AN EMPIRICAL EVIDENCE OF OVER REACTION HYPOTHESIS ON KARACHI STOCK EXCHANGE (KSE)

Muhammad Kashif ¹⁺ --- Sanyah Saad² --- Imran Umer Chhapra³ --- Farhan Ahmed⁴

^1,2,3,4Department of Management Sciences, Shaheed Zulfikar Ali Bhutto Institute of Science and Technology (SZABIST), Karachi, Pakistan

Keywords:Efficient market hypothesis Contrarian strategy CAPM Emerging markets KSE.

ARTICLE HISTORY: Received:8 January 2018. Revised:8 February 2018. Accepted:1 March 2018.Published:7 March 2018.

Contribution/ Originality:The paper contributes the first logical anlsysis in investigating the risk adjusted performance of portfolios based on contrarian strategies by using not only CAPM but also 3-factor and 5-factor Fama and French models (1996 and 2016) on Karachi Stock exchange.

1. INTRODUCTION

A substantial part of the traditional finance theory is the Efficient Market Hypothesis (EMH). According to this hypothesis, share prices fully reflect all available information. Any new information that comes in is immediately and fully incorporated in its price, thus no chances of earning excess abnormal returns. In such a market best strategy is to purchase and hold the market portfolio. The basic assumption behind this strategy is that markets are fully efficient and investors are rational and any arbitrage that arises is quickly removed.

Over the past couple of decades, major critique has been subjected to EMH as the existence of anomalies has called the definition of market efficiency into question. Any evidence that contradicts the traditional finance theory is called an anomaly. Financial literature is replete with evidence of anomalies (see: Fama and French (2008)). The winner-loser anomaly is also such an example; it is also one of the several anomalies that have refuted the EMH. It has highlighted a trading strategy that makes earning of abnormal profits possible (see: (Bondt and Thaler, 1985; Conrad et al., 1997; Mazouz and Li, 2007)). According to them stocks that have outperformed previously tend to perform poorly in the corresponding periods and vice versa. This anomaly refers that a negative correlation exists between excess returns. The strategy is based on the belief that past performance will reverse and buying past losers and selling past winners will generate a significant excess return. Persistence and presence of this anomaly have been proven in various financial markets however causes are still subjected to considerable disagreement.1

Supporters of EMH, Fama (1970;1991;2004) and Lo and MacKinlay (1988) debate that these excess abnormal returns are nothing other than temporary deviations from its intrinsic price, yet its presence has been proven in various financial markets for several decades. Persistent predictability of stock returns may imply that stock markets are inefficient. There are research studies that give explanations to the persistent predictability of stock returns due to the survivorship, statistical and data-snooping, biases (see: (Lo and MacKinlay, 1990; Brown et al., 1992)). Another explanation is presented by Schwert (2003) in line with the Fama (1970;1991;2004) that market inefficiencies are potential shortcomings in the implied asset pricing models. Further, behavioural theorists by using various psychological and sociological behaviours have tried to explain this deviation from efficiency.

The existence of winner-loser anomaly has been confirmed in international data. In a number of European Markets, Bird and Whitaker (2003) document significant return reversals. Additional evidence has been recorded by Dubois and Bacmann (1998) in France, Baytas and Cakici (1999) in Italy, France, UK and Germany, Brouwer et al. (1997) for UK, France, Netherlands, and Germany, Schiereck et al. (1999) and Stock (1990) in Germany, Forner and Marhuenda (2003) and Alonso and Rubio (1990) in Spain. Apart from the European markets evidence of the contrarian returns throughout the world surfaces from China (Kang et al., 2002; Wang and Xie, 2010) Australia (Lo and Coggins, 2006) New Zealand (Chin et al., 2002) Japan (Chou et al., 2007; McInish et al., 2008) and India (Locke and Gupta, 2009). Finally, Barros and Haas (2008) proved this anomaly in 15 developing markets report significant abnormal returns by applying the contrarian investment strategy. Various studies have been conducted in the developing markets of the world to detect the presence and causes of this anomaly, however, no significant literature is available for Pakistan. This research study for the first time aims to fill this gap. The Pakistani market is still in its phase of transition and its history is full of surprises related to security returns and trading activities. Because this market is not fully developed there is a possibility that fund managers are earning abnormal profits by following the contrarian strategy. This study incorporates all stocks registered in KSE from 2000 to 2015 to detect the presence of the overreaction effect using Cumulative abnormal return (CAR) adopted by Bondt and Thaler (1985).

The second aspect of this study focuses on the risk-adjusted performance of contrarian strategy using commonly used asset pricing models in line with Schwert (2003) and Fama (1970;1991;2004). Chan (1988) proves CAPM is fully able to explain the profitability of the contrarian returns. According to him, these abnormal returns are a compensation for the additional risk undertaken in this strategy. In the UK contrarian returns are explained by three-factor Fama French model (see: Galariotis et al. (2007)). They suggest size and value risk factors drive these abnormal returns. In line with Chan (1988); Clements et al. (2009) confirm the disappearance of abnormal returns of the contrarian strategy, when risk factors are accounted. Jordan (2012) provides evidence that a time-varying CAPM explains the profitability of the winner-loser anomaly. On the other hand, several studies such as De Bondt and Thaler (1987); Balvers et al. (2000) and Nam et al. (2001) establish that risk factors are unable to account for the excess abnormal returns generated by these contrarian strategies. The rest of this study is structured as follows. Section 2 explains the literature review in detail. Section 3 provides the details for the employed dataset and empirical procedure. Section 4 offers the empirical results and Section 5 concludes the study.

2. LITERATURE REVIEW

The winner-loser anomaly was first discovered by Bondt and Thaler (1985); De Bondt and Thaler (1987). According to them, stocks that have performed poorly in the past 3 to 5 years have a tendency to yield excess abnormal returns over the accompanying 3 to 5 years, and vice versa for winner stocks. They incorporated monthly data from the New York Stock Exchange (NYSE) from the time period 1926-1982 and discovered that in the 16 non-overlapping three-year test periods, the loser portfolio outperforms the market by an average of 19.6%. On the other hand, the winner portfolio underperformed the market by almost 5%, indicating 24.6% profitability from the contrarian strategy. The presence of this anomaly rejects the EMH and bring forward plenty of related examination throughout the world. In the similar guidelines, Richards (1997) applied the contrarian methodology on national indices and provided evidence of excess abnormal returns greater than 6%, with this tendency being greater in small capitalization markets. In US Conrad and Kaul (1993); Mun et al. (2001); Larson and Madura (2003) and Balvers and Wu (2006) documents significant contrarian returns. Statistically and economically significant returns have been reported in the UK stock market by Mazouz and Li (2007) even after taking into account for time-varying risk, firm size and seasonality. Further evidence of a long-run reversal in the UK has been provided by Power and Lonie (1993); Campbell and Limmack (1997) and Dissanaike (2002).

Often short-run reversals and long-run return reversals are not distinguished. Short run return reversals have been recorded over varying holding periods such as Howe (1986) monthly Lehmann (1990) weekly, Bremer and Sweeney (1988) daily. As observed by Bremer and Sweeney (1988) stocks whose value had fallen by greater than 10% earned returns of 3.95% over the next five consecutive days. Such results were reinforced by Cox and Peterson (1994) who found that after extreme price declines, return reversals were observed for the first three days. Larson and Madura (2003) observed extreme one-day events were caused due to significant overreaction to events. Evidence that considerable one-week reversals remained after taking into account bid-ask spreads and transaction costs were shown by Lehmann (1990). It was also found that a profit was yielded 90% of the time by a one-week contrarian strategy and the unusual returns were most likely the product of investor overreaction or short run illiquidity. This anomaly has also been proved on daily price changes in Japan, Korea and Hong Kong by Schaub et al. (2008) and they found that the overreaction phenomena is limited to securities that have a history of poor performance. Following an excessive decline, the indices of the three countries reversed by 35 to 45%. For past winners, no such reversal was documented.

However, all evidence does not exist in support of this anomaly. In the Australian stock market, Allen and Prince (1995) and Brailsford (1992) found no evidence of this anomaly, while a similar conclusion was reached by Kryzanowski and Zhang (1992) for the Canadian stock market.

Multiple explanations of the causes for the winner-loser anomaly exist. According to the defenders of the EMH, the reason of the anomalous returns has to do with model misspecification, which is in turn caused by inaccurate quantification of costs and risks that are involved in executing a contrarian strategy. On the other hand, according to the behavioural paradigm return reversals do in fact exist and remain due to the irrationality of investors which may be caused by cognitive biases such as overconfidence, noise trading, herding and overreaction. January and size effects have also been identified as the root causes of return reversals.

3. DATA AND METHODOLOGY

3.1. Data

The data set is collected through Thomson Reuters DataStream and Karachi Stock Exchange from (Jan 2000- Dec 2015. 1 The unit of analysis is (KSE) all index, both listed/delisted (dead or alive) companies. Mutual Funds, Unit Trust and ADRs have been excluded from this study (see: (Fletcher and Kihanda, 2005; Florackis et al., 2011)). A screening criterion on the sample has been imposed, firms with any missing value for 24 consecutive months have been excluded as the 24-month rank period return is necessary to calculate the CAR statistics. The Number of companies available for the analysis is 655 out of 895 for the period of 2000-2015. The reason to incorporate both dead and alive companies is to avoid the potential survivorship bias (see: Florackis et al. (2011)). KSE Value Weighted Index and Pakistan 6-month T-Bills rate are used as proxies for the market returns and the risk-free rate, respectively. To construct Small minus Big (SMB) we use Thomson Reuters DataStream yearly market value (MV). To calculate High minus Low (HML) loading factor following Gregory et al. (2001); Hussain (1996) and Lin et al. (1999) we have used Thomson Reuters data stream common equity (WC03501) minus total intangibles (WC02649). For investment factor (RMW-robust minus weak) following Fama and French (2016) we used Thomson Reuters data type total asset (WC02999) every year at the end of December 2000-2015. To calculate the profitability factor (CMA-conservative minus aggressive), operating profit (WC01250) minus dividends paid (WC04551), is used. Details on the construction of SMB, HML, RMW and CMA factor loadings are available in the appendix-A.

3.2. Methodology

This research tests for the existence of the winner-loser anomaly in KSE, by adopting the CAR method. The CAR technique is identical to that of Bondt and Thaler (1985) and has two steps. Firstly, firms with a complete set of returns from January 2000 to December 2001 are identified (rank period). Their monthly performance relative to the market is calculated using the following formula:

Where u_it is the market-adjusted excess return of stock ‘i’ in month ‘t’, R_it is the monthly continuous return on stock ‘i’ in month ‘t’, and R_mt is the monthly return of Value Weighted KSE All index in month ‘t’. At the end of the ranking period (December 2001), securities are arranged in ascending order based on their CAR.

Where,CAR_i is the cumulative market adjusted excess return for stock ‘i’ over the period from 24 months prior to the start of the test period.

Decile portfolios are constructed based on CAR, with the loser portfolio comprising of 10% stocks with the lowest CAR value and the winner portfolio comprising of 10% stocks with the highest CAR. This process of formation of the winner-loser portfolio is repeated for 24-month non-overlapping periods for the rank periods, 2001-2, 2002-3, 2004-5.....2013-2014. For each of the rank period, a non-overlapping 12, 24 & 36 months test periods for the decile portfolios have been defined. Average CAR of the winner and loser portfolio of the test periods are then calculated using the following formula:

Where ACAR_wt ( ACER_lt) is the average cumulated excess return of the winner (loser) portfolio during ‘t’ months in the test period. ACRR_wt ( ACRR_LT) is the average cumulative raw return of the winner (loser) portfolio in month ‘t’. CAR_mt is the cumulative return of the value-weighted market index up to month ‘t’.

Difference between the average cumulative excess returns of the winner and loser portfolios can be defined as

If the winner-loser anomaly holds in the long run then the loser (winner) portfolio will outperform (underperform) the market and investors will be able to generate excess abnormal returns by constructing portfolios based on this contrarian strategy.

We also use the following commonly used asset pricing models to see the risk-adjusted performance of decile portfolios. Firstly, we estimate Jensen alpha from the CAPM:

Where: (𝑅i,) is the return of portfolio ‘i’ in month t, (𝑅ft) is the risk-free rate for month ‘t’ captured by 6 monthly T-bill rate, (𝑅m) is the return on market portfolio, captured by Karachi Stock Exchange all index, (𝑅m, − 𝑅ft) is the excess market portfolio return in month ‘t’, (𝛽i,MKT) is the exposure of portfolio ‘i’ to the (market return). Secondly, we compute the 3-factor alpha the intercept of the Three-factor Fama and French (1996) model:

which captures the risk sensitivity of size and value factors. Thirdly, we estimate the 5-factor alpha the intercept of the five-factor Fama and French (2016) model:

In order to be able to test for the joint significance of the ten portfolio’s alphas and to mitigate the potential errors-in-variable problem. We use a system-based estimation. In particular, we report alphas estimated via the Generalized method of moments (GMM) with Newey-West standard errors corrected for heteroscedasticity and serial correlation (see; Cochrane (2005)). [See Appendix B for GMM explanation]. Apart from the significance of the return differential among the extreme deciles, an interesting question is to what extent an asset pricing model can explain the time series behaviour of CAR sorted portfolios. To evaluate the significance of the model’s pricing errors, we test the joint significance of the estimated alphas of all portfolios. To this end, we use a Wald test which is equivalent to Gibbons et al. (1989). For every model specification considered, the Wald test rejects the null hypothesis of jointly zero alpha estimates.

4. RESULTS AND DISCUSSION

4.1. Portfolio Characteristics

Table 1 below contains various descriptive statistics for each CAR portfolio for the whole sample period, January 2000- December 2015. The rank periods for these portfolios are 24 months and the test period is 36 months. We first report that there is a significant variation in average CAR across the ten portfolios, showing that CAR is a meaningful sorting criterion. Even though there is no particular size pattern across CAR portfolios, it is important to note that P10 (highest CAR shares) typically contains shares with significantly higher average market value relative to the remaining portfolios. Similarly, even though there is no gradient in the portfolio returns betas, shares in P10 exhibit significantly higher betas than the counterpart shares in portfolio P1 (lowest CAR firms). As a result, according to the mean-variance framework, we would expect P10 to yield a higher average return relative to P1. Instead, the portfolio with the lowest CAR value shares (P1 = -2.71 %p.a. for EW and 14.08 %p.a. for VW , P2 =-5.26 %p.a. for EW and 9.53 %p.a. for VW , P3 = -1.30 %p.a. for EW and 10.95 %p.a. for VW ) yield a significantly higher average excess return relative to highest value CAR shares (P10 = -12.60 %p.a. for EW and 10.45 %p.a. for VW , P9 =-2.49 %p.a. for EW and 7.19 %p.a. for VW , P8 = -5.88 %p.a. for EW and 12.35 %p.a. for VW ) in panel A with test period 36-months. A similar pattern is evident in both the 24-months and 12 months test periods. The spread P1-P10 for the case of value- (equally-) weighted returns for a 36-month test period is equal to a statistically significant 3.64% (9.89%) per annum (p.a.). As the test periods are reduced (i.e 24 & 12 months) these spreads disappear. In line with the findings of Mazouz and Li (2007) for the UK market, our study provides strong support for the argument that contrarian anomaly persists in the long run.

4.2. Risk-Adjusted Performance

Table 2 below exhibits the alphas of 10 value-weighted portfolios formed on the basis of CAR. Results show that the contrarian premium we documented in Table 1 panel-A for 36-month test period remains intact even after adjusting for market risk factor of CAPM. The spread strategy P1–P10 yields an abnormal performance of 10.49% p.a. (t-value=1.78) under the CAPM. However, under 3-factorFama and French and 5-factor Fama and French models, the abnormal performance disappears as the alphas become statistically insignificant (7.47% p.a. t-value=0.92 and 4.99% p.a. t-value=0.56). These findings support the argument that the contrarian investment strategy is profitable only in the long run (i.e. 36-months test period) and CAPM fails to explain this anomaly. However, more risk factors like SMB, HML, CMA and RMW are incorporated; the profitability of this investment strategy disappears.

Apart from the significance of the return differential among the extreme deciles, an interesting question is to what extent an asset pricing model can explain the time series behaviour of CAR portfolios. To evaluate the significance of the model’s pricing errors, we test the joint significance of the estimated alphas of all portfolios. To this end, we use a Wald test which is equivalent to Gibbons et al. (1989). For CAPM, the Wald test rejects the null hypothesis of jointly zero alpha estimates. This result shows that portfolios constructed on the basis of CAR yield abnormal returns that cannot be accounted by CAPM. However large values of Wald statistics for both 3 and 5 factor Fama and French models support the joint hypothesis that there is no difference between the alphas of portfolios formed on CAR 36-month investment strategy. As the test periods are reduced to 24 and 12 months, CAPM, 3-factor and 5-factor Fama French models all explain the profitability of the contrarian anomaly.

Similarly, Table 3 below exhibits the alphas of 10 Equally Weighted portfolios sorted on the basis of CAR. Results show that the contrarian premium, we documented in Table 1 also remains intact even after adjusting for the commonly used risk factors in the long run (i.e. 36-months test period). Specifically, the spread strategy P1-P10 yields an abnormal performance of 10.71% p.a (t-value=2.73) under the CAPM, 12.41% p.a. (t-value=2.42) under the 3-factor Fama and French model and 10.37% p.a. (t-value=1.87) under the 5-factor Fama and French model. It is evident from the results that contrarian strategy is profitable in the long run (i.e. 36 months) and above commonly used asset pricing models fails to explain this anomaly for the 36-month test period. This is further confirmed by the Wald test, which is applied to test the joint significance of Alphas. These results are also inconsistent with the results of VW portfolio returns, where CAPM unable to explain the contrarian profitability for the 36-month test period. However, as the test period is reduced to 24 and 12 months results are different and commonly used asset pricing models used above all explain the profitability of the contrarian anomaly. 1

Table-1. Characteristics of CAR with Rank Period = 24 months and Test period = 12,24 & 36 months in Deciles Portfolios of Sample, (2000-2015)

The table represents the characteristics of CAR with Rank Period = 24 months and Test Period = 12, 24 & 36 months in deciles portfolios from the period of Jan 2000-Dec 2015. All the shares listed in KSE during this time period are sorted by month (t) in ascending order and then they are divided into 10 portfolios. P1 comprises of firms with the lowest CAR whereas, P10 represents the highest CAR companies. P1-P10 shows the level of the spread between extreme adjacent portfolio which if results in positive significant value shows that the overreaction hypothesis exists in KSE. Equally Weighted (EW) returns are the annualized average monthly returns of EW portfolios. Value Weighted (VW) represents annualized average monthly returns of VW portfolios. MV represents the average market value of shares in each portfolio. CAPM beta shows the sensitivity of market risk which is an estimate of VW returns. The last column shows the t-statistics which represent the significance of each characteristic. Where the single (*) means 10% chance of rejecting the true null hypothesis that there exists no difference in means between the P1 & P10 characteristic. On the other hand, (**) and (***) shows 5% and 1% respectively.

Table-2.Value Weighted Returns of CAR Rank Period = 24 months and Test period = 12,24 & 36 months in Deciles Portfolios of Sample, (2000-2015)

This table reports the abnormal performance of the decile value-weighted CAR portfolios with Rank Period = 24 months and Test Period = 12, 24 & 36 months in deciles portfolios from the period of Jan 2000-Dec 2015. All the shares listed in KSE during this time period are sorted by month (t) in ascending order and then they are divided into 10 portfolios. P1 comprises of firms with the lowest CAR whereas, P10 represents the highest CAR companies. P1-P10 shows the level of spread i.e. the hedge portfolio which if results in positive significant value show that the overreaction hypothesis does exist in KSE. Portfolios are rebalanced on monthly basis. CAPM alpha is the annualized alpha estimate derived from the Capital Asset Pricing Model. Three-Factor Fama-French alpha is the annualized alpha estimate derived from the Fama-French three-factor model. Five-Factor Fama-French alpha is the annualized alpha estimate derived from the Fama-French five-factor model. T-statistics are reported in parentheses at 1%, 5% and 10% level respectively. The last column reports the chi-square statistic of the Wald test referring to the null hypothesis that the 10 portfolio alphas are jointly equal to zero; p-values are reported below the statistic.

Table-3.Equally Weighted Returns of CAR Rank Period = 24 months and Test period = 12,24 & 36 months in Deciles Portfolios of Sample, (2000-2015)

This table reports the abnormal performance of the decile equally-weighted CAR portfolios with Rank Period = 24 months and Test Period = 12, 24 & 36 months in deciles portfolios from the period of Jan 2000-Dec 2015. All the shares listed in KSE during this time period are sorted by month (t) in ascending order and then they are divided into 10 portfolios. P1 comprises of firms with the lowest CAR whereas, P10 represents the highest CAR companies. P1-P10 shows the level of spread i.e. the hedge portfolio which if results in positive significant value show that the overreaction hypothesis does exist in KSE. Portfolios are rebalanced on a monthly basis. CAPM alpha is the annualized alpha estimate derived from the Capital Asset Pricing Model. Three-Factor Fama-French alpha is the annualized alpha estimate derived from the Fama-French three-factor model. Five-Factor Fama-French alpha is the annualized alpha estimate derived from the Fama-French five-factor model. T-statistics are reported in parentheses at 1%, 5% and 10% level respectively. The last column reports the chi-square statistic of the Wald test referring to the null hypothesis that the 10 portfolio alphas are jointly equal to zero; p-values are reported below the statistic.

5. CONCLUSION

The overreaction hypothesis proposed by Bondt and Thaler (1985) has attracted a lot of attention from both academic and practitioners. In most studies, overreaction hypothesis has occupied a central place in asset pricing literature. In this regard, results of the CAR method indicate loser portfolios outperform winners in 36 months after portfolio formation in the non-overlapping test period. The EW & VW returns of the hedge portfolio (P1-P10) are 9.89% and 3.64% respectively. For both EW & VW portfolio returns, CAPM fails to explain this anomaly as it rejects the null hypothesis for the 36-month test period. However, as more risk factors like SMB, HML, CMA and RMW of 3-factor and 5-factor Fama and French models are incorporated in the risk-adjusted performance of portfolios formed on CAR, the profitability of contrarian anomaly disappears. It is evident from the t-statistics of the hedge portfolios and the Wald test of EW & VW returns of the test periods of 12 and 24 months that CAPM, 3-factor Fama and French and 5-factor Fama and French models, all explain the profitability of the contrarian anomaly. Therefore, we can conclude that contrarian strategy is profitable only in the long run on KSE and investors can long the portfolios with lowest CAR value shares and short the higher CAR values portfolios.

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APPENDIX A

Construction of Mimicking Portfolios for SMB, HML, RMW and CMA Factors:

To construct the portfolios for the Fama-French three-factor model, we followed mimicking portfolio construction used by Fama and French (1993). The size factor data was divided into two sub-groups, small (S) and bid (B) market capitalization firms, by using median as a breakup point and book-to-market equity factor data was divided into three sub-groups, high (H), neutral (N) and low (L) book-to-market equity firms, by using 30th and 70th percentiles as breakup points. The portfolios were made on 2x3 sort; where SMB factor is a simple average of returns on small market capitalization portfolios minus big market capitalization portfolios and the HML factor is a simple average of returns on high book-to-market equity portfolios minus low book-to-market equity portfolios. On the basis of 2x3 sort of SMB and HML factors the six portfolios formed, are as under:

SH = Portfolio of small market capitalization firms and high book-to-market equity ratio firms.

SN = Portfolio of small market capitalization firms and neutral book-to-market equity ratio firms.

SL = Portfolio of small market capitalization firms and low book-to-market equity ratio firms.

BH = Portfolio of big market capitalization firms and high book-to-market equity ratio firms.

BN =Portfolio of big market capitalization firms and neutral book-to-market equity ratio firms.

BL =Portfolio of big market capitalization firms and low book-to-market equity ratio firms.

The construction of portfolios for the Fama-French five-factor model, the study used 2x3 sort, used by Fama and French (2015). The size factor and book-to-market factor data were divided into 2 and 3 categories similarly to three-factor model. The profitability factor data was divided into three sub-groups, robust (R), neutral (N) and weak (W) operating profitability firms, by using 30th and 70th percentiles as breakup points. Moreover, the investment factor data were also divided into three sub-groups, conservative (C), neutral (N) and aggressive (A), same as the previous factors by using 30th and 70th percentiles as breakup points. Here, the construction of size factor is different from the three-factor asset pricing model. The size factor (SMB) was constructed by subtracting nine portfolios of big stocks from nine portfolios of small stock. On the basis of 2x3 sort, the study formed eighteen portfolios, are as under:

SH = Portfolio of small market capitalization firms and high book-to-market equity ratio firms.

SN = Portfolio of small market capitalization firms and neutral book-to-market equity ratio firms.

SL = Portfolio of small market capitalization firms and low book-to-market equity ratio firms.

BH = Portfolio of big market capitalization firms and high book-to-market equity ratio firms.

BN =Portfolio of big market capitalization firms and neutral book-to-market equity ratio firms.

BL =Portfolio of big market capitalization firms and low book-to-market equity ratio firms.

SR = Portfolio of small market capitalization firms and robust profitability firms.

SN = Portfolio of small market capitalization firms and neutral profitability firms.

SW = Portfolio of small market capitalization firms and weak profitability firms.

BR = Portfolio of big market capitalization firms and robust profitability firms.

BN = Portfolio of big market capitalization firms and neutral profitability firms.

BW = Portfolio of big market capitalization firms and weak profitability firms.

SC = Portfolio of small market capitalization firms and conservative investment firms.

SN = Portfolio of small market capitalization firms and neutral investment firms.

SA = Portfolio of small market capitalization firms and aggressive investment firms.

BC = Portfolio of big market capitalization firms and conservative investment firms.

BN = Portfolio of big market capitalization firms and neutral investment firms.

BA = Portfolio of big market capitalization firms and aggressive investment firms

Construction of Size, Book to Market Value, Profitability and Investment factors is explained as follows.

1 - Size Factor (SMB)

For three-factor asset pricing model, the study follows Fama and French (1993) mimicking portfolio construction and for the five-factor model, we use 2x3 sort of portfolios constructed by Fama and French (2015). The construction of SMB factor for three-factor asset pricing model is given in equation as follows:

For five-factor asset pricing model, first the study has to construct three size factors by taking weighted averages on the basis of book-to-market, profitability and investment factors than constructing the final size factor for the model by taking an average of all sub-factors, (see Fama and French (2015)).

2 - Book to Market Value Factor (HML)

For both three-factor and five-factor model the construction of HML factor is the same which is as follows:

3 - Profitability Factor (RMW)

For the construction of portfolios for profitability, the study used 2x3 sort also used by Fama and French (2015). The construction formula is given as follows:

4 - Investment Factor (CMA)

The construction of investment factor is given as follows:

Appendix B

To estimate the Alpha’s of the portfolios the following equation is used:

Where

R = Excess return on portfolio i in time period t

N = Number of portfolio

T = Time period

F = K * 1 vector of excess return factor portfolio

B = Vector of beta’s

This equation assumes that the excess returns of the portfolio are linearly related to its beta’s. For simplicity sake the above equation is restated as follows:

Footnote: