Precious metal mutual fund performance appraisal using DEA modeling

Precious metal mutual fund performance appraisal using DEA modeling

Resources Policy 39 (2014) 54–60 Contents lists available at ScienceDirect Resources Policy journal homepage: Pre...

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Resources Policy 39 (2014) 54–60

Contents lists available at ScienceDirect

Resources Policy journal homepage:

Precious metal mutual fund performance appraisal using DEA modeling Ioannis E. Tsolas n National Technical University of Athens, School of Applied Mathematics and Physics, 9 Iroon Polytechniou, Zografou Campus, Athens 157 80, Greece

art ic l e i nf o

a b s t r a c t

Article history: Received 30 December 2010 Received in revised form 25 October 2013 Accepted 8 November 2013 Available online 27 November 2013

The purpose of this paper is to evaluate the performance of a sample of sixty-two precious metal mutual funds by applying a two-stage procedure. In the first stage, data envelopment analysis (DEA) is used to measure the relative efficiency of funds. In the second stage, a Tobit model is employed to identify the drivers of performance. The purpose for and intended contribution of this paper is twofold: to provide consolidated measures of relative performance of precious metal mutual funds using for first time the DEA framework and to explain fund performance by employing a Tobit model. Correlation results among DEA-based performance measures and traditional indicators of fund performance (Sharpe ratio and Jensen's α) are mixed; no correlation has been found for the Sharpe ratio; whereas in the case of Jensen's α, the correlation is not high. Moreover, the mean-variance efficiency hypothesis holds for the inefficient funds of the sample. In addition, DEA-based fund performance can be explained by fund size, fund persistence, and beta coefficient. & 2013 Elsevier Ltd. All rights reserved.

JEL classification: C14 G20 G23 Keywords: Precious metal mutual funds Efficiency Data envelopment analysis

Introduction Mutual funds are portfolios of stock-exchange securities and/or bonds consisting of shares with the purpose of echoing the overall market. Fund prices are quoted daily on the market, providing a margin for the various types of costs (e.g. management costs and costs for buying and selling securities) (Chiodi et al., 2003). Precious metal mutual funds (e.g. gold mutual funds) are similar in definition to stock mutual funds, in that they invest in a portfolio of shares of mining companies or in tangible metal. Investors who purchase precious metal mutual funds hope to experience greater returns in the long run by buying shares in groups rather than individually. Trading in key precious metals (e.g. gold, silver, platinum, and palladium) comprised a US$0.4 trillion in December 2008, about 9 percent of the trading in commodity markets (e.g. precious metals, oil, agricultural, and other resource commodities) (Batten et al., 2010). Investors can take a position in precious metal price risk by investing in precious metal mutual funds. On average, gold mutual funds provide greater absolute returns than an investment directly in gold itself. Investors expecting a change in the gold price (positive or negative) can expect the gold mutual funds to change


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even more gold, but evidence also supports the assertions that mutual fund returns are disrupted by no-gold-related risk. In regard to empirical research on the correlation between gold and the stock market, see Blose (2010). The prices of precious metal mining stocks do not always move in the same direction as the market price of precious metals. This is due to a number of factors such as mining cost, which can vary significantly among precious metal mining companies and the length of mine life; for instance, a long mine life is associated with better geological conditions; whereas a short mine life implies that a deeper, more costly process will be necessary to extract the precious metal. Precious metal mutual funds offer a diversified portfolio of precious metal mining stocks, and savvy investors should seek funds based on their aggregated performance measures (Blose, 1996). The performance evaluation of mutual funds has become an important issue for both fund managers and researchers. The performance of mutual funds since the pioneering works of Sharpe (1964, 1966), Treynor (1965), and Jensen (1968, 1969) has been investigated using mainly the Capital Asset Pricing Model (CAPM). The CAPM-based performance measurement techniques are within the risk-return framework and are dependent on two factors: the benchmark portfolio used and risk measurement. Most studies investigate the performance of mutual funds while taking into account the expected excess return of the portfolio and a risk measure without incorporating cost categories such as the transaction costs and management fees charged by the funds (Galagedera and Silvapulle, 2002; Murthi et al., 1997; Sengupta and Zohar, 2001).

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Since the late nineties, there has been a growing body of research applying DEA (Charnes et al., 1978) on mutual fund performance evaluation. DEA was first proposed by Murthi et al. (1997) as a measure of portfolio performance. It can easily capture the multidimensional aspect of mutual fund performance and alleviate some of the problems associated with CAPM-based performance measures. DEA, based on the efficiency measurement method of Farrell (1957), permits appraisal and rank of precious metal mutual funds in a risk-return framework using other variables such as the expense ratio. A DEA-based performance measure is important because it enables investors to potentially pinpoint the reasons behind poor performance of funds; moreover, it assists fund managers in the performance appraisal for their funds (Alexakis and Tsolas, 2011). The present study offers two main contributions into the finance literature. In a first stage, the performance of a sample of precious metal mutual funds is assessed using DEA modeling. In the second stage, a Tobit model is employed to identify the performance drivers. The first stage of analysis deals with the derivation of consolidated fund performance measures, the classification of funds into efficient and inefficient, the analysis of slacks to test whether the mean-variance efficiency hypothesis holds for the underperformer funds, and the comparison of traditional indices of fund performance with the derived DEA measures. The second stage deals with Tobit regression analysis. In this paper, the following questions are addressed: (1) What is the most efficient level of risk and other transaction cost associated with sampled precious metal mutual fund returns? (2) Which are the top performers among the sampled precious metal mutual funds? (3) Is there statistical significant correlation among the proposed DEA-based performance measures and the traditional indices of fund performance evaluation? (4) Does the mean-variance efficiency hypothesis holds for the underperformer funds? (5) Which are the drivers of fund performance? The rest of the paper unfolds as follows: Section 2 reviews the literature on DEA-based mutual fund performance evaluation. Section 3 briefly outlines DEA methodology and the proposed model. The data, along with identification of inputs and outputs for the case of precious metal mutual fund industry, are reported in Section 4. Section 5 presents and discusses the results of the two stages of the analysis. Section 6 provides some policy implications, and the last section concludes.

Survey of DEA-based mutual fund performance evaluation In recent years, a growing body of studies has applied frontier estimation methodologies for evaluating the performance of mutual funds. The methods on efficiency measurement use either a parametric or a nonparametric approach (Førsund et al., 1980). Studies that apply the parametric approach in frontier analysis to mutual funds include the works by Briec and Lesourd (2000), where an application of the stochastic parametric approach is provided, and Annaert et al. (2003), who apply the stochastic Bayesian approach (van den Broeck et al., 1994). The first use of DEA to assess fund performance dates back to the pioneering work by Murthi et al. (1997), who developed the DEA portfolio efficiency index (DPEI) to evaluate the performance of mutual funds using costs (inputs) and returns (output). They modified the basic idea employed in the Sharpe index (Sharpe, 1966) by incorporating transaction costs. The motivation of Murthi et al. (1997) to use DEA was to overcome a number of


shortcomings of traditional two-dimensional (risk-return) performance measures. DEA offers a multidimensional performance analysis compared to the above two-dimensional performance measures, since it does not require any theoretical model as a benchmark. Moreover, DEA-based performance is a combination of multiple fund attributes. These include mean returns (outputs), risk (total or systematic), expenses (e.g. transaction costs and administration fees), loads (subscription or/and redemption costs), minimum initial investment, and net asset value (inputs) (See Morey and Morey, 1999; Choi and Murthi, 2001; Sengupta and Zohar, 2001; Anderson et al., 2004). The analysis has been extended to introduce other output variables such as a stochastic dominance indicator (Basso and Funari, 2001, 2005) and input variables such as an ethical indicator (Basso and Funari, 2003), value-at-risk (VaR), and conditional value-at-risk (CVaR) measures (Chen and Lin, 2006). For recent reviews, see Galagedera (2003) and Glawischnig and Sommersguter-Reichmann (2010). Employing essentially radial DEA models like CCR (Charnes et al., 1978) or BCC (Banker et al., 1984) models without or with weight restrictions (McMullen and Strong, 1998; Glawischnig and Sommersguter-Reichmann, 2010) and non-radial DEA models like the directional distance function (Chambers et al., 1998) or the range-adjusted measure (RAM) of performance (Cooper et al., 1999), the efficiency of funds is compared within a category or between several categories. Other approaches that appear in the relevant literature are the minimum convex input requirement set (MCIRS) approach (Chang, 2004), the concept of order m frontier (Daraio and Simar, 2006), the concept of α-quantile efficiency scores (Daouia and Simar, 2007), as well as DEA modeling based on the mean-variance (Briec et al., 2004) and mean-varianceskewness framework (Joro and Na, 2006; Briec et al., 2007). Briec and Kerstens (2009) extended the multi-horizon mean-variance portfolio analysis of Morey and Morey (1999), and more recently, Bãdin et al. (2010) presented a data-driven approach for conditional efficiency measures of mutual funds. A recent classification of modeling approaches by Brandouy et al. (2013) distinguishes models directly derived from production theory, models combining a fund traditional performance measure (e.g. Sharpe ratio) with other variables, models based on portfolio theory, and hedonic price models (Kerstens et al., 2011).

Conceptual framework DEA methodology DEA methodology was first proposed by Charnes et al. (1978) to evaluate the relative efficiency of production units, referred to as decision-making units (DMUs). This is a nonparametric method, in that it does not require assumptions regarding the shape of the production frontier using simultaneously multiple inputs and outputs. In portfolio management, the objective is to analyze the performance of investment portfolios. Risk (volatility or variance) and the return of a portfolio are analogous to inputs and outputs in model of production; in the DEA setting, other variables that reflect cost can be incorporated into the input side of the DEA. Also in the DEA setting, the use of mutual funds such as DMUs may raise some questions about the homogeneity of those mutual funds. It is worth noting that the objective of the DEA is to measure the relative efficiency among similar units that share the same technology (procedure) for similar goals (outputs, returns), by using similar resources (inputs). DEA maps a piecewise linear convex isoquant (i.e. a nonparametric efficient frontier) over data points to determine the efficiency of each of the DMUs relative to the isoquant. DEA accomplishes this by constructing the efficient frontier from a linear combination of the perfectly


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efficient funds and determines fund deviations from that frontier that represent performance inefficiencies. The efficiency scores of DMUs are bounded between zero and one, with fully efficient funds having an efficiency score of one. A DEA model can be formulated in two versions: input and output orientation. An input orientation analysis determines the proportional reduction of the inputs without changing the output level for an inefficient fund to become DEA efficient. An output orientation analysis provides information on the proportional expansion of output levels of an inefficient fund that is necessary, along with the maintenance of current input levels, for the fund to become DEA efficient. Apart from the input- and output-oriented efficiency measures there are also the so called non-oriented or graph efficiency measures. In the mutual fund rating literature, examples include the works of Briec et al. (2004, 2007) and Briec and Kerstens (2009). Input orientation analysis is most cited in the relevant literature and in particular the BCC (Banker et al., 1984) model. This is due to the fact that the input-oriented BCC model is translation invariant with respect to output variables, and thus it can be used to overcome the possible problem posed by the presence of negative returns. DEA input orientation analysis defines an efficiency measure of a fund by its position relative to the frontier of the best fund performance established mathematically by the ratio of the weighted sum of outputs to the weighted sum of inputs. The estimated frontier of best performance characterizes the efficiency of funds and identifies inefficiencies (Alexakis and Tsolas, 2011). More generally, in a DEA framework (Charnes et al., 1978), the management of n mutual funds, j¼1,…,n, is characterized by a set of k inputs X A ℜm þ to produce quantities of outputs Y A ℜ ; the amounts of the ith input and rth output, used by the jth mutual fund are denoted by xij and yrj, respectively. The following VRS input-oriented BCC (Banker et al., 1984), or value-based model (Thanassoulis, 2001) (1) can be used to assess the performance of funds. k


h ¼ ∑ μr yrjo þ ω r¼1

s:t: m

∑ vi xijo ¼ 1

i¼1 m




∑ μr yrj  ∑ vr xrj þ ω r 0

j ¼ 1; 2; …; j0 ; …n

μr Zε

r ¼ 1; 2; …; k

vi Z ε ω free on sign

r ¼ 1; 2; …; m

( Yj ¼

j ¼ 1; 2; :::; n

Y nj


Y nj 4 0



Y nj r0

ð3aÞ ð3bÞ

Simar and Wilson (2007) claim that this DEA/Tobit two-stage approach is invalid due, among other factors, to complicated and unknown serial correlation among the estimated efficiencies. In addition, it can lead to inaccuracies if the number of the units located on the efficient frontier represents a large proportion of the sample (Nahra et al., 2009). Simar and Wilson (2007) propose in the second-stage bootstrap procedures truncated (rather than Tobit) regression analysis. See Johnson and Kuosmanen (2012) for additional qualification of these conclusions. Estimation method alternatives to Tobit regression have appeared in the relevant literature. Ordinary least squares (OLS) linear regression has proved to be a consistent estimator (Banker and Natarajan, 2008; McDonald, 2009). McDonald (2009) further argued that DEA scores are more consistent with a fractional logit model; whereas Estelle et al. (2010) conclude that multiple regression approaches such as nonparametric regression, OLS, Tobit, and fractional logit provide very similar results. Recent contributions to this bulk of literature are the works of Ramalho et al. (2010) and Guan and Chen (2012), who employed partial least squares regression (PLSR) to the second stage of DEA formulation modeling regression.

Data and identification of input and output variables Data

Two-stage approach A two-stage approach is applied in this research, combining the input-oriented BCC (BCC-I) model in the first stage with a censored Tobit regression model in the second. The BCC-I model provides the most efficient level of the value factors of the sample funds and the best funds (top performers), whereas the censored Tobit model is used to examine whether fund-specific factors interfere with the fund ratings produced. Regression analysis The first-stage inefficiency score is the dependent variable that is regressed on the explanatory variables according to the model: j ¼ 1; 2; :::; n

Y nj ¼ βZ j þuj :


where ε 40, a convenient small positive number (non-Archimedean), see also Charnes et al. (1994), μr ¼output weights estimated by the model and vi ¼input weights estimated by the model.

Y j ¼ f ðZ j ; βÞ þ uj ;

where Y j is the dependent variable, Z j and β are vectors of explanatory variables and unknown parameters, respectively, uj is the error term and n is the number of observations. The first stage of the analysis produces DEA efficiency fund ratings that are distributed between zero and unity; therefore, the fund rating becomes a limited dependent variable in the second stage of analysis. To analyze such type of data, a censored Tobit model (Tobin, 1958) is usually applied as an appropriate multivariate statistical model (Hoff, 2007; Sueyoshi et al., 2010). When the dependent variable Y j is censored at zero, the Tobit model may be described as follows (Greene, 1997)


The input and output variables on sixty-two precious metal mutual funds were used in this study. The annual data, publicly available on the Google Finance website (, is from Morningstar, which provides data on net assets, risk measures (i.e. standard deviations and the beta coefficient (β) of the CAPM), annualized returns, fund characteristics and traditional indices (Sharpe ratio and Jensen's α) of mutual fund performance evaluation. Sixty-two funds were analyzed due to the availability of complete information on these funds. Input and output variable specification for DEA There is no consensus among researchers and investors as to which input and output variables should be unambiguously included in a DEA fund performance model. One output variable, namely, the annualized 3-yr return, is considered in this paper to capture the medium-term gross performances (Galagedera and Silvapulle, 2002). The input variables used in the DEA analysis are the following: (i) standard deviation of 3-yr gross performance as a measure of risk; (ii) operating expenses generally referred to as the management expense ratio (MER); (iii) front load; and (iv) deferred load. The BCC-I model is used to examine whether

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the fund managers have employed inputs (risk, MER, front and deferred load) efficiently to produce output (annualized yearly returns). Risk is proxied by standard deviation (i.e. the dispersion of return) that represents the fund's total risk, which may be important for the not-well-diversified small funds. The MER is the percentage of fund assets paid for operating expenses and management fees, including administrative fees and all other assetbased costs incurred by the fund except brokerage costs. The front load, or sales charge, as a percentage of investment, is the entry fee paid by the investors at the time of purchasing shares of mutual funds, while the deferred load is the fee paid when shares are sold. Descriptive statistics of inputs and outputs used in the DEA assessment are presented in Table 1. Variable specifications for the Tobit regression model The second stage of analysis involves explaining the variation in the DEA-based relative inefficiencies by Tobit regression model that include independent variables to proxy a fund's operational characteristics. The explanatory variables include the logarithm of the fund's net assets, which controls for fund size, persistence (i.e. annualized 1-yr return) that reflects momentum, and beta coefficient to proxy the systematic risk that cannot be further reduced through diversification.

Results The following section first presents and discusses the results of the BCC-I model (first stage), before turning to the second-stage Tobit regression results. First stage analysis Precious metal mutual fund performance The estimated efficiency scores of precious metal mutual funds derived using the BCC-I model are summarized in Table 2. The

Table 1 Descriptive statistics of precious metal mutual funds data used in the assessments.

Min Max Mean Median Standard deviation Q1 Q3 Number of funds: 62

3 yr-standard deviation (%)

MER (%)

Frond load (%)

Deferred 3 yr-returns (%) load (%)

25.72 36.32 30.08 29.96 1.77 29.24 30.89

0.26 3.57 1.46 1.29 0.57 1.05 1.87

0.00 5.75 1.20 0.00 2.26 0.00 0.00

0.00 5.00 0.60 0.00 1.32 0.00 1.00

 26.12  12.50  17.17  16.70 2.56  18.93  15.72


mean efficiency is 87 percent; whereas the median efficiency is of the order of 87 percent. Out of the sixty-two funds, four (6 percent of the total sample) were found relatively efficient. The results indicate that there is scope for efficiency improvement in fund performance by minimizing inputs of about 13 percent (¼ 1  0.87) (Table 2). Using the results of the dual of Model (1), one can discriminate among funds that have excelled in performance; these could, therefore, be proposed as benchmarks across sampled funds. Among the four efficient funds, one could further differentiate based on the frequency of their appearance in the reference sets of the inefficient funds, an idea firstly developed by Charnes et al. (1985) (See also: Adler et al., 2002). The frequency of appearance of an efficient fund in an inefficient fund's reference set provides information on how many inefficient funds are affected by the presence of the efficient fund. Therefore, one can further rank the efficient funds. Corresponding results for the top efficient funds are included in Table 3. The top four funds that can be used as benchmarks are: First Eagle Gold Fund, A (SGGDX); First Eagle Gold Fund, C (FEGOX); First Eagle Gold Fund, I (FEGIX); and Vanguard Precious Metals and Mining Fund, Investor (VGPMX). A comparison among nonparametric and traditional indices of precious metal mutual fund performance Table 4 shows the results of the correlation analysis among DEA-based (nonparametric) and traditional indices (Sharpe ratio and Jensen's α) of mutual fund performance evaluation. From the correlation analysis, the following findings emerge: First, Sharpe ratio and Jensen's α indicators are positively correlated to each other across the sampled precious metal mutual funds. This is an expected finding, since the measures by Sharpe (1966) and Jensen (1968) are highly correlated in terms of fund ranking (see also Daraio and Simar, 2006). Second, DEA-based indicators are not highly correlated with Jensen's α, and they are not correlated with the Sharpe ratio. This is not a surprise, due to the different perspectives taken by the two approaches. To investigate further among the nonparametric and traditional indices in the comparative analysis of mutual funds management, a back-testing analysis comparing DEA-based ratings and traditional ratings may be employed (Brandouy et al., 2013; MatallínSáez et al., 2014). The issue is beyond the scope of the current paper, but we look forward to seeing more research addressing this issue.

Table 3 The top efficiency precious metal mutual funds.

Notes: 3 yr-standard deviation: standard deviation of 3 yr gross performance, MER: management expense ratio, 3 yr-returns: annualized 3-yr return, Q1: first quartile, and Q3: third quartile.


Appearance in the reference set (number of times)


11 17 58 16

Table 2 Mean (standard deviation), median, quartiles (Q1 and Q3), min, max values of efficiency measures, number and percentage of efficient funds.

Efficient and inefficient funds Inefficient funds

Mean (SD)

Median (%)

Q1 (%)

Q3 (%)

Min (%)

Max (%)

Efficient funds, number (%)

87.11% (5.43%) 86.22% (4.37%)

86.94 86.91

83.93 83.93

89.82 88.77

70.90 70.90

100.00 95.34

4 (6%)

SD ¼ standard deviation, Q1 ¼ first quartile, and Q3 ¼ third quartile.


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Table 4 Correlation matrix among DEA and traditional indices for the sampled precious metal mutual funds. Jensen's α

BCC-I Pearcon's correlation coefficient BCC-I 1 Jensen's α 0.568* (0.000) Sharpe index 0.159 (0.217) Kendall's rank correlation coefficient BCC-I 1 Jensen's α 0.277* (0.002) Sharpe index  0.001 (0.990) Spearman's rank correlation coefficient BCC-I 1 Jensen's α 0.403* (0.001) Sharpe index 0.002 (0.990)


Min Max Mean Median Standard deviation Q1 Q3

1.63 7.72 5.72 6.10 1.44 5.05 6.85

 44.35  28.03  35.40  35.10 2.96  37.89  33.92

0.47 1.30 0.65 0.61 0.17 0.52 0.75

Table 7 Results of Tobit regression for fund efficiency. Variable


Notes: p-values in parentheses. n



1 0.726* (0.000)

Persist (%)

Notes: size: logarithm of funds' net assets; persist: funds' annualized 1 yr-return; beta: beta coefficient.

1 0.562* (0.000)

Size Sharpe index

1 0.618* (0.000)

Table 6 Explanatory variables. Descriptive statistics.

Correlation is statistically significant at a level of 1%.

Table 5 Mean slacks in inputs (3 yr-standard deviation, 3 yr-beta, MER, frond load and deferred load).


t-Ratios significant at a level of 1%.

Frond load (%)

Deferred load (%)









The DEA measures that stem from Model (1) yield only firststage measures of mutual fund performance. What is not known is the reason for variations in such performance patterns, and it is evident that DEA metrics may not be enough for both consulting purposes and policy analysis. Therefore, a second-stage analysis is called for, as performance may be affected not only by inadequate fund management but also by other explanatory variables. In the sequential step that follows DEA, mutual fund performance measures are regressed using the Tobit regression methodology to identify the impact of a series of explanatory variables listed in Table 6. Between the DEA and Tobit regression, this study uses as dependent variable the transformed variable “h′ ¼1  h”, where h is the performance metric derived from Model (1). For computational purposes, Greene (1997) suggested the use of censoring at zero for Tobit regression (see also Sueyoshi et al., 2010)


Notes: size: logarithm of funds' net assets; persist: funds' annualized 1 yr-return; beta: beta coefficient. p-Values in parentheses

MER (%)

Second stage analysis – Tobit regressions

Standard error

Panel A: censored Tobit model (dependent variable (DEA run 1) ¼ 1 h) Constant  0.1420 0.0820  1.73 (0.089) Size  0.0123 0.0042  2.89* (0.005) Persist  0.7422 0.2049  3.62* (0.001) Beta 0.1179 0.0362 3.26* (0.002) Sigma 0.0464 0.0044 Log likelihood ¼90.235

3yr-standard deviation (%)

Analysis of slacks In the first stage analysis, the sources of inefficiency for the non-efficient funds can be identified by examining the slacks of the input variables. Table 5 depicts the relative mean slacks (absolute mean slack of an input divided by the mean value of the input) of the input variables (Murthi et al., 1997) (see also Daraio and Simar, 2006; Alexakis and Tsolas, 2011). A striking result derived is that risk measured by the standard deviation has no slacks throughout all funds. This is consistent with the notion that mutual funds are on average mean-variance efficient (Murthi et al., 1997). With respect to the other input variables, the slacks for MER are the largest, indicating that this direction may be of higher priority for the precious metal mutual fund managers.



50% 40% 30% 20% 10% 0%












Efficiency Fig. 1. Distribution of efficiency measures of funds. BBC-I1: four-input/one-output model (base case); BCC-I2: five-input/one-output model.

The results of the analysis explaining the performance scores derived by the DEA are given in Table 7. The effect of the logarithm of a fund's net assets and 1-yr returns, which control for fund size and persistence respectively, are significant in explaining fund efficiency at the 0.01 level; the signs of variables are negative as expected. The beta coefficient is significant in explaining fund efficiency at the 0.01 level; according to the findings, high-beta funds seem to be more inefficient compared to the low-beta funds. An interesting topic to be examined further is the use of control variables found to be statistically significant after the Tobit regression in the input side of DEA. Fund size has been selected to perform such analysis; the results are available upon request from the author. The distribution of efficiency scores (Table 2) produced using the four input and one output variables described in Section 4 (base case) and the efficiency scores produced by adding fund size in the input side of DEA (five-input/one-output model) are presented in Fig. 1. As it can be seen from this figure, the use of fund size decreases the discriminating power of the BBC-I model by providing more funds as efficient.

I.E. Tsolas / Resources Policy 39 (2014) 54–60

Policy implications The information provided in the previous section can be interpreted in different ways, according to the objectives of the reader/user. More specifically, it can be used by financial analysts to monitor the performance of precious metal mutual funds industry at a sectorial level. Financial investors could acquire more information on their investments by the derived metrics and could use the potential competitors scenario to compare mutual fundholding politics. Fund managers may be interested in monitoring the performance of their funds, along with their efficiency. The best-in-class funds may be candidates to be picked up by investors that aim to be exposed in the precious metal investing market. Hence, the proposed approach can be a useful tool for practitioners and investors.

Conclusions This paper summarizes a study carried out by employing DEA to monitor the performance of a sample of precious metal mutual funds. DEA is a nonparametric methodology; therefore, it does not need to assume a particular functional form for the returngenerating process. In contrast to traditional methods, the applied methodology provides an efficiency index for each mutual fund under evaluation relative to the best set of funds. A series of research questions presented in the first section are addressed in this study. In order to address these questions, the BCC-I model was employed. The empirical results, providing answers to Questions (1) and (2), indicate that there is scope for efficiency improvement by decreasing inputs of about 13 percent. Moreover, the derived DEA scores can be used to discriminate among funds that have excelled in performance and, therefore, could be proposed as benchmark funds from those in the sample. Results that provide answers to Question (3) do not point out positive links in terms of Pearson's correlation coefficient and rank correlation coefficients, among DEA-based performance measures and Sharpe ratio; DEA scores are not highly correlated with Jensen's α. The mean-variance efficiency hypothesis holds for the inefficient funds of the sample (Question (4)). In addition, to provide answers to Question (5), this paper uses a Tobit regression model to examine factors that significantly influence mutual fund performance. A series of variables were employed to examine the model. The results revealed that DEA-based fund performance can be explained by fund size, persistence, and beta coefficient. An understanding of the DEA-based performance of the sampled funds and of the factors that affect them can be extremely beneficial to both practitioners and investors and can provide helpful references for future studies.

Acknowledgments The author acknowledges the constructive comments of two anonymous reviewers who helped him to significantly improve the quality of this article.

References Adler, N., Friedman, L., Sinuany-Stern, Z., 2002. Review of ranking methods in the data envelopment analysis context. Eur. J. Oper. Res. 140 (2), 249–265. Alexakis, P., Tsolas, I., 2011. Appraisal of mutual equity fund performance using Data Envelopment Analysis. Multinatl. Finance J. 15 (3–4), 273–296. Anderson, R.I., Brockman, C.M., Giannikos, C., McLeod, R.W., 2004. A nonparametric examination of real estate mutual fund efficiency. Int. J. Bus. Econ. 3 (3), 225–238.


Annaert, J., van den Broeck, J., Vennet, R.V., 2003. Determinants of mutual funds underperformance: a bayesian stochastic frontier approach. Eur. J. Oper. Res. 151 (3), 617–632. Bãdin, L., Daraio, C., Simar, L., 2010. Optimal bandwidth selection for conditional efficiency measures: a data-driven approach. Eur. J. Oper. Res. 201 (2), 633–640. Banker, R.D., Charnes, A., Cooper, W.W., 1984. Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manage. Sci. 30 (9), 1078–1092. Banker, R., Natarajan, R., 2008. Evaluating contextual variables affecting productivity using data envelopment analysis. Oper. Res. 56 (1), 48–58. Basso, A., Funari, S., 2001. A Data Envelopment Analysis approach to measure the mutual fund performance. Eur. J. Oper. Res. 135 (3), 477–492. Basso, A., Funari, S., 2003. Measuring the performance of ethical mutual funds: a DEA approach. J. Oper. Res. Soc. 54 (5), 521–531. Basso, A., Funari, S., 2005. A generalized performance attribution technique for mutual funds. Cent. Eur. J. Oper. Res. 13, 65–84. Batten, J.A., Ciner, C., Lucey, B.M., 2010. The macroeconomic determinants of volatility in precious metals markets. Resour. Policy 35 (2), 65–71. Blose, L.E., 1996. Gold price risk and the returns on gold mutual funds. J. Econ. Bus. 48 (5), 499–513. Blose, L.E., 2010. Gold prices, cost of carry, and expected inflation. J. Econ. Bus. 62 (1), 35–47. Briec, W, Kerstens, K., Lesourd, J.B., 2004. Single-period Markowitz portfolio selection, performance gauging, and duality: a variation on the Luenberger shortage function. J. Optim. Theory Appl. 120 (1), 1–27. Briec, W., Kerstens, K., 2009. Multi-horizon Markowitz portfolio performance appraisals: a general approach. Omega 37 (1), 50–62. Briec, W., Kerstens, K., Jokung, O., 2007. Mean–variance–skewness portfolio performance gauging: a general shortage function and dual approach. Manage. Sci. 53 (1), 135–149. Briec, W., Lesourd, J.B., 2000. The efficiency of investment fund management: an applied stochastic frontier model. In: Dunis, C.L., Kluwer, Boston (Eds.), Advances in Quantitative Asset Management, pp. 41–59. Brandouy, O., Kerstens, K., Van de Woestyne, I., 2013. Backtesting superfund portfolio strategies based on frontier-based mutual fund ratings. In: Pasiouras, F. (Ed.), Efficiency and Productivity Growth: Modelling in the Financial Services. Wiley, Industry, New York, pp. 135–170. Chambers, R.G., Chung, Y., Färe, R., 1998. Profit, directional distance functions, and Nerlovian efficiency. J. Optim. Theory Appl. 98 (2), 351–364. Chang, K.P., 2004. Evaluating mutual fund performance: an application of minimum convex input requirement set approach. Comput. Oper. Res. 31 (6), 929–940. Charnes, A., Clark, C.T., Cooper, W.W., Golany, B., 1985. A developmental study of data envelopment analysis in measuring the efficiency of maintenance units in the US Air Forces. Ann. Oper. Res. 2 (1), 95–112. Charnes, A., Cooper, W., Lewin, A., Seiford, L., 1994. Data Envelopment Analysis: Theory, Methodology, and Application. Kluwer Academic Publishers, Boston. Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2 (6), 429–444. Chen, Z., Lin, R., 2006. Mutual fund performance evaluation using data envelopment analysis with new risk measures. OR Spectrum 28 (3), 375–398. Chiodi, L., Mansini, R., Speranza, M.G., 2003. Semi-absolute deviation rule for mutual funds portfolio selection. Ann. Oper. Res. 124 (1–4), 245–265. Choi, Y.K., Murthi, B.P.S., 2001. Relative performance evaluation of mutual fund: a non-parametric approach. J. Bus. Finance Account. 28 (7–8), 853–876. Cooper, W.W., Park, K.S., Pastor, J.T., 1999. RAM: a range adjusted measure of inefficiency for use with additive models, and relations to other models and measures in DEA. J. Prod. Anal., 11; , pp. 5–42. Daouia, A., Simar, L., 2007. Nonparametric efficiency analysis: a multivariate conditional quantile approach. J. Econ. 140 (2), 375–400. Daraio, C., Simar, L., 2006. A robust nonparametric approach to evaluate and explain the performance of mutual funds. Eur. J. Oper. Res. 175 (1), 516–542. Estelle, S.M., Johnson, A.L., Ruggiero, J., 2010. Three-stage DEA models for incorporating exogenous inputs. Comput. Oper. Res. 37 (6), 1087–1090. Farrell, M.J., 1957. The measurement of productive efficiency. J. R. Stat. Soc. 120 (3), 253–290. Førsund, F.C., Lovell, A.K., Schmidt, P., 1980. A survey of frontier production functions and their relationship to efficiency measurement. J. Econ. 13 (1), 5–26. Galagedera, D.U.A., 2003. Investment performance appraisal methods with special reference to data envelopment analysis. Sri Lankan J. Manage. 8 (1–2), 48–70. Galagedera, D.U.A., Silvapulle, P., 2002. Australian mutual fund performance appraisal using data envelopment analysis. Managerial Finance 28 (9), 60–73. Glawischnig, M., Sommersguter-Reichmann, M., 2010. Assessing the performance of alternative investments using non-parametric efficiency measurement approaches: is it convincing? J. Bank. Finance 34 (2), 295–303. Greene, W.H., 1997. Econometric Analysis, 3rd ed. Prentice Hall, New Jersey. Guan, J., Chen, K., 2012. Modeling the relative efficiency of national innovation systems. Res. Policy 41 (1), 102–115. Hoff, A., 2007. Second stage DEA: comparison of approaches for modeling the DEA score. Eur. J. Oper. Res. 181 (1), 425–435. Jensen, M.C., 1968. The performance of mutual funds in the period 1945–1964. J. Finance 23 (2), 389–416. Jensen, M.C., 1969. Risk, the pricing of capital assets and the evaluation of investment performance. J. Bus. 42 (2), 167–247. Johnson, A.L., Kuosmanen, T., 2012. One-stage and two-stage DEA estimation of the effects of contextual variables. Eur. J. Oper. Res. 220 (2), 559–570.


I.E. Tsolas / Resources Policy 39 (2014) 54–60

Joro, T., Na, P., 2006. Portfolio performance evaluation in a mean–variance– skewness framework. Eur. J. Oper. Res. 175 (1), 446–461. Kerstens, K., Mounir, A., Van de Woestyne, I., 2011. Non-parametric frontier estimates of mutual fund performance using C- and L-moments: some specification tests. J. Bank. Finance 35 (5), 1190–1201. Matallín-Sáez, J.C., Soler-Domínguez, A., Tortosa-Ausina, E., 2014. On the informativeness of persistence for evaluating mutual fund performance using partial frontiers. Omega 42 (1), 47–64. McDonald, J., 2009. Using least squares and tobit in second stage DEA efficiency analyses. Eur. J. Oper. Res. 197 (2), 792–798. McMullen, P.R., Strong, R.A., 1998. Selection of mutual funds using Data Envelopment Analysis. J. Bus. Econ. Stud. 4 (1), 1–12. Morey, M.R., Morey, R.C., 1999. Mutual fund performance appraisals: a multihorizon perspective with endogenous benchmarking. Omega 27 (2), 241–258. Murthi, B.P.S., Choi, Y.K., Desai, P., 1997. Efficiency of mutual funds and portfolio performance measurement: a non-parametric approach. Eur. J. Oper. Res. 98 (2), 408–418. Nahra, T.A., Mendez, D., Alexander, J.A., 2009. Employing super-efficiency analysis as an alternative to DEA: an application in outpatient substance abuse treatment. Eur. J. Oper. Res. 196 (3), 1097–1106.

Ramalho, E., Ramalho, J., Henriques, P., 2010. Fractional regression models for second stage dea efficiency analyses. J. Prod. Anal. 34 (3), 239–255. Sengupta, J.K., Zohar, T., 2001. Non-parametric analysis of portfolio efficiency. Appl. Econ. Lett. 8 (4), 249–252. Sharpe, W.F., 1964. Capital asset prices: a theory of market equilibrium under conditions of risk. J. Finance 19 (3), 425–442. Sharpe, W.F., 1966. Mutual fund performance. J. Bus. 39 (1), 119–138. Simar, L., Wilson, P., 2007. Estimation and inference in two-stage, semi-parametric models of production processes. J. Econ. 136 (1), 31–64. Sueyoshi, T., Goto, M., Omi, Y., 2010. Corporate governance and firm performance: evidence from Japanese manufacturing industries after the lost decade. Eur. J. Oper. Res. 203 (16), 724–736. Thanassoulis, E., 2001. Introduction To The Theory And Application Of Data Envelopment Analysis: a Foundation Text With Integrated Software. Kluwer Academic Publishers, Dordrecht, The Netherlands. Treynor, J.L., 1965. How to rate management of investment funds. Harv. Bus. Rev. 43 (1), 63–75. Tobin, J., 1958. Estimation of relationships for limited dependent variables. Econometrica 26 (1), 24–36. van den Broeck, J., Koop, G., Osiewalski, J., Steel, M.F.J., 1994. Stochastic frontier models: a Bayesian perspective. J. Econ. 61 (2), 273–303.