A passive investment strategy for Stichting Pensioenfonds Gasunie

A passive investment strategy

for

Stichting Pensioenfonds Gasunie

A comparative analysis of four investment alternatives

Guido Driever & Thijs Vollenbroek Groningen

A passive investment strategy

for

Stichting Pensioenfonds Gasunie

A comparative analysis of four investment alternatives

G.P.M. Driever Nassaulaan 7a 9717 CE Groningen Student number 1138308 T. Vollenbroek Heymanslaan 28 9714 GM Groningen Student number 1323733 Institution: Faculty of Economics University of Groningen Departments:

Finance, Investment & Accounting International Economics & Business Supervision N.V. Nederlandse Gasunie: Drs. J. de Boer CT

Drs. C.J.G.M. Hendriks

Supervision University of Groningen: Dr. M. Koetter

PREFACE

This thesis is the result of a five month internship at the treasury department of N.V. Nederlandse Gasunie. It is our final paper to fulfil our Master’s degree in Finance & Investment. In addition, it completes Guido’s Master’s degree in International Economics & Business, too.

We would like to thank Michael Koetter and Auke Plantinga of the University of Groningen for their constructive feedback during our meetings and for guiding us through the process of writing our thesis. Furthermore, we thank Johan de Boer, Cor Hendriks, Chris van Winsum and the rest of the treasury department of N.V. Nederlandse Gasunie for their willingness to provide us with relevant information and for creating a pleasant working environment during our internship. Finally, we thank all people who contributed to some extent to the realization of this thesis.

MANAGEMENT SUMMARY

Selecting a passive investment strategy for Stichting Pensioenfonds Gasunie (SPG) requires the consideration of several factors: the treatment of dividends, dividend withholding tax and the reclaim of (part of) it, costs, index changes and stock lending. All factors influence return and tracking error, but the effects are different for the various types of passive investment alternatives available in the market. This research analyzes mutual index funds, exchange traded funds, equity swaps and an own managed portfolio of stocks in further detail and composes a ranking of these alternatives based on return and tracking error. The analysis focuses on two European indices (DJ Stoxx 50- and DJ Euro Stoxx 50 index) for the period 2003-2005.

TABLE OF CONTENTS PREFACE... III MANAGEMENT SUMMARY ... IV TABLE OF CONTENTS...V 1 INTRODUCTION... 1 2 BACKGROUND... 3

2.1THE RATIONALE FOR PASSIVE INVESTMENT... 3

2.1.1 Passive versus active management ... 3

2.1.2 Empirical evidence ... 4

2.2PASSIVE INVESTMENT ALTERNATIVES... 7

2.2.1 Mutual index funds ... 7

2.2.2 Exchange traded funds... 8

2.2.3 Equity swaps ... 8

2.2.4 Managing a portfolio of stocks ... 10

2.3FACTORS OF IMPORTANCE FOR A PASSIVE INVESTMENT STRATEGY... 11

2.3.1 Treatment of dividends ... 11 2.3.2 Effects of taxes... 12 2.3.3 Index changes... 12 2.3.4 Costs... 13 2.3.5 Stock lending ... 14 2.4TAXATION ISSUES... 14

2.4.1 The landscape of tax systems in Europe... 14

2.4.2 The position of pension funds... 18

3 DATA & METHODOLOGY ... 21

3.1CONCEPTS... 21

3.1.1 Total Shareholder Return ... 21

3.1.2 Tracking error... 21 3.2THE MODEL... 22 3.3DATA... 23 3.4HYPOTHESES... 26 3.5METHODOLOGY... 27 3.5.1 Normality ... 27 3.5.2 Autocorrelation ... 28 3.5.3 Regression analysis ... 28

3.5.4 The bootstrap t-test ... 29

3.5.5 The information ratio... 31

4 RESULTS... 32

4.1ASSUMPTIONS... 32

4.1.1 Normality ... 32

4.1.2 Autocorrelation ... 32

4.1.3 Regression analysis ... 33

4.2THE BLOCK BOOTSTRAP T-TEST... 34

4.3THE INFORMATION RATIO... 35

4.4ANALYSIS OF THE RESULTS... 36

4.4.1 Reclaim of dividend withholding tax... 36

4.4.2 Managing the reinvestment of dividends... 37

4.4.3 Qualitative aspects ... 38

4.5COMPARISON OF THE INDICES... 39

5 CONCLUSION ... 40

BIBLIOGRAPHY ... 42

APPENDICES ... 47

APPENDIX AADDITIONAL FACTORS OF IMPORTANCE FOR A PASSIVE INVESTMENT STRATEGY... 48

APPENDIX BHISTORICAL DEVELOPMENTS IN EUROPEAN TAX SYSTEMS... 50

1 INTRODUCTION

Pension funds invest huge amounts of money to accumulate sufficient assets in order to satisfy all pension obligations on a timely basis. In order to achieve this objective, pension funds make use of investment strategies, which can be broadly classified as active management and passive management. Active management tries to outperform the market index with a portfolio that is exposed to more risk than the index. Passive management does not seek to outperform the index, but often tries to mimic it. This can be accomplished in two ways. On the one hand, there is a full replication strategy where all the stocks making up an index are held in their respective weights. On the other hand, under a partial replication strategy, only a subset of stocks is held from the index.

The growth in passive investments has been significant over the last decade. This substantial growth is partly due to the fact that actively managed mutual funds (on average) underperform the market after costs (Frino et al., 2005). Furthermore, growth in passive investments accelerated due to products such as exchange traded funds (ETF’s), which combine the advantages of an index fund and a stock in a single security with relatively low costs.

Stichting Pensioenfonds Gasunie (SPG) is interested in this trend of passive investment and noticed that it could benefit from further knowledge in this field. This research has the objective to explore the market for full index-tracking investments in further detail in order to provide SPG with an optimal investment strategy based on return and tracking error (the measure of deviation of the investment from the benchmark). The analysis takes the main factors of index investment into account: treatment of dividends, effects of dividend withholding tax, index changes, costs and stock lending. All factors may influence return and tracking error, but the effects are different for each of the investment alternatives. As a result, the investment alternatives may perform better or worse compared to each other. The question arises which investment alternative brings the highest total shareholder return (TSR) in combination with the highest positive tracking error.

We focus on the research question:

Which of the four index-tracking investments (mutual index funds, exchange traded funds, equity swaps and own managed portfolio of stocks) on the DJ Stoxx 50- and DJ Euro Stoxx 50 index has provided the highest Total Shareholder Return (TSR) in combination with a maximum positive tracking error for SPG over the years 2003-2005?

In order to answer the research question, the following subquestions have to be taken into account. First, what is the rationale for passive investment? Second, what are the characteristics of various index-tracking investments? Third, which factors have to be taken into account when applying a passive investment strategy? Fourth, what is the influence of the diversified landscape of tax systems in Europe and how does this influence the position of pension funds?

2 BACKGROUND

2.1 The rationale for passive investment

The choice between an active and a passive investment strategy is a major issue to pension funds. In order to provide a rationale for passive investment, one first has to compare both strategies in further detail (section 2.1.1). The question arises whether one can systematically outperform the market return by applying an active management portfolio strategy. The answer depends on the degree of market efficiency. Section 2.1.2 reviews empirical evidence on the Efficient Market Hypothesis (EMH), on active fund performance and on whether this active fund performance is persistent in the market. The outcomes imply that passive management would be a reasonable portfolio strategy to invest in.

2.1.1 Passive versus active management

The choice for a portfolio strategy of passive or active management depends on whether to accept or reject the hypothesis of efficient markets. The EMH states that equilibrium market prices reflect all available information. Therefore, prices are unbiased in the sense that they reflect the collective beliefs of all investors about future prospects (Fama, 1970). Fama distinguishes three forms of market efficiency. Weak form efficiency states that it is impossible to earn abnormal risk-adjusted returns based on the knowledge of past prices and returns. The semi-strong form of the EMH states that stock prices reflect all relevant information that is publicly available. As soon as information becomes publicly available, it is immediately incorporated into prices, and hence, investors cannot gain by using this information to predict returns. The strong form of the EMH implies that inside information is incorporated as well into prices, indicating that it is not possible to earn abnormal risk-adjusted returns at all.

Both active and passive investment strategies have their advantages and disadvantages. An overview of these advantages and disadvantages is presented in table 1.1

Active management Passive management

Advantages:

• Expert analysis – decisions are based on experience, judgement and prevailing market trends.

• Possible higher-than-index returns – managers aim to beat the performance of an index.

• Defensive measures – managers may adapt their portfolio if they believe the market makes a downturn.

Advantages:

• Relatively low transaction costs, operating expenses and management fees.

• No action required – there is no decision-making required by the fund manager or the investor.

Disadvantages:

• Relatively high transaction costs, operating expenses and management fees

• Risk of mistakes – managers may make unwise choices on behalf of investors, which could reduce returns.

• Investors are exposed to unsystematic risk, since one does not hold the market portfolio.

• Complex investment processes – this makes performance measurement and monitoring of an investment more difficult.

Disadvantages:

• Performance is dictated by the index – investors must be satisfied with market returns, because that is the best any passive investment can do.

• Lack of control – Managers can not take action. Passive managers are usually prohibited from using defensive measures, such as moving out of stocks, if they think stock prices are going to decline (assuming they have the correct information). Table 1 Overview of advantages and disadvantages of active and passive management

2.1.2 Empirical evidence

The main question that has to be answered in order to select the preferable portfolio strategy is to what extent markets are efficient. The EMH yields a number of testable predictions about the behaviour of financial asset prices and returns. Consequently, a vast amount of empirical research has been devoted to testing whether financial markets are efficient. Beechey et al. (2000) review empirical evidence on the EMH and form an opinion about the degree of market efficiency. The evidence concentrates on stock markets, although much of the discussion is relevant to other asset markets, such as bond, foreign exchange and derivatives markets, too. The majority of empirical work reviewed concerns US stock market data. Since US markets can be considered as the deepest and most competitive financial markets in the world, they provide a favourable testing ground for the EMH.

Beechey et al. (2000) review literature on the following five predictions concerning the EMH: 1) asset prices move as random walks over time, 2) new information is rapidly incorporated into asset prices, 3) technical analysis should provide no useful information, 4) fund managers can not systematically outperform the market and 5) asset prices remain at levels consistent with economic fundamentals. According to the literature reviewed, the EMH can be (partially) accepted for some predictions: asset price movements over short horizons are close to a random walk, most new information is rapidly incorporated into asset prices and fund managers rarely outperform the stock market on a consistent basis. Nevertheless, other aspects of asset-market behaviour seem much harder to reconcile with the EMH, e.g.

the misalignment in aggregate stock prices. An overview of the conclusions as formulated by Beechey et al. (2000) is summarized in table 2.

Predictions of the Efficient Market Hypothesis

Prediction Empirical evidence Study

Asset prices move as

random walks over time. Approximately true. However: -Small positive autocorrelation for short-horizon (daily, weekly and monthly) stock returns.

-Fragile evidence of mean reversion in stock prices at long horizons (3-5 years).

- Samuelson (1965) - Campbell (1997)

- Poterba & Summers (1988) - Fama & French (1988) New information is rapidly

incorporated into asset prices and currently available information can not be used to predict future excess returns.

New information is usually incorporated rapidly into asset prices, although there are some exceptions. On current information: -In the short run, stocks with high returns continue to produce

high returns (momentum effects).

-In the long run, stocks with low price-earnings ratios, high book-to-market-value ratios and other measures of ‘value’ outperform the market (value effects).

- Fama et al. (1969) - Fama & French (1992) - Jegadeesh & Titman (1993)

Technical analysis should provide no useful information.

Technical analysis is in widespread use in financial markets.

Mixed evidence about whether it generates excess returns. - Brock et al. (1992) - Sullivan et al. (1999) - Allen & Karjalainen (1999) Fund managers can not

systematically outperform the market.

Approximately true. Some evidence that fund managers

systematically underperform the market. - Sharpe (1966) - Jensen (1968)

- Grinblatt & Titman (1988) Asset prices remain at levels

consistent with economic fundamentals; that is, they are not misaligned.

At times, asset prices appear to be significantly misaligned for extended periods

- Summers (1986) - French (1988) Table 2 Predictions on the EMH and empirical evidence

Study Data (frequency) Methodology Results

Malkiel (1995) 1971-1991 (quarterly) US equity mutual funds, except those investing in foreign securities or in a specific sector.

Regression analysis to calculate CAPM alphas after expenses.

Mutual funds generate a negative alpha (underperformance). However, the results are not significantly different from zero. Gruber (1996) 1985-1994 (monthly)

270 US open-end funds, except those listed as foreign stock funds, specialized stock funds and balanced funds.

Performance is measured by a single index model and a four index model.

Returns are measured after expenses, but before load-fees

Mutual funds generate a negative alpha (underperformance) both for the single index model and the four index model. Wermers (1997) 1975-1994 (quarterly)

US mutual funds Comparison of the average fund return as a group with the CRSP-value weighted index before expenses and transaction costs.

1975-1982: outperformance of the average mutual fund.

1983-1994: underperformance of the average mutual fund (averaging 0.53 percent).

Otten and

Bams (2002) 1991-1998 (monthly) 506 Open-end equity mutual funds in France, Germany, Italy, the Netherlands and the United Kingdom

Unconditional and conditional versions of the Carhart (1997) 4-factor model

Returns are measured after management fees.

Aggregate country levels report a positive alpha (outperformance) for 4 of the 5 countries. However, only the result for the UK is significantly different from zero at the 5% level.

Table 3 Literature on active fund performance

Although some actively managed funds on average may fail to add value, this may not be true for all of them. If actively managed funds with an above average return in a certain period also have an above average return in the next period, then it is possible to obtain outperformance by selecting those funds. The importance of persistence analysis is stressed by Sirri and Tufano (1998), who document large money inflows into last year’s top performers and extractions from last year’s losers.

Empirical evidence on performance persistence shows mixed results: some studies show persistence of performance (e.g. Grinblat and Titman (1992), Wermers (1997)), whereas other studies found mixed support for it (e.g. Hendricks et al., (1993), Malkiel (1995), Otten and Bams (2002)).

Overall, the performance of actively managed funds is broadly supportive of the efficient market hypothesis. After deducting management fees and transaction costs, actively managed funds usually do not outperform the market. Consequently, after costs, the return on the average actively managed funds is often less than the return on the average passively managed funds. This implies that applying a portfolio strategy of passive management would be a rational choice.

2.2 Passive investment alternatives

Several kinds of alternatives exist in the market to obtain a position in a passive investment. All these alternatives can be classified as either securities or derivatives. In short, this list of alternatives consists of mutual index funds, exchange traded funds (ETF’s), managed portfolios of stocks, equity swaps, optimized portfolios as listed securities (OPALS), futures and index certificates. We only focus on the first four instruments, since they make up the majority of passive investments available in the market and have been of importance for SPG in the past or are likely to be of interest for them in the future.

This section continues with a description of the four selected index tracking instruments and their characteristics. Mutual index funds are discussed in section 2.2.1, exchange traded funds in section 2.2.2, equity swaps in section 2.2.3 and the management of a portfolio of stocks in section 2.2.4.

2.2.1 Mutual index funds

A mutual index fund is a form of collective investment that pools money from many investors and invests that money in a portfolio of securities. The assets of a mutual index fund are managed to track the performance of a particular index. This can be achieved either through a full replication strategy, where all the stocks making up an index are held in their respective weights, or a partial replication strategy, where a representative sample of stocks are hold from the index. The preferred strategy involves a trade-off between the reduced transaction costs of partial replication against the risk of not matching the index return.

2.2.2 Exchange traded funds

Exchange traded funds (ETF’s) are portfolios of stocks tracking an index, which trade throughout the day on a stock exchange, comparable to a normal stock. They combine the advantages of investment funds (diversification and investor protection) with those of a share (tradability). In addition, the composition of the fund is published daily, making them completely transparent. ETF’s are only redeemable in large blocks in return for the underlying portfolio of stocks. Due to the ‘in-kind’ redemption of ETF’s, arbitrage by institutional investors will ensure that ETF prices on the stock exchange do not deviate much from their net asset value. Redemption against stocks is more tax-friendly than redemption against cash, due to the fact that a cash position is subject to capital gains taxes at the end of the year, whereas a position in stocks can defer taxes until the investment is sold.

ETF’s differ in their characteristics compared to mutual index funds. Whereas mutual index funds can be redeemed in return for cash only once a day against net asset value, ETF’s can be sold in the marketplace during market opening hours or redeemed in exchange for the portfolio of stocks.

The first exchange traded fund, Standard & Poor’s Depositary Receipts (SPIDERS), was introduced by State Street in America in 1993. Beginning in the late nineties, ETF’s have also been conquering Europe and are now among the fastest growing financial products. In May 2004, 105 ETF’s were being traded in Europe, covering the most important national and international equity markets as well as regions, sectors, bonds and commodities. According to Morningstar, Barclays Global Investors and State Street currently are the largest institutions that offer ETF’s.

2.2.3 Equity swaps 2

Equity swaps offer another possibility to invest in an index. A swap is an over-the-counter derivatives transaction where streams of payments are exchanged over time according to specified terms. When at least one set of payments is determined by a stock or a stock index, the transaction is referred to as an equity swap.

An equity swap on a stock index works as follows: one party pays (receives) the positive (negative) rate of return of the underlying index to a pre-determined principal. The counterparty pays an inter-bank interest rate, often LIBOR (London Inter Bank Offered Rate) or EURIBOR (Euro Inter Bank Offered Rate), plus or minus a certain number of basis points (a spread). Principals themselves are not exchanged between the two parties, but banks often require collateral to cover credit risk. The amount of collateral depends on the counterparty and the underlying(s) of the swap.

The investor paying the interest component of the swap can place the amount to invest in the money market and receive LIBID (London Interbank Bid Rate), in order to fulfill the interest payment. SPG hedges fluctuations in interest rates through investments in mortgage-backed securities (debt obligations representing claims in a pool of mortgages). Almost all credit risk is covered through investments in

multiple AAA-rated loans. These mortgage-backed securities provide SPG with additional proceeds (a spread) above the interest rate. According to Barclays Capital, the spread over LIBOR has been fluctuating between 16 and 55 basis points for AAA-rated securities over the period 1999-2005 (figure 1). It is preferable for SPG to receive interest on mortgage-backed securities on a basis equal to the settlement of the swap. Then, SPG runs no interest rate risk.

0 50 100 150 200 250 300 350 ju n 99 ok t 99 feb 00 ju n 00 ok t 00 feb 01 ju n 01 ok t 01 feb 02 ju n 02 ok t 02 feb 03 ju n 03 ok t 03 feb 04 ju n 04 ok t 04 feb 05 ju n 05 ok t 05 feb 06 ju n 06 AAA A BBB

6 per. Zw. Gem. (BBB) 6 per. Zw. Gem. (A) 6 per. Zw. Gem. (AAA)

Figure 1 Mortgage-backed securities average issuance spreads (basis points over LIBOR) Source: Barclays Capital 2006

Figure 2 depicts an equity swap for SPG graphically. SPG has several positions in equity swaps, where it receives the return on an index. In turn, it pays an inter-bank interest rate, often EURIBOR plus or minus a spread. Additional proceeds are received from the mortgage-backed securities. The spread over LIBOR is comparable to the spread over EURIBOR.

Euribor +/- spread Euribor Index (negative)

+ spread Index (positive)

Figure 2 An equity swap for Stichting Pensioenfonds Gasunie

Equity swaps are mainly an investment alternative for institutional investors and are fully customizable for the user. Investors may have specific time horizons, portfolio compositions or other terms and conditions that are not matched by exchange listed derivatives. Typically, the return of an equity swap includes dividends. These are referred to as total return swaps. Furthermore, an equity swap is usually settled every three months to limit the risk of default of the counterparty. Settlement may occur on fixed contracts- or fixed notional conditions. A fixed contracts settlement keeps the number of contracts in the index fixed (the value of the equity swap may deviate from the initial investment), whereas a fixed notional settlement holds the value of the equity swap constant (at the settlement date, redundant contracts are sold in a bull market; additional contracts are bought in a bear market). Swap transactions are often traded under a

standard International Swap Dealers Association (ISDA) agreement, which includes agreements on payment, credit, collateral provisions, events of default and methods for calculating payments on early termination.

In case SPG wants to place an equity swap in the market, it contacts its partner banks in order to set up a competitive bidding process. The bank providing the most competitive quote would rationally be the preferred party to enter the swap with. The range of this quote is dependent on three factors. First, a banks’ funding level generally indicates whether or not it has cheap access to money in order to enter the swap. Here, a banks’ credit rating plays an important role: the better a banks rating, the lower the price it will pay to obtain additional funding. Second, banks differ in their effectiveness to reclaim dividend withholding taxes from tax authorities. This depends on the existence of the banks’ taxable profits in all countries that have stocks included in the indices. If a bank has taxable profits in a certain country, it can reclaim the whole amount of dividend withholding tax. The more profitable branch offices the bank has in various countries, the more effective it can reclaim the tax. Third, stock lending provides banks with an additional return, which may appear in the competitiveness of a quote. Overall, banks submit quotes which are on a comparable level with previous ones.

2.2.4 Managing a portfolio of stocks

Another investment option is to invest directly in stocks and manage the portfolio yourself. An investor can buy all stocks in the same proportion as they are represented in the index or hold a representative sample of stocks. The stocks are bought via a brokerage account. A small part of the money has to remain uninvested in order to pay for transaction costs. These costs consist of a fixed amount and a variable amount. Furthermore, the broker can charge a minimum cost (in case of small transactions) and a maximum cost (in case of large transactions).

2.3 Factors of importance for a passive investment strategy

Various factors influence return and tracking error. These factors are of importance when one likes to compare an investment in a mutual index fund, an ETF, an equity swap and a portfolio of stocks. Return is defined in this research as total shareholder return (TSR) and measures the change in value of the index over a specific period of time assuming reinvestment of dividends. Furthermore, additional proceeds and costs might be added/subtracted, arising from factors explained in this section. Tracking error is defined as the amount by which the performance of the investment differs from that of the benchmark.3

Although an extensive list of factors influencing TSR and tracking error can be composed, we have chosen to discuss in this section the five factors that are quantifiable and most relevant. An overview of other, less relevant factors is included in Appendix A. The factors that will be discussed are:

• Treatment of dividends (section 2.3.1) • Effects of taxes (section 2.3.2) • Index changes (section 2.3.3) • Costs (section 2.3.4)

• Stock lending (section 2.3.5)

2.3.1 Treatment of dividends

The DJ Stoxx 50- and DJ Euro Stoxx 50 total return indices assume immediate reinvestment of dividends on the ex-dividend date. This has consequences for TSR and tracking error on the investment alternatives. Dividend payments cause tracking error when investors hold the underlying portfolio of stocks. This is due to the fact that investors reinvest dividends on the payment date, whereas the index assumes reinvestment on the ex-dividend date. An investor also has the option to receive dividends immediately by selling the stocks right before closure on the day before the ex-dividend date and buy the stocks at the opening price on the ex-dividend date. This option is neglected in this research, since one would be exposed to overnight price fluctuations that may lead to a considerable tracking error.

Index funds often reinvest dividend payments immediately in the underlying stocks. This is possible through the use of cash futures. Dividends for ETF’s are received and held in an interest-bearing account. While these dividends are in the account, the ETF manager uses cash futures to equitize those dividends. The dividends are paid out on a quarterly basis to the holders of ETF contracts. Here, a time lag arises between the ex-dividend date and payment date of those dividends.

Equity swaps are often negotiated in terms of total return. With regard to dividend payments, there is no tracking error for the party who receives the return on the index.

2.3.2 Effects of taxes

Investors holding passive investments face tax externalities. This is the result of a varying degree of tax exposure towards the index-tracking investments and a differential tax treatment of the investments in the various countries. Dividend withholding tax and capital gains tax are the most important, as will be explained below. The former has to deal with the distribution of dividends, whereas the latter becomes effective with the realization of an appreciation of a capital asset from its purchase price.

All investment alternatives are exposed to dividend withholding tax. Countries apply dividend withholding tax rates in a wide range. However, preferential tax treaty rates are often applied. These treaties define that the source state may tax dividends up to a rate of 15%. The difference between both rates can be reclaimed by the countries’ tax authorities. A more in-depth discussion of dividend withholding tax is provided in section 2.4.

Capital gains tax is not always of importance, since countries diverge in the way they treat the taxation of capital income. In addition, capital gains tax is often only of concern for individual investors and not for pension funds, since most countries exempt pension funds on the taxation of their investment income4_.

The Netherlands belongs to the group that exempts pension funds from taxation on investment income and therefore capital gains taxation is not included in this research.

2.3.3 Index changes

A fund manager has to rebalance its portfolio each time an index change occurs. This can be the result of (Frino et al., 2004):

• Index revisions: to ensure that indices are always accurate and follow the changes in the stock markets as closely as possible, they are reviewed on a regular basis.

• Repurchase/issuance of stocks by companies, which influences the weightings of the company in the index.

• Entry/exit of stocks due to M&A activity, spin-offs, right offerings or bankruptcies.

The DJ Stoxx 50- and DJ Euro Stoxx 50 index are reviewed annually in September. Then, the stocks are ranked for each of the sectors in terms of their free float market capitalization (the portion of a stocks total market capitalization that is available for trading). Subsequently, a selection rule determines which stocks are added and removed from the index. In addition to the annual index revision, both indices are adapted for remaining index changes during the year.

Index changes do influence TSR and tracking error, since they involve transaction costs and also timing costs/earnings. The latter can be caused by fund managers, who trade in the period between the announcement and the actual index revision date or managers, who rebalance their portfolio after the revision date, due to e.g. market illiquidity.

4 _{Of the country sample applicable for research, only Denmark, Italy and Sweden tax the investment income of their}

It might be easier for a manager of a portfolio of stocks to profit from index changes, due to their smaller size of the investment. Managers of mutual index funds or ETF’s also may beat the index by smart timing policies regarding index changes. Equity swaps follow the index perfectly and use the actual change date to implement index changes.

2.3.4 Costs

Transaction costs and a funds’ operating expenses influence TSR and tracking error. Transaction costs often consist of commission fees paid to a broker. Mutual index funds may face additional costs, such as front-end load (the amount you pay when buying stocks in a mutual fund), back-end load (the amount you pay when selling stocks in a mutual fund), additional purchase fees and redemption fees.

Carrel (2006)5 _{notes that no-load mutual index funds have an advantage compared to ETF’s, since trading}

entails no commission costs. However, this advantage is disappearing rapidly, since commission fees are decreasing.

Transaction costs for equity swaps are quite low. It is relatively easy to enter into a position and dealers charge relatively few costs to hedge a position. Chance (2002) states that additional transaction costs in the form of legal and documentation costs are also very low.

Transaction costs for the management of a portfolio of stocks will be relatively high, since an investor has to buy all underlying stocks and adjust the portfolio when index changes occur. The transfer of stocks in Ireland, Switzerland and the UK imposes an extra transaction cost: stamp duty. At the end of 2005, stamp duty in Ireland was relatively high (1%) compared to corresponding rates at the United Kingdom (0.5%) and Switzerland (0.15%). ETF’s and equity swaps are free of stamp duty.

A fund’s operating costs are accumulated in the so-called expense ratio, which includes management fees, custody, investment advisory and shareholder servicing expenses. These costs are expressed as a percentage of the funds average net assets over a year.

In general, ETF’s have a lower expense ratio than mutual index funds. Harper et al. (2001) note that these lower ratios are due to the fact that asset-management firms sponsor the ETF’s and do not directly deal with the individual investor through expensive telephone centers and retail offices. Brokers and financial advisors perform that function. Gastineau (2001) shows that mutual funds incur between 5 and 35 basis points higher expenses due to their duty to keep track of stockholders transactions and other paper work. Operating costs for equity swaps are reflected in the negotiated quote. Furthermore, an investor has to be aware of the requirements to supervise the (ISDA) agreements. Understanding these agreements requires specific knowledge.

2.3.5 Stock lending

Stock lending involves the temporary exchange of stocks with an obligation to redeliver the same quantity of the same stocks at a future date. Usually, this happens for other stocks or cash of an equivalent value. In most stock lending agreements, the borrower is given legal title to the stocks for the life of the transaction. In general, the borrower fee is determined in advance and the lender has contractual rights similar to the ownership of the stocks. The lender has the right to receive all dividend payments and to have the stocks returned. The past few decades have shown a huge growth in the stock lending market for all types of equities in order to earn additional revenue. This expansion is reflected in daily intermediate market volumes, especially in the USA.

Mutual index funds, ETF’s and banks involved in equity swaps often engage in stock lending. Credit Suisse measures annual proceeds from stock lending for her index fund products to be 10-20 basis points in the Eurozone region, whereas Barclays’ iShares reports proceeds of 25 basis points a year. An investor managing a portfolio of stocks might gain from stock lending. However, banks estimate proceeds to be nil up to an amount of € 100 million. Stock lending proceeds from equity swaps are reflected in the negotiated quote.

2.4 Taxation issues

This section analyzes the importance of dividend taxation on index-tracking investments. Dividend withholding tax is more or less interrelated with corporate taxation, since the level of corporate tax influences the amount of dividends that can be distributed to shareholders. In turn, the level of dividend withholding tax influences dividend return on the investments. Since dividend withholding tax rates may vary a lot between countries, this section is included to provide further insights in this field.

This section continues as follows. First, the diversified landscape of tax systems in Europe is explained in further detail in section 2.4.1 and discusses the implications of corporate tax and dividend withholding tax. Section 2.4.2 discusses the tax position of pension funds concerning these taxes.

2.4.1 The landscape of tax systems in Europe

Corporate taxes are commonly distinguished according to what extent they reduce the double taxation on distributed profits. Economic double taxation refers to income that is first taxed at the corporate level when it is realized and then taxed a second time at the shareholder level when it is distributed (Lindhe, 2001). Most European countries have integrated the corporate and shareholder taxation to a certain extent and a variety of systems has been employed over the years. There is considerable room for variation within each of these tax systems, particularly in relation to what is classed as a tax deduction, or equivalently as taxable income. This can lead to significantly different tax effects, even under the same system (Officer, 1982).

Cnossen (1993) distinguishes three broad types of tax systems. Their interaction is depicted in figure 3.

Figure 3 Integration types of corporate and personal income tax systems

On the one hand, there is no integration at all between corporate and personal income tax. This so-called classical system implies that (distributed or retained) corporate profits are first taxed under corporate income tax and are then subject to personal income tax (double taxation). On the other hand, the corporate tax system is fully integrated with personal taxes and the corporation is regarded as a ‘conduit’ (pass-through) of all corporate source income of shareholders (distributed as well as retained profits). The corporate tax represents only a prepayment on the personal income tax liability of the shareholder. Furthermore, integrated systems partly mitigate the economic double taxation of corporations and shareholders. Relief can be applied directly at the corporate level or at the shareholder level:

• Dividend deduction system: dividends are fully deductible from taxable profits of the corporation. Personal income tax is imposed on the gross (= net) dividend.

• Split-rate system: takes account of the double taxation of dividends by differentially taxing distributed and undistributed (retained) profits. The distributed profits (dividends) are taxed at a lower rate of company tax than the undistributed profit.

Integration of distributed profits No integration:

Classical system Full integration: Conduit system

Corporate level Shareholder level

Dividend

• Imputation system: partial or full elimination of double taxation of dividends through the provision of a tax credit for the company tax paid on the dividend receipts of shareholders.

• Partial double taxation system: a flat-tax rate is applied to dividends and other corporate income, where the tax rate is often identical to the lowest marginal rate of personal income tax. This guarantees partial relief from double taxation for shareholders with a marginal income tax rate above the flat-rate.

Over the years, many countries reformed their tax systems to so-called modified classical systems.6 _These

reforms have narrowed the range of traditional forms of double taxation relief (e.g. imputation systems) and increased the degree of integration. Table 4 presents an overview of the countries’ tax systems for the years 2000 and 2006, including the years when noticeable shifts in tax regimes have taken place (IBFD, 2000-2006). The table confirms the trend of a shift to modified classical systems. This can be a) a half income system, where 50% of the dividends is exempted from taxation and the other 50% is taxed at the applicable rate, or b) a system of partial double taxation, where a reduced flat rate is applied for dividend income at the personal level.

Country Tax system 2000 Tax system 2006 Reform

Austria Partial double taxation Partial double taxation 20057

Belgium Partial double taxation Partial double taxation 20037

Denmark Partial double taxation Partial double taxation

Finland Imputation (full) Partial double taxation 2005

France Imputation (partial) Half income system 2005

Germany Imputation (full) Half income system 2001

Greece Dividend exemption Dividend exemption

Ireland Classical system Classical system

Italy Imputation (full) Partial double taxation 2004

Luxembourg Partial double taxation Half income system 2002

The Netherlands Classical system Partial double taxation 2001

Portugal Imputation (partial) Half income system 2002

Spain Imputation (partial) Imputation (partial)

Sweden Partial double taxation Classical system 2004

Switzerland8 _{Classical system Classical system}

United Kingdom Imputation (partial) Imputation (partial)

Table 4 Tax systems in Europe: an overview for the years 2000 and 2006

A reform of a country’s tax system often goes hand in hand with a decline of the corporate income tax rate, aiming to increase the country’s international competitiveness. Table 5 summarizes the corporate income tax rates of the countries for the years 2000-2006 (Ernst & Young, 2000-2006). As expected, corporate income tax rates have declined over the years.

6 _{Appendix B includes a description of historical developments in European tax systems regarding capital income.}

7 _{The Austrian and Belgian tax reform brought no change in the type of tax system, but provided measures to}

increase the country’s international tax competitiveness.

8 _{Taxation in Switzerland occurs at the federal and cantonal level. As a result, double taxation may occur both in}

Country 2000 2001 2002 2003 2004 2005 2006 Remarks

Austria 34.0 34.0 34.0 34.0 34.0 25.0 25.0

Belgium 40.17 40.17 40.17 33.99 33.99 33.99 33.99 Includes a 3% surtax Denmark 32.0 30.0 30.0 30.0 30.0 28.0 28.0

Finland 29.0 29.0 29.0 29.0 29.0 26.0 26.0

France 37.8 36.4 35.4 35.4 35.4 34.9 34.4 Includes surtaxes; standard rate is 331_/3%

Germany 51.63 38.36 38.36 39.58 38.29 38.31 38.34 Includes 5.5% surtax & add. municipal tax Greece 40.0 37.5 35.0 35.0 35.0 32.0 29.0

Ireland 24.0 20.0 16.0 12.5 12.5 12.5 12.5

Italy 41.25 40.25 40.25 38.25 37.25 37.25 37.25 Includes a regional tax of 4.25% Luxembourg 37.45 37.45 30.38 30.38 30.38 30.38 30.38 Includes surtaxes; standard rate is 22% The Netherlands 35.0 35.0 34.5 34.5 34.5 31.5 30.5

Portugal 35.2 35.2 33.0 33.0 27.5 27.5 27.5 Includes a 10% municipal surcharge Spain 35.0 35.0 35.0 35.0 35.0 35.0 35.0

Sweden 28.0 28.0 28.0 28.0 28.0 28.0 28.0

Switzerland 25.1 24.7 24.5 24.1 24.1 21.3 21.3 Federal tax rate of 7.83%; add. cantonal tax United Kingdom 30.0 30.0 30.0 30.0 30.0 30.0 30.0

Table 5 Overview of corporate income tax rates 2000-2006

Double taxation of dividends is further relieved through tax treaties. Already in 1929, the practicability of uniform multilateral treaties by which double taxation could be eliminated became noticeable (Reinhold, 2004). However, the system that evolved consisted largely of bilateral tax treaties among countries. Nevertheless, treaties are thought to be a helpful step on the path to a coherent and uniform regime of international taxation, which may lead to a multilateral tax agreement.

Tax treaties typically classify and assign taxing jurisdiction through provisions, such as dividends, interest and royalties. For the purpose of this thesis, only tax treaties concerning dividends are taken into account. Under a tax treaty, the source state may tax dividends at a rate up to 15%, which is defined in a country’s tax protocol, whereas non-treaty rates for 2005 range from e.g. 15% in Spain up to 35% in Switzerland. The difference between the two rates can be reclaimed by a country’s tax authority.

A complete overview of dividend withholding tax rates is presented in table 6 (Ernst & Young, 2000-2006). It also includes the tax treaty rates applicable to the other countries of the research. All rates hold for portfolio investments. Greece and the United Kingdom are not included in the table, since they do not impose dividend withholding tax.

Country 2000 2001 2002 2003 2004 2005 2006 Tax treaty rate

Austria 25 25 25 25 25 25 25 10/15 Belgium 25 25 25 25 25 25 25 10/15 Denmark 25 25 28 28 28 28 28 0/10/15/18 Finland 28 29 29 29 29 28 28 0/10/13/15 France 25 25 25 25 25 25 25 0/15 Germany 25 21.1 21.1 21.1 21.1 21.1 21.1 10/15 Ireland 22 22 20 20 20 20 20 0 Italy 27 27 27 27 27 27 27 15 Luxembourg 25 25 25 20 20 20 20 7.5/15 The Netherlands 25 25 25 25 25 25 25 10/15 Portugal 30 30 25 25 25 25 25 10/15 Spain 25 18 18 18 15 15 15 10/15 Sweden 30 30 30 30 30 30 30 0/10/15 Switzerland 35 35 35 35 35 35 35 0/10/15

It is well known that most investment funds are located in Luxembourg and Ireland, due to their favourable tax climate. Dividend withholding tax rates for both countries are among the lowest in Europe. In addition, it is possible to reclaim the whole amount of dividend withholding tax in Ireland and the Irish corporate tax rate is by far the lowest in Europe. Other factors contributing to the attractiveness of Ireland and Luxembourg are their well developed financial infrastructure and their conducive regulatory environment.

2.4.2 The position of pension funds

In most European countries, domestic pension funds meeting certain requirements can benefit from a special corporate income tax regime (EFRP, 2006). When the pension fund is a regulated company pursuant to the domestic civil pensions act, preferential tax treatment may apply for corporate income tax and withholding taxes on distributions of dividends and interest payments from domestic investments. The tax treatment of domestic pension funds may result in a full exemption from corporate income tax or a reduced rate corporate income tax. Furthermore, withholding taxes may provide relief through an exemption at source, a refund of withholding tax levied, or a credit of withholding tax levied against corporate income tax due. This is different in the case of foreign pension funds, which can not benefit from such beneficial exemption or refund procedures. The treatment has brought foreign pension funds in a discriminatory position, where cross-border dividends paid to European pension funds are subject to a higher level of taxation compared to domestic pension funds. Fortunately, it is becoming clear that such difference in treatment based on the location of the pension fund is contrary to the EU principles of the internal market. This has resulted in many complaints, which have been submitted by the European Federation for Retirement Provision (EFRP) and PriceWaterhouseCoopers (PWC) to the European Commission (EC). They claim that EU member states should stop discriminating foreign pension funds. In December 2005, 16 EU member states were levying a higher tax on dividends paid to foreign pension funds. Ten countries, which are of concern for this research, are part of this group: Austria, Denmark, France, Finland, Germany, Italy, The Netherlands, Portugal, Spain and Sweden. The position of Switzerland, as a non-EU member, towards this discriminatory practice is unclear. The discriminatory treatment of cross-border investments can be further classified into three categories (EFRP, 2006). An overview of this classification is presented in table 7.

In the second category, domestic pension funds are not exempt from corporate tax, but do benefit from an exemption of withholding taxes, whereas foreign pension funds do not. In the end, the effective tax burden on domestic pension funds is lower compared to the tax burden on foreign pension funds. This might be the result of e.g. a lower tax base or a lower corporate income tax rate. Countries that belong to this second category are Denmark, Finland, Italy and Sweden.

In the third category, domestic pension funds are subject to withholding tax and corporate tax, where it is allowed to credit the withholding tax against the corporate tax due. Since foreign pension funds are not subject to corporate income tax in the source country, they are not entitled to credit withholding tax. Germany is the only country belonging to this category. Since Germany makes a distinction between two types of pension funds, the country is present in two categories. The status of SPG in Germany is unclear.

Domestic pension fund Foreign pension fund

Category 1 • Exemption, reduced rate, or refund/credit of

domestic withholding tax • Exemption from corporation tax

• Subject to withholding tax (no exemption, reduced rate, refund or credit)

Category 2 • Exemption from withholding tax

• Corporation tax levied a) on a net basis

b) on the basis of a deemed (low) yield c) at a rather low corporation tax rate

• Subject to withholding tax (no exemption, reduced rate, refund or credit)

Category 3 • Subject to withholding tax

• Subject to corporation tax, but withholding tax is credited against corporation tax due

• Subject to withholding tax

• No credit against corporation tax due Table 7 Classification of tax treatment for domestic and foreign pension funds

The procedure of submitting a complaint for this discriminatory treatment is relatively straightforward and is form- and cost-free (Schonewille, 2006). The complaint only has to contain a quote of the national provisions, which are thought to be not in conformity with the EC Treaty. After receiving a complaint, the EC has one year to either close the case, if it concludes that there is no infringement, or to send a ‘letter of formal notice’ to the member state of concern. Member states have to reply within two months. If the reply is negative and there are still beliefs of the existence of an infringement, the EC might send a so-called ‘reasoned opinion’ to the member state. Again, the member state has two months to reply. If the member state is still not prepared to adjust its legislation and there still exist thoughts about infringement, the case can be brought to the European Court of Justice (ECJ). Up to now, the complaints procedure has proved to be of great benefit to the EC to find unjustified obstacles in the internal market and pension funds seem to formally file procedures with local tax authorities in the source states if they think they have to pay more withholding tax than local funds.

3 DATA & METHODOLOGY

3.1 Concepts

In this section, we explain two main concepts of this research: total shareholder return and tracking error. Both concepts need further explanation before one can start with the interpretation of forthcoming results.

3.1.1 Total Shareholder Return

Total shareholder return (TSR) is defined as the change in value of the investment over a specific period of time, assuming reinvestment of tax dividends plus (minus) additional proceeds (costs). These additional proceeds/costs may arise from the factors mentioned in section 2.3: taxes on dividends and the reclaim of (part of) it, index changes, costs and stock lending. Not every investment is exposed to all factors. Table 8 provides an overview of the factors of concern for the investment alternatives. The sign reflects the expected effect on TSR (+ = positive effect; - = negative effect; 0 = no effect).

Dividend

withholding tax Reclaim (part of) dividend

withholding tax

Stock lending Costs Index changes

Index fund - 0 + - +/-

ETF - + + - +/-

Equity swap9 _{- + + - 0}

Portfolio of stocks - + 0 - +/-

Table 8 Additional proceeds and costs for every investment alternative

3.1.2 Tracking error

Tracking error is a measure of how closely the investment follows the benchmark. There are a number of ways in which tracking error can be measured. In this research, tracking error is measured using two methods defined by Frino and Gallagher (2001). First, standard tracking error on day t is calculated as the difference in returns of the investment p and the benchmark index b (Rpt – Rbt). The daily average tracking

error over n days (TE1,t) is defined as:

n

TE

∑

=

)

R

-(R

9 _{Additional proceeds/costs for equity swaps are received/paid indirectly, since they are reflected in the negotiated}

An alternative test for tracking error, and the typical standard methodology used, is the standard deviation of

tracking error, measuring day-to-day variability of the difference in returns between the investment and the

benchmark index return (TE2,t). It is expressed as follows:

[

]

_∑

Where

R

R

return of the index over the research period.

3.2 The model

We construct a three-step model that provides further insights in the components that constitute total shareholder return and tracking error for each of the investment alternatives on both indices. The model is graphically depicted in figure 4. The first step in the process is to calculate daily TSR of all investment products. The second step is to calculate daily tracking error by subtracting the benchmark return from the TSR of the investment products. The third step is to rank the investment products. We perform a ranking based on a) hypotheses testing and b) the information ratio.

This chapter continues with discussing the first two steps of the model and the construction of the data samples (section 3.3). Thereafter, the methodology concerning hypotheses testing and the calculation of the information ratio is explained in further detail.

Figure 4 The model for calculating TSR and tracking error DJ Stoxx 50 50 Index DJ Euro Stoxx 50 50 Index Total Shareholder Return (TSR) DJ Stoxx 50 50 Index DJ Euro Stoxx 50 50 Index Tracking error (TE) Additional effects on TSR: • Dividend withholding tax • Reclaim (part of) dividend

3.3 Data

A variety of investment products is available on the DJ Stoxx 50- and DJ Euro Stoxx 50 index. We have selected for each of the investment alternatives an investment product on both indices in order to calculate TSR and tracking error. Table 9 presents an overview of the selected investment products.

DJ Stoxx 50 index DJ Euro Stoxx 50 index

Exchange traded fund iShares offered by Barclays GI iShares offered by Barclays GI

Index fund KBL Equity Fund Europe 50 Credit Suisse Index Match Fund

Equity swap Negotiated with BNP Paribas Negotiated with BNP Paribas

Portfolio of stocks Brokerage account of ABN AMRO Brokerage account of ABN AMRO

Table 9 Overview of selected investment products on the four investment alternatives

iShares, offered by Barclays Global Investors (BGI), are selected for the analysis of ETF’s. Barclays is a reputable party in the market and offers ETF’s in a wide range of varieties, including the indices of concern. In addition, SPG currently has iShares included in its investment portfolio.

TSR for ETF’s is calculated on a daily basis using the net asset value (NAV) of the product. This NAV includes all relevant proceeds and costs as mentioned in section 3.1.1. By using the NAV, we are not exposed to daily noise in the bid-ask spread. The amount to invest, net of the purchase fee, is divided by the NAV in order to determine the number of ETF contracts the investor has to buy. This number of contracts increases at the moment BGI distributes dividends to the holders of ETF contracts. The dividend inflow and the current cash position determine the new number of contracts the investor has to buy. Our aim is to keep the cash position close to zero, though transaction costs and custodian fees lead to deviations. Interest is calculated on the cash position using the EONIA interest rate. Data of daily NAV’s and quarterly distributed dividends are obtained from Bloomberg. The iShares are bought at Euronext Amsterdam.

The two index funds - KBL Equity Fund Europe 50 and CS Index Match Fund - have been selected after reviewing the supply of open-end index funds available in the market. The main selection criteria were: 1) the extent to which the fund would track the underlying index, thereby applying a full replication strategy; 2) the availability of daily NAV’s and 3) the availability of a detailed prospectus of the fund. Both funds satisfied the conditions.

Equity swaps are different from the other investments, since historical prices (quotes) are not available on a daily basis. This is due to the illiquid over the counter market of equity swaps. The negotiated quote is applicable from the start of the swap and holds for the entire duration; intermediate quotes are not known. However, it is still possible to approximate the value of the equity swap on a daily basis and translate this into a TSR. As mentioned in section 2.2.3, banks submit quotes which are on a comparable level with previous ones. For that reason, one can assume SPG is able to enter a swap on more or less comparable conditions as in the past. Historically, quotes of BNP Paribas have been the most competitive ones for SPG. Therefore, a weighted quote has been composed out of historical equity swaps of SPG settled with BNP Paribas. A disadvantage of this procedure is that it underestimates the daily standard deviation of tracking error, since it excludes the day-to-day variation in the quote of the equity swap. According to Mr. Rinkes of Morgan Stanley, this day-to-day variation is primarily caused by changes in the three factors that constitute the competitiveness of a bank’s quote: its funding level, its effectiveness to reclaim dividend withholding tax and its proceeds from stock lending. Although this procedure is not optimal in a methodological sense, it is inevitable given the characteristics of the swap.

same proportion as they are represented in the index. Furthermore, an interest-bearing cash balance contains money to pay for transaction costs.

In order to hold the stocks in their respective weights, the portfolio needs to be rebalanced each time an index change occurs (see section 2.3.3). We apply the method of contingent rebalancing, where a position is rebalanced to its optimal value when the value of the stock in the portfolio differs more than x% of the optimal value of the stock in the portfolio. The optimal value is defined as the weight of the position in the index multiplied by the sum of cash and total portfolio holdings. As mentioned in section 2.2.4, the choice for the rebalancing percentage x in the model is debatable. According to Morningstar10_{, investors}

would not worry about minor divergences from the optimal portfolio allocation of e.g. 2%, but allocations differing from target allocations by 5% or more should definitely encourage action from the investor. Since varying values of x result in different outcomes of TSR and tracking error, there is no clear-cut value for x. By setting x at 3.5%, which is halfway the rebalancing range as indicated by Morningstar, we take a neutral position with regard to the trade-off between transaction costs and tracking error. At this percentage, the cash balance is always less than 2% for both indices. Although this procedure fails to account for correlations and differences in volatilities between stocks, it is relatively easy to implement. Furthermore, a reclaim procedure of dividend withholding tax has been implemented in the model. Investors have the opportunity to reclaim (part of the) dividend withholding tax from tax authorities twice a year. We added the reclaim procedure in the model at the end of June and December. The amount that can be reclaimed is added about two weeks later to the cash position and is automatically reinvested in the portfolio. Data of all index members (weight of the company in the index, number of stocks of the company in the index, closing price and dividend payouts) is obtained from Bloomberg.

A fictive amount of € 10 million is invested in each of the investment products. TSR and tracking error is calculated and analyzed over this amount applying a research period of three years (2003-2005). This research period has been selected, since equity swaps for SPG have a duration of three years. Extending the research period would lead to a bias in the results. Then, the use of a 3-year quote would be an incorrect reflection of the quote that holds for a longer duration. (Quotes on equity swaps change when the duration of the swap is extended). The data sample for each investment product is around 760 observations of TSR and tracking error. Since not all investment products have observations on the same date, adaptations to the data samples are required. An observation of a product is considered to be non-existing when there is a missing value in the product to which it is compared. Finally, input figures of operational expenses, transaction costs and custodian fees of all investment products are summarized in Appendix C. Furthermore, this appendix includes the quotes on the equity swaps and monthly proceeds on mortgage-backed securities. Administrative costs to manage all investment products have been ignored, since these are hard to quantify.

3.4 Hypotheses

Hypotheses testing is one of the ranking methods applied in this research in order to select the optimal investment alternative for SPG. Intuitively, one would expect that index tracking investments have zero tracking error, since the objective of these products is to follow the index as perfect as possible. Nevertheless, due to the additional proceeds and costs as mentioned in section 2.3, tracking error might deviate from zero.

We are interested in the investment alternative providing the highest TSR in combination with a maximum positive average tracking error. We test two investment alternatives jointly in order to determine whether intraday tracking error of an investment is significantly higher than the other. A ranking list is composed, sorting the investment products on TSR over the research period. On the basis of this ranking, the following hypotheses are formulated:

Hypotheses regarding the DJ Stoxx 50 index:

- Ho,1: Tracking error of the equity swap = tracking error of the portfolio of stocks.

- Ha,1: Tracking error of the equity swap is higher than of the portfolio of stocks.

- Ho,2: Tracking error of the equity swap = tracking error of the iShares.

- Ha,2: Tracking error of the equity swap is higher than of the iShares.

- Ho,3: Tracking error of the equity swap = tracking error of the KBL index fund.

- Ha,3: Tracking error of the equity swap is higher than the KBL index fund.

- Ho,4: Tracking error of the portfolio of stocks = tracking error of the iShares.

- Ha,4: Tracking error of the portfolio of stocks is higher than of the iShares.

- Ho,5: Tracking error of the portfolio of stocks = tracking error of the KBL index fund.

- Ha,5: Tracking error of the portfolio of stocks is higher than of the KBL index fund.

- Ho,6: Tracking error of the iShares = tracking error of the KBL index fund.

- Ha,6: Tracking error of the iShares is higher than of the KBL index fund.

Hypotheses regarding the DJ Euro Stoxx 50 index:

- Ho,7: Tracking error of the equity swap = tracking error of the portfolio of stocks.

- Ha,7: Tracking error of the equity swap is higher than of the portfolio of stocks.

- Ho,8: Tracking error of the equity swap = tracking error of the iShares.

- Ho,9: Tracking error of the equity swap = tracking error of the CS index fund.

- Ha,9: Tracking error of the equity swap is higher than the CS index fund.

- Ho,10: Tracking error of the portfolio of stocks = tracking error of the iShares.

- Ha,10: Tracking error of the portfolio of stocks is higher than of the iShares.

- Ho,11: Tracking error of the portfolio of stocks = tracking error of the CS index fund.

- Ha,11: Tracking error of the portfolio of stocks is higher than the CS index fund.

- Ho,12: Tracking error of the iShares = tracking error of the CS index fund.

- Ha,12: Tracking error of the iShares is higher than of the CS index fund.

3.5 Methodology

Before it is possible to select the appropriate test for the hypotheses, two assumptions need to be examined: normally distributed data (section 3.5.1) and independent observations (absence of autocorrelation, section 3.5.2). In addition, a regression analysis is included in section 3.5.3 to examine to what extent the investment products follow the indices. Section 3.5.4 deals with statistical tests appropriate for hypothesis testing. Section 3.5.5 discusses the second ranking technique, the information ratio, in further detail.

3.5.1 Normality

A normality test checks whether the data set is a random sample from a normal distribution. The normality assumption (ut ~ N(0, σ2)) is required in order to conduct hypothesis testing. This assumption

can be tested by applying the Jarque-Bera test for normality in Eviews, which is based upon four statistical characteristics of distributions: mean, standard deviation, skewness and kurtosis (Brooks, 2002). Skewness measures the extent to which a distribution is not symmetric about its mean value and kurtosis measures how fat the tails of the distribution are. A normal distribution has a skewness of zero and a kurtosis of three.

3.5.2 Autocorrelation

Besides normality, the independence of observations (or the absence of autocorrelation) is measured. Pope and Yadav (1994) warn for potential estimation bias in tracking error arising from the use of high frequency data (i.e. daily or weekly data). Their research suggests that negative serial correlation in tracking error can bias upwards its estimate. A test for autocorrelation, which does not assume normally distributed data, is the Runs test. This test counts the number of times there is an increase (+) and the number of times there is a decrease (-) in the observation at time t in relation to the observation at time t-1. A run is defined as the number of times there is a change in sign. The number of runs (R) is compared with the number of runs expected in a random process (

μ

r r

R

Z

σ

μ

−

=

The number of runs expected in a random process (

μ

2 1 2 1

2

1

n

n

n

n

+

+

=

μ

Where n1 and n2 are the number of observations with a positive sign (+) and the number of observations

with a negative sign (-), respectively.

The standard deviation (

σ

) 1 ( ) ( ) 2 ( 2 2 1 2 2 1 2 1 2 1 2 1 − + + − − = n n n n n n n n n n r

σ

The null hypothesis of no autocorrelation is rejected if the Z-statistic is higher than the critical level of 1.645 (5% significance level, one-tailed test).

3.5.3 Regression analysis

Regression analysis is used as an extra check to determine the index-tracking capabilities of the various investment products. The most commonly used technique is the Ordinary Least Square (OLS) regression, which is defined as:

Where:

Rpt = return of the investment product

αp = alpha (vertical intercept) of the investment product

βp = beta (slope) of the investment product

Rbt = return of the benchmark

ε pt = error term

The objective of the regression analysis is to estimate the coefficient for βp, which is the percentage of

return of the product that can be explained by variation of the market return. A product perfectly tracking the index has a β equal to one. The more the beta deviates from one, the less the product tracks the underlying index.

The use of an OLS regression assumes no autocorrelation in the error terms, a constant variance of the error terms (homoscedasticity), normally distributed data and a linear relation between the return of the benchmark and the return of the product (Brooks, 2002). If one of these assumptions is violated, other regression techniques have to be applied, e.g. the GARCH (1,1) model. This model accounts for variance of the error terms and volatility clustering and is defined as:

pt bt p p pt

R

R

=

α

+

β

+

ε

ε

~

N

(

0

,

σ

)

+

+

=

γ

δ

ε

θ

σ

σ

This model (8) forecasts the variance of date t return as a weighted average of a constant (γp), yesterday’s

squared error (

δ

ε

σ

θ

3.5.4 The bootstrap t-test

The bootstrap method of resampling is described by Efron and Tibshirani (1993). In a bootstrap, the original sample is duplicated B times by repeatedly sampling with replacement from this one random sample. Each resample is of the same size as the original sample. The bootstrap distribution of a statistic collects the values of the statistic from many resamples and gives information about the sample distribution.

The bootstrap method allows for hypotheses testing, including the two-sample test:

1. Two independent random samples are observed, z = (z1, z2, z3, ... , zn) and y = (y1, y2, y3, ... , yn),

drawn from possibly different probability distributions F and G.

2. The null hypothesis of no difference between F and G (Ho: F = G) is tested based on a test