Canadian Socially Responsible Investment Mutual Funds Performance Evaluation Using Data Envelopment Analysis

Abstract

Socially responsible investment (SRI) mutual funds, which rely on social, environmental and ethical considerations in the investment decision-making process, have experienced significant growth over the past 20 years worldwide. This chapter examines the performance, over the 2008–2011 period, of a survivorship bias-free sample of 85 Canadian SRI funds, using a Data Envelopment Analysis (DEA) approach. This technique does not require the specification of benchmarks and allows measuring the relative efficiency of decision making units/funds in the presence of a multiple input-output setting. Various performance indicators or efficiency scores are derived using higher-order moments and tail-risk measures, fee structures, net returns, and fund size. The results confirm the suitability of the DEA-based performance setting and suggest that front-end loads and fund size are the main causes of the inefficiency of Canadian SRI mutual funds. These findings carry important implications for the fund-selection process and performance persistence, and would be of interest to regulators, practitioners, and institutional and individual investors.

1 Introduction

Performance measurement and evaluation of actively managed funds continue to receive wide interest among academics and practitioners. The variety of interested parties who are involved in and benefit from the assessment of fund performance suggests the need for a robust measure. At first, it was simply about computing the historical returns without taking into account other factors: the higher the return, the better the performance. With the development of modern portfolio theory by Markowitz (1952), risk was included into the decision-making process, and pioneering measures were proposed by Treynor (1965), Sharpe (1966), and Jensen (1969). Since these contributions, alternative approaches have been proposed in the literature; where they differ is in the way risk is considered, such as the use of multifactor models (Lehmann and Modest 1987; Carhart 1997) and the adoption of the stochastic discount factor-based methodology (Chen and Knez 1996; Farnsworth et al. 2002; Ayadi and Kryzanowski 2005, 2008).

Nevertheless, there is an ample literature arguing that different managerial attributes and other fund characteristics can affect mutual fund performance. These characteristics include the fund size (Indro et al. 1999), management fees (Elton et al. 1993), expenses (Malkiel 1995), and loads (Carhart 1997). Furthermore, Glosten and Jagannathan (1994) provide evidence that actively managed mutual funds have non-normal return distributions with negative skewness and fat tails due to investment restrictions or limitations, such as short-selling restrictions, the use of derivative instruments to hedge risk, and the increasing use of option-like trading or dynamic strategies. They contend that traditional or classical measures of performance would be inappropriate and would lead to a biased assessment of fund managers’ true selection ability.¹ This finding was recently corroborated by Ayadi and Kryzanowski (2013) on a sample of Canadian equity mutual funds, and by Agarwal et al. (2014) for several hedge fund portfolios. Both papers advocate the use of nonlinear benchmarks for such investment portfolios.²

The inadequacy of traditional measures in a non-normal world and for portfolios with nonlinear payoffs has led to the development of alternative methods named frontier analysis methods. Data Envelopment Analysis is a powerful non-parametric frontier method founded by Charnes et al. (1978) that takes into consideration the dynamics of fund strategies and the various fund characteristics. DEA is suitable to assess and rank mutual fund performance in a (nonlinear) risk-return framework based on several input and output variables, even with a non-parametric relationship for these variables. DEA-based measures of performance offer insights into the level of fund efficiency, given the set of input and output variables. Such information is useful to individual and institutional investors as well to fund managers to uncover the importance of the included variables through their efficiency contributions.

One type of investment portfolio that has experienced tremendous growth in the past 20 years is the socially responsible investment (SRI) mutual fund.³ The investment strategies of such funds are governed by ethical rules and social screens to select or exclude assets. Advocates of these special investments argue that the inclusion of social and environmental considerations in the investment decision-making process improves investment returns. Therefore, assessing the performance of SRI investments or mutual funds is of interest to various players in the financial system.⁴ We build on the previous research by using the DEA method to develop new performance measures for a comprehensive sample of Canadian SRI funds over the 2008–2011 period.⁵ Our approach takes into consideration key variables such as net returns, linear and nonlinear risk measures, total assets, and fee structures. In this vein, Basso and Funari (2008) study the performance of ethical mutual funds on the European market and develop new efficiency scores. They find that ethical funds have higher scores only when the employed DEA model considers the ethical level among the output variables. In parallel, Pérez-Gladish et al. (2013) use the same method to examine the performance of a sample of US mutual funds. They conclude that there are no significant performance (efficiency scores) differences between conventional and SRI funds.

The remainder of this chapter is organized as follows. In the next section we introduce socially responsible investments mutual funds and their strategies, with a brief review of the literature on their performance. In Sect. 3, we discuss the DEA approach as an alternative non-parametric performance index. We also highlight the use of DEA in the evaluation of mutual fund performance. Section 4 explains the empirical implementation of the DEA approach, with a description of the data and key variables. It also discusses the obtained results. Finally, the conclusion reviews the major results and identifies possible avenues of future research.

2 Socially Responsible Investments Mutual Funds

Socially responsible investments (SRI) mutual funds, also known in the literature as ethical funds, are special investments that aim to harmonize investors’ financial and ethical objectives. Instead of relying solely on financial criteria, ethical funds integrate moral and social issues. The Social Investment Organization defines socially responsible investing (SRI) as the inclusion of social, environmental, and governance (ESG) considerations into the management and selection of investments.⁶ This organization claims that socially responsible mutual funds, when compared to conventional funds, offer an additional level of analysis and investment by using one SRI strategy or a combination of several. These strategies and previous SRI performance research are presented and discussed in the next sub-section.

2.1 SRI Strategies

Several organizations, such as the US Sustainable and Responsible Investment Forum, the European Sustainable Investment Forum, the Association for Sustainable and Responsible Investment in Asia, the Responsible Investment Association Australasia, and the Canadian Social Investment Organization, recognize five major investment strategies (Social Investment Organization 2013).

Screening

This is the most adopted strategy and can be divided into three groups: negative screening, positive screening, and standards-based screening. Negative screening is used to exclude companies that are involved in unethical activities, such as tobacco manufacturing, alcohol production, military or weapons-related contracting, gambling, nuclear power, or pornography. Positive screening “is a proactive process designed to select companies that demonstrate leadership in a variety of environmental, social, and governance issues.”⁷ This, for example, includes protection of the environment, protection of human rights, ensuring employee standards, or supporting alternative energy. Finally, standards-based screening involves the selection of investments that respect international standards, such as the United Nations Universal Declaration of Human Rights or the UNICEF Convention on the Rights of the Child.

Integration

This involves the consideration of ESG factors in investment research and in the decision-making process. It differs from screening in the sense that it combines ESG data, research, and analysis, together with financial and other factors, in making investment decisions.

Sustainability-themed funds

Sustainability-themed investing involves selecting assets on the basis of investment themes such as clean energy, green technology, or sustainable agriculture. Investments are directed at companies or industries that offer innovative solutions to existing problems or that otherwise enhance sustainability practices.

Impact investing

Impact investing refers to targeted investments that are made in private markets and that aim at solving social or environmental problems while also generating financial returns. Impact investing includes community investing, where capital is specifically directed to traditionally underserving individuals or communities, to businesses with a clear social or environmental purpose, or to revenue-generating non-profits.

Corporate engagement and shareholder action

This strategy aims at influencing corporate behaviour through various strategies including communicating with senior management and/or boards of directors, filing shareholder proposals, and proxy voting.

2.2 Literature Review

Viewed from three different perspectives, the phenomenon of ethical funds has been discussed by several researchers. Each of these standpoints is based either on an underperformance, outperformance, or no-effect hypothesis (Hamilton et al. 1993). The first hypothesis claims that ethical funds underperform their conventional peers. The reasons for this underperformance are discussed by Bauer et al. (2007): First, investing in ethical funds limits the diversification of the portfolio because ethical funds can exclude companies with a good financial performance, for ethical considerations. Second, there are costs to developing ethical investment screens and corporate-social-responsibility rankings. Third, irresponsible activities are perceived as more lucrative and recession-proof than are responsible investments. The second hypothesis suggests that ethical funds can outperform conventional funds. The outperformance of ethical funds occurs when “sound social and environmental performance signals high managerial quality, which translates into favourable financial performance” (Renneboog et al. 2008). Outperformance could also be related to the fact that responsible investments avoid paying for the consequences of non-ethical behaviours, for instance, government fees. Finally, the ‘no-effect-hypothesis’ supposes that there is no significant difference between the performance of ethical and conventional funds. In other words, the social responsibility feature does not affect the stock price (Hamilton et al. 1993).

Several empirical studies have been conducted in various countries to confirm or disconfirm these hypotheses. The majority of the studies focus on the US market, such as Hamilton et al. (1993), Statman (2000), Bauer et al. (2005), Benson et al. (2006), and Renneboog et al. (2008). They all conclude that there is no significant performance difference between ethical and conventional funds. The same conclusion is drawn by Luther et al. (1992), Mallin and Saadouni (1995), Gregory et al. (1997), Kreander et al. (2005), and Renneboog et al. (2008), who examine the performance of ethical funds in the European market. Furthermore, the Australian and Canadian evidence (Bauer et al. 2006, 2007; Humphrey and Lee 2011; Ayadi et al. 2015) supports the no-effect hypothesis. Nevertheless, few studies confirm the underperformance or outperformance hypothesis, such as Chang and Witte (2010), whose findings show a significant underperformance of US SRI funds over 5-, 10- and 15-year periods, but not over the 3-year period.

The above-mentioned studies use classic performance measures, mainly Jensen’s alpha, based either on the CAPM, or on the Carhart four-factor-model, Sharpe ratio, and Treynor ratio. However, the comparison is regarded as meaningless if the ethical and conventional funds do not have the same characteristics (age, size, market, investing area, etc).

3 Data Envelopment Analysis for Performance Evaluation

3.1 Introduction

Most classical or parametric performance measures rely on the Markowitz portfolio theory (1952). This approach uses the efficient-frontier concept, which is defined as a set of non-dominated portfolios in the mean-variance space; in other words, the efficient frontier consists of portfolios that maximize returns for a given level of risk, or alternatively, minimize risk for a given expected return (Kroll et al. 1984). Similarly, alternative methods of frontier analysis are based on the concept of the production frontier, which illustrates the maximum potential output that a production unit can achieve under a given set of inputs. These methods were initiated by Farrell (1957) in an attempt to present an efficiency measure that overcomes the problems of index numbers in dealing with multiple inputs. All production units aim at reaching the efficient frontier but may fail due to reasons within or beyond their control. Farrell assumed that a production unit can be inefficient either if it produces less than the maximum output available from a set of inputs (technical inefficiency) or if it does not consume the best proportion of inputs in view of their prices (price or allocative inefficiency).

One non-parametric frontier-analysis approach referred to as Data Envelopment Analysis (DEA) was developed by Charnes, Cooper, and Rhodes in 1978 as a solution to the problem introduced by Farrell (1957) in measuring efficiency. It has been a useful tool to evaluate non-profit and public sector organizations. Unlike parametric methods, which require the specification of a functional form of the efficient frontier, the DEA approach is based on mathematical programming to define the efficient frontier and to calculate the efficiency scores. Moreover, it does not assume a precise relation between input and output variables, which would offer flexibility and less susceptibility to specification error. However, DEA does not allow for random error; instead, it attributes all deviation from the frontier to inefficiencies. Further, DEA is sensitive to the choice of input and output variables; adding an important number of inputs and outputs may decrease the model’s accuracy. DEA is also vulnerable to the curse of dimensionality, which is related to problems associated with a low number of decision-making units (DMU)⁸ relative to the number of input-output variables.⁹ Finally, the DEA model relies on the following basic assumptions: (1) The positivity of the employed variables; (2) Conditions on the number of DMU to be evaluated; for example, Cooper et al. (2007) claim that if the number of DMUs (n) is less than the combined number of inputs plus outputs (m + s), a large portion of the DMUs will be identified as efficient, and efficiency discrimination among DMUs is lost; (3) The homogeneity of the DMUs.

3.2 The DEA Model

We adopt the BCC (Banker, Charnes, and Cooper 1984) DEA model based on variable returns to scale, because if one can assume that economies of scale change as fund size increases, then constant-return-to-scale-type DEA models are not an adequate choice. Further, we choose an input-oriented model that emphasizes the reduction of inputs to improve efficiency, as we suppose that mutual-fund managers have more control over inputs than outputs.

The DEA model can be formulated in its dual form as follows:

$$ \begin{array}{ll}\mathrm{M}\mathrm{i}\mathrm{n}\hfill & {z}_o-\varepsilon \left({\displaystyle {\sum}_{i=1}^m{S}_i^{-}}+{\displaystyle {\sum}_{r=1}^s{S}_r^{+}}\right)\hfill \end{array} $$

(1)

$$ \mathrm{Subject}\ \mathrm{t}\mathrm{o}\kern1em \begin{array}{ll}{\displaystyle {\sum}_{j=1}^n{x}_{ij}\ {\lambda}_j+{S}_i^{-}}={z}_o{x}_{io}\hfill & i=1,2,\dots, m\hfill \end{array} $$

$$ {\displaystyle {\sum}_{j=1}^n{y}_{rj}\ {\lambda}_j+{S}_r^{+}}={y}_{ro}\kern1.6em r=1,2,\dots, s $$

$$ {\lambda}_j\ge 0\kern8.6em j=1,2,\dots, n $$

where we denote by: j = 1, 2, … , n funds; r = 1, 2, … , s outputs; i = 1, 2, … , m inputs; y _rj amount of output r for the fund j, x _ij amount of input i for fund j. ${S}_i^{-}$ and ${S}_r^{+}$ represent input and output slack variables, respectively. z _o represents the efficiency score for the fund under evaluation. λ _j (j = 1, … , n) are non-negative scalars. ε is a non-Archimedean element (a very small positive number).

The dual leads to the same value of the objective function as the primal. However, while the number of constraints of the primal depends on the number of the DMU evaluated, the dual constraints depend on the number of inputs and outputs. Ramanathan (2003) argues and demonstrates that the use of the dual formulation is computationally more efficient because the computational efficiency of linear programing codes depends upon the number of constraints.

According to Cooper et al. (2011), an efficient fund is one that satisfies the following conditions: z _o * = 1 and all slack variables are equal to zero. When a fund has an efficiency score equal to one and there are some slacks different from zero, it is considered weakly efficient.

Cooper et al. (2007) explain that a DMU can become efficient by reducing its inputs by the ratio z _o and eliminating the negative slacks ${S}_i^{-}$. A similar efficiency can be attained if output values are augmented by the positive slacks ${S}_r^{+}$. The gross improvements of inputs and outputs are given by the following formulas:

$$ \varDelta {x}_{io}={x}_{io}-\left({z}_o{x}_{io}-{S}_i^{-}\right)=\left(1-{z}_o\right){x}_{io}+{S}_i^{-} $$

(2)

$$ \varDelta {y}_{ro}={S}_r^{+} $$

The projection of the inefficient DMU into the frontier is defined by the following formulas:

$$ \tilde{x_{\iota o}} = {x}_{io} - \varDelta {x}_{io} $$

(3)

$$ \tilde{y_{ro}}={y}_{ro}+\varDelta {y}_{ro} $$

While the CCR model relies on two assumptions, namely, the convexity of the efficient frontier and the constant returns to scale, the BCC model (Banker et al. 1984) relaxes the latter assumption in order to handle variable returns to scale. The following constraint was introduced into the envelopment model:

$$ {\displaystyle {\sum}_j^n{\lambda}_j=1} $$

(4)

3.3 Literature Review on DEA Applications to Evaluate Mutual Fund Performance

Murthi et al. (1997) are the first researchers attempting to apply the DEA methodology to assess the performance of mutual funds. Their objective is to overcome the shortcomings of traditional performance measures, especially their inability to consider transaction costs in the analysis. They propose a new performance index called the DEA portfolio efficiency index that takes into account risk, return and transactions costs. The main CCR DEA model is applied to 731 mutual funds in 1993 using the actual return as the output variable, and four input variables: expense ratio, loads, turnover, and standard deviation of returns. As a result, Murthi et al. indicate that mutual funds are approximately mean-variance-efficient and that efficiency is not related to transaction costs. While Murthi et al. (1997) adopt the basic DEA assuming constant returns-to-scale and do not survey the issue of scale effects on mutual funds, McMullen and Strong (1998) estimate a DEA model that assumes variable returns-to-scale to analyze 135 common stock mutual funds. They consider as outputs the returns over different lengths of time and, as inputs the sales charge, expense ratio, minimum initial investment (instead of turnover), and semi-deviation of return measured over 3 years. In addition, seeing that DEA can assign very low weights to some undesirable inputs and outputs in order to increase the efficiency measure, they set constraints upon the weights in order to ensure that not all attributes are disregarded. In a second step, Choi and Murthi (2001) apply a different DEA formulation to the data they used before, and propose a non-oriented additive model that considers the same inputs and outputs of the DPEI index. This approach allows for the control of the scale effects.

Whereas pioneering works focused on return as an output in the DEA model and considered only standard deviation and transaction costs as inputs, subsequent studies include other variables. Basso and Funari (2001) propose a DEA-based performance index taking into account different risk measures and investment costs. They consider both subscription and redemption costs. The risk measures include the return standard deviation, the beta coefficient, and the half-variance risk. Furthermore, they define a new index that reflects an additional output, a stochastic dominance indicator in order to describe the investor’s preferences, and the occurrence of returns. In an empirical analysis of the Italian financial market, these authors evaluate the performance of 47 mutual funds and find that redemption costs are an important variable in determining fund rankings. In a subsequent paper, Basso and Funari (2003) develop DEA models that encompass ethical criteria, as in recent decades, investors have become more concerned with satisfying both their financial and their ethical aims. First, they propose a generalization of DEA indexes by adding the ethical measure as a second output. Then, they develop an exogenously fixed output model that contains an ethical level and presents it as a fixed variable. However, these indexes do not take into account the nature of the information available about the ethical level, as in practice, only binary information on the ethical/non-ethical nature, or a ranking of funds according to their ethical level are available. For this reason, these authors present a DEA categorical model with an exogenously fixed output. They test these indices on 50 simulated mutual funds. Subscription and redemption costs, the standard deviation of returns, and beta coefficient are chosen as inputs; and the expected return and an ethical indicator are selected as outputs. Moreover, Basso and Funari (2005) extend their previous indexes so that they can take into account the results of traditional performance measures. Hence, a generalized DEA performance metric, which adds to the outputs the value of the traditional performance indexes, is proposed. Moreover, they present the cross-efficiency matrix, which makes it possible to measure the performance of each fund, using different optimal weights for the other funds.

Considering that the risk measures introduced in previous DEA models do not reflect the characteristics of the funds’ return distributions, such as asymmetry and fat-tailedness, Gregoriou et al. (2005) focus on different downside risk measures to examine 614 hedge funds for the period from 1997 to 2001. Chen and Lin (2006) propose a DEA model that considers the value at risk (VaR) and the conditional value at risk (CVaR) as inputs in a test of 22 different input-output specifications. Lamb and Tee (2012) develop a new method with a suitable form of returns to scale and convenient risk measures. Their model directly allows for diversification and employs the mean return as an input, and the maximum between CVaR and zero as an output. Recently, Pérez-Gladish et al. (2013) use the DEA to evaluate the performance of a sample of 46 US domiciled large-cap equity mutual funds. They use the following inputs: turnover ratio, annual report gross, expense ratio, deferred loads, and front loads. As outputs, they use a financial criterion, namely, the mean return, as well as nonfinancial criteria, namely, social and environmental responsibility (SER) level, and quality of the SRI management.

4 Data, Implementation, and Results

We first present the sample of SRI funds and the key variables used in different DEA models. A discussion of the descriptive statistics of these variables is also provided. In the second part, we fully show the construction of various DEA models, with a discussion of the efficiency results implied by each model. All the tests and efficiency scores of SRI mutual funds are conducted using the “FxDEA,” software.

4.1 Data and Variables

The sample used in the present chapter is provided from the Fundata database and consists of monthly data for 85 Canadian SRI mutual funds over the period of May 2008 to December 2011. To control for selection and survival biases, we include all active and terminated funds in our portfolio tests. Summary statistics of SRI mutual fund returns are provided in Table 1.

Table 1 Summary statistics for Canadian SRI mutual funds returns

We use various input/output variables to assess the performance of our sample of Canadian SRI funds. Most of them are based on earlier studies. The output variables include the net return of the fund and the skewness of fund returns. The return is given by the changes in the net asset values per share (NAVPS), and is adjusted for all distributions. The skewness of fund returns is estimated by the third moment and measures the asymmetry of the return distribution (Joro and Na 2006; Pendaraki 2012). The set of input variables includes the following fund characteristics: (1) The fund size, which is proxied by total net asset (TNA) value (Daraio and Simar 2006); (2) The return standard deviation is given by the second moment and is a measure of fund total risk (Basso and Funari 2003; Daraio and Simar 2006; Chen and Lin 2006; Joro and Na 2006); (3) The value at risk (VaR 95 %), which describes an investment’s possible loss that is not exceeded with a probability of 95 % (Gregoriou et al. 2005; Chen and Lin 2006); (4) The kurtosis of fund returns is given by the fourth moment and measures of the degree of the peakness of the return distribution; (5) The management expense ratio (MER), defined as the mutual fund’s annual fees, which includes the management fees and other operating expenses, expressed as a percentage of the total fund value (Daraio and Simar 2006; Chen and Lin 2006; Ayadi et al. 2015); This is an important variable that differentiate SRI and non-SRI funds. In effect, management expenses are expected to be higher for SRI versus non-SRI mutual funds for one or more of the following reasons: First, SRI funds incur additional monitoring costs of the firms in which they invest to ensure that they maintain socially responsible policies (Gil-Bazo et al. 2010); Second, investors in SRI funds are likely to be less performance sensitive (Gil-Bazo et al. 2010) and studies find that management fees are inversely related with investor performance sensitivity (Christoffersen and Musto 2002; Gil-Bazo and Ruiz-Verdu 2009); and third, SRI funds may have higher management expenses since the smaller size of their sponsors and their assets under management lead to less economies from scale (as reported by Bauer et al. 2005, for German and UK funds, and by Bauer et al. 2006, for Australian funds). (6) Front-end loads and back-end loads, representing sales and deferred sales charges (Daraio and Simar 2006). Our framework is consistent with the axiomatic microeconomic theory suggesting that investors prefer positive skewness and have an aversion to kurtosis (Scott and Horvath 1980; Hwang and Satchell 1999).

Table 2 reports summary statistics of the included input/output variables. It is clear that some of the funds of our sample exhibit negative average returns and negative skewness. In order to satisfy the DEA’s non-negative requirement on variables used, we use the translation invariance property of the input-BCC model and normalize returns and skewness through the addition of a constant.

Table 2 Summary statistics for employed variables for Canadian SRI mutual funds

Furthermore, since every variable should be able to bring new information to the analysis, a desired property for each model is the independence of the selected variables. Jenkins and Anderson (2003) reveal that including highly correlated variables in the DEA can significantly affect the efficiency results. Therefore, it is necessary to make sure that the variables are not highly correlated. The input variables’ correlation matrix is shown in Table 3. It can be seen that the correlation between back-end loads and front-end loads is equal to 0.75. In order to avoid including the same type of information twice, it is necessary to drop one of the highly correlated variables from the analysis.

Table 3 Input/output correlation matrix

4.2 Results and Discussion

The DEA program is designed and tested in four different forms that have different combinations of input and output variables. In the first model (DEA-1), standard deviation is considered an input, and net returns, an output (which resembles the mean-variance framework). An extended model, where the management-expense ratio (MER), front-end loads, and total assets are added as inputs, is proposed for DEA-2. The third model, DEA-3, relies on the value at risk as a measure of risk instead of the standard deviation of returns. Finally, model DEA-4 incorporates higher-moment risk variables into the analysis (kurtosis and skewness). Our setup in all DEA models is consistent with the rule of thumb suggested by Banker et al. (1989) where n = 85 > max(s × m, 3(s + m)) = max(2 × 6, 3 × (2 + 6)) = 24.

Table 4 reports the input and output data for each fund and the empirical results of the analysis. In addition, Table 5 compares the efficient set and the minimum and average efficiency scores obtained with each of the employed models.

Table 4 Empirical results of the analysis of the performance of the Canadian SRI mutual funds

Table 5 Comparison of the efficient set and the minimum and average efficiency scores obtained with DEA-1, DEA-2, DEA-3, and DEA-4 models

In the mean-variance framework (DEA-1), only two funds are identified as efficient. However, the other funds have efficiency scores of less than one; thus, they are inefficient. This evidence suggests that not all SRI mutual funds are mean-variance efficient (this result is further confirmed using the Sharpe ratio measure).

By adding the front-end loads, MER and total-assets variables into the standard mean-variance framework (DEA-2), the number of efficient funds and the average efficiency increase significantly. In effect, the average efficiency score is 12.5 % and 49.9 % in the first and second applications, respectively. In addition, the number of efficient funds becomes twelve, representing almost 14 % of our sample. Ten inefficient funds in the mean variance framework turn out to be efficient according to the second application. It is worth noting that adding back-end loads into the analysis did not alter these results.

In the third application (DEA-3), we introduce the value at risk as a measure of tail risk, instead of the standard deviation. The results show that the efficient set did not change considerably from the second application since only one additional fund is a member of the new efficient set.

In the fourth application (DEA-4), we incorporate higher-moment risk variables (kurtosis and skewness) into the analysis. The results improve in a substantial manner, where six additional funds turn out to be efficient, in comparison with the DEA-2 results. This would suggest the importance and the contribution of these higher moment variables in the assessment of the performance of our sampled funds. This last specification is consistent with the higher moment SDF model of Ayadi and Kryzanowski (2013) for the evaluation of Canadian domestic equity funds. For this extended DEA model, the efficient target values, efficient peer groups, optimal weights, and lambda values for the fourth DEA model are reported in Tables 6, 7, 8, and 9, respectively.

Table 6 Target values of input and output variables for the fourth DEA model

Table 7 Peer groups of SRI funds for the fourth DEA model

Table 8 Optimal weights in the fourth DEA model

Table 9 Lambda values in the fourth DEA model

Twelve Canadian SRI funds are efficient under the DEA runs: DEA-2, DEA-3, and DEA-4. This persistency characterizes them as the best-performing SRI funds of the sample under evaluation. On the other hand, 67 funds are found to be inefficient in all DEA runs, which qualify them as the worst-performing funds of the sample.

In order to uncover the reasons for poor fund performance, we compute for each fund the input slack variables, which reflect the improvements needed for an inefficient fund to become efficient (Table 10). The investigation of these slack variables and the relative mean slacks shows that the size of the fund, measured by the total assets, and the loads are the major sources of inefficiency. In this regard, inefficient funds basically need to reduce their loads and size in order to improve their efficiency.

Table 10 Slacks of input and output variables for the fourth DEA model

These results present some advantages to either potential investors or mutual fund managers. On the one hand, they help investors identify the best-performing SRI mutual funds and offer insight into the factors they should consider when investing in SRI mutual funds. On the other hand, the results help mutual-fund managers to identify which of their peers are outperforming them, and what are the success factors for SRI funds in order to improve their operational behaviour.

5 Conclusion

The present chapter uses the non-parametric technique of data envelopment analysis (DEA) to investigate the efficiency of 85 Canadian SRI funds during the period of 2008–2011. It extends the previous research in at least two ways. First, and so far as we are aware, it represents the first attempt to apply the DEA to assess the performance of SRI mutual funds in Canada. Moreover, by specifically focusing on the input slacks, measured using the DEA, this chapter offers insights into specific aspects of managerial behaviour that can be improved, rather than merely addressing the summary efficiency score. The evidence suggests that loads and the SRI fund’s size are the main sources of inefficiency.

There are at least three ways in which this research could be extended. First, we can use DEA models that can highlight changes in the efficiency of SRI funds over the years. A second extension would be to compare the results of DEA with those of parametric frontier analysis methods. Finally, we can develop advanced models that would include both efficiency and effectiveness components into the performance analysis.