Combination value investing and momentum investing to stock selection using data envelopment analysis

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1 International Research Journal of Applied and Basic Sciences 2013 Available online at ISSN X / Vol, 4 (3): Science Explorer Publications Combination value investing and momentum investing to stock selection using data envelopment analysis Mohsen Alvandi 1, Safar Fazli 2, Ahmad HashemiSiavoshani 3 1. Member of scientific board, Imam Khomeini International University, Iran, Qazvin 2. Member of Scientific board, Imam Khomeini International University, Iran, Qazvin 3. Department of social science, Imam Khomeini International University, Iran, Qazvin Corresponding Author ahmad_hashemi09@yahoo.com ABSTRACT: This paper examines the applicability of data envelopment analysis (DEA) as a basis of selection criteria for equity portfolios. In Iran, it is the first DEA application for constructing a combined equity investment strategy that aims to integrate the benefits of both value investing and momentum investing. Efficiency score are calculated by DEA models and then highest score should be in the optimal portfolio. The performance of portfolio is evaluated on the basis of the average return and several riskadjusted performance metrics throughout the sample periods.the result shows the capability of the DEA approach to add value to equity portfolio selection. The outperformance is slightly more significant when the stock price momentum is included in the DEA variables. DEA is particularly useful as a multi-criteria methodology in cases in which the number of stock in the sample is large. Keywords: Data envelopment analysis (DEA), Value investing, Momentum investing, Performance measurement INTRODUCTION One of the important issues raised in the capital markets and should be considered by investors, is discussed the optimal portfolio selection (Abzari et al, 2006). Portfolio optimization problems in early 1952, was noticeable. Modern portfolio theory was first proposed by Markowitz organized a paradigm of the portfolio with the highest expected rate of return for a given level of risk created(garkaz et al 2010). Considerable evidence against the efficient stock market hypothesis has been documented over the past three decades. On the one hand, numerous studies have identified the existence of price momentum on stock returns (e.g., see Jegadeesh and Titman, 1993, 2001; Chan et al., 1996,2000; Lewellen, 2002; Billio et al., 2011), which refers to the tendency of recent winner stocks to generate abnormal returns also in the near future. On the other hand, there is plenty of international evidence of value premium (e.g., see Fama and French, 2006; Brown et al., 2008), which refers to the tendency of value stock to outperform glamour stock for most of the time. Momentum investing has been documented to perform best in the short term (e.g., see Jegadeesh and Titman, 2001; Cooper et al., 2004; Lam et al., 2010), whereas value investing performs better when using longer holding periods (see e.g., Bird and Whitaker, 2003; Rousseau and van Rensburg, 2004; Bird and Casavecchia, 2007a). Bird and Whitaker (2004) report that the added value attributable to each value and momentum strategy is basically uncorrelated, which enables performance improvement by combining these two strategies. Recently, further evidence of added-value of combining value and momentum strategies has been documented (e.g., see Bird and Casavecchia, 2007a; Bettman et al., 2009; Leivo and patari, 2011). However, the major problem with such a research design is how to combine the value indicator and the momentum indicator into a single selection criterion. In this paper, we test whether data envelopment analysis (DEA) is applicable to resolve this dilemma. Literature review During the past three decades, a large number of studies have documented the anomalous outperformance of naïve strategies that are based on relative valuation difference between value and glamour

2 stock. Many later studies have shown not only that the value premium in stock markets is a word-wide phenomenon, but also that the relative efficiency of different valuation criteria varies across both stock markets and the sample period examined. For example, Fama and French (1998) compare the value premiums obtained from using four different portfolio-formation criteria (i.e. B/P, CF/P, E/P and D/P) in 13 major stock markets. According to their results, the classification criterion leading to the greatest value premium varies across countries. Later studies have shown further that the relative efficiency of different valuation criteria also varies across the sample period examined. E.g., according to Dhatt et al. (2004), the most efficient individual valuation multiples in the US stock market during the period were CF/P and S/P.Bidgoli and sarnj (2008), measure of stock liquidity portfolio as one of the most important measures introduced in the Tehran Stock Exchange.thus, evidence is somewhat supportive of the use of multicriteria methodology for the purpose of separating value stock from glamour stocks. To our knowledge, the interaction of value and momentum strategies was first discussed by Asness (1997) who concludes that momentum and value are negatively correlated across stocks, yet each is positively related to the cross-section of average stock returns. Parallel to the results of Asness (1997), Bird and Whitaker (2004) report that the best long-only (i.e. no short sales allowed) portfolio performance would be achieved by investing in valueloser stock if a 6-month price momentum were used as a timing indicator and B/P as a value indicator. The study Khajue et al (2006), that the DEA had used as a benchmark for the portfolio, we in this paper from the DEA as a measure of portfolio composition and valuation indicators, momentum indicators share will use. Data and methodology Sample description The portfolios employed in testing the applicability of DEA as the basis of stock selection criteria are composed of Tehran Stock Exchange during the period. To solve problems related to the liquidity of our shares of companies that are in use at least 60 percent of liquidity. In order to avoid survivorship bias, the sample also includes the stock of the companies that were delisted during the sample period. Adjustment for dividends, splits and capitalization issues are made appropriately. If an issuer has had two or more stock series listed, only the one with a higher liquidity is included in the sample. The stock of companies with a negative book value and/or whose fiscal year is not a calendar year are excluded. The final sample size ranges from 63 companies (2001) to 142 (2010). Data envelopment analysis The concept of efficiency is derived from physical and engineering science and indicates the relationship between inputs and outputs (Hwang and Chang, 2003). Charnes et al (1978) (CCR) introduced the ratio definition of efficiency, also known as the CCR ratio definition, which generalized the single-output to single-input ratio definition used in classical science to multiple output and inputs without requiring pre-assigned weights. The main strength of the CCR ratio as it is applied in this study lies in its ability to combine multiple inputs and outputs into a single summary measure to select efficient firms for investment. Charnes et al (1978) proposed that the efficiency,, of a decision-making unit (DMU 0 ) can be determined by solving the following CCR model:!" # $% "& In this study, the # $ rpresent the outputs for DMU j with the ranges for '" and j indicated in equation (1). Additionally, denotes the weight given to input ' represents the weight given to output " is the number of outputs, is the number of inputs, is the number of DMUs, and is the efficiency value of DMUo. The outputs and inputs may take the form of theoretically prescribed values or they may take the from of observations. The constraints in equation (1) ensure that an optimal ( will always satisfy $ ( with the optimal solution values ( ( #$& The CCR model as equation (1) allows each DMU to specify its own weights to maximize its own efficiency value. The flexibility for this model to choose its input and output weights produces the efficient DMUs in general (Ertay and Ruan, 2005). Therefore, the efficiency value of any DMU can be estimated and rated via equation (1). This study defines a DMU as a listed firm. And the amounts of output and input will be determined based on the real values in the financial statements.

3 The CCR model was developed based on the assumption of constants return to scale. Banker et al (1984) (BCC) extended the CCR model by introducing a new separate variable and enabled the determination of the efficiency of any DMU, whether operations were conducted in regions with increasing, constant or decreasing returns to scale. The model proposed by Banker et al (1984) is equivalent to fractional programming problem, and can be expressed as the following BCC model: ) * +, +-.* / (2)!" #$% " & With unconstrained in sign. Since being proposed by Charnes et al (1978) and Banker et al (1984), the DEA models have been widely applied in evaluating the efficiencies of manufacturing and service industries (Hwang and Chang, 2003; Ertay and Ruan, 2005). A recent research by Mostafa (2007) employed DEA to evaluate the relative efficiency of the top 100 Arab banks. However, the DEA models are rarely used in portfolio management. Research on stock selection using DEA models to assess the efficiency of the firms listed on the Tehran Stock Exchange and constructs portfolio by selecting the stocks with high efficiency values. Portfolio-formation We report the results for eight variants of a portfolio-formation criterion. The number of variants stems from the fact that we test four combinations of input and output variables using two variants of DEA models. The first combination employs the stock price and enterprise value-per-share (EVPS) as input parameters, and book valueper-share (BPS), dividend-per-share (DPS) and EBIT-per-share (EBITPS) as output parameters and can thus be interpreted to represent a pure composite value (i.e. value-only) criterion without any momentum indicator. The second combination also includes the momentum indicator as the output parameter alongside with the variable combination. For validity reasons, the momentum output variable is constructed by multiplying the stock price of the nineteen trading day of March by the stocks past 6-month return denoted as the investment relative (i.e. one plus return). The third combination differs from the second in that it only includes one input variable (i.e. the stock price). The fourth combination is similar to third, except that earnings-per-share (EPS) is substituted for EBITPS. The choice of input and output variable for the basis of DEA is based on recent results of Leivo and Patari (2012). Test procedures for performance comparisons The performance evaluation of portfolios is based on a time series of their monthly returns. The portfolios are equally weighted every time they are reformed in the nineteen of March each year, and then monthly returns are calculated by taking account of changes in the portfolio weights during 1-year holding period. The intermediate cash flow obtained from delisted stocks within the holding period are reinvested in the remaining stocks of the same portfolio according to prevailing portfolio weights in the beginning of rebalancing implications, continuous stacked time-series of monthly returns for portfolios are generated throughout the 10-year sample period. The performance of portfolios is evaluated based on the average return, the Sharp ratio and Jensen alpha. In order to avoid validity problems stemming from the negative excess returns in the context of the Sharp ratio comparisons we use modified versions of Sharp ratios throughout the study, as follow: :; = <:;< (3) 4 Where " = the average monthly return of a portfolio '" > = the average monthly risk free rate of the return, the standard deviation of the monthly excess returns of a portfolio ', and ER= the average excess return of portfolio i. we use Sharp ratio as a representative of total risk-based performance metrics. Jensen on the other benchmark studies to assess the performance of the company is based on the capital asset pricing model. The model yields a linear function of the risk-free rate of return and risk only during maintenance. Spend a function of systemic risk is the risk that the criterion based on the beta () are expressed as a share of it. Jensen s alpha coefficient expresses the company s excess return relative to the returns expected from the capital asset pricing model: " )" )" > (4)

4 Where = Jensen s alpha coefficient of portfolio j, " = the average monthly return of portfolio j, " > = risk-free return, " = Market return and = Beta coefficient of portfolio j. positive alpha coefficient expresses better than expected performance of the stock, while a negative value means a lower alpha coefficient of performance shares, performance is expected. Unlike Jensen coefficient of variation in the Sharp ratio for portfolio performance evaluation is not only to focus on systemic risk. Statistical tests and adjustments To compare the monthly returns of CCR and BCC model portfolios with the Market portfolio, we used repeated measures test. Repeated measures consist of a certain variable rates in some different situation. The plan that aims to assess these rates is known as the repeated measures plan. This is the generalized from of paired comparison test. However there is a difference that in a paired comparison test, a group is compared in two conditions but in a repeated measures test, a group is compared in two or more conditions.for example, comparing different methods of calculating return on equity. According to the ten-year period ( ) and the number of the portfolios, we compare the yields of the efficient portfolios. Based on sampling time length and the different compositions of the portfolios, we used 40 repeated measure tests for examining the monthly yields. Furthermore, the significances of the differences between the portfolio alphas and Sharp ratio are tested by the appropriate t- statistics. Table 1. Performance comparison of DEA portfolios during full sample period ( ) Portfolio-formation criterion Average Average Jensen alpha SR (sign.) SR(sign.) annual monthly (sign.) P return(%) return(%) i vs.market CCR i vs.bcc j CCR i vs.bcc j CCR1(inpust: stock price and EVPS- outputs: BPS, (0.01) CCR 1 vs.bcc 1 (0.012) 7.06 (0.008) DPS and EBITPS) CCR2(inputs: stock price and EVPS-outputs: BPS, DPS, EBITPS and price (0.03) CCR 2 vs.bcc (0.05) CCR3(input: stock priceoutputs: BPS, DPS, EBITPS and price CCR4(input: stock priceoutputs: BPS, DPS, EPS and price momentum indicator) BCC1(inputs: stock price and EVPS- outputs: BPS, DPS and EBITPS) BCC2(inputs: stock price and EVPS-outputs: BPS, DPS, EBITPS and price BCC3(input: stock priceoutputs: BPS, DPS, EBITPS and price BCC4(input: stock priceoutputs: BPS, DPS, EPS and price momentum indicator) (0.05) (0.04) CCR 3 vs.bcc 3 (0.021) CCR 4 vs.bcc 4 (0.032) (0.02) (0.05) (0.07) (0.06) (0.007) (0.007) Market portfolio The table presents average annual return, performance metrics (the Sharp ratio (SR) and Jensen s alpha) for portfolios formed on the basis of four portfolio formation criteria (1-4 in first column) and two DEA models (CCR and BCC). The numbers following SRs and Alphas (in parentheses) indicate significance differences between two DEA models and market based on the Paired comparison test statistics for the Sharp ratio (SR) difference and Jensen s alpha difference, respectively). The pairs of DEA portfolios being compared in the last two columns are indicated by second column from the right.

5 Table 2. Repeated test results between DEA portfolio and the Market portfolio during full sample period ( ) Year Portfolio Sig (CCR i &BCC j &Market) 2001 CCR 3 &BCC 3 &MARKET CCR 4 &BCC 4 &MARKET CCR 2 &BCC 2 &MARKET CCR 3 &BCC 3 &MARKET CCR 4 &BCC 4 &MARKET CCR 1 &BCC 1 &MARKET CCR 4 &BCC 4 &MARKET CCR 1 &BCC 1 &MARKET CCR 2 &BCC 2 &MARKET CCR 4 &BCC 4 &MARKET CCR 3 &BCC 3 &MARKET CCR 4 &BCC 4 &MARKET CCR 1 &BCC 1 &MARKET CCR 4 &BCC 4 &MARKET CCR 2 &BCC 2 &MARKET CCR 3 &BCC 3 &MARKET CCR 4 &BCC 4 &MARKET CCR 1 &BCC 1 &MARKET CCR 2 &BCC 2 &MARKET CCR 4 &BCC 4 &MARKET CCR 1 &BCC 1 &MARKET CCR 2 &BCC 2 &MARKET CCR 3 &BCC 3 &MARKET CCR 4 &BCC 4 &MARKET CCR 1 &BCC 1 &MARKET CCR 2 &BCC 2 &MARKET CCR 3 &BCC 3 &MARKET CCR 4 &BCC 4 &MARKET Results show that the monthly returns of CCR portfolio has better than monthly returns of BCC portfolio. DISCUSSIONS This paper examines the applicability of DEA as a basis for selection criteria, using the Tehran Stock Exchange over the period portfolios on the basis of their DEA efficiency score. The performance of each portfolio is evaluated on the basis of stacked time-series of monthly returns throughout the 10-year period. The result shows that the DEA efficiency score provide a useful basis for equity portfolio selection. The outperformance improves slightly when stock price momentum is included in the DEA variables. According to the results, it seems that the DEA has a selective approach in forming portfolios, since many of the variables used to classify and thereby shares have outperformed the market portfolio had an effective portfolios. Also based on the results of the Sharp ratio and Jensen s alpha, CCR portfolios have better performance than BCC portfolios. The best combination of input and output variables in the fourth compound was obtained, which had the best performance in terms of return and risk metrics compared with the other portfolios. The results of this research verify the Patari et al (2012) and Chen (2008) research results about the use of DEA method in portfolio performance optimizing. Long-time sampling compared with other studies on the Tehran Stock Exchange portfolio, lead to providing the best combination for comprising the portfolio. For the future studies, the DEA weighting system seem to try make changes in the content and functionality portfolio will be conducted based on several methodologies. Furthermore, the size of the sample in our study is not large in spite of its comprehensiveness from the local stock market aspect. Thus, DEA method employed in this paper could be applied to other large stock markets to examine to what extent our results are

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