Are sector mutual funds superior to
country mutual funds?
Name: Kevin Kwong Shing Lam
Student number: 1525379
Supervisor: Dr. A. Plantinga
Date: 3 October 2006
Faculty: Management &
Are sector mutual funds superior to
country mutual funds?
Abstract
This paper investigates if Dutch sector funds have higher returns than country funds during the period 2000 – 2005. This question will be answered using a 4 factor model, which covers 4 geographical investment areas. The sample contains 109 country funds and 29 sector funds. Additionally, a larger sample of sector (72) and country funds (182) will be used to compare the performance during the period 2003 – 2005.
The results show that in the long run sector funds are superior to country funds. Sector funds have 0.0648% per week higher return than country funds. On annual base, sector funds significant outperform country with 3% per year during the period 2000 – 2005.
Table of content
Section 1: Introduction... 4
Section 2: Literature Review ... 4
Section 3: Overview methodology to measure excess return... 10
Section 4: Research questions... 12
4.1 Hypothesis and theoretical background... 13
Section 5: Data description ... 15
5.1: Methodology ... 16
5.2: Additional tests ... 19
Section 6: Results additional tests ... 20
6.1: Results 4 factor model... 21
6.2: Results sub period 1... 24
6.3: Results sub period 2... 26
6.4: Results 1 factor model... 27
6.5 Results sample period 2003... 27
7. Conclusion and Discussion ... 29
References ... 31
Appendix A: Regression results with dummy variable... 33
Appendix B: Regression results 6 factor model ... 35
Appendix C: Regression results 1 factor model... 36
Appendix D : Regression results 3 factor model... 37
Section 1: Introduction
RTLZ news (www.rtlz.nl, 29-12-05) reported the 10 best performing Dutch mutual funds of last year. On this list there were 6 country funds and just two sector funds. The best
performing country fund was the Indocam Himalayan Fund with a return of 101%, while the best sector fund, Postbank Energy fund had a return of 51%. Does this suggest that country funds are a better investment than sector funds? On the other hand, the rapidly increasing supply of sector funds would suggest the reverse. Otherwise, why should financial
institutions develop all those sector funds if they do not perform better?
This paper tries to answer the question; “are country funds superior to sector funds or vice versa”? This question is relevant for private investors because sector funds have increased rapidly in the Netherlands in the last years. Therefore, should private investors invest in sector funds or are county funds a better opportunity? To my knowledge this relationship has not yet been investigated by academics. This paper will provide a first impression in the relationship between the performance of sector and country funds.
Furthermore, the Dutch mutual funds performance will be analysed for the period 1999 – 2005. Prior studies conclude that on average mutual funds underperform the market by the cost of management. If this hypothesis is true, investors should choose funds with the lowest costs to maximize their return. Differences in investment styles will become irrelevant. Most studies on mutual funds performance are done in the U.S. while studies on Dutch mutual funds are scare. This study will also provide more insight in the mutual fund performance in the Netherlands. Mutual fund performance has attracted my attention because almost all private investors invest in funds. If mutual funds indeed underperform the market by the cost of management, why should investors put their money in funds? Other alternatives like, indexation or trackers1 would be more profitable.
This paper is organized as followed: section 2 will deal with prior studies on mutual funds performance, especially in the U.S. Section 3 describes different methodologies to measure the excess return. Sections 4 discuss the research questions, hypotheses and the theoretical background. Section 5 defines the data collection and the research methodology. Section 6 shows the main regression results and section 7 concludes the paper.
Section 2: Literature Review
Mutual funds have been investigated extensively by academics in the U.S. A large part of this study is devoted to mutual funds performance. The mutual fund performance is usually interpreted as the fund manager’s forecasting ability (Jensen, 1968). Jensen (1968, pp 389) defines this ability as:
1www.euronext.com defines trackers as passively managed investment funds that track indices very
“The ability to earn returns through successful prediction of security prices which are higher than those which we could expect given the riskiness of this portfolio”
This suggests that fund managers have stock selection ability, when they can earn excess return in comparison with the market. The first study was done by Sharpe (1966), who uses the reward to risk ratioto measure the performance of U.S. mutual funds from the period 1954 -1963. Sharpe (1966) demonstrates that the gross performance of U.S. mutual funds is at least as good as the Dow Jones Industrials. When the management costs of mutual funds are taken into account, funds underperformed the Dow Jones Industrials. Moreover, Jensen (1968) uses a performance measure inspired by the Capital Asset Pricing Model (CAPM) to measure the excess mutual fund performance. This measure is known as the Jensen alpha. If this Jensen’s alpha is positive, then the fund manager has stock selection ability.
Eventually, Jensen’s alpha became the basic measure to examine fund performance until the 1990’s. Jensen (1968) investigates 115 U.S. mutual funds for the period 1945 - 1964 and concludes that mutual funds on average underperform the passive benchmark. Additionally, McDonald (1974) examines a sample of 123 U.S. mutual funds from the period 1960 -1969. As a result, 5% of the funds have a Jensen alpha that is significantly different from zero at a significant level of 95%. Based on this result McDonald (1974) concludes that mutual funds in general do not outperform / underperform the market because the number of signified alphas is caused by chance. Grinblatt et al. (1989) use another approach to measure the fund performance. Instead of actual fund returns, hypothetical returns are used to measure the stock selection ability. Based on fund holdings, hypothetical returns are calculated. Grinblatt et al. (1989) believe that stock selection ability can only be measured with gross (hypothetical) returns. In their opinion, fund manager will charge a higher cost when they have stock selection ability. This will makes measuring stock selection ability with net return impossible. Furthermore, they argue that the difference between the hypothetical return and actual return should be the average transaction costs. They also use three other benchmarks to compare the results. The results show that some fund managers have superior
performance. Especially, aggressive growth funds, growth funds and fund with the lowest assets are able to beat the benchmark. However, whenmanagementcosts are taken into account, the abnormal performance vanishes. The transaction costs are estimated at 2.5% which is larger than prior studies suggested.
parameters: the S&P 500 index, bond index and non - S&P stocks. Elton et al. (1993)
present evidence that the alphas in Ippolito’s sample eventually become negative. Moreover, in their study, turnover and management fees have a negative influence on the performance. This study shows three remarkable facts about mutual fund performance. First of all, the benchmark has great influence on the performance (α). Lehman and Modest (1987) show how the benchmark choice can influence the results. Using four different methodologies to form benchmarks, the sensitivity of performance evaluation has been analysed. The result shows that using different benchmark will lead to different excess return. The sample size and the number of explanatory variables will also affect the results. In their study the CAPM gives better performance in comparison with the APT benchmarks. Secondly, still no
evidence is presented that mutual funds can beat the market. Finally, the single index model may not be well enough to explain the variation in fund performance. Still, academics are wondering if active management will be profitable and which determinants have influence on fund performance.
Academics also examine the persistence of mutual fund returns. Hendricks et al. (1993) argue that past fund performance can predict future performance. Good performance will be followed by good returns in the future, the so - called ‘’hot hand” phenomenon. While the “cold hand” phenomenon assume that funds with bad performance will followed to have bad performance. Hendricks et al. (1993) examine fund performance from 1974 - 1988 and demonstrate that poor performers will underperform their benchmarks significantly, while good performers do not significant outperform the benchmark. The difference between the top and the worst performers is about six to eight percent per year, even when the
performance is corrected for the known anomalies (firm size, dividend yield) or the
survivorship bias. Malkiel (1995) also examine the performance persistence. The results both support the “hot hand” and “cold hand” phenomenon during the 1970’s. However, this
relationship becomes weaker in the 80’s. Malkiel (1995) also developed investment
strategies to exploit this phenomenon. Buying last year’s best performers leads to an excess return during 1973 - 1981. This excess return will vanish in a later period and eventually becomes negative in 1987 -1991. In addition, Elton et al. (1996) not only found evidence supporting the short run persistence but also long term persistence of mutual fund
performance. Using modern portfolio theory (MPT) techniques, a strategy is constructed that significantly outperforms the strategy of buying past winners. Moreover, Carhart (1997) uses a 4 factor model to explain the causes of performance persistence. This model is an
performers invest a larger proportion in small caps and have lower expenses and transaction costs than the poor performers. This result indicates that active management does not pay. Furthermore, the “hot hand” phenomenon is mainly driven by the one year momentum effects.
Another issue is the impact of survivorship bias on the outcomes of academic research. Prior to the study by Malkiel (1995), academics focussed on samples that include funds that existed through the entire period of study. Funds that were terminated during this period were excluded. Malkiel (1995) confirms that survivorship bias has influence on the
performance and shows that the effects are more important than prior studies indicate. Only use a sample of survived funds, will every year lead to significant higher average return than when all funds are included during the period 1982 - 1990.This confirms the view that using only survivors will overestimate the performance. Furthermore, the study supports the general hypothesis that mutual funds underperform their benchmark, even before deduction of management costs.
Wermers (2000) continues to investigate whether mutual funds can beat their benchmark. As a result, funds on average outperform the market with 130 basis points before deduction of costs during the period 1975 -1994. When the expense ratio is taken into account funds underperform the market with 100 basis points. Wermers (2000) analyses the excess return using the three measures of Daniel et al. (1997). Daniel et al. (1997) develop three
benchmarks based on the stock characteristics (size, book to market ratio and the momentum effect) held by the portfolios that are evaluated. The three measures are the stock selection ability (CS), timing ability (CT) and return on average style (AS).
Wermers (2000) shows that fund managers on average have a CS of 71 basis point. This indicates that fund managers indeed have stock selection ability. The other 60 basis points can be attributed to AS, while there is no evidence of timing ability. The underperformance is largely due to the expense ratio and transaction costs (160 basis points).The low
performance of the non - stock holding accounts for the remaining 70 basis points. Finally, the results demonstrate that turnover has effect on the fund performance. Normally active management goes in hand with higher turnover. If active management indeed can create value, funds with a higher turnover should have a higher return than funds with a low turnover. Wermers (2000) concludes that high - turnover funds indeed outperform low - turnover funds. The difference between the top and bottom fractile is 4.3% per year. The largest part are due to the AS (2.2%) and CS (1.22%). Additionally, the highest two turnover funds are able to outperform the Vanguard Index 500 fund, even when the costs are
Prior studies usually have not focussed on the performance of sector funds. The samples mainly contain domestic funds, which also include sector funds. However, sector funds were not examined as a different group. In some studies, sector funds are excluded because these funds are not well diversified and due to there low turnover (Malkiel, 1995; Wermers, 2000). One of the first studies on sector funds is done by Della et al. (2002). Della et al. (2002) examine the stock selection and timing ability of sector fund managers. Also the sensitivity of the benchmark has been investigated. The results show that Fidelity sector mutual funds have selection ability during the period 1989 to 1998. However, the results are sensitive to the choice of the different benchmarks. When the S&P 500 is use as benchmark few sector funds have selection ability, while using the Dow Jones Industry Group or
Subgroup Index many funds have selection ability. Finally, no evidence of positive timing ability has been presented, but the negative timing ability was significant. These results are not affected by the choice of benchmark. Kacperczyk et al. (2005) investigate whether mutual funds overweight industries in comparison with their benchmark, can outperform a well diversified portfolio. Kacperczyk et al. (2005) argue that fund managers will only
indicate that concentrated funds indeed can outperform diversified portfolios. The better performance is mainly caused by better stock selection ability of concentrated funds.
Studies about mutual funds performance in Europe is done by Otten and Bams (2002). They investigate whether the 5 largest mutual funds countries in Europe (France, Germany, Italy, Netherlands and UK) are able to beat their benchmark. Both the Fama & French 3 factor model and Carhart 4 factor model are used to measure the performance. Otten and Bams (2002) show that European mutual funds are able to outperform the benchmark. Especially small caps can outperform their benchmark even when the costs are deducted. These results violate prior studies on mutual fund performance in the U.S., which indicate that on average funds underperforms the market by the cost of management. In their case the 4 factor model outperforms the 3 factor model (the adjusted R² is always higher). If the Fama & French 3 factor model will be used, the results will be affected. First of all, the performance of U.K and German funds will decrease, while the funds performance in Italy and the
Netherlands will improve. When the costs are not taken into account 4 out of the 5 countries outperformed their benchmark. Finally, there is evidence that expense ratio and age of the fund are negative related with the excess return, while the asset of the fund has a positive influence. Horst (1999) investigates the performance of 287 Dutch mutual funds for the period 1990 - 1997. The funds are divided in five groups and the performances are
measured with the reported investment style and with the estimate style. The estimated style is formed by the return base style analysis of Sharpe (1992). The results show that mutual funds, which mainly contain Dutch stocks, outperform their benchmark. In table 1 the main studies on mutual funds performance are summarized.
Table 1: summary of studies on fund performance
Auteur Period Sample Model Conclusion
Jensen ( 1968) 1945 -1964 115 funds measure Jensen Funds underperform the benchmark
McDonald (1974) 1960 -1969 123 funds measure Jensen No evidence of out – or underperformance
Grinblatt and
Titman ( 1989) 1975 - 1984 279 funds
Jensen measure
Funds underperform after costs
Ippolito (1989) 1965 - 1984 143 funds measure Jensen benchmark after costs Funds outperform the
Elton et al. (1993) 1965 - 1984 143 funds 3 factor model Funds underperform the benchmark
Malkiel ( 1995) 1971 - 1991 239 funds
Jensen measure
Funds underperform the benchmark even before costs
Wermers ( 2000) 1975 - 1994 1,788 funds DGTV (1997) measure Funds underperform the benchmark after costs
Otten ( 2002) 1991- 1998 506 funds Carhart 4 factor measure outperform the benchmark. European funds can
Kacperczyk (2005) 1984 - 1999 1,771 funds DGTV measure
Section 3: Overview methodology to measure excess return
The performance of mutual funds can be measured with different models. Prior to the 1990’s the CAPM was normally used to measure the expected return. The CAPM was developed independently by Sharpe (1964), Linter (1965) and Mossin in the 60’s. The model assumes that investors are risk averse, have homogeneous expectations and the market portfolio is efficient. CAPM predicts that the expected return is positive linear related with the β of a stock (systematic risk) and that β only affects expected return. This prediction is formalized in the so - called Security Market Line (SML). The SML can be described by equation 1. If the expected stock return is above the SML, investors will buy this stock and they are able to earn a return above the equilibrium level. Through the higher demand, the stock price will increase and the expected return will be again on the SML.
• Ri,t = Rf + βi (Rm - Rf) + εit { 1 }
Rit = expected stock return
Rf = risk free rate
βi = βi of a stock
Rm - R f = excess return on market portfolio
βi = Cov (Ri,t , Rm ) { 2 }
T²
When the SML is able to model stock returns appropriately, the excess return can be calculated with a modification of the SML (Jensen, 1968). Jensen (1968) shows that the excess return can be estimated with equation 3.
• Ri,t - Rf = αi + βi (Rm - Rf) + εit { 3 }
Rit - Rf = excess return
αi = excess return fund ( Jensen’s alpha)
βi = β of a fund
Rm - R f = excess return on market portfolio
If αi is equal to zero, the fund has performed the same as the market. When αi is larger or
smaller the fund has performed better or worse than the market.
returns are different. An investor exploits this opportunity by shorting the stock with the lowest return and buying the stock with the higher return. The investor will gain a positive return with no initial investment and risk. By exploiting this opportunity the demand and supply of the stocks will affected its price and this will lead to the new equilibrium price. The APT assumes that multiple factors can affect the expected return, while CAPM assumes that only the stock market has influence on the expected return.
In general there is no standardized APT model for calculating the excepted stock return. Factors that could explain stock return can be included in the model. Equation 4 gives a general APT model with 3 factors. The factors are oil price, interest rate and growth GDP.
• Ri,t = αi + β0 I1 + β1 I2 + β1 I3 + εit { 4 }
• Ri,t - Rf = α + β0 (Rm - Rf) + β1 SMB + β2 HML + εit { 5 }
Ri,t - Rf = excess fund return
Rm - Rf = excess return on market portfolio
SMB = difference in return between small cap portfolio and large cap portfolio HML = difference in return between a portfolio with high to market ratio and a
portfolio with a low book to market ratio.
Carhart (1997) extends the Fama & French 3 factor model with the ‘’ momentum effect’’. The momentum effects indicate an investment strategy which focuses on buying past
winners and selling past losers. This trading strategy can lead to an excess return for a short investment horizon. Carhart (1997) uses the 4 factor model to explain the persistence of mutual funds performance, by forming portfolios based on last year performance. The results show that the difference between the top and the bottom deciles is 67 basis points per month. Buying last year best performer and selling worst performers will lead to an excess return of 8% per year. Of this 67 basis point spread, almost the half (31 basis points) can be attributed to the momentum effects. Furthermore, the market factor, size, book to market ratio, expense ratio and turnover also explains a large part of the spread. Additionally, Carhart (1997) shows that expense ratio and turnover are negative related with fund performance. Every 100 basis points increase in expense ratio or turnover will decrease the return with 154 or 95 basis points. This result also supports the view that active management does not pay.
Section 4: Research questions
Main question
• Are Dutch sector funds superior to Dutch country funds during the period 2000
- 2005? Sub questions
• How was on average, the performance of Dutch mutual funds in comparison with their appropriate benchmarks during the period 2000 - 2005?
• What was the performance of Dutch sector funds during the period 2000 - 2005?
• What was the performance of Dutch country funds during the period 2000 -2005?
• Is there a difference in performance between sector funds and country funds during the period 2000 -2005?
4.1 Hypothesis and theoretical background
Mutual funds performance has been investigated extensively by academics, especially in the U.S. Most studies indicate that mutual funds on average underperform their benchmark by the cost of management (Jensen, 1968; Grinblatt et al., 1989; Elton et al., 1993; Malkiel, 1995; Wermers 2000). The underperformance indicates that fund managers are not able to pick stocks to compensate the costs. If active management does not pay, then investors should hold funds with the lowest cost to maximise their return. Based on prior studies, we will assume that Dutch mutual funds on average underperform their benchmark. The first hypothesis will be defined as.
• H1: Dutch mutual funds on average underperform their benchmark during the
period 2000 - 2005.
Furthermore, Kacperczyk et al. (2005) show that more concentrated funds can outperform well diversified funds during the period 1984 -1999. On average, diversified funds have an excess return of 0.09% per quarter, while concentrated funds have an excess return of 0.53% per quarter. These returns are measure before expenses, indicating that funds indeed can outperform their benchmark. When the cost of management is deducted similar results are presented. More concentrated funds still outperform diversified portfolio. Additionally, excess returns of concentrated funds remain positive, while the excess returns of the
• H2: Sector funds on average outperform their benchmark during the period
2000 - 2005.
The performance of country funds is harder to predict. First of all, to my knowledge there are no studies especially on the performance of country funds relative to sector funds.
Secondly, international funds are excluded in prior researches (Malkiel, 1995; Wermers, 2000; Otten 2002). However, international funds are included in my sample. Therefore, prior results on fund performances are not useful. These two restrictions make it difficult to draw a conclusion on the performance of country funds.
Moreover, there are studies on the impact of country and sector influences on diversification. Heston and Rouwenhorst (1994) investigate whether there is a relationship between country and sector effects. This relationship has been analysed using data of 12 European countries and 7 sector groups during the sample period 1978 – 1992. Heston and Rouwenhorst (1994) demonstrate that the correlation between countries are on average smaller (0.407) than the correlation between the sectors (0.704). Furthermore, industry effects have very small impact on country returns (1%). While country effects have a larger influence on industry returns (19%). This evidence shows that country effects are greater than industry effects. It could be concluded that investing in countries have more diversification effects than sector investing. Additionally, Rouwenhorst (1999) also investigates the country and industry effects in the EMU countries during the period 1978 – 1998. The results confirm that the correlation between countries (0.41) is indeed smaller than the correlation between industries (0.71). In addition, country returns are more volatile than industry returns and country effects are still larger (2.76) than industry effects (1.47), despite the greater co – operations of the EMU countries. Both studies suggest that country effects are more important than industry effects for international diversification. Thus, country funds should perform at least as well as sector funds because of their better diversified portfolio. The performance of country funds will be tested with the following hypothesis.
• H3: Country funds on average outperform their benchmark during the period
2000 – 2005.
As mentioned before country allocation has more diversification effects than industry allocation. This could lead to a higher performance than sector funds. The difference in performance between country and sector funds will be tested with hypothesis 4.
• H4:Country funds on average outperform sector funds during the period 2000 –
Section 5: Data description
The Dutch mutual funds performances are obtained from Datastream. Instead of monthly data, weekly data will be used. Otherwise, the number of observations (72 instead of 312) will be too small to draw any reliable conclusion on fund performance. The weekly return is calculated as the asset value at t minus the value at t -1 divided by 100%.
Working backwards from 1998 till 1980, all Dutch funds performances in Datastream are collected. The data is almost free of survivor bias, because all Dutch funds are included in this research. Only funds that meet the following criteria will be used for this investigation. First, funds should have at least one year of data starting from January 2000. The year 2000 is chosen as base data instead of 1999 because now two sub periods of 3 year can be formed. Sub periods of three years are used to make the results more comparable with the additional test which also has a three year time period. Furthermore, a relative short time period will be used because in 1999 the Euro was introduced in business for 12 European countries. Before this period, fund returns are affected by the exchange rate. While after the introduction of the Euro, exchange rates within these countries vanish. This difference makes it unable to use both periods in one research. Eventually, the period after the introduction of the Euro will be used. Now, most recent data can be examined and the exchange rate has almost no influence on the performance.
The second criterion is that only funds that invest at least 80% of their assets in equities should be included. Because the fund compositions were not all available. The ISIN code or fund name will be used to examine if the funds meet this criterion. After creating the
database, funds are classified into three groups: country, sector and worldwide funds. Country funds are defined as funds that are investing at least 50% of their assets into one investment area (country or region).While sector funds invest at least 50% of their assets in one sector and worldwide funds are funds that meet all the criteria but do not have one major investment area or sector. Additionally, funds are divided further into two groups: survivors and dead funds. Survivors are defined as funds which contain data for the whole time period. This suggests that the fund is active (traded) during the whole period. While a dead fund is not traded during the whole period. Due to mergers or cancellations there is only data available for a part of the time period. Starting from 2000 there are 158 funds who meet the criteria. Of these funds, 85 are classified as active funds and 73 as dead funds. Additionally, 109 funds can be classified as country funds, 29 as sector funds and 20 as worldwide funds. Dividing the sample period into sub periods will only affect the number of funds for sub period 2. In this period the number of dead funds has decreased with 19 to 54 funds.
from Datastream. When the funds did not meet the stated criteria they are removed from the database. Eventually, this database contains 182 active funds and 72 dead funds. These funds can also be classified in 182 country and 72 sector funds. The worldwide funds are not included in this sample, because the main objective is to measure the performance of
country and sector funds with a larger sample.
All data of the explanatory variables are also collected from Datastream. For the 4 factor model (see section 5.1) the MSCI Indices are used. This model contains the indices All Country Asia, Emerging Markets, EMU and Northern America. The weekly market return will be measured in the same way as the fund return. Additionally, the 1 month Euribor will be used as the risk free rate. Because this rate is annualised, it will be converted into weekly data by dividing it by 52. Furthermore, the FTSE Sector Index will become the explanatory variable in the1 factor model. This index contains ten sector groups: oil & gas, basic materials, industrials, consumer goods, consumer services, health care, telecom, utilities, financials and technology. Both models will be extended with two bond factors Default and Maturity to capture the bond influence. The default factor is measured as the difference between the return of MSCI Dutch AAA Corporate Bond and the MSCI Dutch BBB Corporate Bond. While the maturity is measured as the difference in return between MSCI Netherlands average long term bond (maturity over ten years) and the weekly Euribor.
5.1: Methodology
As mentioned before most studies prior the 1990’s used the modification of the SML by Jensen (1968) to predict the excess return of mutual funds. The intercept α, also known as the Jensen’s alpha measure the performance of the mutual fund compared with the market.
• Ri,t - Rf = αi + βi (Rm - Rf) + εit { 6 }
Rit - Rf = excess fund return
αi = excess return of the mutual fund ( Jensen’s alpha)
βi = β of the mutual fund
Rm - R f = excess return on market portfolio
If αi is equal to zero, the fund has performed the same as the market. When αi is larger or
smaller and significant the fund has performed better or worse than the market.
(size) or the book to market ratio for all the funds. Due to this restriction, a modification of the Jensen’s alpha will be introduced to measure the fund performance.
Ordinary least square (OLS) method will be used to measure excess return. Both CAPM as APT assume there is a linear relationship between β and other factors with excess return. This makes it reliable to assume OLS is an appropriate method for measuring the excess return. Two models will be used to measure the excess returns. First of all, a 4 factor model, which covers 4 geographical investment areas (Asia, Emerging Market, EMU and North America) will be used. Mutual funds normally invest in liquid and developed market. In my opinion these 4 factors should explain some variation in excess return. The performance of the investment areas will be measured with the MSCI Indices, All Countries Asia, All Countries Emerging Market, EMU and North America. Finally, the risk free rate will be measured with the 1 week Euribor. Equation 7 describes the first model of this paper.
• Ri,t - Rf = αi + β1,i (Rm, t - Rf,t) + β2,i (Rm, t - Rf,t) + β3,i (Rm, t - Rf,t) +β4, i (Rm, t - Rf, t) + εit {7}
Rit - Rf = excess fund return
αi = stock selection ability of fund
βi,j = β of the different investment areas
Rm, t - Rf, t = excess market return
However, fund managers will normally be evaluated with a benchmark, which is in line with their investment strategy. Country funds should be benchmarked with their allocation in different countries, while sector funds should be benchmarked with their sector allocation. Because prior models do not capture the sector influences a second model will be
introduced. This model just contains 1 variable. For country and worldwide funds the MSCI All Country Index will be used as explanatory variable. A broad index will be used to make the performance of country funds more comparable. Additionally, the performance of sector funds will be measured with the FTSE All Country Sector Index.
Both models will be used to examine if the results are sensitive to the choice of the
benchmark. Furthermore, two criteria will be set up to choose the appropriate model for this research. First of all, the model will be selected on the value of the average adjusted R2. The
adjusted R2 gives an indication of the explanatory power of the model. A higher adjusted R2
would indicate that the model explains the excess return better than the other model. Secondly, the model will be chosen on the average sum of the β. This value gives an
highest average R2 will eventually be chosen. In my opinion a better model would measure β
more accurately, while the reverse does not always hold.
Additionally, mutual funds do not fully invest their money in equities. Fund managers also invest a small part of their assets into bonds and cash. To capture these influences equation 7 should be adjusted for bond factors. Fama & French (1993) discover two factors related to the bond market: the maturity and default risk. These two factors explain about 97% of the excess return for high grade bonds and 49% for the low grade bonds.
Comer (2006) uses a four index model to investigate the performance of hybrid mutual funds. The four factors are high quality bonds, low quality bonds, long maturity bond and short maturity bonds. Eventually, the bond factors describe by Fama & French (1993) will be used to capture the bond influence. Only the default factor will be measured on a different way. Instead of taking the difference between the return of long term corporate bond and long term government bond return. We will measure default as the spread between the MSCI Dutch long term AAA Corporate Bond and the MSCI Dutch long term BBB Corporate Bond. This factor should capture the default on corporate bonds. Furthermore, the maturity will be measured as the difference in return between the return on MSCI Netherlands long term bond and the 1 week Euribor.
The 4 factors of Comer (2006) will not be used; otherwise the model will contain 8 factors. This will makes it hard to interpret the results. In addition, Fama & French (1993) show that their bond factors explain most of the variation in excess return. The 6 factor model is given by equation 8.
• Ri,t - Rf = αi + β1,i (Rm, t - Rf,t) + β2,i (Rm, t - Rf,t) + β3,i (Rm, t - Rf,t) + β4,i (Rm, t - Rf,t)
+ β5,i (Rca, t - Rcb,t ) + β6,i (R g,t - Rf ,t ) + εit { 8 }
Rit - Rf = excess return fund
αi = stock selection ability of fund
βi, j = β of investment areas
Rca, t - Rcb, t = difference between the return of AAA corporate bond and the return on BBB
corporate bond (default risk)
Rg, t - Rf, t = difference between the return of long term government bond the 1 week
Euribor (maturity)
5.2: Additional tests
After the appropriate model is chosen, based on the highest adjusted R2 and the average
sum of β. Some additional tests are required to ensure that OLS is the appropriate method for measuring the fund performance. Brooks (2002) describes 5 assumptions to make OLS estimators become best linear unbiased estimators (BLUE). The five assumptions to make the OLS estimators BLUE are; the average value of the errors should be zero. Secondly, the variance of the errors is constant. Thirdly, the covariance of the errors is zero. Fourthly, the values are non – stochastic and finally the errors are normally distributed. The last
assumption is optional and is necessary to make valid inference about the population. We will conduct additional test to examine if the assumptions are not violated.
When all the assumptions are meet, Brooks (2002) argues that the estimators will contain four main characteristics. First, the estimator β has the minimum variance in comparison with other estimators (Best). Secondly, the estimators have a linear relationship (Linear). Thirdly, on average the estimators will be equal to the actual values (Unbiased). Finally, the
estimators estimate the true values (Estimators).
Brooks (2002) states that the first assumption will never be violated when there is a constant in the model. Because there is a constant in the model assumption 1 is not violated. The second assumption can be tested with White’s heteroscedasticity test. If the errors are heteroscedastic, OLS estimators will no longer be BLUE. The estimators will become inappropriate and could lead to misleading inference. When there is heteroscedasticity, this problem will be solved by rerunning the regressions with White’s heteroscedasticity
consistent error estimates. The third assumption can be examined with the Durbin - Watson (DW) test. The DW test assumes that errors at time t -1 are not correlated with the errors at time t. The presence of autocorrelation will be analysed with the 5% critical values of DW. When autocorrelation is presence the OLS estimators will not be efficient anymore. The estimators will not have the lowest variance in comparison with other models. Also the standard errors will be measured inappropriate which could lead to wrong conclusions. The presence of autocorrelation can be solved by rerunning the OLS regressions with Newey - West standard errors. Furthermore, Brooks (2002) states that (chapter 3, pp. 56):
residuals normal distributed. Moreover, Elton et al. (2003) state that factors in a multi index model should be uncorrelated. The correlation matrix shows that the correlations between the factors are relatively high. The highest correlation (0.81) is between EMU and Northern America, while the lowest is correlation (0.48) is between EMU and Asia. This suggests that the factors should be made uncorrelated before it can be used. The factors are made uncorrelated using the methodology describes by Elton et al. (2003).
Section 6: Results additional tests
Based on the regression results of the 1 and 4 factor model, the main model of this study will be
selected. The average adjusted R2 is 0.41 for the 4 factor model and 0.28 for the 1 factor
model. According to the first criteria the 4 factor model seems to be superior to the 1 factor model. Furthermore, the average sum of beta will also be used to evaluate the models. Normally the sum of betas should be 1. If this is the case, the model explains all the
allocation of a fund. In my case, the 4 factor model has an average sum of beta of 0.90 and 0.57 for the 1 factor model. This suggests that 90% of the exposure is explained by the 4 factor model. Both tests indicate that the 4 factor model is indeed outperforming the 1 factor. As a result, the 4 factor model should be used as the leading model.
After the main model has been selected, additional tests will be conducted to explore if the 5 assumptions described in section 5.3 are not violated. Assumption 1 and 4 are not violated because a constant is included in model, namely α. This makes the errors have an average value of zero and that the coefficients are non – stochastic. The presence of
heteroscedasticity is examined with White’s heteroscedasticity test. This test shows that almost two - third (101 out of 158) of the funds rejects H0 at 10% level. The rejection of H0
indicates the presence of heteroscedasticity. Rerun the regressions with White’s
manipulate the data too much. Rerun the regressions with a dummy variable, will increase the number of residuals with a normal distribution with 19 funds to 41 funds. Still the non – normal distribution is dominated. The regression results with a dummy variable are
presented in Appendix A1.The result of a t - test confirms that the performance measured with a dummy variable are not significant different than without a dummy variable.
To sum up, the main results of the additional tests. The data show presence of heteroscedasticity and negative autocorrelation. When this is corrected with White’s
heteroscedasticity consistent error estimates or Newey - West standard errors the magnitude of α is not affected. Only the standard error of α will reduce, which result in more funds significantly underperform / outperform the benchmark. Furthermore, adding a dummy variable in the model will lead to a small increase in the number of normal distributed residuals. The dummy variable will affect the magnitude of α but the differences are not significant. Therefore, OLS with no correct or a dummy variable will be used to measure α.
6.1: Results 4 factor model
Table 2 reports the main variables of the regressions over the period 2000 – 2005. The first variable is the excess return (α) of the fund groups. The excess return is measured in percentage per week. The first figure shows that Dutch mutual funds underperform the benchmark with 0.0249% per week and is significant at 5% level. When this performance is annualized, funds on average underperform the benchmark with 1.30%. This result is in line with prior studies, which suggest that funds underperform the benchmark by the cost of management. Because Dutch funds normally charge a cost between the 1 and 2 percentage. Furthermore, excluding the worldwide funds make the underperformance lower (0.0203%) but it is still significant at 10% level. The worldwide funds are excluded in the second column because these funds have the poorest performance, which could affect the results.
Both results support H1 that Dutch mutual funds underperform the benchmark by the costs.
The performances of sector and country funds are also presented in table 2. Country funds significant underperform the benchmark with 0.0339% per week, while sector funds have a positive α of 0.0309% per week. The positive α, supports the results of Kacperczyk et al. (2005). Kacperczyk et al. (2005) demonstrate that more concentrated funds are able to outperform the benchmark. Because the results are insignificant, hypothesis 2 can not be accepted or rejected. As a result, no evidence is presented that sector funds are able to outperform their benchmark. In contrast, country funds do significant underperform the benchmark. Therefore, H3 can be rejected. When the performances of sector and country
funds are combined, H4 can also be rejected. Country funds are not superior to sector funds,
Table 2 also presents the average exposure (β) of the 4 factor model. In general, Dutch mutual funds have a long position in the European Union (0.59), Asia (0.33) and in the Emerging Markets (0.01), while there is a short position in Northern America (-0.03). Country funds have similar exposure as the average Dutch fund. On the other hand, sector funds have a negative exposure in the Emerging market (-0.08) and a positive exposure in Northern America (0.09). A t - test confirms that the exposure in the Emerging Markets and Northern America are significant different at 1% level for sector and country funds. This difference could be a reason of the underperformance of country funds. Unfortunately, data of fund holdings are not available. This makes it impossible to investigate whether sector funds indeed have a larger allocation in Northern America and a smaller in the Emerging Markets than country funds.
Besides the 4 factor model a 6 factor model will be used to measure the Dutch funds performance. The extended model contains two bond factors (default and maturity). This model will be introduced to examine if bond factors have influence on prior results. The results of the 6 factor model are presented in appendix B1.The figures show that the 6 factor model has no influence on the conclusion. Dutch mutual funds still underperform the benchmark and sector funds are also superior to country funds. Although, both model will lead to the same conclusion two remarks should be placed. First of all, the excess returns of all funds groups have decreased and secondly the underperformance has become more significant. The decline in excess return is caused by the allocation of bond. Mutual funds invest some of their assets in bonds and bonds normally have a lower return than stocks. Eventually, this will reduce the expected return. Through the lower return the
underperformance will also become more significant. Only the excess return of country funds has decreased significant when the bond factors were added in the model. This result
demonstrates that country funds have a larger allocation in bonds in comparison with sector funds. This difference could also be a reason for the underperformance of country funds. Finally, the adjusted R2 has increased with 3 % for all fund types, indicating that the bond
factors have explanatory power on excess return.
6.2: Results sub period 1
that 54 of the residuals have a normal distribution. Using a dummy variable in the model will increase this number with 32 to 86. As mentioned before, the presence of heteroscedasticity and negative autocorrelation will not affect the magnitude of α, while using a dummy variable does. Rerun the regressions with White’s heteroscedasticity consistent error estimates and the Newey - West standard error confirms this view. However, the dummy variable will affect α. The regression results with a dummy variable are shown in appendix A2. Using a t - test shows that the excess returns of sector and country funds are not significant different. Therefore, “normal” regression will also be used for sub period 1.
The results of sub period 1 (2000 – 2002) are given in table 3. Now, all funds groups underperform the benchmark. Only sector funds do not significant underperform the benchmark. These results again support H1 that funds underperform the benchmark. On
average, Dutch mutual funds underperform the benchmark with -0.1375% per week. When this performance is annualized, Dutch funds underperform the benchmark with 7% per year during this period. This underperformance is larger than prior studies suggests. One possible explanation of this large underperformance could be that mutual funds have a riskier portfolio than the market portfolio. During a bear period (sub period 1) mutual funds will have a
greater loss than the benchmark. We have classified sub period 1 as a bear period because all the four MSCI indices have a negative average weekly return during this period.
Unfortunately, this explanation is not supported by the results. The 4 factor model shows that the sum of β is just 0.85. Because the β is below unity, the portfolio is less risky than the market portfolio. Moreover, table 3 shows that country funds underperform the benchmark with 0.1604% per week, while sector funds have a return of -0.0281% per week. Thus H2 can
not be accepted or rejected, while H3 can be rejected. Still there is no evidence presented
that sector funds can outperform the benchmark. However, the result shows that country funds on average underperform the benchmark. Using a t - test demonstrates that the difference in performance between sector and country funds is significant at 1% level. This result also supports the rejection of hypothesis 4 and shows again that sector funds are superior to country funds.
Finally, table 3 shows the average exposure of the funds during sub period 1.
6.3: Results sub period 2
For sub period 2 similar results are found for the additional tests. The data contains the same amount of heteroscedasticity and normal distributed residuals as prior period. However, the amount of negative correlation has reduced to over 50%. The regression results with dummy variable are presented in appendix A3. The dummy variable will increase the number of normal distributed residuals with 33 to 91. But the excess returns are still not significant different than without the dummy variable.
The results of sub period 2 (2003 – 2005) are more striking. Besides the worldwide funds, all other funds significant outperform their benchmark. These results are presented in table 4. The results support the rejections of H0 that Dutch mutual funds do underperform their
benchmark. Instead of the underperformance, funds are able to significant outperform the market. The average excess return is 0.0748% per week for all the Dutch funds. This shows that mutual funds are able to outperform the benchmark in the short run. While in the long run funds underperform the market significant.
Further, the results show that country funds have an excess return of 0.0889% and sector funds 0.0859% per week. These results support H2 and H3 that sector and country funds can
outperform the benchmark. While, H4 can not be accepted or rejected because the difference
in performance is not significant. The results indicate that there is no clear evidence on the performance of country funds in comparison to sector funds. Eventually, this paper shows that in the long run sector funds indeed have higher returns than country funds. However, this result is not consistent for both sub periods. During sub period 2 the exposure of both fund types has also changed. Now, both funds only have long positions. But still there is a difference in the amount of exposure in Northern America.
the four MSCI indices had a positive average weekly return during this period. The 4 factor model confirms this view for sub period 2. During this period the average sum of beta is 1.15. This indicates that funds indeed have a riskier portfolio than the market.
6.4: Results 1 factor model
The 4 factor model seems a better model than the1 factor model for this research. Still, the 1 factor model will be used to examine the Dutch mutual funds performance. This model will be used to investigate whether a complete different model will support my prior conclusions. For sector funds the FTSE Sector Indices will be used as explanatory variable and the MSCI Worldwide Index for the country and worldwide funds. The regression results are shown in appendix C. The results for the whole sample period and sub period 1 are in line with the 4 factor model. During these periods Dutch mutual funds underperform the benchmark and sector funds have significant higher return than country funds. Additionally, during sub period 2 sector funds perform better than country funds. The difference is not significant but it supports the view that sector funds are better investment than country funds.
Extending the model with bond factors will only influence the conclusions for sub period 2. Dutch mutual funds and country do not significant outperform the benchmark, while sector funds do. The results of the 3 factor model are shown in appendix D. The 3 factor model shows that sector funds are indeed superior to country funds even in the short run.
6.5 Results sample period 2003
Prior tests contain a relative small sample of sector funds. Just 29 sector funds are used for the whole sample period and sub period 1, while during sub period 2 there are just 26 sector funds. Especially, during the last period there is no clear answer on the performance of sector funds. The 4 factor model shows that sector underperform country funds while the other three models show the reverse. In my opinion this could be caused by the small sample of sector funds. To increase the sample of sector funds, an additional test will be conducted with data from 2003. Starting the test from 2003 will increase the number of sector funds with 43 to 72 and country funds with 73 to 182. This new sample will be used to
without the dummy variable (see appendix A4). Table 5 shows the regression results of sample period 2003.
Table 5: regression results sample period 2003
All Funds All Country Funds All Sector Funds
All All Survivors Dead All Survivors Dead
Mean α 0.0327* 0.0253** 0.0169 0.0510** 0.0512* 0.0525** 0.0492*** T statistics 2.64 1.68 0.92 2.04 2.40 1.89 1.45 SDTV 0.0020 0.0020 0.0021 0.0017 0.0018 0.0019 0.0018 R 0.59 0.62 0.60 0.66 0.54 0.48 0.65 Average DW 2.38 2.44 2.46 2.37 2.23 2.22 2.26 Average BJ 1,540 1,564 2,057 76 1,481 2,351 30 Average βas 0.15 0.15 0.17 0.09 0.13 0.15 0.11 Average βem 0.21 0.19 0.11 0.42 0.26 0.22 0.33 Average βeu 0.80 0.80 0.79 0.81 0.81 0.74 0.93 Average βna 0.12 0.03 0.04 0.00 0.35 0.26 0.50 N 254 182 137 45 72 45 27
* = significant at 1 % level; ** = significant at 5 % level; *** = significant at 10% level The results are in line with prior results of sub period 2. Dutch mutual funds still significant outperform the benchmark during a bull market. The same results are presented for sector and country funds. However, sector funds now outperform country funds. Table 5 shows that sector funds have an excess return of 0.0512% per week and country funds 0.0253% per week. Although the difference is not significant, it confirms prior results that sector funds are indeed superior to country funds.
7. Conclusion and Discussion
In this paper the performance of sector and country funds has been investigated for the period 2000 – 2005. The Dutch mutual funds performance has been analysed with a 4 factor model, which covers 4 geographical investment areas (Asia, Emerging Markets, Europe and Northern America). This model has been chosen because it had a higher sum of beta and R2
than the 1 factor model. Although, the data contain heteroscedasticity and negative autocorrelation, the magnitude of α has not been affected. This result is confirmed by adjusting the regression results with White’s heteroscedasticity consistent error estimates and the Newey - West standard errors. The residuals also showed a domination of non - normal distribution. This problem has been solved by adding a dummy variable in model. The dummy variable made more residuals normal distributed but the non - normal distribution still dominates. Finally, the results with a dummy variable were not significant different than without a dummy variable. This made it reasonable to use the 4 factor model to measure α. Furthermore, a second model has been used to control the test results. This 1 factor model covers a broad index to measure the performance. The FTSE Sector Index has been used for the sector funds and the MSCI Worldwide Index for country and worldwide funds. Both models were extended with two bond factor (default and maturity) to capture the bond influence.
Finally, a second test was conducted for sub period 2 because of the small sample of sector funds. This test examined whether the results are not affected through outliers. The new sample contains 72 sector funds and 182 country funds. In contrast to the 4 factor model, the three other models showed that sector funds significant outperform country funds. This result confirmed that sector funds were indeed superior to country funds even in the short run. In conclusion, this paper showed that in the long run sector funds had significant higher returns than country funds. Also evidence for outperformance in the short run is presented. Furthermore, Dutch mutual funds significant underperform the benchmark in the long run, while in the short run funds can both underperform / outperform the benchmark.
The results of this paper could be affected by the small sample of sector funds. For this research only 29 sector funds are included. Due to this small sample, the performance of sector funds could be measured to high through outliers. In my case, real estate funds
significant outperform the benchmark. Because the models do not contain a real estate factor there could be a benchmark error. The benchmark problem can be solved by using Daniel et al. (1997) measures. Daniel et al. (1997) form benchmarks base on stock characterises (size, book to market ration and) and not on stock allocation.
Furthermore, this investigation uses a small time frame (6 years) in comparison with prior studies, which use a time period of at least 10 years. Additionally, this paper does not give a clear explanation of the causes of the superior performance of sector funds. Including fund characteristics (size, turnover, age, and costs) could explain the different.
On a final note, the 4 factor model has a relative low adjusted R2 (0.41) in comparison with
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