Searching for the return on locality
in the Province of Groningen
Abstract: The home equity bias of investors and the closely related regional bias are a predominant theme within behavioral finance. The popular explanation for these two phenomena is that investors prefer stocks of nearby companies because of their familiarity. However it may also be possible that home biased investors benefit from an informational advantage because of their vicinity. This hypothesis is studied for the Dutch province of Groningen. I have built a portfolio of local stocks, and have evaluated its performance between 2003 and 2009. As I do not find a statistically significant alpha (Jensen (1968)), the portfolio does not benefit from an informational advantage.
JEL Codes: G11, D03
Searching for the return on locality
in the Province of Groningen
Master Thesis
University of Groningen Faculty of Economics
1. Introduction
An important topic in behavioral finance is the home bias of investors. Investors display a strong preference to holding stocks of companies located in their home country (French and Poterba (1991)) and even more specifically in their own region (Coval and Moskowitz (1999), Ivković and Weisbenner (2005)). Focusing predominantly on local stocks may hurt an investor’s expected returns. Moreover, an investor can reduce the variance of his returns by diversifying internationally (Levy and Sarnat (1970))
Notwithstanding the benefits of international diversification, a higher emphasis on investments in one’s vicinity may have some merits of its own. An investor who focuses on his own region can be better informed than an investor who has to monitor an entire country or continent. This informational advantage could give the private investor a superior stock picking ability. Ivković and Weisbenner (2005) find that individual investors gain higher returns on their local stocks than on their non-local stocks. Furthermore, by investing locally, one can reap indirect benefits by stimulating the local economy. Lastly, as Huberman (2001) describes, investors are drawn to familiar, and thus local, companies. As the familiarity of investment opportunities increases, investors feel more competent to make decisions regarding such investments.
This means that investors are faced with an implicit tradeoff between on the one hand the gains from diversification, and on the other hand the feeling of familiarity which is hard to put a price on. In addition, they may also benefit from a hypothetical informational advantage due to living close to their investments. This tradeoff is unclear. As a matter of fact, it is questionable whether investors even make a conscious decision between either diversification or familiarity when it comes to their investment portfolios. This is why I want to research how an investment strategy with a regional bias actually performs. Is its performance acceptable or not? I have chosen to direct my attention to a regional investment strategy for the province of Groningen. My research question is whether an investor wins or loses if he invests in a regional portfolio instead of a passive market portfolio.
Using employment records about the province, I have built a portfolio of stocks representing the regional economy of Groningen. The weights of the stocks are based on the number of
The portfolio’s performance is analyzed by regression analysis to calculate Jensen’s alpha (Jensen (1968)). Jensen´s alpha is often used to test whether a portfolio has a higher return than a passive portfolio with an equal systematic risk. I use three asset pricing models to calculate Jensen´s alpha. The first model is the Capital Asset Pricing Model1, which assumes the only
source of systematic risk is the portfolio´s sensitivity, β, to the return on the market (Rmt). The
second model is that of Fama and French (1993), who find that the market return beta alone is insufficient to explain the variance of portfolio returns. Fama and French find that returns can be explained better when market capitalization (SMBt; Small Minus Big) and market-to-book value
(HMLt; High Minus Low) are added as explanatory variables. The final model is that from Carhart
(1997). In the Carhart model, the one year momentum effect in stock returns is added as an explanatory variable (MOMt). The alpha that is left when these four explanatory variables (or
“factors” in financial terminology) are taken account is the risk adjusted return of the portfolio. If the portfolio has a statistically significant positive alpha, there is added value from following a regional strategy. On the other hand, the return of the portfolio can also be interpreted as an anchoring point for the return an investor in Groningen can earn from following a regional strategy.
The empirical research in this thesis is relevant for the following reasons. If there is indeed added value from following a regional strategy, e.g. a significant positive alpha, then the “return on locality” as hypothesized by Ivkovic and Weisbenner (2005) is validated as a rational
explanation for the home equity bias. But even when there is no added value, and the home equity bias is indeed an irrational trait of investors, is that really that bad? Just as long as Jensen’s alpha is not significantly lower than zero, the investor still earns a risk adjusted return comparable to that of a passive market portfolio.
The rest of this thesis is structured as follows; section two is a literature review of the home bias. Section three further explains the research methodology. Section four presents details about the data used, the portfolio’s composition and summary statistics. The results from the regressions are in section five. The conclusions from my research are in section six.
1 As developed by Sharpe (1964); Lintner (1965); Mossin (1966); referred to in the rest of this thesis as
2. Literature review
In this thesis I explore whether the preference of investors for geographically close investments is sensible or not. Since the preference for geographically close investments is present at both the national and the regional level I make a distinction between the home bias and the regional bias. In this thesis, the home or home equity bias refers to the tendency of investors to hold equity portfolios consisting of predominantly domestic stocks. The regional or local bias refers to the preference for nearby stocks within the investors’ country (Coval and Moskowitz (1999))
In the following sub sections, I explain first why the home bias is seen as an anomaly. Then I present two economic explanations for the home bias that are predominant in literature: firstly, barriers to and costs of international investment, and secondly, hedging needs of investors. Since both are unable to explain the home and regional bias, I argue that it is a behavioral matter. In the last section, it is debated whether or not this type of investor behavior has a rational grounding: the return on locality.
A. Home and regional bias puzzle
International diversification of portfolios is beneficial for investors in two ways. First of all, going abroad can increase the expected return on a portfolio. This can be done for instance by investing in foreign markets with positive abnormal returns. But more importantly,
international diversification of equity portfolios reduces their risk. Because large positive and negative returns cancel each other out, the variance of the portfolio’s returns is reduced. Ample evidence on particularly the reduction of variance through international diversification can be found in Grubel (1968), Levy and Sarnat (1970) and Solnik (1974).
French and Poterba (1991) is one of the seminal papers about the home equity bias of investors. At the time the paper was written, investors from the US, Japan and the UK invested respectively 93.8 %; 98.1% and 82% of their equity portfolios in stocks from their home country. It is
contradictory to modern portfolio theory. Kang and Stulz (1997) states: “if investors care only
about the mean and variance of their real return of their invested wealth (...) one would expect investors, as a first approximation, to hold the world portfolio of stocks..”, yet studies consistently
show that investors are investing the majority of their wealth in domestic equity (Tesar and Werner (1995), French and Poterba (1991)).
B. Barriers and costs of international investment
The home equity bias of investors might be explained by the fact that international
diversification of equity holdings is harder to achieve and more costly than simply holding domestic equity. International investment may be hampered by the following factors: (1) restricted access to capital markets for foreign investors, (2) institutional limits on foreign investment, (3) differences in taxes and (4) higher transaction costs. All these four factors fall short in explaining the home country bias and bear no relation to the regional bias at all.
French and Poterba (1991) debunk the first three explanations. First of all, most countries have abolished regulation that prevented or limited foreign parties from having access to their capital markets. Second, institutional limits on foreign investments still exist for pension funds and the like, but the proportion of foreign investment in those cases is still less than what is explicitly allowed. And thirdly, while withholding taxes on dividends etc. differ from country to country, the actual differences in taxes paid are marginal. Also, in general an investor can use withheld taxes from abroad as a tax credit in his home country.
C. Hedging needs of investors
A different type of explanation for the home bias in equity portfolios is that investors hold domestic assets in order to hedge against inflation and price uncertainty in their home country. Residents of different countries consume different baskets of goods, which leads to different levels of inflation per country. This country specific inflation risk is then hedged by investors by holding a portfolio with a home equity bias. Adler and Dumas (1983) develop a model of how inflation risk is hedged in this manner. Not only do the baskets of goods consumed by residents differ from country to country, residents also own (non-equity) assets and consume goods that are not traded across borders. These non-traded assets and goods are subject to inflation and price shocks. Residents therefore face uncertainty with regard to their future wealth and
consumption levels. Stockman and Dellas (1989) develop a model wherein residents hold equity in their home country in order to hedge against this price uncertainty.
However, this is not the whole picture. Cooper and Kaplanis (1994) use the model from Adler & Dumas (1983) and extend it with the assumption that all investors have an equal risk tolerance. The empirical test of their model has a rather counter intuitive conclusion. It concludes that risk averse investors will not hedge inflation risk by holding a home biased equity portfolio. Since the average investor is risk averse, hedging inflation risks is not an explanation for the home bias as proposed by Adler and Dumas (1983). The hypothesis that hedging against price uncertainty and inflation of non-traded goods explains the home bias (Stockman and Dellas (1989)) is refuted by Baxter and Jermann (1997). Baxter and Jermann argue that human capital is the most important non-traded good, since about 60% of a nation’s income is generated through labor. The wages received by workers can be seen as the return on human capital, and the wages received are positively correlated with the returns on the domestic capital market. Baxter and Jermann establish in their paper that if an investor wants to hedge price risk regarding non-traded goods, e.g. his own salary, he should take a short position in domestic equity rather than a long position. Given the findings from Cooper and Kaplanis (1994) and Baxter and Jermann (1997), hedging motives are not a credible explanation for the home equity bias.
D. Investor behavior and return on locality
Huberman (2001) offers the most persuasive justification for this view. Huberman shows that the majority of shares of Regional Bell Operating Companies (RBOCs) are held by investors from the same region. These shareholders are often also customers from the same RBOC. This
phenomenon is driven by investors’ preference for stocks of familiar companies. Because the companies in which they invest are familiar to them, they feel comfortable about where they place their wealth.
Apart from feeling more comfortable about investing in familiar stocks, investors may also have an informational advantage if they invest in nearby companies. Coval and Moskowitz (2001) show that professional fund managers earn better returns on their nearby investments than on their remote investments. Individual investors may also be able to benefit from the same informational advantage; the “return on locality”. Ivković and Weisbenner (2005) find that private investors earn a 3.2% higher annual return on their local shares then on their remote holdings. This difference is even larger for stocks outside of the S&P 500. An explanation for this excess return is that investors have a better ability to monitor investment opportunities within their region, especially for smaller companies that attract less media attention.
However, Seasholes and Zhu (2010) challenge the findings from Ivković and Weisbenner (2005); criticizing mainly their methodology. Seasholes and Zhu (2010) apply a different methodology to the same dataset. They find that when a local equity risk premium is added as a control variable, local holdings do not outperform non-local holdings. Their second finding comes from aggregate portfolios of investors’ buys minus their sells. These portfolios consistently have an
economically and statistically significant negative alpha on both local and non-local holdings, both inside and outside the S&P 500. This leads Seasholes and Zhu to the conclusion that private investors do not possess superior information on local companies. Given these findings, it is questionable whether individual investors are able to exploit the return on locality the way professional fund managers can.
3. Methodology
In this section I explain how the regional portfolio returns are analyzed using the framework of Jensen (1968), the CAPM model, Fama and French (1993) and Carhart (1997). First, it is
important to explain how the portfolio is formed and how the returns are defined. The
portfolio’s returns are measured on a weekly interval using return indices from Datastream. The weighting of companies is based on their employee count within the province of Groningen; sub-section A goes in to more detail on this. Sub-sub-section B explains how the performance of the portfolio is evaluated using regression analysis. Sub-section C presents my hypotheses regarding the results from the regression analysis.
A. Portfolio composition and returns
Consider an investor from the province of Groningen who has a preference for nearby and familiar investments. Based on which attributes would he choose his stocks? Would the weights of the companies be based on their number of subsidiaries, the size of terms of their local revenues or the amount of people it employs?
In the regional portfolio I have built, the weights of the companies are based on the quantity of employees in Groningen of each company. This is done for a number of reasons. First of all, regional data about revenues of firms are unavailable or otherwise restricted. Basing weights on the number of subsidiaries would be too arbitrary since it would mean that any subsidiary would have the same weighting, regardless of its size or economic importance. Thus, basing the weighting on employment data makes more sense. It also makes more sense from the viewpoint of the investor to pick stocks in such a manner. The larger the employer, the more familiar its name becomes to the investor. Individual investors are biased towards familiar and local stocks because they feel more confident about their investment decisions that way (Huberman (2001)). Given that employment is the easiest variable to measure and is closely related to familiarity, the weights of stocks are based on the number of people each listed company within the province of Groningen employs.
The weight of each stock within the portfolio is determined at the start of each year given the number of employees it has in that year. This yearly rebalancing ensures that portfolio weights stay in line with changes in employment. The total numbers of employees per company change only gradually every year the weight wij of each stock i is calculated as follows:
(3.1)
Where i denotes the listed company and j denotes the year on which the employment data are based, with 2003 as year 0. Simply put: a company’s portfolio weight in year j is equal to the number of employees it has in year j divided by the sum of all employees in that year’s data sample.
Given these portfolio weights, the portfolio’s weekly return Rpt is measured as:
(3.2)
Where RIi,t is the return index number of stock i at time t and RIi,t-1 is the return index number
from one week before time t. Note that I take the natural logarithm of the portfolio’s simple return to alleviate issues with non-normality due to outliers. This also gives the returns the property that they are continuously compounded. These weekly returns are used in the time series regressions that are explored in the following sub-section.
B. Portfolio evaluation
In order to evaluate the performance of the regional portfolio which was developed in the previous section, I calculate Jensen’s alpha (Jensen (1968) based on three different asset pricing models. The following three asset pricing models are used: the Capital Asset Pricing Model, the Fama and French (1993) three factor model and the Carhart (1997) four factor model. When in any of the three regressions alpha is found to be positive, it means the portfolio’s return is in excess of what can be explained by the model in question. Such an excess return means that there is added value from the portfolio’s composition. The calculations of the respective alphas are in equations 3.2, 3.4 and 3.4.
(3.4)
(3.5)
In these equations Rpt is the portfolio’s weekly return as defined in equation 3.2 and Rft is the 3
month Euribor rate. The constants αCAPM, αFF and αCAR are the alphas calculated with respectively
the CAPM, Fama and French (1993) three factor and the Carhart (1997) four factor models. The variable Rmt - Rft, is the excess return of the equity market over the risk free interest rate;
commonly known as the equity risk premium. SMBt, and HMLt respectively represent the excess
returns of small cap over large cap stocks and those of value over growth stocks. MOMt
represents the one year momentum factor from a portfolio long on last year’s winners and short on last year’s losers. Finally, εt represents the residuals in the regression. I use index data from
MSCI to proxy for these four variables. The returns of the four factors are calculated with continuous compounding just as in equation 3.2. The indices used as proxies can be found in table 3 in the data section.
C. Hypotheses
A priori I do not expect the portfolio to have an excess return in the form of a statistically
significant positive alpha for any of the three asset pricing models. The following hypotheses will be tested:
H1:
H2:
H3:
I do not expect the regional portfolio to beat any of the benchmarks. The regional portfolio is rebalanced every year as of January 1, based on changes in employment. This type of
rebalancing makes any market timing effects very unlikely. There is also no expected gain from stock picking because all listed companies in the province are included. Finally, I do not expect that the portfolio can benefit from any “return on locality” as described in Ivkovic and
their location. This last statement deserves a more elaborate explanation, which can be found in the next two paragraphs.
The average distance between investors and company headquarters is a lot smaller in the Netherlands than in the US. Both Ivkovic and Weisbenner (2005) and Seasholes and Zhu (2010) define local companies as those headquartered within 250 mile radius of the investor. In the Dutch case, that would make any company in the Netherlands a local company. Coval and Moskowitz (2001) narrow this definition down to companies within a 100 kilometer radius of a fund manager. But even then, for a fund manager based in the Randstad area, the majority of companies in the Netherlands would be considered local. The small average distance between investor and company headquarters makes any informational advantage based on location less likely. For an investor in Groningen there is another problem as there are no listed companies headquartered in Groningen, Friesland or Drenthe.
The way in which companies seek financing also differs greatly between the US and the
Netherlands. In the US, it is very common for small and relatively unknown companies to go to the stock market to raise capital (Rajan and Zingales (2003)). However, in the Netherlands, such companies often seek financing through intermediaries such as banks. The companies that are traded on the Dutch stock market are generally well known and active across the whole country. Thus there are probably not that many “dark horses”; stocks that earn an excess return to compensate for their relative anonymity (Garcia and Norli (2010)).
In conclusion, the small average distance between investors and firms and the conjectured lack of dark horse stocks make any return on locality unlikely for the regional portfolio. As was explained earlier, there are also no expected gains from selective stock picking or market timing. It is therefore not probable that the portfolio yields an alpha significantly different from zero. Consequently, hypotheses H1, H2 and H3 are that Jensen’s alpha is zero for all three models.
4. Data
The empirical research in this thesis is done using secondary data about employment in the province of Groningen and return data on stocks from Thomson’s Datastream. The first part of this section describes how the employment data have been processed in order to build a portfolio of stocks and sheds some light on the companies which are included in this portfolio. The second part will give the more details on the return data used in the regression analysis. Because of issues with non-normality and availability of return data, summary statistics are only presented as of the 2nd of June 2003 until the 31st of December 2009. But to paint the most
complete picture, statistics about the employment data and portfolio composition are presented from 1996 until 2009. This section is concluded by a discussion of the summary statistics on the variables used in regression analysis.
A. Portfolio composition
The employment data used to build a stock portfolio for the province of Groningen are taken from the Lisa database. The Lisa database is an initiative of several public and private
organizations which cooperate to keep track of developments in employment across economic sectors and regions within the Netherlands. Examples of cooperating organizations are
provinces, municipalities and the Central Bureau of Statistics. Lisa keeps a registry on economic “establishments”, which can either be a branch office or subsidiary of a listed company or an independent business. Information about location, economic activity and employment is available for every separate establishment. The exchange of information between many actors enables Lisa to compile a very complete database. Lisa releases a new database every year which includes revisions of former years, when applicable. Thanks to the Lisa data it is possible to build an accurate stock portfolio with weightings based on employees.
During the years for which Lisa data is available, the number of listed companies active within the province has risen from 73 in 1996 to 111 in 2009. However, the data does not suffer from survivorship bias because a total of 120 listed companies were identified between 1996 and 2009. Over the years, more listed companies established themselves rather than left. More specific figures can be found in table 1. A different trend that is visible in the data is that the fraction of the effective working population that is employed by a listed company2 has risen
from 6.36% in 1996 to 9.39% in 2009. This trend could be explained by small companies being consolidated by larger, often listed, companies.
In the next step, the data about listed companies were enriched with sector information following the ICB3 classification system. The weights of the ICB sectors within the portfolio can
be found in table 2. It can be inferred from table 2 that a large proportion of the listed companies in Groningen operate in the consumer services (30.7%) or industrial (26.6%) sector. Health care (0.2%) and Oil & Gas (0.8%) companies are very marginally represented. At a first glance, the portfolio appears to be out of balance in terms of spreading among sectors. Particularly the small share of oil & gas companies is at odds with the fact that this sector was earmarked as one of the region’s economic frontrunners by the government in the report “Pieken in de Delta” (Ministry of Economic Affairs (2006)).
In sum, the portfolio does not suffer from survivorship bias. However, its sector composition is tilted towards industrials and consumer services. As a consequence, the diversification among sectors may leave something to be desired.
2 The Central Buro of Statistics defines the total workforce as the total of employees working at least 12
Table 1: Employment data from 1996 until 2009.
This table presents figures about employment in the province of Groningen. Row 1: Number of listed companies present in portfolio. Row 2:
“Employed by listed companies” denotes the number of people employed by listed companies within the province. Row 2: Employed in total denotes the total amount of people that are employed for at least 12 hours a week within the province. Sources: CBS Statline, Lisa, own research.
Year: 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Listed companies 73 75 74 81 85 89 94 95 95 96 97 97 109 111
Employed by listed companies
(x1000) 14,6 15,4 16,7 17,2 18,7 19,6 21,4 20,9 19,7 19,5 20,5 20,3 22,7 24,4
Employed in total (x1000) 229,0 234,0 239,0 239,0 244,0 243,0 247,0 247,0 253,0 252,0 250,0 265,0 263,0 260,0 Ratio (listed/total) 6,36% 6,59% 6,98% 7,18% 7,68% 8,08% 8,65% 8,47% 7,77% 7,73% 8,21% 7,68% 8,63% 9,39%
Table 2: Composition of portfolio among ICB sectors from 1996 until 2009 and on average. Weights are based on the amount of employees per sector divided by the total number of employees.
B. Return Data
To calculate the portfolio’s returns as defined in equation 3.2, the portfolio weights are multiplied with weekly stock returns. The four factors used in the regression analysis are proxied by stock market indices. All return data has been sourced from Thomson’s Datastream, except for the MSCI Barra Momentum index, which was downloaded from the MSCI website. Returns are calculated using a total return index. In this manner, gross dividends and other distributions such as stock splits are also taken into account. The stocks’ return indices (RI) are denominated in Euros. The portfolio return in Euros is the relevant return since that would be the return incurred by an investor in the Netherlands. Aside from that, when equity indices are calculated, the stock prices of the constituents are always converted into one single currency. Calculating the portfolio returns with the inclusion of the effect of exchange rate fluctuations is thus the most consistent when doing performance evaluation.
Transaction costs are not taken into consideration in the calculation of the portfolio’s returns. This is because the benchmarks I use to analyze the portfolio’s performance are not adjusted for transaction costs either. Rebalancing is done only once a year, with very gradual shifts in
portfolio composition. Because of such a low turnover, transaction costs are expected to be marginal.
The indices I use as a proxy for the four factors Rmt, SMBt, HMLt and MOMt, are from MSCI. The
risk-free rate is proxied by the 3 month Euribor interest rate. Some more details can be found in table 3. The method that I use for proxying factors is similar to that used in Kramer (2009), who uses the Dutch counterparts of the indices in table 3 to proxy for Rmt, SMBt and HMLt. Given that
89%4 of the companies in the portfolio are listed on a European exchange, European indices are
specific Fama and French factors. Moerman finds that due to increased financial integration in Europe, the difference in accuracy has gotten less acute. I am therefore confident that European indices are the correct benchmarks.
Table 3. Indices used as proxies for factors in regression analysis.
Rmt is the equity market’s return; Rft is the 3 month Euribor rate. SMBt is the excess return of
small cap over large cap stocks; HMLt is the excess return of value over growth stocks. MOMt is
the one year momentum factor. Variable: Proxy:
Rmt MSCI Europe index
Rft Euribor 3 month interest rate
SMBt Long: MSCI Europe Small Caps index, short: MSCI Europe Large Caps index.
HMLt Long: MSCI Europe Value index, short: MSCI Europe Growth index
C. Summary statistics
Summary statistics on the regional portfolio’s weekly returns and on the other variables used in the regression analysis can be found in panel A of table 4. The portfolio has a weekly return of 0.24%, which corresponds to an annual return of 12.3%. The annual return is 4.8 % higher than the return on the MSCI Europe index, which is used to proxy for the equity market return. At the same time the portfolio’s standard deviation is 2.75% versus the benchmark’s 2.71%. The Sharpe ratio (Sharpe (1966)) of the portfolio is 0.066 whereas the MSCI Europe index has a Sharpe ratio of 0.034; both numbers are based on weekly data. A tentative conclusion is that the portfolio composition has succeeded in increasing expected return without adding too much volatility.
The average values of the four factors Rmt – Rft, SMBt, HMLt and MOMt are all positive which is
consistent with the theory of the CAPM, Fama and French and Carhart models. Nonetheless, the 2007 credit crunch and its aftermath have put downward pressure on the equity market premium. The average factor premium on HMLt is quite low, at 1.7% annually. On the other
hand, the MOMt premium is rather high on average with 10.7% annually. This is not surprising
since it is proxied by a portfolio which is long in last year’s winning stocks and short in last year’s losers.
The kurtosis of all dependent and independent variables, except the risk free rate, is higher than 3. Since a kurtosis of 3 is considered ideal if data are expected to follow a normal distribution, it is obvious that the data suffers from leptokurtosis. Leptokurtosis, or fat tails is quite common in financial time series data. Initial regression analysis using the ordinary least squares method yielded residuals that were non-normally distributed. For all three regression equations, the residuals failed the Jarque-Bera test. Heteroskedasticity is also present in the data as the residuals failed White’s test for heteroskedasticity. Further testing confirmed that the data suffered from ARCH effects5. I use the model from Glosten, Jagannathan and Runkle (1993) for
stock price volatility in my regression analysis to tackle the issues with ARCH effects in the data. The correlations between the variables used in regressions (3.1); (3.2) and (3.3) can be found in panel B of table 4. The variables Rpt and Rmt – Rft have a near perfect correlation of 0.922. Since
only Rmt – Rft is an explanatory variable, multicollinearity does not pose a problem. The correlation between Rmt – Rft and MOMt is also high which may give problems with near
significant or not. A second issue is that the high correlation between Rmt – Rft and MOMt makes it
harder to distinguish which factor is actually driving the return on the portfolio. As these issues with multicollinearity are only applicable to regression equation (3.5), I ignore them for now and pay extra attention to them in the discussion of the results.
Table 4. Summary statistics on variables used in regression analysis.
Panel A presents summary statistics on 343 weekly data points starting on the 2nd of June 2003
and ending on the 28th of December 2009. Returns are calculated with continuous compounding.
Rpt is the portfolio’s return; Rmt is the equity market’s return; Rft is the 3 month Euribor rate;
SMBt is the excess return of small cap over large cap stocks; HMLt is the excess return of value
over growth stocks. MOMt is the one year momentum factor. Panel B presents the correlations
between the portfolio’s return and the four factors used as explanatory variables in the regression analysis.
Panel A: Summary Statistics
5. Results
A. Results from main regression analysis
The results from the time series regressions using the regular portfolio weighting can be found in table 5; panel B. The main finding from the regression analysis is that Jensen’s alpha is not statistically significant for any of the three models. The portfolio thus does not significantly outperform a passive market portfolio. However, the alpha is positive for all three models and there is no underperformance. Thus an investor will not impact wealth negatively if he decides to follow a regional investment strategy.
Under the assumptions of the CAPM model (eq. 3.3), the portfolio has a beta (β1) of 0.95
with respect to the market return, Rmt - Rft. Thus, the portfolio has a slightly lower
systematic risk compared to the market. A beta of one would imply that the portfolio has a systematic risk equal to that of the market. The intercept or Jensen’s alpha is 0.04% a week. Whilst this value is not statistically significant, it does have a positive sign. When the weekly alpha is multiplied by 52, the “outperformance” compared to the MSCI Europe index is 2.3% annually. The adjusted R2 of the regression is 85%. This is already
very good fit given that the CAPM is the simplest model for explaining asset returns. For instance in Fama and French (1992), similar regressions only have a fit of around 70%.
When the other two factors from Fama and French (1993), SMBt and HMLt, are added
into the regression (eq. 3.4), Jensen’s alpha decreases somewhat to 0.03% per week or 1.33% annually. The fit of the regression is increased somewhat to 89%. SMBt is the only
added explanatory variable that is statistically significant. The SMBt beta (β2) is 0.45,
which means the portfolio’s style is moderately tilted towards small cap stocks. The returns on small cap stocks are on average more volatile than on large cap stock, which is compensated by a higher expected return. However, the standard deviation of the portfolio6 (2.75%) is not significantly higher than that of the market proxy (2.71%) so
added volatility is not an issue. HMLt is not statistically significant.
market beta (β1) increases by 0.16 with respect to the betas in equations 3.3 and 3.4.
The factors Rmt – Rft and MOMt have a correlation coefficient of 0.88 which causes the multicollinearity problem. The standard error7 for β1 also increases, as the z-statistic
drops from 47.27 to 29.72 between the Fama and French and Carhart model. Both the wrong attribution of explanatory variables and the higher standard errors are textbook examples of near perfect multicollinearity (Brooks (2008), page 172). As such, the results from the Carhart model are not reliable. If there were no issues with
multicollinearity, I would expect β4 not to differ significantly from zero because the
portfolio does not follow a specific momentum strategy. A negative beta would imply that the portfolio return is hurt because previous winning stocks are sold in favor of losing stocks. An investor or a fund manager with a comparable portfolio might worry about this. The solution would be simple. Each year the investor could sort which stocks had the best and worst returns that year, and take the momentum effect into account when determining his rebalance.
Given these findings, the hypotheses H1, H2 and H3 are confirmed. Jensen’s alpha does
not significantly deviate from zero for either the CAPM or the Fama and French model. The evidence for H3 is less clear because of the multicollinearity problem. But because
the employment figures per company only change gradually, the changes in portfolio weights are only marginal. It is therefore unlikely that the portfolio has a very high positive or negative momentum tilt which would make Jensen’s alpha differ significantly from zero for the Carhart model. The regional portfolio outperforms the passive market portfolio by between 1.3% and 2.3% annually; this excess return should be enough to cover trading costs.
Table 5. Results from time series regression
This table presents the results from the time series regressions as specified in equations 3.3, 3.4 and 3.5. Weekly returns with continuous compounding are used in the
regressions. The regressions are done using the model of Glosten, Jagannathan and Runkle (1993) to cope with ARCH effects. The annual α is calculated by multiplying the weekly α (the intercept) by 52. Panel A presents the results using the portfolio
weighting scheme as specified in equation 3.1. Panel B presents results from a sensitivity analysis of the same portfolio only using the previous year’s employment records to determine portfolio weights. Z-statistics are in parentheses; * denotes a variable significant at the 99% confidence level.
Panel A: Results from times series regression with companies’ portfolio weights based on same year’s employment records
CAPM Fama and French Carhart
α 0.0004 0.0003 0.0005 (0.82) (0.53) (0.98) Annual α 2.30% 1.33% 2.35% β1 (Market) 0.9486 * 0.9362 * 1.1044 * (44.12) (47.27) (29.72) β2 (Size) 0.4457 * 0.4663 * (10.66) (11.87) β3 (Book-to-market) -0.0384 -0.0554 (-0.74) (-1.08) β4 (Momentum) -0.1572 * (-5.62) Adjusted R2 84.96% 88.91% 90.16% Observations 343 343 343
Panel B: Results from times series regression with portfolio weighting based on previous year’s employment records
CAPM Fama and French Carhart
Table 5. Results from time series regression (continued)
This table presents the results from the time series regressions as specified in equations 3.3 and 3.4. Weekly returns with continuous compounding are used in the regressions. The regressions are done using the model of Glosten, Jagannathan and Runkle (1993) to cope with ARCH effects. The annual α is calculated by multiplying the weekly α (the intercept) by 52. Panel C presents results using return data from January 1, 2001 until June 2, 2003. Panel D presents results from regression analysis using worldwide indices as proxies. These proxies are listed in appendix IV. Z-statistics are in parentheses; * denotes a variable significant at the 99% confidence level.
Panel C: results from time series regression using return data as of January 1, 2001 until June 2, 2003
CAPM Fama and French
α 0.0006 -0.0005 (0.37) (-0.40) Annual α 3.00% -2.83% β1 (Market) 0.94 * 1.06 * (28.70) (28.70) β2 (Size) 0.30 * (4.03) β3 (Book-to-market) 0.40 * (4.95) Adjusted R2 80.19% 85.15% Observations 126 126
Panel D: results from time series regression using MSCI World stock indices as proxies for CAPM and Fama and French factors
CAPM Fama and French
B. Sensitivity analysis: portfolio weighting based on previous year’s employment
I have also created a portfolio of regional stocks in which each year the portfolio weights of companies are based on employment figures from the year before. This portfolio is tested in the same manner as the regular portfolio. The purpose of this is to see how the portfolio performs if lagged employment data is used instead of the most recent. This is a relevant sensitivity analysis since accurate and recent employment records are hard to come by. It is also a test to see whether the portfolio has a passive character, or whether there are any unexpected timing effects.
For this lagged portfolio, the weight (wij)of each stock i is determined like this:
(3.6)
Where wij is the weight of stock i in year j. Employeesi,j-1 denotes the number of
employees company i had in the year before year j. Year j=0 is 2003.
Summary statistics about the lagged portfolio’s returns and the explanatory variables are listed in Appendix II. The average annual return on the lagged portfolio is
comparable to that of the regular portfolio; 12.7% versus 12.3%. The same goes for its Sharpe ratio: 0.069 vs. 0.066.
The results from the regression analysis of the lagged portfolio’s returns are in table 5; panel B. These results are very similar to those from the regular portfolio in panel A. The annual Jensen’s alphas have gone up somewhat from 2.30% to 2.42% for the CAPM model, and from 1.33% to 1.87% for the Fama and French model. In neither case Jensen’s alpha is statistically significant. The betas β1, β2 and β3 are virtually unchanged
with respect to those in panel A. Again, the results from the Carhart model are tainted by the multicollinearity issue. The adjusted R2’s also remain equal for both the CAPM (85%)
and the Fama & French model (89%). The lagged portfolio’s risk adjusted performance (Jensen’s alpha) is identical to that of the regular portfolio.
C. Robustness check: returns as of January 1st of 2001
Due to the limited availability of the MSCI Barra Europe Momentum index, the
portfolio’s performance is analyzed from the 2nd of June 2003 until the 31st of December
2009. In this sub-section, I analyze the performance of the portfolio using weekly data as of January 1st, 2001 until June 2nd, 2003.8 The goal is to check whether the finding that
Jensen’s alpha is not statistically significant for the CAPM and Fama & French model is robust for a different time span with different market conditions.
Summary statistics about the returns between January 1st, 2001 and June 2nd, 2003 are
listed in Appendix III. What is most striking is that the equity risk premium Rmt – Rft is now negative on average; it is -0.45% weekly which translates into -23.14% annually. Market returns were also more volatile in this period; the weekly standard deviation of Rmt is 3.55% compared to 2.71% for the reference period9. The low average market
returns and the higher volatility are caused by both the early 2000’s bursting of the dot com bubble and the 9/11 attacks. It is interesting to see how the portfolio performs during such a distinct bear market. The portfolio has a less detrimental Sharpe ratio in this period than the market; -0.11 compared to -0.13. What also stands out in this period out is that HMLt is so high on average: 6.39% compared to 1.68% for the reference
period. Presumably, this is caused because many IT and Telecommunications companies were seen as having a high potential for earnings growth during the dot com bubble. After this bubble burst, these overvalued stocks had to go down in value, which would explain the high premium on HMLt during the post dot com bubble period.
The results from the regression analysis can be found in table 5, panel C. Under the assumptions of the CAPM model, the portfolio has a statistically insignificant but positive alpha of 0.06% a week which translates to 3% annually. When the factors SMBt
and HMLt are added into the equation, alpha becomes negative but it remains
non-statistically significant. Its alpha is then -0.05% weekly or -2.83% annually. The regional portfolio’s market beta increases somewhat from 0.96 to 1.06. Around 6% of the annual portfolio performance is explained by a positive sensitivity to SMBt and HMLt, which are
now both statistically significant. In other words, the portfolio composition is tilted towards small capitalization and value stocks. The adjusted R2’s of both regressions
(panel C) are lower than those from the reference period (panel A) because of the higher
volatility in the stock market between January 1, 2001 and June 2, 2003. The residuals from both regressions are nevertheless normally distributed.
It is a new finding that the portfolio composition is tilted towards value stocks e.g. stocks with high book-to-market values, because HMLt was not statistically significant during
the reference period. It is probably due to its higher factor premium that HMLt is
statistically significant for this period. Once again, because of the passive character of the portfolio I conjecture that the portfolio is also tilted towards value stocks between June 2nd, 2003 and December 31st, 2009.
I also performed regression analysis using results from the full period; January 1st of
2001 until December 31st of 2009. But unfortunately the results were unreliable because
the residuals from both the CAPM model and the Fama and French model did not follow a normal distribution. The Jarque Bera values of the residuals from both regressions were higher than 6. I performed the Chow Breakpoint test and it indicated a structural break between the sub samples before and after June 2nd of 2003.
D. Robustness check: World index data
In this section I test whether the European indices from table 3 are the correct
benchmarks for my portfolio. The regressions from equations 3.3 and 3.4 are now done using world indices as proxies. The names of the indices used as proxies for the
explanatory variables are listed in Appendix IV.
Summary statistics about the explanatory variables can be found in Appendix V. The average annual return on the world market between June 2nd, 2003 and December 31st
2009 was 1.9% below that of the European market. The world market portfolio has a Sharpe ratio of 0.021, worse than that of the European market (0.034) and the regional portfolio (0.066).
Now let’s turn to the results in table 5, panel D. For the CAPM model; Jensen’s alpha is 0.09% weekly or 4.69% annually. This is the only instance that alpha is anywhere near being statistically significant; albeit with a 90% confidence interval. The higher alpha is explained by the lower average return on the market, Rmt. When SMBt and HMLt are
The use of worldwide market data lowers the quality of the regressions. The adjusted R2
of the CAPM regression drops from 85% to 78%. For the Fama and French regression the adjusted R2 is decreased from 91% to 79%. The lower adjusted R2 on both
6. Conclusion
The results from the regression analysis confirm the hypothesis that the portfolio does not earn a significant risk adjusted return for either of the three asset pricing models. The absence of any positive and statistically significant Jensen’s alpha indicates that there is no added value from the regional portfolio’s composition. The portfolio does not benefit from the return on locality either.
However, in almost all of the regressions Jensen’s alpha does have a positive sign.
Because I do not find any significant negative alpha in any of the regression, the portfolio yields a return that is acceptable given its risk. In other words, there is no significant underperformance when compared to its appropriate benchmark; the MSCI Europe index. Because the portfolio has such a passive character, it is a viable alternative for investing in ETF’s tracking European equity indices; for instance the iShares MSCI Europe Fund. The portfolio outperforms the risk adjusted benchmark by between 1 and 2% annually. This should cover the higher trading costs of the regional strategy when compared to an ETF. The higher performance of the portfolio compared to the market can be partly explained its tilt towards small capitalization and value stocks. The added benefit of the regional strategy is that it makes an investor feel more familiar with his investments, so he will feel less cognitive dissonance about his portfolio choice.
References Secondary data:
CBS Statline, 1996 - 2009 (Centraal bureau voor Statistiek, Heerlen) Thomson’s' Datastream, 2001 - 2009 (Thomson Reuters, New York, NY) Lisa - Het werkgelegenheidsregister van Nederland, 1995 - 2009 (Stichting Lisa,
Enschede)
MSCI Website, 2003 - 2009 (MSCI, New York, NY)
Orbis – company information around the globe, 2011 (Bureau van Dijk, Amsterdam)
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Appendix I - Listed companies in the province of Groningen
This appendix contains the names of the companies that were part of the portfolio between January 1st of 2001 and December 31st of 2009. The companies are sorted by ICB Sector.
Basic Materials Gerry Weber Imtech
Akzo H&M Kone Cranes
Arcelor Mittal Hornbach Holding Koninklijke BAM
Cameron Hutchinson Whampoa Manpower
Dow Chemical Intersport Olympia Flexgroup
DSM JC Decaux Randstad
FMC Kentucky Fried Chicken Rexel / CDME **
Holmen Laurus / Super de Boer* Saint Gobain Group
PPG Macintosh Retail Group Solar a/s group
Smurfit McDonald’s STORK
Tata Chemicals Mediq TNT
Teijin Limited Metro Trelleborg
Schuitema USG People
Consumer Goods Sligro Food Group UTX
British American Tobacco The Carphone Warehouse
Björn Borg Thomas Cook Int. Oil & Gas
Canon Telegraaf Media Groep BP
Coats Vendex KBB Chevron
CSM Exxon Mobil
Ford Motor Financials Fugro
Henkel ABN Amro SGS
Hunter Douglas Aegon Shell
L'Oreal AON Total
LVMH Fortis
Michelin ING Technology
NBTY SNS Reaal Atos
Philips Van Lanschot Brunel
SCA Cap Gemini
Scania Health Care ICT Automatisering
Unicharm Bayer AG Logica
Ordina Consumer Services Industrials
Accor Adecco Telecommunications
Ahold Arriva Deutsche Telekom
Bidvest Ballast Nedam KPN
Burger King Bilfinger UK Mail Group
Carpetright Cargotec Vodafone
Charles Vögele CRH
Compass Group Draka Holding Utilities
Douglas Holding Eriks Electrabel / GDF Suez***
Domino’s Pizza G4S RWE
Elior GEA Group Suez Environnement
Esprit Grontmij Tieto
Appendix II: Summary statistics - portfolio with previous year’s company weights. The data in the following table correspond to the results presented in table 5, panel B.
Panel A presents summary statistics on 343 weekly data points starting on the 2nd of June 2003
and ending on the 28th of December 2009. Returns are calculated with continuous compounding.
Rpt is the portfolio’s return; Rmt is the equity market’s return; Rft is the 3 month Euribor rate;
SMBt is the excess return of small cap over large cap stocks; HMLt is the excess return of value
over growth stocks. MOMt is the one year momentum factor.
Panel B presents the correlations between the portfolio’s return and the four factors used as explanatory variables in the regression analysis.
Appendix III: Summary statistics - returns as of 1/1/2001
The data in this table correspond to the results presented in table 5, panel C.
Panel A presents summary statistics on 469 weekly data points starting on the 1st of January
2001 and ending on the 2nd of June 2003. Returns are calculated with continuous compounding.
Rpt is the portfolio’s return; Rmt is the equity market’s return; Rft is the 3 month Euribor rate;
SMBt is the excess return of small cap over large cap stocks; HMLt is the excess return of value
over growth stocks.
Panel B presents the correlations between the portfolio’s return and the four factors used as explanatory variables in the regression analysis.
Appendix IV: Worldwide equity indices used as proxies for Fama and French factors Rmt is the equity market’s return; Rft is the 3 month Euribor rate. SMBt is the excess return of
small cap over large cap stocks; HMLt is the excess return of value over growth stocks. MOMt is
the one year momentum factor. Variable: Proxy:
Rmt MSCI World index
Rft Euribor 3 month interest rate
SMBt Long: MSCI World Small Caps index, short: MSCI World Large Caps index.
Appendix V: Summary statistics - World Data
The data in the following table correspond to the results presented in table 5, panel D. The variables Rmt, SMBt and HMLt in this table are proxied by MSCI World indices instead of MSCI
Europe indices.
Panel A presents summary statistics on 343 weekly data points starting on the 2nd of June 2003
and ending on the 28th of December 2009. Returns are calculated with continuous compounding.
Rpt is the portfolio’s return; Rmt is the equity market’s return; Rft is the 3 month Euribor rate;
SMBt is the excess return of small cap over large cap stocks; HMLt is the excess return of value
over growth stocks.
Panel B presents the correlations between the portfolio’s return and the three factors used as explanatory variables in the regression analysis.
