Socially Responsible Investment
Performance and Diversification
Rients Galema
December 2007
TABLE OF CONTENTS
PREFACE...1
CHAPTER 1 ...4
1. SOCIALLY RESPONSIBLE INVESTMENT AND PERFORMANCE...4
1.1INTRODUCTION... 4
1.2DATA AND METHOD... 8
1.3 RESULTS... 16
1.4. CONCLUSIONS... 25
2. DIVERSIFICATION OF SOCIALLY RESPONSIBLE INVESTMENT PORTFOLIOS: TESTING FOR MEAN-VARIANCE SPANNING ...28
2.1 INTRODUCTION... 28
2.2MEAN-VARIANCE SPANNING AND INTERSECTION... 33
2.3 DATA & PORTFOLIO FORMATION... 41
PREFACE
This master thesis combines two empirical studies on socially responsible investment. Socially responsible investment can be seen as an investment style in which investors not only take the financial consequences but also the societal consequences of their investment decisions into account. There is a large and growing group of individual investors that wants to invest socially responsible, but also institutional investors are increasingly concerned with the social consequences of their investments. The latter is fueled by the increased pressure of the general public on institutional investors to invest in a more socially responsible way. When investment decisions are no longer solely based on financial variables we enter a world which is relatively unfamiliar to economics. In socially responsible investment, investment decisions also depend on tastes so that classic Fisher separation no longer holds.
A central question the socially responsible investment literature has tried to answer is what the influence of moral tastes is on risks and returns of investments. The basic difficulty it has encountered in trying to answer this question is that socially
responsible investment is almost by definition a relatively vague concept, since it depends on moral tastes which differ across persons and across time. Fortunately, in order to better define the concept of socially responsible investment, several dimensions have been identified. For instance, a social dimension, an environmental dimension and a governmental dimension. In addition, there are agencies that have started to rate
companies based on these dimensions and based on a more or less fixed set of criteria. In our research we use data of one of those rating agencies. Of course, there is still
heterogeneity across different rating agencies and across time, implying that it is likely that the literature on socially responsible investment will continue to display sometimes conflicting findings.
Nonetheless, tastes do have an impact on the functioning of capital markets and therefore are worth investigating. In this thesis we are concerned with 2 central questions. The first question we try to answer in chapter 1 is what the performance consequences are of a socially responsible investment strategy. This is interesting since standard economics predicts that a socially responsible investment strategy can only be detrimental to
‘news value’. News about social responsibility can inform investors about the risk and cash flow of companies. The second question we try to answer in chapter 2 is concerned with the diversification consequences of socially responsible investment. Socially
responsible investors necessarily limit their investment universe by choosing not to invest in irresponsible firms. We try to find out whether constraining the universe has
consequences for their diversification possibilities. Our findings suggest that it depends on the criteria used and the assumptions one makes about other constraints encountered in the investment process, such as the existence of a risk-free rate and short sales constraints.
CHAPTER 1
SOCIALLY RESPONSIBLE INVESTMENT AND PERFORMANCE 1.1 Introduction
Socially responsible investing (SRI) has become an investment style that attracts a lot of investor attention. In addition to their financial performance, many companies nowadays also report on their performance in the dimensions of social responsibility, in particular on environmental, social, and corporate governance issues. This tendency to report on non-financial issues is a reflection of a broader movement among investors, who appear to be increasingly concerned about non-financial dimensions of performance. The central issue considered in this paper is whether taking into account these non-financial issues has implications for stock prices and excess stock returns.
The increased interest in socially responsible investment has inspired a substantial amount of research that investigates the link between excess returns and SRI. So far, most of the empirical literature on SRI reports little difference between the risk-adjusted returns of stocks with high scores on SRI and those with low scores. Kurtz (1997)
establishes that socially responsible stocks do not appear to under perform the market as a whole. These findings have been found elsewhere in the literature too (e.g. Bauer et al., 2005; Becchetti and Ciciretti, 2006 and Lee and Faff, 2006) and it appears safe to conclude that there are no significant differences in the performance of socially
responsible funds and stocks and conventional ones. Although there are exceptions. Hong and Kacperzcyk (2007) report higher expected returns for stocks that are excluded from a portfolio because of negative ethical issues (companies producing alcohol, tobacco, and gaming). Furthermore, Brammer et al. (2006) find that their composite SRI indicator is negatively related to UK stock returns. These contradictory findings give rise to the question how the relationship between SRI and excess return manifests itself.
neglect effect hypothesis by Hong and Kacperczyk, 2007). Third, the expected returns of socially responsible firms are higher than those of irresponsible firms. Hamilton et al. (1993) argue that if investors consistently underestimate the probability that positive news will be released about companies that are socially responsible, socially responsible stocks will be relatively underpriced, while irresponsible stocks will be relatively
overpriced. They dub this the underestimation hypothesis. Fourth, SRI can be positively related to expected returns when investors underreact to valuable SRI information, which we dub the underreaction hypothesis. This implies that there is no effect or a small effect on prices, while abnormal returns are positive in case of good SRI news and negative in case of bad SRI news1.
Note the important difference between the second hypothesis and the third and fourth hypotheses. In the second hypothesis, stock prices are influenced due to investors’ discriminating SRI tastes, while in the third and fourth hypotheses SRI information is value relevant (Derwall, 2007). Value relevance implies that markets respond rationally to SRI information since it conveys clear information about a firm’s risks and cash flows. We will come back to value relevance later, after we discuss the theory relating to the second hypothesis.
Most formal theoretical work on the relationship between SRI and expected returns is reminiscent of Merton (1987) and focuses on the discrepancies in prices that are the result of demand differences for different types of stocks. These demand differences can either be due to incomplete information (Merton, 1987), (green) investor preferences (Heinkel et al., 2001) or firms voluntarily internalizing externalities in equilibrium (Dam, 2007). Yet they all share a basic feature, namely that excess demand for socially
responsible stocks and a shortage of demand for irresponsible stocks will lead to overpricing of the first and underpricing of the latter. The shortage of demand for irresponsible firms’ stock implies that the risk sharing opportunities for people investing in these stocks are limited and therefore command a return premium (Merton, 1987, Heinkel et al. 2001).
As a result of limited risk sharing due to differences in demand, Merton (1987) also shows that excess returns depend on other characteristics in addition to market risk. In the context of SRI the increased or decreased risk of a firm acting in a socially
responsible manner could therefore increase or decrease, respectively, its expected return.
1 Note that with good SRI news we mean good SRI news from an investor perspective, since good news for
For instance, Hong and Kacperczyk (2007) mention the increased litigation risk
associated with the products of sin companies.2 As they also note, deviation from CAPM equilibrium due to the neglect effect hypothesis depends crucially on the assumption of limits to arbitrage because of a set of constraints and risks discussed by Shleifer and Vishny (1997) and others.
An interesting market equilibrium version of this ‘limits to arbitrage’ argument is provided by Fama & French (2007). They introduce two groups of investors; A investors that do not have tastes for assets as consumption goods (neutral investors) and D
investors that do have a taste for assets as consumption goods (e.g. SRI investors). In general, the portfolio of the latter group of investors will not be unconditionally mean-variance efficient so that market clearing requires that group A overweights the assets underweighted by group D and vice versa. If group A investors hold the exact
complement of the group D investors’ asset position there is market equilibrium in which Jensen’s alpha is zero for the market portfolio, positive for investor A’s portfolio and negative for investor D’s portfolio. However, due to limits to arbitrage it is possible that neutral investors do not entirely offset the price effect of SRI investors. Still, even if they are able to do so, if SRI investors find that their lower Jensen’s alpha is sufficiently compensated by the utility derived from investing in socially responsible firms, the price effect does not disappear.
The empirical findings of Hong and Kacperczyk (2007) are in accordance with the neglect hypothesis and limits to arbitrage. They find that sin stocks; stocks of firms involved in producing alcohol, tobacco and gambling, are relatively underpriced – they have lower market-to-book values – but do have higher excess returns than other stocks. This is consistent with sin stocks being underpriced due to less demand for these stocks and therefore earning a higher return.
However, the effect of social responsibility on asset returns is not necessarily driven by agents’ non-financial tastes alone. Social responsibility information could also directly predict stock returns just like many stock-specific variables are known to be able to predict stock returns. In that case SRI is informationally relevant to markets so that its asset pricing implications can be explained in a traditional rational-expectations
2 Note that in an asset pricing model with a market-to-book factor included this litigation risk could be
framework, i.e. SRI is value relevant (Derwall, 2007). The literature on variables that are informationally relevant is extensive, but can be divided into three categories. First, it has been found that past returns are able to forecast future returns (Jegadeesh and Titman, 1993)3. Second, several price-scaled variables are able to forecast future returns, of which the market-to-book ratio and market capitalization itself are often deemed to have the most pervasive impact (Fama & French, 1992). Finally, there are a number of studies that investigate the long-term price reaction to specific information events. In particular, we can distinguish these events as being either management decisions or information about firm performance. Daniel, Hirshleifer and Subrahmanyam (1998) review a substantial body of literature that shows that there is considerable evidence that investors underreact to information conveyed by management decisions.
How we should categorize SRI information is not clear a priori. What is clear from this literature is first, to find out whether SRI is value relevant we have to control for the many variables known to be able to predict excess returns. Second, if SRI
information is immediately and correctly priced, it cannot be used to predict excess stock returns. Conversely, if investors underreact to SRI information or even not price this information at all and prices correct in the long term, social responsibility information can be used to predict the cross-section of stock returns.
However, different types of SRI information could have different effects on excess returns and stock prices. We belief that one of the reasons that the empirical literature has yielded so little significant relations between SRI and expected returns may be due to the aggregation over different dimensions, which have confounding effects. For example, it is possible that news pertaining to firms pursuing a strategy towards
environmental friendly production is negatively related to expected returns, while firm news pertaining to good employee relations could be positively related. Therefore, we zoom in on the many dimensions of social responsibility.
For each of these dimensions we investigate the pricing and return implications of SRI to test our hypotheses. In particular, the neglect effect hypothesis predicts a positive relation between SRI and market-to-book ratios but a negative relation between SRI and excess returns. Conversely, the underestimation and underreaction hypothesis predict a
3 This apparent anomaly has been incorporated in an asset pricing model by Carhart (1997) by means of the
positive relation between excess returns and SRI, but a negative or no relation between SRI and market-to-book ratios.
To test the return implications of SRI we form 12 portfolios based on positive scores on the strength and concern screens of six SRI dimensions on the universe of stocks tracked by KLD during the period 1992 to 2006. We test whether each of these portfolios can deliver excess returns by estimating the Fama French (1993) asset pricing model augmented with the Carhart (1997) momentum factor. Since we test multiple portfolios of non-normally distributed returns we test them in a system GMM framework (MacKinlay and Richardson, 1991). Next we investigate the pricing impact of SRI by regressing market-to-book ratio on scores on our six dimensions, using the latest panel techniques. Finally, we take a closer look at the informational impact of SRI scores on excess returns by regressing excess returns on lagged SRI scores for our six dimensions using Fama-MacBeth (1973) regressions.
Our main finding is that the neglect effect hypothesis does not hold for our dataset; SRI dimensions that are related to market-to-book ratios are not related to excess returns and vice versa. The two dimensions that are not related to market-to-book ratios, but are related to excess returns are Community and Employee Relations. So for these two dimensions we can reject the neglect effect hypothesis but we cannot reject the underreaction and underestimation hypothesis. A second finding is that our Employee relations score can predict the cross-section of stock returns. However, if we take a closer look we find that only a few subdimensions are responsible for the explanatory power of Employee relations.
The outline of the rest of the paper is as follows. In section 2 we first discuss the data, after which we discuss the methodology on the portfolio, the market-to-book, and the Fama-MacBeth (1973) regressions. In section 3 we discuss the empirical results from our regressions analyses; we compare these results and discuss additional tests. Finally, section 4 discusses and concludes.
1.2 Data and method
pooled market-to-book regressions. Finally, we perform a series of Fama-Macbeth (1973) regressions to test the direct effect of KLD scores on excess returns.
1.2.1 Data
We obtained data on social responsibility from KLD Research & Analytics, Inc and financial performance measures for each firm from Datastream. Other researchers have used these databases too when investigating the relationship between financial performance and SRI (e.g. Hillman and Keim, 2001; Becchetti et al., 2005). KLD uses screens to monitor SRI and it has expanded its universe of coverage over the last couple of years. In the 1990s, it covered the S&P500 Index and the Domini 400 Social Index. In 2001 the database was extended to include all constituents of the Russell 1000 Index as well. In 2003 the database was further extended to include all stocks from the Russell 2000 as well. KLD does not have historical ratings data available for non-US companies, unless it is a member of the S&P500. In our study we include all stocks covered by KLD.
KLD uses multiple criteria on which firms are evaluated using both positive and negative screens, where positive screens indicate strengths and negative screens indicate weaknesses of the firm. Each screen can be summarized in a binary variable, which reflects whether the firm meets the particular criterion and which are awarded at the end of each calendar year. The screens are summarized in groups of corresponding items referring to a general theme by summing over the screens of each theme4. Six themes are identified: Community involvement, Corporate governance, Diversity, Employee
relations, Environment, and Product. The first theme involves how the firm interacts with its social environment. Corporate governance relates to how the firm is governed and directed. Diversity is about the composition of the workforce, especially senior management and the board. Related to this is Employee relations which is about the relationship between the company and its employees and in particular concerns issues related to employee compensation. Environment is about environmental issues and policies. Finally, the theme Product is about strengths and weaknesses in relation to the quality of the products of the firm. With respect to all six themes, KLD investigates both
4 Note that on critque on summing over subscreens is that we do not know whether each screen should be
strengths and concerns5. More detailed information about the themes and their strengths and weaknesses is provided by Becchetti and Pinnacchio (2007).
Apart from these six themes, KLD also investigates companies’ behavior with respect to human rights. However, as this is undertaken since the year 2000 only, we do not include this item in our analysis because it would result in a substantial reduction of the data available for our analysis. Furthermore, KLD has exclusionary screens for alcohol, gambling, firearms, military, nuclear power, and tobacco. Given the nature of these screens, namely focusing only on concerns, it is excluded from our analyses
Return data and accounting data were obtained from Datastream. This includes monthly data on returns, market values and trading volumes and yearly data on shares outstanding, company age, R&D expenditures, net sales, book equity, number of shares outstanding and net income. The time period covered for these data is June 1992 to July 2006 for our monthly portfolio and Fama-MacBeth (1973) regressions and December 1991 to December 2004 for our yearly market-to-book regressions. Monthly data is measured at the end of each calendar month and yearly data at the end of each calendar year. The return and accounting data were linked with the KLD data based on ticker and name for the oldest data and on CUSIP code for the more recent data. Finally, the
independent variables used in our portfolio regressions; the value-weighted market proxy, the SMB, HML and MOM factors and the risk-free rate were obtained from the website of Kenneth French.
1.2.2 Forming Portfolios
Twelve portfolios are formed for our six CSR dimensions based on whether stocks have a score on a certain strength or concern screen. In forming portfolios we are especially interested in the informational content of the KLD scores. Therefore, we closely follow the approach of Fama and French (1993) in constructing the portfolios. KLD assigns CSR ratings at the end of each year, so to be certain that the social responsibility and financial information for year t-1 is known, we calculate returns on monthly equally weighted portfolios beginning in July of year t to June of year t+1. Equally weighted portfolios are rebalanced at the beginning of July each year. Portfolios that test the positive and negative dimension of a certain screen are not mutually
exclusive since a portfolio can obtain a positive score on both dimensions. Investors can base their trading strategy on the portfolios we construct.
The monthly return performance of the portfolios is assessed using the Fama and French (1993) three-factor model expanded with the Carhart (1997) moment factor.
i t i t i i t i i t i i t i t i i i t i t RF RM RF s SMB h HML mMOM R − =α +β ( − )+ + + +ε (1)
where Rti is the return on one of the portfolios, constructed as explained above. RM is a value-weighted market proxy and RF is the return on a one-month Treasury Bill. SMB is the difference in monthly return between a small and large-cap portfolio. HML is the difference in return between a value and a growth portfolio. MOM is the monthly return on a portfolio long on past one-year winners and short on past one-year losers. It is designed to capture the risk due to the momentum found in stock returns by Jegadeesh and Titman (1993). Summary statistics on the portfolios and factors are reported in panel A of table 1. In addition to testing the returns on the individual portfolios we also test the return on a differenced portfolio similar to Derwall et al. (2005):
i t i t i i t i i t i i t i t i i C i t S i t R RM RF s SMB h HML m MOM R, − , =α +β ( − )+ + + +ε (2) Where Rti,S is the return on one of the six strength portfolios and Rti, C is the return on its accompanying concern portfolio. The independent variables are as defined in (1), although i is now the differential excess performance.
The set of portfolio equations is tested in a GMM system as in Mackinlay and Richardson (1991) and Clare et al. (1997). Estimation in a system allows the errors of equations to be correlated. Given the fact that our portfolios are all correlated with each other with a correlation coefficient of .80 or higher, estimating a system is probably more efficient. Estimating the portfolios in a GMM system as opposed to an OLS or SUR system has the further advantage of being able to rely on weaker assumptions. In particular, GMM does not rely on the assumption of homoskedasticity and normality of returns.
The estimation procedure is to construct a series of errors from equation system 1 so that they are orthogonal to a vector of instruments for al equations. Given the fact that we do not include any conditional information these instruments consist of a constant and our independent variables. The GMM procedure then chooses parameters
TABLE 1: SUMMARY STATISTICS
Panel A: Summary statistics equally weighted SRI portfolios
Variable Portfolio Mean Portfolio Standard Deviation
SRI Difference Portfolios
Community (%) 0.051 1.853 Diversity (%) 0.086 1.735 Employee Rel. (%) -0.001 1.241 Environment (%) 0.004 1.148 Product (%) 0.040 1.966 Governance (%) 0.002 2.249 SRI Portfolios Comstr. (%) 1.287 3.759 Comcon. (%) 1.236 4.523 Divstr. (%) 1.266 4.304 Divcon. (%) 1.180 4.914 Empstr. (%) 1.254 4.477 Empcon. (%) 1.255 5.003 Envstr. (%) 1.160 4.115 Envcon. (%) 1.156 4.242 Prostr. (%) 1.265 4.466 Procon. (%) 1.226 4.052 Govstr. (%) 1.272 4.491 Govcon. (%) 1.270 4.702 Mkt. (%) 0.635 4.131 SMB. (%) 0.262 3.826 HML. (%) 0.455 3.526 MOM. (%) 0.906 4.990
Define xt =[1,(MKTt −RFt)′,SMBt′,HMLt′,MOMt′]′,εt =Rt −Bxt, the moment
conditions used by the GMM estimation of B are: 0 ] [ ] [gt =E xt ⊗ t = E ε (3)
where T is the number of time series observations and P is the number of model parameters.
To test whether coefficients are zero across the system we use a J-test of over identifying restrictions (Hansen, 1982). Since we have 6 instruments for each equation, equation system (1) and system (2) generate 72 and 36 orthogonality conditions, respectively. However, restricting one of the coefficients to be zero across the system implies that the number of parameters to be estimated is restricted to 60 and 30, respectively. So the system is over identified. The test of the 12 and 6 over identifying restrictions are distributed as 2(12) and 2(6) under the null. We also report J-statistics for iterated GMM estimates since Ferson and Foerster (1994) show that iterated GMM statistics are more reliable in finite models with a larger number of equations or instruments.
Panel B: Summary statistics of variables used in market-to-book regressions
Variable Time-Series Average of Means Time-Series Average of Standard Deviations
LogM/B 0.958 0.693 Community 0.277 0.658 Diversity 0.385 1.083 Employee Rel. 0.123 0.822 Environment -0.139 0.838 Product -0.127 0.695 Governance -0.258 0.621 ROE 0.112 0.250 R&D/Sales 0.062 0.846 LogAge 2.730 0.661 Comstr. 0.335 0.634 Comcon. 0.057 0.228 Divstr. 0.603 0.954 Divcon. 0.218 0.401 Empstr. 0.403 0.641 Empcon. 0.280 0.516 Envstr. 0.240 0.491 Envcon. 0.379 0.819 Prostr. 0.150 0.368 Procon. 0.278 0.590 Govstr. 0.088 0.284 Govcon. 0.346 0.524 1.2.3 Market-to-Book Regressions
The KLD scores are formed on six dimensions adding a point when a stock scores positively on a dimension’s strength screen and subtracting a point when a stock scores negatively on a dimensions’ strength screen. The most elaborate specification we test is the following : t i i,t t i c c SRI B M Log( / ) , = 0 + 1 +c2Xi,t +ε , (4) where LogM/Bi,t is the logarithm of the market-to-book ratio of stock i at the end of year t. SRIi,t-1 is a vector containing the (lagged) scores of the six SRI variables; Community, Corporate Governance, Diversity, Environment, Employee Relations and Product. These scores are calculated for each SRI variable as the sum of strength screens minus the sum of concern screens.
Panel C: Summary statistics of variables used in Fama-MacBeth (1973) Regressions
Variable Time-Series Average of Means Time-Series Average of Standard Deviations
Exreturns (%) 0.959 10.154 Beta 0.965 0.400 LogSize ('000) 7.910 1.583 Returns(%) 1.260 10.156 Turnover (%) 0.566 0.903 LogM/B 0.927 0.704 LogAge 3.093 0.504
In this table we report summary statistics for the three sets of regressions. Panel A reports time series averages of cross-sectional means and standard deviations for the time series return regressions. Comstr and Comcon denote the raw returns on an equally-weighted portfolio formed on the basis of a positive score on the
community strength and concern screens, respectively. Community is the raw return on the difference portfolio Comstr – Comcon. The other SRI portfolios in panel A are defined in a similar manner. Panel B reports similar scores. All variables are measured at the end of the year. LogM/B is the logarithm of market-to-book value. The SRI variables Community, Diversity, Employee Relations, Environment, Product and Governance are the scores on the different SRI dimensions computed as the sum of strength subscores minus the sum of concern
subscores. R&D/Sales is the fraction of sales spent on R&D expenditures in year t. R&DMissing is a dummy that is one when the variable R&D/Sales is missing and zero otherwise. LogAge is the logarithm of age based on the base date in Datastream and measured at the end of each year. ROE is the return on equity of firm i in year t winsorized to exclude the 0.5% smallest and largest observations.Panel C reports summary statistics on the variables used in the cross-sectional regressions. The summary statistics of the SRI variables are excluded since they are the same as in Panel B. Exreturns is a stock’s monthly return net of the risk-free rate. Beta is a stocks post-ranking Beta calculated following Black et al. (1972). LogSize is the logarithm of company market capitalization at the end of month t-1. LogM/B is the logarithm of the market-to-book ratio at the end of month t-1. Return is the simple average of returns during the past 12 months, lagged one month. Turnoveri is the 1 month
lagged monthly average of daily share turnover, which is calculated as average shares traded divided by shares outstanding during month t. LogAge is the logarithm of company age measured at the end of the previous year.
The vector Xi,t includes several control variables known to correlate with the market-to-book ratio. It includes, R&D/Salesi,t which is the fraction of sales spent on R&D expenditures in year t. R&DMissingi,t is a dummy that is one when the variable
is in the Russell1000 or Russell2000, but not in the S&P500. This dummy captures any effects that are due to the enlargement of the number of stocks covered by KLD. LogAgei,t is the logarithm of age based on the base date in Datastream and measured at the end of each year. Finally, ROEi,t is the return on equity of firm i in year t winsorized to exclude the 0.5% smallest and largest observations. Summary statistics can be found in panel B of Table 1.
In estimating (4) we do not use Fama-Macbeth (1973) regressions but pooled OLS with robust standard errors. The reason being that Fama-Macbeth approach to estimating panel data is useful in adjusting for correlation in the cross-section, but understates standard errors when the dependent variable is correlated across time (Petersen, 2007). Return data only suffers from minor autocorrelation, however market-to-book ratios are very much correlated across time. In addition, market-market-to-book ratios are correlated in the cross-section. Therefore, we cluster standard errors both by firm and by time, following Thompson (2006)6 However, these standard errors are only
asymptotically correct. For the standard errors clustered by firm this poses no problem, but for standard errors clustered by time it does, since we only have 14 years of data. Therefore, we also report a second specification in which we adjust for autocorrelation by including time dummies.
1.2.4 Cross-Sectional Regressions
We use cross-sectional regressions because we are interested in assessing the direct influence of KLD scores on excess returns. Using the SRI scores defined above along with a host of control variables, we estimate the following regression :
t i i,t t i i,t t t i RF SRI Beta X R, − =β0 + 1 −1+β2 , + 3 −1+ε , (5) where Ri,t is the monthly return of stock i in month t and the risk-free rate is as defined above. The vector SRIi,t again includes the scores of the six SRI variables as in the cross-section regressions, but this time measured at the end of year t. Betai,t, is a stock’s post-ranking beta estimated using the traditional method of Black et al. (1972). Xi,t-1 is a vector of control variables similar to those used by Hong & Kacperczyk (2005).
LogSizei,1 is the natural logarithm of firm i’s market capitalization at the end of month t-1. LogM/Bi, t-1 is the logarithm of the market-to-book ratio of stock i at the end of month
6 We kindly thank Mitchell A. Petersen for providing the STATA program to cluster standard errors both
t-1. Returni, t-1 is the simple average of returns during the past 12 months, lagged one month. Turnoveri, t-1 is the 1 month lagged monthly average of daily share turnover in stock i during month t, which is calculated as average shares traded divided by shares outstanding during month t. Russell3000i,t and LogAgei,t are as defined above, only this time they are measured at the end of month t.
1.3 Results
1.3.1 SRI portfolios
Looking at Panel B of Table 2 we see that none of our SRI portfolios shows significant outperformance, although we should note that the adjustment factor is largely responsible for this result. The necessity of adjusting for a large number of factors and equations can also be seen by comparing the two J-statistics that test whether a
coefficient is zero across all equations. J-statistic A was computed using 2-stage GMM, whereas J-statistic B was computed using iterated GMM. Following J-statistic A we would reject the hypothesis of zero alpha across all equations at the 5% level, whereas following J-statistic B we would not be able to reject this hypothesis. Although we know from Ferson and Foerster (1994) that iterated GMM has somewhat lower power than 2-stage GMM, the difference in p-values is large enough to suspect that 2-2-stage GMM leads to overrejection.
Looking at the difference between SRI strength and concern portfolios has the advantage of reducing the dimensionality of the system, next to being able to assess the difference in factor exposure and performance between strength and concern portfolios. Concerning the first, the difference in p-values of the J-statistics is much smaller so that using different estimation methods does not lead to qualitatively different results. Concerning factor exposure, we see that for four out of six portfolios the strength portfolio has a significant lower exposure to the HML factor than its accompanying concern portfolio, suggesting that these portfolios are more growth oriented than their concern counterparts. Finally, only the community strength portfolio significantly outperforms its accompanying concern portfolio. The excess return associated with this portfolio is 3.4%, although it is only significant at the 10% level.
implies that CSR strength portfolios should have lower performance than concern portfolios, which is clearly not the case and even opposite for the community difference portfolio. To further investigate the pricing impact of SRI scores, we next perform market-to-book regressions.
1.3.2 Market-to-Book Regressions
In the market-to-book regressions we measure both the dependent variable as well as the SRI scores at the end of the year. So our regressions indicate whether a stock that has a high book-to-market ratio at the same time also scores high on one of the SRI dimensions. The result for two specifications is reported in Table 3. In column (1) we report results for the specification including time dummies, clustering standard errors by firm. In column (2) we report results for the specification where we cluster standard errors by both year and firm. The SRI scores are the sum of positive scores on strength screens minus the sum of scores on concern screens7. So following the neglect effect hypothesis we would expect that the SRI scores are positively related to market-to-book ratios, while the underestimation hypothesis predicts the converse.
Looking at Table 3 we see that the former is indeed the case for 3 out of 6 SRI dimensions. Interestingly, governance scores have a significant negative effect on market-to-book ratios. Looking at panel B, we see that the concern part of the score is mainly responsible for this, suggesting that the market values excessive remuneration of top executives, although the causation could also run the other way. Another interesting finding in panel B is that both environment strength and concern scores are negatively related to market-to-book ratios. This indicates that KLD gives environmental scores to industries with lower growth potential.8 Finally, it is interesting to note that the total community and employee relations scores as well as their strength and concern sub scores do not have a significant effect on market-to-book ratios. In other words, stocks obtaining high scores on community and employee relations do not appear to be overpriced relative to other stocks.
7 Note that these scores are not symmetric due to the fact that for some dimensions one can obtain more
strength scores than concern scores or vice versa.
8 Note that at first it might seem strange that the total environmental score has a positive effect, while both
TABLE 2. Carhart Regressions, Equally Weighted KLD portfolios, July 1992 - June 2006
Panel A: KLD Difference Portfolios
t-stat RM - RF t-stat SMB t-stat HML t-stat MOM t-stat
Community 3.40%* 1.852 -0.15*** -3.06 -0.04 -0.77 -0.30*** -4.49 0.01 0.46 Diversity 2.36% 0.95 -0.08 -1.47 -0.25*** -4.64 -0.10 -1.66 0.06 0.92 Employee Rel. 0.50% 0.305 -0.07** -2.08 -0.11*** -3.20 -0.11*** -2.09 0.09** 2.39 Environment 1.13% 0.879 -0.04 -1.52 0.06 1.82 -0.11*** -3.01 -0.03 -1.11 Product 1.48% 0.767 0.02 0.46 0.15** 2.55 -0.25*** -4.01 -0.02 -0.79 Governance 0.92% 0.368 -0.21*** -4.22 0.25*** 3.89 0.10 1.29 -0.06 -1.20 J-stat A 9.37 24.96 27.38 23.67 14.44 (0.154) (0.000) (0.000) (0.000) (0.025) J-stat B 7.32 18.59 19.38 13.22 6.36 (0.293) (0.005) (0.004) (0.040) (0.384)
Panel B: KLD Strength and Concern Portfolios
t-stat RM - RF t-stat SMB t-stat HML t-stat MOM t-stat
Commstr 3.01% 1.45 0.95*** 17.66 0.01 0.17 0.49*** 4.41 -0.11 -1.77 Commcon -0.38% -0.13 1.10*** 13.40 0.05 0.92 0.79*** 5.89 -0.13 -1.48 Divstr 3.37% 1.34 1.03*** 24.25 0.10 1.58 0.39*** 3.53 -0.20** -2.50 Divcon 0.99% 0.28 1.11*** 15.41 0.36*** 3.66 0.49*** 3.96 -0.26*** -4.87 Empstr 2.68% 1.22 1.07*** 24.46 0.20*** 3.14 0.43*** 4.43 -0.22*** -4.12 Empcon 2.18% 0.73 1.13*** 19.79 0.31*** 4.03 0.54*** 4.05 -0.31*** -3.33 Envstr 0.63% 0.25 0.99*** 14.90 0.21*** 3.18 0.64*** 6.43 -0.19** -2.56 Envcon -0.50% -0.19 1.03*** 15.41 0.16*** 2.50 0.75*** 5.95 -0.16 -1.81 Prostr 3.42% 1.19 1.03*** 18.27 0.18* 1.86 0.33*** 3.05 -0.19*** -3.50 Procon 1.91% 0.95 1.01*** 20.34 0.04 0.63 0.58*** 4.67 -0.17** -2.64 Govstr 4.21% 1.14 0.91*** 12.13 0.38*** 3.11 0.46*** 2.69 -0.29*** -3.87 Govcon 3.27% 1.38 1.11*** 28.98 0.13** 2.14 0.36*** 3.57 -0.23*** -4.39 J-stat A 24.32 32.12 31.84 30.96 29.80 (0.018) (0.001) (0.001) (0.002) (0.003) J-stat B 12.91 NA† 22.56 19.67 14.07 (0.376) (0.032) (0.074) (0.296)
In Panel A we estimated for all portfolios in a system GMM framework the regression: R(t) – RF(t) = + [RM(t) – RF(t)] + sSMB(t) + hHML(t) + mMOM(t) + e(t). T-statistics are adjusted following Ferson and Foerster (1994) by a factor T/(T-P), where T is the number of time periods and P the number of parameters. We also test the over identifying restriction generated by the remaining orthogonality conditions when we set one of the parameters to zero for all of the portfolios. For panel A Hansen (1982) shows this test is distributed as 2(6) under the null since in the restricted case the number of instruments is 36 and the number of parameters is 30 so that the number of over identifying restrictions is 6. In panel B this test is distributed as 2(12) under the null since in the restricted case the number of instruments is 72 and the number of parameters is 60 so that the number of over identifying restrictions is 12. J-stat A and B denote J-stats from 2-Stage and Iterated GMM, respectively. P-values are reported between
So the out performance of the community difference portfolio does not seem to be due to the fact that it is underpriced in the first place. However, the fact that the
community strength portfolio seems to outperform its concern portfolio does not necessarily imply that the stocks in the community strength portfolio outperform other stocks in our sample. In addition, in our portfolio regressions we cannot distinguish between firms obtaining a larger or a smaller SRI score. Therefore, to look more directly at the impact of SRI scores on future excess returns, in the next section we discuss the results of our Fama-MacBeth (1973) regressions.
1.3.3 Fama-MacBeth Return Regressions
Looking at the results in Table 4 we see that the effect of most of the control variables are consistent with Hong & Kacperczyck (2007). Betai,t and Turnoveri, t-1 are not significant and LogM/Bi, t-1 and Agei, t-1 have a negative effect on subsequent returns. Furthermore, although LogSizei, t-1 and Returnsi,t-1 do not have a significant influence, they do have the expected signs. Concerning the SRI scores, we see that only the
employee relations score has a significant positive effect on excess returns. Although it is only significant at the 10% level, it is robust to the inclusion of numerous control
variables, including 39 industry dummies. The outperformance of about 0.07% per month per point implies that stocks obtaining the maximum (minimum) score on employee relations of 4 (-4) will outperform (underperform) other stocks in the sample by 3.4% excess returns on an annual basis.
TABLE 3: Pooled Market-to-Book Regressions
Panel A: Full KLD scores
Variable (1) T-stat (2) T-stat
Community 0.016 0.83 0.007 0.311 Diversity 0.047*** 4.44 0.052*** 4.589 Employee Rel. 0.014 1.14 0.013 0.937 Environment 0.042*** 3.25 0.047*** 3.467 Product 0.046** 2.21 0.044** 2.230 Governance -0.108*** -7.08 -0.118*** -4.187 R&D/Sales 0.005*** 3.00 0.005*** 3.595 R&DMissing -0.288*** -11.74 -0.289*** -9.596 Russell3000 0.001 0.03 0.036 0.915 LogAge -0.098*** -7.08 -0.093*** -7.063 ROE 0.567*** 7.94 0.575*** 2.964 Dum. Time Y N Adj. R-sqr. 0,713 0,127
Panel B: Strength and Concern KLD scores
Variable (1) T-stat (2) T-stat
Comstr 0.004 0.20 0.007 0.28 Comcon -0.054 -1.64 -0.049 -1.28 Divstr 0.052*** 3.85 0.066*** 4.18 Divcon -0.048 -2.46 -0.045 -1.71 Empstr 0.013 0.71 0.017 0.78 Empcon -0.023 -1.50 -0.044 -1.35 Envstr -0.080*** -3.41 -0.090*** -3.39 Envcon -0.074*** -5.52 -0.081*** -5.70 Prostr 0.097*** 2.63 0.085** 2.25 Procon -0.017 -0.69 -0.014 -0.48 Govstr -0.018 -0.65 0.001 0.03 Govcon 0.154*** 8.28 0.174*** 5.44 R&D/Sales 0.005*** 3.05 0.003*** 5.16 R&DMissing -0.299*** -12.25 -0.287*** -8.98 Russell3000 0.008*** 0.23 -0.009 -0.25 LogAge -0.085*** -6.13 -0.063*** -4.24 ROE 0.555*** 7.83 -0.003*** -2.99 Dum. Time Y N Adj. R-sqr. 0,718 0,092
Concerning workforce reductions, Hallock (1998) and Farber and Hallock (1999) show that layoffs are negatively related to cumulative abnormal returns (CARs), although the effect has been rather small in recent years.10 Concerning union relations, evidence
TABLE 4: Cross-Section Regressions of Excess Stock Returns, July 1992 - June 2006
Variable (1) (2) (3) (4) (5) (6) (7) Community -0.003 0.011 0.003 0.006 0.058 0.068 0.042 -0.070 0.231 0.062 0.136 1.260 1.469 0.870 Diversity -0.049 -0.022 -0.012 -0.009 -0.012 -0.017 -0.046 -1.018 -0.482 -0.268 -0.202 -0.276 -0.384 -1.104 Employee Rel. 0.045 0.060 0.077* 0.079* 0.071* 0.074* 0.073* 1.028 1.439 1.897 1.951 1.826 1.908 1.720 Environment 0.020 -0.005 0.034 0.037 0.049 0.038 -0.046 0.377 -0.090 0.644 0.698 0.942 0.732 -1.105 Product 0.042 0.010 0.062 0.053 0.049 0.045 0.058 0.615 0.145 0.954 0.850 0.811 0.749 1.146 Governance 0.014 -0.095 -0.093 -0.094 -0.110 -0.104 -0.098 0.173 -1.183 -1.200 -1.221 -1.479 -1.390 -1.312 Beta 0.163 0.037 0.032 0.019 -0.108 -0.124 -0.327 0.304 0.070 0.061 0.038 -0.237 -0.271 -0.776 LogSize -0.117 -0.015 -0.019 -0.031 -0.015 -0.041 -1.913* -0.240 -0.314 -0.507 -0.251 -0.713 LogM/B -0.477*** -0.482*** -0.591*** -0.608*** -0.637*** -4.109 -4.190 -5.570 -5.756 -6.481 Returns 0.025 0.014 0.011 0.016 0.777 0.441 0.351 0.613 Turnover 0.330* 0.291 0.107 1.803 1.591 0.687 Log Age -0.512*** -0.374** -3.779 -2.658 Dum. Russell -0.002 -0.024 -0.044 -0.573 Dum. Industry N N N N N N Y Adj. R-sqr. 0,000 0,000 0,003 0,002 0,003 0,002 0,003 This table reports the results on the Fama-MacBeth (1973) regressions. Variables are described in Table 1. Dum. Industry Y (N) indicates whether 39 industry dummies have (have not) been included in the specification. T-statistics are reported below the coefficients. * 10% significance ** 5% significance *** 1% significance
suggests that union coverage is negatively related to market value (Hirsch, 1991) and that this negative effect is not accompanied by growth changes (Bronars and Deere, 1993). Finally, to the extent that poor union relations increase the chances of strikes it is relevant
10 For an overview on the results of studies on the relationship between job loss announcements and stock
to note that Kramer and Vasconcellos (1996) and Persons (1995) find that strike announcements result in negative CARs.
To disentangle the effect of the sub scores we re-estimate equation (5), this time including the sub screens of employee relations as dummy variables instead of the employee relations score. A description of the sub screens and the results are provided in Table 5. The first thing to notice is that there are only a few subscreens that significantly affect excess returns. The size and significance of these dummies suggests that there are indeed only a few subscreens responsible for the effect of employee relations on excess returns. In particular, they are all larger in absolute terms than 3.4% annually and generally more significant than the total score.
TABLE 5: Cross-Section Regressions of Excess Returns on Employee Relations Screens
Variable (1) (2) (3) (4) (5) (6) (7)
Employee Relations Subscreens
Second, only the concern subscreens have a significant effect on excess returns, but they are not consistent in sign. This implies that simply adding the subscores of strength and concern screens to form overall scores will lead to confounding effects. It also suggests that what is a concern from a social perspective is not always a concern from a financial perspective due to the fact that social objectives do not always align with firm objectives. For instance, Pension/Benefit Concern (Empcon. D) has a positive
influence on future excess returns. This could be due to the fact that investors require a premium for firms with underfunded pension liabilities (Carroll and Niehaus, 1998). Still, in other cases both objectives can be aligned. When we look at Poor union relations (Empcon. A) and Workforce reductions (Empcon. C) we see that they have a negative effect on future excess returns, possibly because they influence future cash flows negatively.11
1.3.4 Robustness Checks
Comparing the results of our three analyses, our most interesting finding is that those dimensions related to initial market-to-book ratios (i.e. Diversity, Environment, Product and Governance) do not seem to be related to subsequent excess returns, neither in our portfolio regressions nor in our Fama-MacBeth (1973) regressions. Conversely, those dimensions that are related to excess returns, i.e. Community in our portfolio regressions and Employee Relations in our Fama-MacBeth (1973) regressions are not related to market-to-book values. Therefore, our results imply that the effect on excess returns does not seem to be due to overpricing (underpricing) induced by the excess demand (lack of demand) of socially responsible (irresponsible) stocks.
To check the robustness of our results we performed some additional analyses which are available on request. As a first check we repeated our portfolio regressions but this time using value-weighted returns instead of equally weighted returns. Results
remain qualitatively the same, except the difference portfolio of employee relations yields a significant positive excess return of 2.81% annually, while the excess return on the Community difference portfolio is insignificant. These results are reported in Appendix 1A.
A second check consists of also splitting the Employee Relations score into its 10 sub scores for our market-to-book regressions. The results of this robustness check are reported in Appendix 1B. In contrast to the return regressions in Table 4, only some of the strength scores significantly influence market-to-book ratios, while the concern scores do not influence market-to-book ratios. A notable exception to this is Workforce
reduction (Empcon C.) which does significantly influence market-to-book ratios, however, the fact that it enters with a negative sign is contradictory to the neglect effect
hypothesis. Yet, the fact that it influences market-to-book ratios negatively and also influences future excess returns is in accordance with the underreaction hypothesis.
1.4. Conclusions
In this paper we set out to investigate three hypotheses concerning the effect of social responsible investment on stock returns; the neglect effect hypothesis, the underestimation hypothesis and the underreaction hypothesis. According to the first, social responsibility is positively related to market-to-book values, but negatively to excess returns. According to the second hypothesis investors consistently underestimate the probability that positive news will be released about companies that are socially responsible. So it predicts that SRI is negatively related to market-to-book values and positively related to excess returns. Finally, according to the underreaction hypothesis, SRI information is a determinant of stock returns due to the fact that investors underreact to the financially relevant information conveyed by SRI scores. This implies that there is no relation between market-to-book value and SRI and that there is a positive relation between SRI and excess returns.
Our results imply that the third hypothesis is most likely to hold for our data. For several of our Employee relations sub screens bad news has a negative effect on stock returns, but no effect on initial market-to-book values. Furthermore, in our portfolio regressions SRI is positively related to excess returns for the Community difference portfolio.
Another aspect illustrated by our analyses is that one should take a very disaggregated look when investigating the relationship between socially responsibility and returns. Even when aggregating over only a few sub scores one risks creating predictors that have confounding effects. Especially when the social responsibility information conveys financial information there are advantages to disaggregating when different sub scores contain different pieces of information that have conflicting effects on returns. In addition, the fact that the scores we investigated are changing from year to year, underlines their informational relevance.
CHAPTER 2
DIVERSIFICATION OF SOCIALLY RESPONSIBLE INVESTMENT PORTFOLIOS: TESTING FOR MEAN-VARIANCE SPANNING 2.1 Introduction
In recent years socially responsible investment (SRI) has become increasingly popular. US investment in socially screened mutual funds and separate accounts has increased from $162 billion in 1995 to $1,685 billion dollar in 2005. Relatively, the largest increase was shown by socially screened mutual funds, whose assets increased from $12 billion to $179 billion in 2005 (Social Investment Forum, 2005). The SRI investment process is characterized as an investment process which in addition to financial consequences also takes account of the social and environmental consequences of investments. As such it is aimed at delivering value to the shareholders as well as to society at large. To achieve this aim, a strategy that is often deployed by investors is screening. Hereby investors choose to hold stocks of companies that perform well in terms of social responsibility and avoid stocks that perform badly.
However, by screening stocks based on non-financial criteria investors limit their investment universe. The constraints imposed by socially responsible investing imply that mean-variance optimization is limited, since there are now less stocks to choose from to achieve an optimally diversified portfolio. In other words, investors might achieve a higher return with a lower variance by also investing in the assets they exclude from their portfolio. Of course, this is only true in a world where unconditional expected returns are equal to expected returns conditioned on social responsibility information. However, proponents of SRI argue that social screening ensures that the stocks that are selected based on social screening are those that offer a higher mean return for a lower variance compared to those that are not selected. The aim of this paper is to provide some empirical evidence in this debate by testing whether a socially responsible investor is better or worse off by not investing in negatively screened assets.
For this purpose we use the methodology of mean-variance spanning and
intersection tests as developed by Huberman and Kandel (1987). These regression-based tests are used to test the effect of additional assets on the mean-variance frontier.
the risk-free rate, we can test whether there is intersection. Intersection means that the mean-variance frontier of the benchmark assets and the mean-variance frontier of the benchmark assets and the new assets have precisely one point in common. If instead we do not make the assumption that there exists a risk-free rate we can test for spanning. Spanning means that the mean-variance frontier of the benchmark assets coincides with the frontier of the benchmark assets and the new assets. This implies that no mean-variance investor can be made better off by investing in the extra assets, regardless of the risk-free rate.
The bulk of recent studies that apply mean-variance spanning and intersection are concerned with the benefits from international diversification. For instance, Bekaert and Urias (1996), Errunza et al. (1999) and De Roon et al. (2001) study whether investors are better off in mean-variance terms when investing in emerging markets. Furthermore, Glen & Jorion (1993) and De Roon et al. (2003) use mean-variance spanning techniques to study how currency hedging can improve international stock portfolios. Finally, Eun et al. (2006) use spanning and intersection analysis to show the difference in diversification possibilities for investors in small cap stocks versus large cap stocks.
In contrast, this study applies the mean-variance spanning and intersection tests to a different area, namely that of socially responsible investing. Specifically, we use the step-down spanning test proposed by Kan and Zhou (2001), which allows us to track down what is causing the rejection of spanning. In addition we test for spanning when there are transaction costs and short-sales restrictions, as in DeRoon et al. (2001). The latter is especially interesting. This is because it allows us to test whether the assets excluded by socially responsible investors can contribute to the optimal portfolio of all assets in a negative or in a positive sense. That is, in order to improve the portfolio in mean-variance terms, should investors take short positions in these assets or long positions?
mean-variance terms, investors could take long positions in the assets initially excluded. This is called the discriminating tastes hypothesis.
The literature concerning this hypothesis originates from Merton (1987) who shows that in the presence of incomplete information and different investor demand preferences, excess returns can depend on other characteristics than market risk. His model for instance predicts that more-widely known firms with larger investor bases will have lower alphas. In a related model Heinkel et al. (2001) show that firms that are not socially responsible will face a higher cost of capital due to a lack of demand for their stocks. Dam (2007) shows that returns can only be higher for irresponsible firms when we compare firms with the same level of damage per output, i.e. firms from the same industry. Finally, a very simple model that only considers investor tastes in determining market equilibrium in a CAPM world is presented by Fama and French (2007). They show that when some investors have tastes for assets as consumption goods, market equilibrium is generically like equilibrium in a world where some investors trade on misinformed beliefs. The only difference is that misinformed beliefs are corrected when investors see the errors of their ways, whereas price effects due to tastes can persist. If a group of investors has a taste for socially responsible assets and if there is a group of investors willing to hold the complement of these investors’ holdings a situation can persist in which SRI investors persistently earn lower returns than SRI neutral investors.
Implicitly, these models assume that CSR does not convey financial information. In contrast, Derwall (2007, p.194) asserts that CSR does convey financial information. This he calls the value relevance hypothesis; ‘markets are rationally responsive to social responsibility because corporate social responsibility (CSR) conveys clear financial information about a firm’s risks and cash flows’. However, in the context of mean-variance spanning, this hypothesis is difficult to investigate since we are dealing with stock returns. This difficulty arises because an increase in stock returns can imply both an increase in expected cash flows or a decrease in expected risk.
diversification of the larger portfolio that includes irresponsible stocks. Here, the value emanates from lower transaction costs associated with a smaller portfolio. So if reject spanning, we reject the transaction cost relevance of CSR. Considering the second, CSR screening can be valuable when it screens out those assets that will perform worse in mean-variance terms, so that investors can possibly take short positions in these assets. As such, CSR information can be used directly to improve the portfolio in mean-variance terms, so it is mean-variance value relevant. Rejecting mean-variance value relevance implies accepting the discriminating tastes hypothesis and vice-versa.
Of course, from an investor perspective it is also valuable to know whether one should take long positions in the assets first excluded. However, economic theory suggests that this is purely due to the demand effect explained above. That is why we refer to this as the discriminating tastes hypothesis. Of course, the reader can be agnostic about whether taking long positions in assets first excluded is due to a pure demand effect induced by tastes or due to risk and return information implicit in CSR information.
The most compelling evidence for this discriminating tastes hypothesis is
provided by Hong and Kacperczyck (2007) who show that sin stocks, i.e. stocks of firms involved in producing alcohol, tobacco and gambling, achieve higher excess returns than other stocks. In addition, they find that these sin stocks are less held by norm-constrained institutions such as pension plans. Related to this are the findings of Arbel et al. (1983) who find that there is a negative relation between institutional holdings and excess returns, even when controlling for size. In a study closely related to ours Geczy et al. (2003) investigate the diversification loss of mutual fund investors that restrict their universe to socially responsible mutual funds. They find that the constraint is costly for investors disallowing manager skill, but believing in pricing models that associate higher returns with exposure to size, value and momentum factors.
performance. Whereas the first corroborates the discriminating tastes hypothesis, the latter corroborates the value relevance hypothesis. This illustrates that these two hypotheses are not mutually exclusive, but depend on which exclusionary screens one considers.
This is consistent with our results differing according to which exclusionary screens one considers. First, we can reject spanning for the excluded Sin, Social,
Environment and Product portfolios but we cannot reject it for the Governance portfolio, when allowing short sales. This implies we can reject transaction cost value relevance for the excluded Sin, Social, Environment and Product portfolios, but we cannot reject it for the Governance portfolio. So investors can benefit in terms of transaction costs by holding a smaller portfolio that excludes Governance concern stocks. Second, we can only reject spanning and intersection for the Sin portfolio when we disallow short sales. This is consistent with Hong and Kacperczyck (2007) and suggests that when investors take long positions in Sin stocks they can improve their portfolio in mean-variance terms. So for Sin stocks we can reject the mean-variance value relevance hypothesis and we have to accept the discriminating tastes hypothesis. For the Social portfolio it is just the other way around; this portfolio receives a significant negative weight in the tangency portfolio when allowing short sales. This implies that we can reject the discriminating tastes hypothesis and we have to accept the mean-variance value relevance hypothesis. Finally, transaction costs of the CSR investment strategies do not qualitatively change our results, which suggests we should not attach too much weight to the results on the
transaction cost value relevance hypothesis.
The rest of this paper is organized as follows. In section 2, we first explain the intuition behind mean-variance spanning tests. Then we present a multivariate framework and explain how this is used when testing for spanning and intersection. Finally, we discuss how we perform these tests when considering short sales constraints and
transaction costs. In section 3, we discuss the results of our mean-variance spanning tests. In addition, we perform the actual Markowitz portfolio optimization to show the
2.2 Mean-Variance Spanning and Intersection
The idea of mean-variance spanning is straightforward. A set of K risky assets spans a larger set of K + N risky assets if an investor cannot become better off in mean-variance terms from investing in the N additional assets. In that case the mean-mean-variance frontiers of the K risky assets and the K + N risky assets coincide. Usually the mean-variance spanning literature refers to the K assets as benchmark assets and to the N assets as test assets. In our case, the K benchmark assets are those assets a socially responsible does invest in and the N test assets are those assets it does not invest in. Mean-variance spanning tests whether there is a difference in the mean-variance frontiers of the K and K + N risky assets and therefore it applies to all possible values of the risk-free rate. As such the concept is most interesting when a risk-free asset does not exist, or when there is no unlimited lending and borrowing at a known risk-free rate.
By contrast, when there is unlimited risk-free lending and borrowing at a known risk-free rate, we no longer consider spanning since investors will only be interested in the portfolio that maximizes their reward to risk ratio (i.e. Sharpe ratio). In other words, when there exists a risk-free rate, we basically fix a parameter which entails that instead of the whole mean-variance frontier we are only interested in one point: the tangency portfolio. In that case we are interested in intersection of two sets of assets, which is formally defined as; there is only value of the risk-free rate (η) for which mean-variance investors cannot improve their mean-variance efficient portfolio by investing in the N additional assets. In other words, the mean-variance frontiers of the K benchmark assets and the K + N assets are said to intersect.
2.2.1 Tests of Mean-Variance Spanning
= = 2 1 ] [ µ µ µ E Rt (1)
and the covariance matrix of the K+N risky assets as
= = 22 21 12 11 ] [ V V V V R Var V t (2)
where we assume that V is invertible. Regressing R2t on R1t:
, 1 2t Rt t
R =α+β +ε t =1,2,...,T (3)
Here we assume the estimated coefficients are constant over time, E[εt]=0N and K
N t tR
E[ε 1′]=0 × , where 0 is an N-vector of zeros and N 0N×Kan N × K matrix of zeros.
Testing for spanning implies that we jointly test for each of the N test assets whether the intercept is equal to zero and whether the sum of the K beta values is equal to one. In order to do so we need estimates of the N intercepts and the N × K beta coefficients
which are given by α =µ2 −βµ1 and 1 11 21
−
=V V
β . The restrictions that need to hold for spanning are: , 0 : 0 N H α = βιK = ιN (4)
where 0 is a vector of N zeros and N ιK and ιN are vectors of K and N ones,
respectively. To see why (4) indicates spanning we consider a simple example in which we take N = K = 1. In that case it is easy to see that spanning implies that
t t t R
R2 = 1 +ε t =1,2,...,T (5)
SinceR1tand εt are uncorrelated we can write the variance of their sum as the sum of
their variances: ) ( ) ( ) ( )
(R2t Var R1t t Var R1t Var t
Var = +ε = + ε t=1,2,...,T (6)
So the variance of the benchmark asset is smaller than that of the test asset under the assumption of spanning. However, the assumption of spanning also implies that the benchmark assets and the test assets have the same mean13. So when there is spanning the benchmark asset has the same mean but a lower variance than the test asset and the benchmark asset spans the test asset.
To describe the multivariate tests of spanning we consider the matrix notation of equation (3):
where R is a T × N matrix of R2t, X is a T × (K + 1) matrix with its typical row [1 R′ , 1t] B is a (K + 1) × N matrix of coefficients containing the N vectors of coefficients
corresponding to each of the N test assets and E is a T × N matrix of errors. Furthermore,
we assume that T is large compared to N and K, XX ′ is invertible and the errors are multivariate iid distributed with mean zero and variance Σ
The unconstrained maximum likelihood (ML) estimators are ) ( ) ( ˆ XX 1 XR B≡ ′ − ′ (8) ) ˆ )( ˆ )( / 1 ( ˆ ≡ T R−XB R−XB Σ (9)
The hypothesis of spanning is given by H0 :θ = AB−C =02×N where
′ − ′ = K K A ι 0 0 1 (10) ′ − ′ = N N C ι 0 (11)
The ML-estimator of θ is given by θˆ= ˆAB−C. Since we have equality restrictions here Seber (1984) shows that we do not need to perform the constrained estimation to obtain test statistics. We can suffice with defining
A X X TA Gˆ = ( ′ )−1 ′ (12) θ θΣ ′ = ˆˆ− ˆ ˆ 1 H (13)
and noting that all invariant tests of (4) (e.g. Wald, Likelihood Ratio and Lagrange multiplier tests) are functions of the eigenvalues of HG−1. From Bernt & Savin (1977) the Wald test is given by
2 2 1 ~ N A Q i i T W λ χ = = (14)
where Q is the number of nonzero roots of HG−1, which are two in this case.
2.2.2 The HK-test statistic
) ( 2 , 2 2 / 1 1 ~ 1 N K T N F N N K T U HK = − − − − − (15)
When N = 1 this statistic should be
N K T F K T U HK = − − − ~ 2, − − 2 1 1 1 (16)
Here U =| Σˆ |/|~Σ| where Σ~ is the constrained ML-estimator of Σ~ .
Kan and Zhou (2001) provide a power analysis of these test statistics and show that the distance between the standard deviation of the two global minimum-variance portfolios is the main determinant of the power of spanning tests, whereas the distance between the two tangency portfolios is relatively less important. This is because in the joint test where the intercept is zero and the beta-parameters sum to one, the former can be estimated much less precisely than the latter. The estimation of the intercepts involves estimating , whereas estimating the other parameters does not. Since the other
parameters can be estimated more precisely, spanning tests place more weight on the part of the test that tests whether the coefficients sum to one.
However, what is statistically important here does not correspond to what is economically interesting. We are primarily interested in the intercept parameter, since the sign of the parameter indicates whether the tangency portfolio has positive or negative weights in the N test assets. So it indactes whether we have to take short positions in the social concern assets first excluded or long positions, respectively.
To take account of the differences in power of the two parts of the spanning test, Kan and Zhou (2001) develop a step-down procedure in which the first step consists of testing whether the intercepts are zero by means of an F-test similar to the HK-test:
N K T N F N N K T F − − − Σ Σ − − = , 1 1 ~ | ˆ | | | (17)
where Σˆ is the unconstrained estimate of Σ and Σ the constrained estimate imposing the
constraint that all intercepts equal zero. In the second step of the step-down test we test conditional on . This F-test is given by
