suggest that TTT, based on the market


26/32


capitalization in determining the allocation weights, is not the most appealing

portfolio while the hypothetical portfolio, based on the Markowitzs theoretical

framework, is showing more attraction during the sample period. In an attempt to

further validate the results, the examination was extended to an out-of-sample

period. Statistical results prove that the newly proposed portfolio is still better

than TTT in two of three performance measures, implying that TTT is relatively

less satisfactory. In other words, investors can employ Markowitzs framework to

construct a better portfolio than the TTT.

After factoring in the various costs of portfolio construction and adjustments

and taxes, the adoption of the theoretical portfolio is still beneficial and preferred.

In other words, an investor will be better off if the TTT could have been

constructed on the ground of the theoretical doctrine instead of market

capitalization. Practically, TTT does provide a diversification and other benefits;

especially, when the Markowitzs doctrine is not well-known and the allocation

weights are not easily accessible to investors. As well, it should be noted that it is

never an attempted goal of any ETF to achieve an efficient portfolio. Therefore,

from the perspective of investment, ETF is a good investment instrument by

combining the merits of stocks and mutual funds; while based on portfolio

theories, the constituents of ETF can be reconstructed and improved to achieve a

more efficient goal.

To expand Taiwans ETF market further and expect that Taiwans financial

institutions can design a better financial instrument for investors, the following

directions are proposed:

First, Taiwan should establish a mechanism to govern share borrowings for those

investors with an intention of ETF creation. There are fluctuation limits on

securities in Taiwans stock market, causing a problem in carrying out the creation

and redemption process. To illustrate, when some shares on the constituent list go

up and hit the upper limit, e.g., +7%, basically the trading of these stocks will be

very limited and thus investors can not buy enough shares for ETF creation.

However, if the regulations about share borrowings exist, investors can borrow

these shares through this avenue, further creating the flexibility and suitability of


27/32


ETFs in Taiwan.

Second, Taiwan should develop the ETF-related financial products in a more

affordable way. To increase the liquidity of TTT and the hedging trading

opportunity, Taiwan introduced TX50 futures and TTT at the same time.

However, currently, the poor trading volume in the TX50 futures market has

admitted the failure in the product design due to its unaffordable contract size. In

the United States, ETF-related financial products, such as options and futures, are

also traded. These derivatives and ETFs encourage and increase liquidity for each

other. In Korea the development of ETF has encouraged the further developments

in the option market, representing positive interactions between various financial

products (Ou, 2003b).

Third, various ETF products with different underlying indexes, markets and

industries should be pursued. According to Taiwans regulations, the targeted

indexes for ETFs have to be designed or approved by Taiwans Stock Exchange

with the requirements of representation, transparency and tradability. However,

those approved indexes are presently designed by MSCI, FTSE and so on.

According to the empirical results in this study, these benchmarks in terms of

market capitalization may not be the optimal portfolios. It is recommended thatTaiwans regulatory authority should approve more benchmarks fitting the

requirements and then the scopes and numbers of ETFs can be further expanded to

create more trading strategies in risk management.


28/32


Notes:

1. The Nasdaq-100 Index Tracking Stock was originally traded with a symbolof QQQ and was changed to QQQQ and moved to NASDAQ on December 1,

2004.

2. One stock basket, the smallest amount for the creation or redemption in theprimary market, is equal to one million shares in this case.

3. 1 lot is equal to 1,000 shares.4.

It is acknowledged and should be kept in mind that at the time of this studythe data set is quite short given the fact of TTTs rather short history. It is not

the intention of this research to generalize the results of this research to all

ETFs. However, the results obtained from this study do provide some

insights and add another dimension to future development and the design and

research of ETF products.

5. The first adjustment was done in January 2004 with Realtek (TSE code: 2377)being deleted and Formosa Petrochemical (6505) being added. The second

modification was completed in April 2004. Cheng Hsin (2105), Ritek (2349),

Inventec (2356) were deleted while Walsin Lihwa (1605), Shin KongFinancial Holdings (2888) and Quanta Display (3012) were taken into TTT

(Polaris SITC, 2004).

6. The program used here for finding an optimal portfolio is designed byAnthony Sun who employs the visual basic application in Excel. Please refer

to the following website: http://www.geocities.com/wallstreet/9245/.

7. For example, in Scenario One, Walsin Lihwa (1605) will take the place ofCheng Shin (2105), Shin Kong (2888) will replace Ritek (2349) and Quanta

Display will substitute Inventec (2356). Other matching scenarios are

presented in the same way with different pairings.

8. The typical transaction cost of 0.1425% of the trading value and a 0.1%transaction taxes (See Table 1) were applied to the calculation. As well, since

TTT is rebalanced every quarter, two complete portfolio adjustments were

assumed and included in the hypothetical portfolio during the studied period.


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