چشم انداز جدید عملکرد بازار سرمایه

The traditional data envelopment analysis (DEA) models assess equity market performance using the risk and return factor values associated only with the assessed equity market. However, in DEA models, the risk and return factors may be valued differently for different equity markets. A measure that incorporates the risk and return factor values of other equity markets to assess the performance of a given equity market is cross-efficiency. The cross-efficiency of an equity market provides a global perspective of its performance. In this paper, each year from 2003 to 2011, we estimate the cross-efficiency of 40 equity markets in a multi-dimensional risk-adjusted return framework. Applying the multiple-correlation clustering algorithm to the estimated cross-efficiency scores we classify the equity markets so that each cluster comprises of the markets that have been ranked similarly by the other equity markets. We highlight that cross-efficiency scores and membership in clusters is useful information to investors when constructing international portfolios.

Performance of financial products such as mutual funds is usually assessed under a risk-adjusted return framework. Two commonly used risk-adjusted return performance measures are, Sharpe ratio and Treynor ratio. These ratios measure risk-adjusted return with one measure of risk and one measure of return and therefore they may be classified as one-dimensional measures. Risk however is multidimensional. The risk positions that investors take may depend on their situation. Examples of risk positions that investors may take are shortfall risk, downside risk and total risk. One-dimensional approaches of performance assessment cannot account for the multidimensional nature of risk (Colson and Zeleny, 1979 and Hurson and Zopounidis, 1995). Nevertheless, formulating a single comprehensive measure of risk that incorporates multiple risk factors is not easy. When there are several measures of risk and several measures of return, the risk metrics and the return metrics has to be aggregated separately to construct a composite measure of risk and a composite measure of return. One way of constructing a composite measure is to use a weighting scheme. Then the performance may be assessed in the ratio of a weighted sum of return to a weighted sum of risk. The non-parametric technique known as data envelopment analysis (DEA) computes such weights allowing each financial product being evaluated to show its performance in the best possible manner. Being a non-parametric technique, having the ability to accommodate multiple risk and return factors and assessing performance based on known levels of attainment rather than with reference to a benchmark makes DEA a powerful performance appraisal tool. A large number of DEA applications are documented in the finance literature. For example, DEA has been used to assess the relative performance of mutual funds (Choi and Murthi, 2001), hedge funds (Gregoriou et al., 2005), banks (Vassiloglou and Giokas, 1990) and insurance companies (Cummins and Zi, 1998). Bainbridge and Galagedera (2009), Meric and Meric (2001) and Galagedera (2010) use DEA to assess equity market performance. If return is the reward for bearing risk, we may consider return factors as output variables and risk factors as input variables of a process that compensates risk (inputs) with return (outputs). In the case of equity markets, the DEA methodology assesses performance by allowing each equity market to show its performance in a manner that is most favourable to that equity market. This is achieved by choosing the weights that gives the highest ratio of weighted sum of outputs to weighted sum of inputs. Each equity market may therefore choose different sets of weights.1 Because of the freedom afforded to each equity market to choose its own weights, such an assessment of performance may be viewed as one of self-appraisal.2 An alternative is to assess the performance of all markets with a common set of weights. This means that the analyst will have to pre-specify a set of weights thereby introducing an element of subjectivity to the analysis. One way of circumventing this problem is to use the weights chosen by a given equity market to assess the performance of the other equity markets as well. The performance of a given equity market assessed with the weights of another equity market may be viewed as peer-appraised performance. In the DEA literature, peer-appraisal is referred to as cross-evaluation and the efficiency obtained through peer-appraisal is referred to as cross-efficiency (Sexton et al., 1986). We use peer-appraised efficiency and cross-efficiency interchangeably. Under peer-appraisal, the performance of a given equity market is assessed with the weights of each of the other equity markets in the sample. When this procedure is repeated for each equity market in the sample, all equity markets will have assessments based on a set of weights chosen by itself and by each of the other equity markets in the sample. Hence, we can obtain an average cross-efficiency score for each equity market indicating how the other equity markets in the sample may perceive its performance on average.3 The average cross-efficiency score is simply the average peer-appraised performance score. Equity markets may be ranked based on the average peer-appraised performance score. Such rankings would be more appealing than the rankings obtained with the self-appraised performance scores.4 As far as we are aware all DEA applications of equity market performance appraisal adopts the self-appraisal procedure and ours is the first to use cross-efficiency. We assess equity market performance with two return factors (described in Section 3.1) as output variables and three risk factors: standard deviation (a proxy for total risk), systematic risk (the capital asset pricing model beta) and downside deviation (a proxy for downside risk) as input variables in the DEA model. We assume that the realisation of the two return factors reflects the reward for the associated risk measured from three different standpoints. According to our chosen set of input–output variables, the performance assessed would be the risk-adjusted return performance. The peer-appraised efficiency scores can be used to sort equity markets into clusters. We do this by adopting the multiple-correlation clustering (MCC) algorithm proposed in Doyle (1992). The MCC algorithm belongs to the divisive technique of clustering where the initial set is divided into two sub-sets and each sub-set is subsequently divided into another two sub-sets and so on until a stopping rule is reached. The MCC algorithm begins by computing the correlation between the peer-appraised efficiency scores of each pair of equity markets. Each correlation coefficient therefore indicates how similarly the two equity markets have been appraised by the other equity markets in the sample. The markets that belong to a cluster are those that are ranked similarly by the other sampled markets. Clustering of equity markets is important for investors as cluster membership provide information valuable for equity market selection and risk management.5 We appraise the performance of 22 developed and 18 emerging markets and therefore the estimated average cross-efficiency score of an equity market reflects the performance from a global perspective. The peer-appraised performance scores and cluster membership is valuable information to investors when forming international portfolios. The remainder of this paper is organised as follows. Section 2 provides a brief description of the self-appraised and the peer-appraised performance assessment procedures and the multiple-correlation clustering algorithm. Section 3 describes the data and the input–output variables used in the DEA models. A discussion of the results is given in Section 4. Section 5 highlights the empirical usefulness of the findings. After robustness check of the results in Section 6, the paper concludes with some remarks in Section 7.

Many risk-adjusted return performance measures are proposed in the literature. Evidence suggests that choice of the measure may have an impact on performance appraisal. Further, as risk is multidimensional, performance measures based on one output metric (single measure of return) and one input metric (single measure of risk) may not be adequate. A technique that allows multiple outputs and multiple inputs in performance appraisal is data envelopment analysis (DEA). DEA has other advantages. It is a non-parametric technique and therefore it is not necessary to specify a functional form for the efficient frontier. All studies that adopt the DEA methodology to assess equity market performance use models that allow the equity market being assessed to show its performance in the most favourable manner. This process is referred to as self-appraisal. In such assessments, weights are assigned to each input and output factor considered in the DEA model. These weights which are equity market specific can be interpreted as the values that the equity market attaches to the input and output factors to achieve optimal performance. We assess a given equity market's performance with the weights of each of the other equity markets separately and thereby obtain for the assessed equity market a set of efficiency scores referred to as peer-appraised efficiency scores. This is a novel approach because a given equity market's performance is assessed from the perspective of a large number of other equity markets and that gives a global perspective of performance rather than a restricted view of performance through self-appraisal. Peer-appraised efficiency scores have other uses. Applying the multiple-correlation clustering algorithm on the peer-appraised efficiency scores, equity markets may be classified into clusters so that each cluster comprises of the equity markets that is ranked similarly by the other equity markets in the sample. We apply these methodologies to a large data set comprising of 40 equity markets (22 developed and 18 emerging) with daily returns from January 2003 to December 2011. When assessing the equity market performance using DEA, we consider two components of return as output factors and three factors of risk as input factors. Through this empirical investigation we show that peer-appraised efficiency scores of equity markets and their membership in clusters become valuable information when constructing international portfolios.