Role of human assets in measuring firm performance and its implication for firm valuation

Maiti, Moinak; Vuković, Darko Article Role of human assets in measuring firm performance and its implication for firm valuation Journal of Economic Structures Provided in Cooperation with: Pan-Pacific Association of Input-Output Studies (PAPAIOS) Suggested Citation: Maiti, Moinak; Vuković, Darko (2020) : Role of human assets in measuring firm performance and its implication for firm valuation, Journal of Economic Structures, ISSN 2193-2409, Springer, Heidelberg, Vol. 9, Iss. 47, pp. 1-27, https://doi.org/10.1186/s40008-020-00223-3 This Version is available at: https://hdl.handle.net/10419/261594 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Role ofhuman assets inmeasuring firm performance andits implication forfirm valuation Moinak Maiti1*† and Darko Vuković1,2† 1 Introduction Knowledge-based economy gained momentum over manufacturing-based economy in last few decades. Business firms nowadays specially giving significant importance to develop their human assets to gain competitive advantages over the other firms. Human assets are intangible in nature and generally not captured by balance sheet items. Accurate measurement of firm’s human assets is bit complex; one reason could be as Bontis etal. (2000) pointed out that human assets of a firm are not under direct control of the firm. In spite of knowing the fact that human assets are important in valuing the firm still most of the firm valuation are done considering only the balance sheet items. Collins etal. (1997) added investors could gain additional by gathering information on the firms’ human assets. Last few decades are spectator of several risk factors and factor models for firm valuations [see Maiti (2020a, b)]. CAPM [Sharpe (1964), Lintner (1965) and Mossin (1966)] was the seminal model that challenged over the period of time by several researchers like Fisher Black (1972), Fama and MacBeth (1973), Ross (1976), Banz (1981), Reinganum (1981), Gibbons (1982), Basu (1983), Shanken (1985) and Bhandari (1988). There after several multifactor models developed and challenged such as Ross (1976) APT model, Fama–French (1993) three-factor model, Fama–French (2015) five-factor model and others. Further studies by Haugen and Baker (1996), Cohen Abstract The purpose of the study is to evaluate the role of human asset in firm performance and its implication for firm valuation. To do so a modified five-factor model with human asset designed for capturing the size, value, profitability and investment in average portfolio returns that performs better than both Fama–French (1993) three- and Fama–French (2015) five-factor model. Study redefines CMA factors as CvMAv that includes human assets in it. The main problem with the modified five-factor model with human asset is the microcap with conservative investment stocks whose returns behave like that low-value unprofitable firms. Keywords: Human asset, Factor models, Asset Pricing, Risk JEL Classification: G12 Open Access © The Author(s) 2020. 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RESEARCH Maitiand Vuković Economic Structures (2020) 9:47 https://doi.org/10.1186/s40008-020-00223-3 *Correspondence: [email protected] †Moinak Maiti and Darko Vuković contributed equally to this work 1 Department for Finance, St. Petersburg School of Economics and Management, National Research University Higher School of Economics, Kantemirovskaya St. 3A, Saint Petersburg 194100, Russia Full list of author information is available at the end of the article Page 2 of 27 Maitiand Vuković Economic Structures (2020) 9:47 etal. (2002), Fairfield etal. (2003), Titman etal. (2004), Novy-Marx (2013), Hou etal. (2014), Clarke (2016), Chiah etal. (2016), Balakrishnan and Maiti (2017), Maiti and Balakrishnan (2018, 2020), Maiti (2019a, b, c), Maiti (2020a, b) and others find that these model are not global and there is a scope for more robust valuation model. Most of the studies discussed above do not include a measure for human assets in their valuation models. Notably it was the Campbell (1992, 1992) studies that strongly argued firm valuation excluding human assets may lead to serious errors. Other studies by Fama and Schwert (1977), Jagannathan and Wang (1996), Jagannathan etal. (1998), Rosett (2001) and Qin (2002) also find that human asset is an important factor in explaining the cross-sectional risk return variations. The present study will examine the role of human asset investment in firm valuation in Indian context. Present study will use Fama–French (1993) three-factor and Fama–French (2015) five-factor model in a time series setup to test the risk return relationship and finally results will be compared to newly proposed model to justify its robustness than the former two models. The nobleness of the present study lies in several ways first altogether a new robust five-factor asset pricing model developed with human asset investment which found to be superior than existing valuation models; second, in Indian context human asset investment factor is almost untouched by previous studies except Maiti (2019a, b, c), Maiti and Balakrishnan (2018, 2020) and few others. 2 Literature review Campbell (1996) shows that by ignoring human asset CAPM overstates the risk investing in financial assets and understates the risk aversion coefficient. Study also finds intertemporal model using human asset to be more robust than the traditional CAPM in explaining risk return relationship. Similarly, Jagannathan and Wang (1996) study also find that the intertemporal model with human asset is more sustainable than CAPM. The study also argues that human assets are tradable such as in mortgage and life insurance markets. Thereafter Rosett (2001) and Qin (2002) added that human asset is positively related to the equity returns. Chen etal. (2005) study find that during the period between 1977 and 2001, there is significant increase in the gap between the book value and market value of the US companies. The study mentioned that ignorance of valuable assets by the financial statement could be the reason behind the gap between the book value and market value as similar to the Collins etal. (1997) findings. The study also confirms that 80% of the firm’s market value is missing in the financial statement of the firm. Knowledge-based aspect of the firms’ human asset is considered by Crook etal. (2011). Study argues that human asset characteristics are unique for each firm; human asset of a firm is difficult to copy, replicate and duplicate. Hence, a firm could gain sustainable competitive advantages over other firms by developing its human asset. In general successful firms pay higher compensation to develop human assets that in turn leads to higher productivity and increase value of the firm. Pantzalis and Park (2009), Edmans (2011) and others study show empirically that market is often unable to price the human asset accurately especially for the small-size firms. From the above discussion it is clear that human asset factor is important in relationship to determining the firm valuation. The main problems lie with human asset is that it is very difficult to measure and none of the available techniques that are used by previous study are able to Page 3 of 27 Maitiand Vuković Economic Structures (2020) 9:47 measure the human asset factor accurately. Human asset investment seems to be one of the very important factors that are related to the stock returns and on the other hand, very limited number of studies are done on human asset in this aspects. Considering the emerging markets, very limited number of studies are done on human asset and firm valuation in Indian context. All such factors justify the need of present study and study results will have serious implication for the other emerging and developed markets. 3 Data andmethodology 3.1 Data The study uses monthly data for total 431 companies those are listed in the BSE 500 index and the study period is from July, 2003 to November, 2016. Study uses Market capitalization (MC) as proxy for Size; Price to Book (P/B) ratio as proxy for Value; BSE 200 index monthly return as proxy for Market (Rm) and 91-day T-Bills return as proxy for risk-free rate (Rf). Total asset growth (TA) without human asset act as the proxy for Investment (CMA) and it is calculated by the formula [(TAt − TAt−1)/TAt−1)] as similar to Hou etal. (2015) and return on equity (ROE) used as the proxy for profitability as similar to Haugen and Baker (1996). Total salary and wage expense used as the proxy for human asset (HA) as similar to Hansson (2004), Draca etal. (2011), and Bell and Machin (2016). Traditionally investment in human asset considers as the cost to the company and not as the investment Petty and Guthrie (2000). But significant number of studies by Bontis (2003) and Wright etal. (2001) argued that human asset should be considered as the investment of the firm rather than expenses in today’s knowledge-based economy where human asset has greater importance in determining the value of the firm. So present study defined a new factor for investment with human asset (CvMAv) as the total asset growth (TAM = TA + HA) including human asset that acts as the proxy for Investment factor (CvMAv) and it is calculated by the formula [{(TA + HA)t − (TA + HA)t−1}/ (TA + HA)t−1)]. 3.2 Portfolio construction methodology Single and double shorting techniques are deployed to construct the study and mimicking portfolios. Every year in the month of June (t) based on market capitalization of the stocks using single sorting technique five equal weighted portfolios are constructed. Five market capitalization (MC)-based portfolios are named P1 to P5 in ascending order of size. Then again in the month of June next year (t + 1) the rank revised using the same process and continued every year till 2016. Following the same procedure other portfolios based on P/B, ROE, TA and TAM are constructed and named. Then every year in the month of June (t) using double sorting technique 25 value weighted portfolios are constructed from the cross of five MC and P/B sorted portfolios. Portfolio consists of small size (MC) and low P/B stocks named as the MP11, similarly portfolio with big size (MC) and high P/B stocks named as MP55. Then again in the month of June next year (t + 1) the rank revised using the same process and continued every year till 2016. Following the same procedure using double sorting technique three sets of 25 portfolios are constructed from the each individual crosses of five ‘MC & ROE’, ‘MC & TA’ and ‘MC & TAM’ sorted portfolios, respectively. The portfolios were named in the similar fashion as Page 4 of 27 Maitiand Vuković Economic Structures (2020) 9:47 explained in case of ‘MC & P/B’ cross and again in the month of June next year (t + 1) the rank revised using the same process and continued every year till 2016. Using the similar process, other portfolios are constructed to derive the mimicking portfolios as described below. Every year in the month of June (t) based on market capitalization (MC) of the stocks using single sorting technique two equal weighted portfolios are constructed similar to Balakrishnan and Maiti (2017), Maiti and Balakrishnan (2018, 2020), Maiti (2019a, b, c) and other studies. The portfolios are named Small (S) and Big (B) in ascending order of size (MC). Then again in the month of June next year (t + 1) the rank revised using the same process and continued every year till 2016. Then using Fama–French (1993) breakpoints (30:40:30) based on P/B three weighted portfolios are constructed. Portfolio consists of bottom 30% stocks with low P/B ratio named value (V), top 30% stocks with high P/B ratio named growth (G) and rest 40% stocks were placed into the neutral portfolio. Then again in the month of June next year (t + 1) the rank revised using the same process and continued every year till 2016. Then every year in the month of June (t) using double sorting technique six value weighted portfolios are constructed from the cross of two MC and three P/B sorted portfolios. These formed six portfolios are named as S/L, S/N, S/G, B/L, B/N and B/G, where S/L consists of small size and low P/B stocks whereas B/G consists of big size and high P/B stocks. Similarly using Fama–French (1993) breakpoints (30:40:30) based on ROE, TA and TAM three sets of three weighted portfolios are constructed from each of these variables. Portfolio consists of bottom 30% stocks with low ROE named Weak (W), top 30% stocks with high ROE named Robust (R) and rest 40% stocks were placed into the neutral portfolio. Then portfolio consists of bottom 30% stocks with low TA named Conservative (C), top 30% stocks with high TA named Aggressive (A) and rest 40% stocks were placed into the neutral portfolio. Similarly portfolio consists of bottom 30% stocks with low TAM named Conservative Value (CV), top 30% stocks with high TAM named Aggressive value (AV) and rest 40% stocks were placed into the neutral portfolio. Then again in the month of June next year (t + 1) the rank revised using the same process and continued every year till 2016. Then every year in the month of June (t) using double sorting technique three sets of six value weighted portfolios are constructed from the each individual cross of ‘two MC & three ROE’, ‘two MC & three TA’ and ‘two MC & three TAM’ sorted portfolios, respectively. Then formed portfolios were named in similar fashion as described in case of ‘two MC & three ROE’ cross. 3.3 Mimicking portfolios Study uses five mimicking portfolios SMB (Size), LMH (value), RMW (profitability), CMA (Investment without human asset) and CvMAv (Investment with human asset) and they are calculated as explained below: (1) SMB = (S/L + S/M + S/H)/3 − (B/L + B/M + B/H)/3, (2) LMH = (S/L + B/L)/2 − (S/H + B/H)/2, (3) RMW = (S/R + B/R)/2 − (S/W + B/W)/2, Page 5 of 27 Maitiand Vuković Economic Structures (2020) 9:47 The present study uses three regression models: Fama–French three-factor model where SMB and LMH mimic the risk factors whereas s and l are the portfolio’s responsiveness to (sensitivity coefficients) SMB and LMH factors, respectively. Fama–French Five-factor model where SMB, LMH, RMW and CMA mimic the risk factors whereas s, l, p and t are the portfolio’s responsiveness to (sensitivity coefficients) SMB, LMH, RMW and CMA factors, respectively. Modified five-factor model with Human Asset where SMB, LMH, RMW and CvMAv mimic the risk factors whereas s, l, p and t are the portfolio’s responsiveness to (sensitivity coefficients) SMB, LMH, RMW and CvMAv factors, respectively. 4 Explanatory variables Descriptive statistics of the explanatory variables are shown in Table1. The average monthly market premium of 1% (t = 2.151), size premium of 1.3% (t = 5.177) and value premium of 0.8% (t = 2.164) seem quite attractive in terms of investment; results are similar to Fama–French (1993, 2015) in US market. Investment based on size of the firms has higher probability to yield more returns to the investors. Profitability, investment and human asset factor yields comparatively much lower average monthly premium than market, size and value factor. That implies that risks associated with these factors are lower and risk adverse investors should consider these factors while making investment decision. Correlation matrix for the explanatory variables is shown in Table2. Market is negatively related to the profitability and investment factors whereas positively related to size, value and investment with human asset factors. Theoretically findings are correct and similar to Fama–French (2015) in US context. Value and investment with human (4) CMA = (S/C + B/C)/2 − (S/A + B/A)/2, (5) CvMAv = (S/Cv + B/Cv)/2 − (S/Av + B/Av)/2. (6) RPt − RFt = a + b(RMt − RFt) + sSMBt + lLMHt + et (7) RPt − RFt = a + b ( RMt − RFt )+ s SMB t + l LMH t + p RMWt + t CMAt + et (8) RPt − RFt = a + b(RMt − RFt) + sSMBt + lLMHt + pRMWt + hCvMAvt + et Table 1 Descriptive statistics fortheindependent variables Rm SMB LMH RMW CMA CvMAv Mean returns 0.010 0.013 0.008 0.001 0.001 0.002 Standard deviations 0.059 0.031 0.047 0.006 0.028 0.012 T-statistics 2.151 5.177 2.164 2.115 0.617 2.115 Page 6 of 27 Maitiand Vuković Economic Structures (2020) 9:47 asset factors are positively related to other factors except profitability factor. The correlations between the explanatory variables are within the limit and in all cases standard errors are less. 5 Empirical results Figure1 shows the average return pattern for 25 portfolios constructed based on MC_ PB, MC_ROE, MC_TA and MC_TAM. In all the cases portfolio 1 returns outperformed the returns from other portfolios and similarly portfolio 25 has the lowest average returns in all the cases. The return patterns clearly reveal that investors can gain abnormal returns by following size-based investment strategy. Figure1 also reveals that there is manifestation of other factors (value, profitability, investment) too and there exists certain patterns which need to be identified. Details of each portfolio formed from each cross are shown in Table3 for further discussion. MC_PB: First portfolio consists of small size and low P/B stocks yield average monthly return of 4.6% (t = 5.490) which is at least four times higher than the average monthly return of last portfolio. Holding value (P/B) constant in each column the average monthly return decreases with increase in size and this is known as the size effect. Consider first column keeping low-value (P/B) constant first portfolio at the top of Table 2 Correlation matrix forexplanatory variables RM SMB LMH RMW CvMAv CMA RM 1 SMB 0.283 1 LMH 0.329 0.063 1 RMW − 0.352 − 0.041 − 0.843 1 CvMAv 0.306 0.287 0.171 − 0.338 1 CMA − 0.133 0.286 0.215 − 0.346 0.162 1 Fig. 1 Radar graph shows 25 portfolios mean returns based on MC_PB, MC_ROE, MC_TA and MC_TAM crosses Page 7 of 27 Maitiand Vuković Economic Structures (2020) 9:47 Table 3 Summary statistics of25 portfolios formed onMC_PB, MC_ROE, MC_TA andMC_ TAM Panel A(mean excess returns) MC_PB MC_ROE Low 2 3 4 High Low 2 3 4 High Small 0.046 0.039 0.034 0.027 0.021 0.043 0.039 0.032 0.034 0.035 2 0.039 0.023 0.022 0.017 0.019 0.022 0.021 0.019 0.019 0.024 3 0.020 0.020 0.014 0.017 0.016 0.018 0.016 0.017 0.016 0.021 4 0.014 0.014 0.019 0.016 0.014 0.010 0.013 0.018 0.018 0.021 Big 0.016 0.010 0.011 0.015 0.010 0.010 0.007 0.012 0.013 0.013 MC_TA MC_TAM Low 2 3 4 High Low 2 3 4 High Small 0.042 0.037 0.029 0.040 0.039 0.038 0.039 0.037 0.030 0.022 2 0.024 0.021 0.019 0.018 0.023 0.028 0.026 0.019 0.022 0.014 3 0.019 0.013 0.013 0.014 0.016 0.021 0.016 0.020 0.012 0.014 4 0.014 0.017 0.019 0.015 0.018 0.019 0.013 0.018 0.013 0.019 Big 0.014 0.011 0.009 0.017 0.010 0.013 0.014 0.014 0.015 0.011 Panel B (standard deviations) MC_PB MC_ROE Low 2 3 4 High Low 2 3 4 High Small 0.106 0.101 0.093 0.083 0.087 0.109 0.164 0.095 0.090 0.091 2 0.149 0.100 0.084 0.084 0.078 0.111 0.099 0.086 0.086 0.083 3 0.109 0.104 0.082 0.088 0.076 0.112 0.101 0.092 0.086 0.082 4 0.116 0.097 0.108 0.089 0.067 0.110 0.100 0.089 0.084 0.069 Big 0.108 0.104 0.087 0.089 0.067 0.103 0.100 0.086 0.080 0.078 MC_TA MC_TAM Low 2 3 4 High Low 2 3 4 High Small 0.103 0.107 0.099 0.145 0.104 0.110 0.099 0.141 0.092 0.087 2 0.099 0.094 0.088 0.085 0.096 0.112 0.093 0.088 0.088 0.085 3 0.096 0.088 0.093 0.093 0.101 0.103 0.091 0.087 0.101 0.083 4 0.093 0.089 0.088 0.087 0.111 0.101 0.079 0.084 0.089 0.075 Big 0.082 0.074 0.080 0.086 0.094 0.092 0.104 0.089 0.082 0.077 Panel C (T-statistics) MC_PB MC_ROE Low 2 3 4 High Low 2 3 4 High Small 5.490 4.843 4.615 4.187 3.086 4.953 3.043 4.228 4.803 4.902 2 3.324 2.961 3.330 2.633 3.101 2.465 2.673 2.854 2.873 3.610 3 2.347 2.436 2.159 2.508 2.742 1.991 1.987 2.299 2.405 3.241 4 1.510 1.851 2.204 2.327 2.718 1.195 1.650 2.502 2.774 3.851 Big 1.927 1.267 1.659 2.093 1.841 1.233 0.921 1.719 2.017 2.117 MC_TA MC_TAM Low 2 3 4 High Low 2 3 4 High Small 5.123 4.425 3.736 3.538 4.708 4.344 4.946 3.304 4.186 3.138 2 3.022 2.800 2.755 2.701 2.982 3.187 3.474 2.719 3.189 2.076 3 2.507 1.942 1.848 1.972 1.980 2.595 2.236 2.934 1.569 2.140 Page 8 of 27 Maitiand Vuković Economic Structures (2020) 9:47 column with small-size stocks’ portfolio yields average monthly return of 4.6% (t = 5.490) whereas average monthly return reduced more than thrice to 1.6% (t = 1.927) for the bottom portfolio in the column with big-size stocks. Same observation is observed for all other columns that indicate there is a strong size effect in portfolio return patterns. Similarly holding size (MC) constant in each row the average monthly return decreases with increase in value and this is known as the value effect. Consider first row keeping small-size constant first portfolio at the extreme left of the first row with low-value stocks’ portfolio yields average monthly return of 4.6% (t = 5.490) whereas average monthly return reduced almost half to 2.1% (t = 3.086) for the bottom portfolio in the column with big-size stocks. Similar observation reflects in all other rows also indicate that there is a strong value effect in portfolio return patterns. The study findings are similar to Fama–French (2015) study in US context. MC_ROE, MC_TA and MC_TAM: Clear size effect is observed in portfolios formed from MC_ROE, MC_TA and MC_TAM crossed portfolios. In MC_ROE cross portfolio holding size constant for first three rows shows no clear pattern but last two rows with big-size portfolios show weak profitability effect as similar to Novy-Marx (2013) and Fama–French (2015) findings. Holding size constant for both the MC_TA and MC_ TAM crosses no much clear portfolio return pattern observed while traversing through any of the other rows. Figure2 shows the 3D view of return patterns for all the portfolios formed from MC_PB, MC_ROE, MC_TA and MC_TAM crosses, respectively. More complex return patterns are observed in case for MC_ROE, MC_TA and MC_TAM cross portfolios as frequent change in slope can be observed in Fig.2. 6 Asset pricing results 6.1 Three-factor regression Three-factor regression results with market, size and value are shown in Table4. A regression model is said to be a best model which is able to capture all alpha values equal to zero. Five portfolios found significant (alpha values not equal to zero where t(a) is more than 1.96) for MC_PB, MC_ROE & MC_TA and four portfolios found significant in case of MC_TAM portfolios. Average alpha value (intercepts) for MC_PB, MC_ROE, MC_TA and MC_TAM cross portfolios found to be 0.0034, 0.0049, 0.0034 and 0.0033, respectively. The average values of intercepts are not closer to zero for all the cases and average R-Square value (%) for MC_PB, MC_ROE, MC_TA and MC_TAM cross portfolios are 78.7, 76.4, 76.6 and 73.8, respectively (see Table7). Expect for the MC_TAM cross portfolio consists of microcaps (First portfolio) that are not captured by the threefactor regressions. The study findings are similar to the global findings of Aharoni etal. (2013) and Fama–French (2015). Table 3 (continued) MC_TA MC_TAM Low 2 3 4 High Low 2 3 4 High 4 1.984 2.436 2.729 2.130 2.095 2.418 2.056 2.734 1.809 3.120 Big 2.165 1.859 1.388 2.453 1.346 1.748 1.759 2.067 2.390 1.752 Page 15 of 27 Maitiand Vuković Economic Structures (2020) 9:47 Table 5 (continued) Panel C MC_TA aRM Low 2 3 4 High Low 2 3 4 High Small 0.010 0.006 0.002 0.018 0.005 1.098 1.156 1.074 0.592 1.089 2 0.001 0.002 0.001 0.002 0.001 1.082 1.038 0.950 0.917 1.022 3− 0.001 − 0.002 − 0.003 0.001 − 0.003 1.110 0.996 1.124 1.097 1.012 4 0.004 0.008 0.007 0.003 0.011 1.036 1.002 0.986 0.963 1.189 Big 0.007 0.004 0.001 0.008 0.003 0.968 0.829 0.996 1.020 1.109 S L Low 2 3 4 High Low 2 3 4 High Small 1.438 1.246 1.055 1.638 1.528 0.214 0.402 0.415 0.028 0.479 2 0.654 0.662 0.652 0.449 0.933 0.383 0.034 0.150 0.253 0.070 3 0.553 0.297 0.378 0.201 0.712 0.188 0.194 0.166 0.075 0.235 4 0.143 − 0.022 0.003 0.031 0.120 − 0.137 0.014 0.205 0.238 − 0.532 Big − 0.029 − 0.164 − 0.122 − 0.254 0.066 − 0.245 0.128 − 0.037 0.232 − 0.422 R T Low 2 3 4 High Low 2 3 4 High Small − 0.187 − 0.109 − 0.038 − 1.517 0.065 0.716 0.322 0.083 − 1.940 − 0.383 2− 0.182 − 0.366 − 0.376 − 0.196 − 0.396 0.207 0.169 0.031 − 0.020 − 0.724 3− 0.283 − 0.113 − 0.106 − 0.199 − 0.304 0.460 0.416 − 0.155 − 0.199 − 1.101 4− 0.399 − 0.366 − 0.145 − 0.170 − 0.925 0.134 0.096 0.098 − 0.214 − 0.742 Big − 0.419 − 0.169 − 0.139 0.057 − 0.681 0.350 0.142 − 0.003 − 0.238 − 0.603 t(a) t(RM) Low 2 3 4 High Low 2 3 4 High Small 2.316 1.385 0.373 1.803 1.014 18.752 18.242 17.314 4.406 15.812 2 0.350 0.441 0.146 0.407 0.329 19.149 17.292 18.852 16.965 16.805 3− 0.236 − 0.569 − 1.024 0.250 − 0.727 23.439 18.659 24.216 21.480 15.793 4 0.836 2.131 2.035 0.935 2.314 17.092 20.515 19.855 20.993 18.111 Big 2.110 1.291 0.342 3.054 1.014 22.806 21.628 31.404 28.133 27.144 t(s)t(l) Low 2 3 4 High Low 2 3 4 High Small 11.095 8.881 7.684 5.504 10.026 1.428 2.471 2.610 0.082 2.710 2 5.227 4.978 5.846 3.753 6.928 2.641 0.221 1.158 1.822 0.446 3 5.271 2.516 3.683 1.775 5.022 1.548 1.416 1.397 0.570 1.429 4 1.067 − 0.207 0.031 0.308 0.826 − 0.879 0.111 1.609 2.025 − 3.161 Big − 0.307 − 1.937 − 1.740 − 3.167 0.734 − 2.253 1.307 − 0.461 2.493 − 4.027 t(r)t(T) Low 2 3 4 High Low 2 3 4 High Small − 1.126 − 0.605 − 0.218 − 3.970 0.330 4.690 1.950 0.516 − 5.531 − 2.134 2− 1.130 − 2.142 − 2.623 − 1.275 − 2.292 1.401 1.078 0.235 − 0.143 − 4.562 3− 2.100 − 0.744 − 0.804 − 1.371 − 1.667 3.724 2.986 − 1.279 − 1.493 − 6.585 4− 2.315 − 2.638 − 1.028 − 1.306 − 4.957 0.849 0.750 0.754 − 1.788 − 4.330 Big − 3.471 − 1.548 − 1.539 0.554 − 5.859 3.158 1.423 − 0.039 − 2.519 − 5.657 Page 16 of 27 Maitiand Vuković Economic Structures (2020) 9:47 Table 5 (continued) Panel D MC_TAM aRM Low 2 3 4 High Low 2 3 4 High Small 0.003 0.014 0.009 0.004 − 0.004 1.317 0.845 0.673 0.962 0.934 2 0.005 0.006 0.002 − 0.001 − 0.001 1.170 0.989 0.982 0.938 0.935 3− 0.003 0.001 0.008 − 0.002 0.002 1.212 1.037 1.031 1.085 0.901 4 0.005 0.000 0.007 0.004 0.007 1.158 0.837 0.867 0.891 0.923 Big 0.009 0.005 0.003 0.008 0.003 0.947 1.264 1.069 0.956 0.985 S L Low 2 3 4 High Low 2 3 4 High Small 1.544 0.900 1.717 1.135 0.817 0.152 0.581 0.277 0.294 0.643 2 0.814 0.798 0.399 0.741 0.269 0.234 0.047 0.238 0.570 0.264 3 1.031 0.348 0.298 0.221 0.021 − 0.070 0.035 − 0.141 0.286 0.324 4 0.388 0.149 0.168 − 0.245 0.160 − 0.224 0.296 0.143 0.392 0.035 Big − 0.166 0.018 0.060 − 0.231 0.028 − 0.345 − 0.281 0.009 0.064 − 0.325 R T Low 2 3 4 High Low 2 3 4 High Small 0.104 − 0.105 − 1.180 − 0.051 0.383 0.357 − 0.005 − 1.397 0.140 0.285 2− 0.435 − 0.490 − 0.062 0.174 − 0.063 0.033 0.009 0.207 0.096 0.091 3− 0.312 − 0.264 − 0.278 − 0.241 − 0.081 0.074 0.183 0.002 − 0.458 0.039 4− 0.546 − 0.072 − 0.273 − 0.193 0.060 0.000 0.124 − 0.410 − 0.095 0.098 Big − 0.630 − 0.432 − 0.137 − 0.147 − 0.254 − 0.092 − 0.342 − 0.116 − 0.011 − 0.017 t(a)t(RM) Low 2 3 4 High Low 2 3 4 High Small 0.637 2.478 0.981 0.837 − 0.896 19.324 10.802 5.219 14.804 15.251 2 0.914 1.357 0.457 − 0.338 − 0.223 16.360 17.119 16.745 16.075 16.655 3− 0.680 0.241 1.880 − 0.579 0.632 18.807 18.607 18.885 18.519 18.273 4 1.151 0.026 1.731 1.158 1.964 18.841 16.329 15.398 18.368 19.411 Big 1.907 1.329 0.943 3.020 1.250 14.882 25.835 22.560 25.124 27.341 t(s)t(l) Low 2 3 4 High Low 2 3 4 High Small 10.232 5.194 6.015 7.886 6.028 0.871 2.895 0.837 1.762 4.093 2 5.146 6.241 3.078 5.738 2.164 1.274 0.317 1.580 3.807 1.832 3 7.232 2.826 2.469 1.702 0.195 − 0.423 0.247 − 1.007 1.906 2.558 4 2.850 1.310 1.349 − 2.286 1.516 − 1.422 2.252 0.992 3.153 0.291 Big − 1.177 0.163 0.572 − 2.747 0.349 − 2.112 − 2.241 0.071 0.657 − 3.519 t(r) t(T) Low 2 3 4 High Low 2 3 4 High Small 0.535 − 0.470 − 3.218 − 0.275 2.201 2.008 − 0.027 − 4.151 0.825 1.785 2− 2.142 − 2.981 − 0.372 1.047 − 0.394 0.175 0.059 1.354 0.628 0.621 3− 1.704 − 1.667 − 1.789 − 1.446 − 0.575 0.440 1.262 0.016 − 2.999 0.306 4− 3.125 − 0.494 − 1.708 − 1.399 0.446 − 0.002 0.928 − 2.794 − 0.749 0.794 Big − 3.483 − 3.105 − 1.021 − 1.355 − 2.478 − 0.557 − 2.680 − 0.940 − 0.115 − 0.184 Page 17 of 27 Maitiand Vuković Economic Structures (2020) 9:47 for microcap portfolio indicate that first portfolio with low profitability microcaps is dominated by firm whose stocks behave like unprofitable firms with aggressive investment. MC_TA: Six portfolios found to be significant with average alpha value of 0.0043 and 78.9 average R-square (%). Here also like previous case high positive investment (CMA) and less negative profitability (RMW) coefficient for microcap portfolio indicate that first portfolio with low profitability microcaps is dominated by firm whose stocks behave like unprofitable firms with aggressive investment and the problem with microcap remains unsolved. MC_TAM: Four portfolios found to be significant with average alpha value of 0.0047 and 74.9 average R-square (%). The biggest problem lies with Fama–French (2015) is microcaps due to high negative profitability (RMW) and investment (CMA) factor but it is well captured with MC_TAM cross portfolio. So, it indicates that it is not the asset pricing problem but the way how portfolios constructed are of much importance. From the above discussion, it is very much clear that microcap is the problem for most of the crosses as similar to Fama–French (2015) findings. Study result also confirms that Fama–French (2015) five model is not better than Fama–French (1993) three-factor model in Indian context. Further study confirms Fama–French five-factor model is not a global similar to studies by Hou etal. (2014), Clarke (2016), and Chiah etal. (2016). Then study runs modified five-factor model with human asset investment with market (Rm), size (SMB), value (LMH), profitability (RMW), and investment with human asset (CvMAv). 6.3 Modified five-factor regressions (with human asset investment) The regressions’ result of the modified five-factor model with human asset investment is shown in Table6. Table 5 (continued) Panel E R2 MC_PB MC_ROE Low 2 3 4 High Low 2 3 4 High Small 0.740 0.744 0.762 0.789 0.777 0.768 0.452 0.733 0.771 0.741 2 0.571 0.734 0.757 0.801 0.794 0.770 0.782 0.762 0.764 0.768 3 0.827 0.829 0.747 0.832 0.799 0.768 0.810 0.792 0.790 0.817 4 0.854 0.780 0.845 0.818 0.778 0.798 0.800 0.774 0.747 0.799 Big 0.876 0.888 0.908 0.881 0.856 0.882 0.884 0.886 0.850 0.832 MC_TA MC_TAM Low 2 3 4 High Low 2 3 4 High Small 0.800 0.782 0.757 0.467 0.730 0.763 0.613 0.484 0.693 0.694 2 0.799 0.748 0.797 0.753 0.753 0.749 0.763 0.727 0.728 0.732 3 0.851 0.771 0.845 0.815 0.750 0.759 0.766 0.757 0.792 0.784 4 0.736 0.816 0.802 0.827 0.782 0.771 0.738 0.725 0.815 0.754 Big 0.833 0.834 0.902 0.890 0.884 0.705 0.863 0.824 0.865 0.863 Page 18 of 27 Maitiand Vuković Economic Structures (2020) 9:47 Table 6 Regression results of Modified Five-Factor Model with human asset for 25 portfolios RPt − RFt = a + b (RMt − RFt) + s SMBt + l LMHt + p RMWt + h CvMAvt + et Panel AMC_PB a b Low 2 3 4 High Low 2 3 4 High Small 0.007 0.009 0.011 0.002 − 0.001 0.950 1.017 1.034 0.971 1.093 2 0.010 0.003 0.001 − 0.004 0.004 0.833 0.987 0.886 1.017 0.977 3− 0.004 − 0.001 − 0.001 0.001 0.003 1.099 1.145 0.930 1.123 0.957 4− 0.003 0.002 0.010 0.003 0.005 1.021 0.896 1.145 1.062 0.814 Big 0.004 0.001 0.003 0.007 0.002 0.984 1.097 1.014 1.100 0.883 S L Low 2 3 4 High Low 2 3 4 High Small 1.157 1.047 0.828 1.109 1.262 1.128 0.402 0.045 0.014 − 0.458 2 1.634 0.613 0.660 0.902 0.557 0.629 0.106 0.186 0.015 − 0.333 3 0.666 0.475 0.463 0.439 0.304 0.582 0.287 0.114 − 0.100 − 0.088 4− 0.248 − 0.208 − 0.345 0.103 0.133 1.098 0.553 − 0.120 − 0.144 − 0.261 Big − 0.374 − 0.400 − 0.308 − 0.223 0.140 0.924 0.462 0.293 − 0.162 − 0.449 Rh Low 2 3 4 High Low 2 3 4 High Small 0.641 − 0.012 − 0.175 − 0.060 − 0.375 0.665 0.410 0.320 0.197 − 0.095 2− 1.033 − 0.409 − 0.120 − 0.171 − 0.231 − 0.458 0.358 0.315 − 0.031 0.158 3− 0.296 − 0.233 − 0.233 − 0.045 0.036 0.017 0.227 − 0.126 0.073 0.130 4− 0.029 − 0.143 − 0.466 − 0.100 − 0.041 0.151 0.258 0.475 0.391 0.271 Big − 0.095 − 0.213 − 0.013 − 0.134 − 0.228 0.025 − 0.014 0.049 0.094 0.087 t(a)t(RM) Low 2 3 4 High Low 2 3 4 High Small 1.543 1.924 2.535 0.635 − 0.284 13.802 15.171 17.172 19.059 19.974 2 1.006 0.582 0.314 − 1.089 1.221 6.094 14.510 16.288 20.033 20.538 3− 0.854 − 0.280 − 0.235 0.251 0.842 17.952 20.050 16.908 22.639 20.965 4− 0.724 0.423 2.464 0.839 1.608 17.293 14.842 20.224 21.469 19.427 Big 1.093 0.371 1.032 2.522 1.004 19.383 23.261 28.576 26.745 25.836 t(s)t(l) Low 2 3 4 High Low 2 3 4 High Small 7.459 6.935 6.107 9.664 10.241 6.505 2.380 0.294 0.109 − 3.322 2 5.309 3.999 5.385 7.892 5.195 1.826 0.618 1.359 0.114 − 2.777 3 4.832 3.693 3.734 3.928 2.958 3.774 1.997 0.819 − 0.797 − 0.764 4− 1.867 − 1.529 − 2.705 0.924 1.408 7.382 3.635 − 0.840 − 1.157 − 2.471 Big − 3.268 − 3.766 − 3.857 − 2.411 1.815 7.221 3.891 3.272 − 1.563 − 5.214 t(r)t(h) Low 2 3 4 High Low 2 3 4 High Small 3.450 − 0.067 − 1.079 − 0.438 − 2.540 4.217 2.670 2.320 1.684 − 0.759 2− 2.800 − 2.227 − 0.820 − 1.250 − 1.795 − 1.461 2.295 2.529 − 0.269 1.453 3− 1.792 − 1.509 − 1.571 − 0.334 0.289 0.122 1.731 − 1.000 0.645 1.240 4− 0.179 − 0.878 − 3.051 − 0.751 − 0.365 1.115 1.865 3.657 3.449 2.821 Big − 0.690 − 1.669 − 0.137 − 1.211 − 2.470 0.211 − 0.129 0.607 0.994 1.114 Page 19 of 27 Maitiand Vuković Economic Structures (2020) 9:47 Table 6 (continued) Panel B MC_ROE a b Low 2 3 4 High Low 2 3 4 High Small 0.007 0.017 0.004 0.003 0.004 1.013 0.727 0.964 1.030 1.082 2− 0.003 0.000 0.002 − 0.003 0.003 1.041 0.983 0.982 1.095 1.065 3− 0.003 0.004 0.000 − 0.003 0.005 0.979 1.043 1.054 1.016 0.966 4− 0.002 0.001 0.009 0.008 0.010 1.049 0.938 0.917 0.915 0.873 Big 0.002 − 0.001 0.005 0.004 0.003 1.073 1.076 1.018 0.983 0.996 S L Low 2 3 4 High Low 2 3 4 High Small 1.542 1.212 1.014 1.108 1.241 0.471 0.218 0.481 0.606 0.277 2 0.791 0.549 0.622 0.972 0.668 0.455 0.289 − 0.036 − 0.046 0.193 3 0.379 0.145 0.222 0.451 0.020 0.364 − 0.137 0.292 0.474 0.267 4 0.068 − 0.143 − 0.228 − 0.194 0.234 − 0.045 0.429 0.171 0.192 − 0.213 Big − 0.301 − 0.277 − 0.138 − 0.071 − 0.051 0.027 0.088 − 0.084 − 0.144 − 0.010 R h Low 2 3 4 High Low 2 3 4 High Small − 0.185 − 1.324 0.032 0.508 0.497 0.288 − 0.124 0.193 0.187 0.288 2− 0.451 − 0.349 − 0.280 0.028 0.238 0.135 0.268 0.072 − 0.112 − 0.081 3− 0.509 − 0.752 0.062 0.261 0.350 0.541 0.168 0.175 − 0.057 0.438 4− 0.837 − 0.320 − 0.240 0.080 − 0.015 0.304 0.221 0.142 0.228 0.156 Big − 0.625 − 0.487 − 0.390 − 0.148 0.256 0.156 0.110 − 0.067 0.119 0.125 t(a)t(b) Low 2 3 4 High Low 2 3 4 High Small 1.502 1.430 0.872 0.772 0.928 14.323 4.186 14.738 17.767 17.609 2− 0.565 0.050 0.431 − 0.681 0.917 14.486 16.084 17.441 19.352 19.736 3− 0.674 1.052 − 0.081 − 0.853 1.698 14.103 17.653 18.884 18.775 21.662 4− 0.397 0.203 2.332 2.153 3.398 15.977 15.427 16.143 16.296 21.330 Big 0.754 − 0.280 1.776 1.458 0.873 22.691 23.645 26.214 23.062 23.150 t(s)t(l) Low 2 3 4 High Low 2 3 4 High Small 9.679 3.097 6.881 8.484 8.969 2.643 0.498 2.921 4.146 1.789 2 4.886 3.990 4.901 7.630 5.501 2.514 1.876 − 0.257 − 0.322 1.419 3 2.426 1.087 1.762 3.702 0.199 2.080 − 0.919 2.074 3.477 2.374 4 0.458 − 1.044 − 1.785 − 1.531 2.539 − 0.273 2.797 1.197 1.355 − 2.061 Big − 2.826 − 2.700 − 1.579 − 0.741 − 0.521 0.223 0.764 − 0.862 − 1.345 − 0.091 t(r)t(h) Low 2 3 4 High Low 2 3 4 High Small − 0.971 − 2.821 0.181 3.243 2.997 1.779 − 0.311 1.285 1.404 2.044 2− 2.323 − 2.113 − 1.844 0.181 1.636 0.820 1.912 0.555 − 0.861 − 0.654 3− 2.715 − 4.714 0.409 1.788 2.903 3.399 1.241 1.365 − 0.459 4.281 4− 4.726 − 1.948 − 1.566 0.529 − 0.137 2.018 1.582 1.092 1.774 1.666 Big − 4.895 − 3.964 − 3.721 − 1.284 2.204 1.439 1.052 − 0.755 1.220 1.270 Page 20 of 27 Maitiand Vuković Economic Structures (2020) 9:47 Table 6 (continued) Panel C MC_TA a b Low 2 3 4 High Low 2 3 4 High Small 0.009 0.005 0.001 0.017 0.003 0.968 1.034 1.007 0.829 1.056 2 0.001 0.001 0.000 0.001 0.001 1.025 0.991 0.940 0.912 1.087 3− 0.001 − 0.002 − 0.004 0.000 − 0.005 1.039 0.935 1.126 1.064 1.096 4 0.003 0.007 0.007 0.003 0.008 0.986 0.951 0.955 0.978 1.148 Big 0.007 0.005 0.001 0.007 0.001 0.934 0.856 0.991 1.005 1.105 S L Low 2 3 4 High Low 2 3 4 High Small 1.393 1.063 0.918 1.467 1.292 0.249 0.547 0.524 0.166 0.667 2 0.590 0.608 0.639 0.428 0.809 0.434 0.077 0.160 0.269 0.169 3 0.555 0.306 0.322 0.039 0.487 0.186 0.187 0.212 0.203 0.415 4 0.069 − 0.115 − 0.037 − 0.015 − 0.280 − 0.078 0.087 0.237 0.275 − 0.214 Big 0.023 − 0.038 − 0.135 − 0.387 − 0.185 − 0.287 0.028 − 0.027 0.338 − 0.222 R h Low 2 3 4 High Low 2 3 4 High Small − 0.278 0.019 0.087 − 0.970 0.383 0.450 0.598 0.372 − 0.508 0.393 2− 0.155 − 0.342 − 0.368 − 0.171 − 0.130 0.254 0.211 0.047 0.041 − 0.043 3− 0.373 − 0.201 − 0.018 0.006 0.139 0.213 0.177 0.065 0.298 0.023 4− 0.348 − 0.289 − 0.122 − 0.082 − 0.369 0.243 0.270 0.144 0.010 0.620 Big − 0.540 − 0.327 − 0.124 0.240 − 0.305 0.040 − 0.240 0.031 0.210 0.324 t(a)t(b) Low 2 3 4 High Low 2 3 4 High Small 2.086 1.066 0.116 1.572 0.641 15.137 16.100 15.723 5.385 14.610 2 0.204 0.325 0.112 0.363 0.135 17.303 15.719 17.718 16.027 15.933 3− 0.262 − 0.568 − 1.140 − 0.098 − 0.930 20.169 16.257 22.939 20.032 14.357 4 0.688 1.925 1.928 0.827 1.633 15.551 18.772 18.313 20.050 16.423 Big 2.138 1.672 0.293 2.641 0.344 20.259 21.547 29.695 26.274 24.082 t(s)t(l) Low 2 3 4 High Low 2 3 4 High Small 9.668 7.349 6.364 4.232 7.934 1.547 3.380 3.247 0.428 3.664 2 4.421 4.282 5.345 3.341 5.264 2.907 0.482 1.199 1.878 0.984 3 4.782 2.362 2.908 0.327 2.834 1.432 1.290 1.712 1.517 2.157 4 0.485 − 1.005 − 0.314 − 0.133 − 1.781 − 0.489 0.683 1.802 2.237 − 1.213 Big 0.224 − 0.421 − 1.803 − 4.493 − 1.792 − 2.472 0.278 − 0.319 3.504 − 1.918 t(r)t(h) Low 2 3 4 High Low 2 3 4 High Small − 1.609 0.108 0.503 − 2.334 1.961 3.068 4.063 2.533 − 1.440 2.371 2− 0.967 − 2.012 − 2.568 − 1.110 − 0.703 1.872 1.458 0.388 0.313 − 0.273 3− 2.682 − 1.296 − 0.133 0.042 0.676 1.808 1.346 0.574 2.444 0.131 4− 2.034 − 2.113 − 0.868 − 0.622 − 1.956 1.674 2.323 1.206 0.086 3.870 Big − 4.336 − 3.046 − 1.379 2.326 − 2.463 0.376 − 2.634 0.405 2.391 3.086 Page 21 of 27 Maitiand Vuković Economic Structures (2020) 9:47 Table 6 (continued) Panel D MC_TAM a b Low 2 3 4 High Low 2 3 4 High Small 0.000 0.011 0.010 0.005 − 0.002 1.138 0.691 0.912 1.002 1.006 2 0.002 0.005 0.002 0.000 − 0.001 1.027 0.944 0.954 0.969 0.938 3− 0.006 0.001 0.007 − 0.003 0.002 1.079 0.995 0.995 1.142 0.905 4 0.003 0.000 0.006 0.004 0.008 1.077 0.796 0.873 0.912 0.976 Big 0.007 0.003 0.002 0.009 0.004 0.864 1.212 1.048 0.969 1.011 S L Low 2 3 4 High Low 2 3 4 High Small 1.229 0.504 1.769 1.292 1.114 0.402 0.895 0.237 0.169 0.407 2 0.464 0.686 0.412 0.858 0.314 0.512 0.136 0.227 0.478 0.228 3 0.724 0.316 0.207 0.184 0.046 0.174 0.061 − 0.068 0.316 0.304 4 0.181 0.094 0.019 − 0.228 0.333 − 0.060 0.339 0.262 0.379 − 0.103 Big − 0.416 − 0.250 − 0.039 − 0.205 0.087 − 0.146 − 0.068 0.087 0.043 − 0.372 R h Low 2 3 4 High Low 2 3 4 High Small 0.361 0.305 − 0.967 − 0.240 0.022 0.934 0.958 − 0.791 − 0.316 − 0.585 2− 0.079 − 0.375 − 0.115 0.035 − 0.127 0.867 0.278 0.067 − 0.237 − 0.067 3− 0.009 − 0.265 − 0.183 − 0.115 − 0.114 0.781 0.167 0.223 − 0.129 − 0.041 4− 0.332 − 0.039 − 0.041 − 0.193 − 0.138 0.501 0.191 0.166 − 0.087 − 0.375 Big − 0.354 − 0.090 − 0.013 − 0.172 − 0.312 0.564 0.488 0.185 − 0.070 − 0.152 t(a)t(b) Low 2 3 4 High Low 2 3 4 High Small 0.092 2.066 1.032 1.112 − 0.372 17.528 9.182 6.493 14.802 16.266 2 0.380 1.141 0.463 − 0.116 − 0.137 14.907 15.710 15.380 15.890 15.869 3− 1.340 0.159 1.693 − 0.599 0.682 17.380 16.959 17.466 18.046 17.422 4 0.791 − 0.107 1.422 1.201 2.443 17.291 14.824 14.429 17.864 20.151 Big 1.519 0.750 0.714 3.091 1.448 13.468 24.320 21.128 24.206 26.912 t(s)t(l) Low 2 3 4 High Low 2 3 4 High Small 8.407 2.976 5.592 8.473 7.997 2.457 4.721 0.669 0.990 2.613 2 2.991 5.069 2.951 6.245 2.359 2.949 0.902 1.452 3.109 1.529 3 5.177 2.389 1.612 1.291 0.392 1.112 0.414 − 0.476 1.982 2.324 4 1.292 0.779 0.142 − 1.984 3.055 − 0.383 2.507 1.719 2.943 − 0.841 Big − 2.883 − 2.227 − 0.350 − 2.274 1.029 − 0.904 − 0.543 0.700 0.427 − 3.934 t(r)t(h) Low 2 3 4 High Low 2 3 4 High Small 2.059 1.502 − 2.550 − 1.315 0.130 6.278 5.552 − 2.457 − 2.035 − 4.129 2− 0.426 − 2.312 − 0.687 0.213 − 0.796 5.487 2.017 0.470 − 1.696 − 0.493 3− 0.051 − 1.673 − 1.192 − 0.675 − 0.810 5.489 1.241 1.712 − 0.889 − 0.345 4− 1.976 − 0.271 − 0.251 − 1.396 − 1.057 3.513 1.555 1.199 − 0.742 − 3.381 Big − 2.042 − 0.666 − 0.095 − 1.591 − 3.074 3.841 4.268 1.631 − 0.761 − 1.768 Page 22 of 27 Maitiand Vuković Economic Structures (2020) 9:47 MC_PB: Two portfolios found to be significant with average alpha value of 0.0040 and 80.1 average R-square (%). Market and value slopes found to be highly positive; here, size slopes become positive for big-size portfolio (which was not in case with Fama–French (2015) five-factor regression results). Similar to Fama–French (2015) in column one with low-value stocks, the coefficient of profitability (RMW) factor have positive slopes for microcaps whereas it changes its sign on increase of size. This indicates that first portfolio with combination of low value and microcaps is much dominated by the low-value stocks with aggressive investment and marginal profitability but yields higher returns than other portfolios as shown in Table3. The biggest problem that lies with Fama–French (2015) is microcaps due to high negative profitability (RMW) and investment (CMA) factor but it is well captured by modified five-factor model with human asset as these factors become more positive. MC_ROE: Three portfolios found to be significant with average alpha value of 0.0043 and 77.9 average R-square (%). Profitability (RMW) changes its sign on moving from low ROE stock portfolios to the high ROE stock portfolios but not investment (CMA) coefficient as in case with Fama–French (2015) five-factor regressions. Biggest problem with Fama–French (2015) is that first portfolio with low profitability microcaps is dominated by firm whose stocks behave like unprofitable firms with aggressive investment due to high positive investment (CMA) and less negative profitability (RMW) coefficient which is well captured by the modified five-factor model with human asset as an addition of human asset reduces high positive investment factor. MC_TA: Three portfolios found to be significant with average alpha value of 0.0043 and 78 average R-square (%). Here also like previous case high positive investment (CMA) and less negative profitability (RMW) coefficient for microcap portfolio indicate that first portfolio with low profitability microcaps is dominated by firm whose Table 6 (continued) Panel E R2 MC_PB MC_ROE Low 2 3 4 High Low 2 3 4 High Small 0.766 0.755 0.768 0.791 0.777 0.767 0.376 0.736 0.770 0.748 2 0.535 0.742 0.765 0.795 0.794 0.768 0.787 0.759 0.756 0.767 3 0.824 0.832 0.749 0.821 0.797 0.784 0.811 0.794 0.777 0.833 4 0.855 0.785 0.847 0.828 0.782 0.803 0.795 0.775 0.752 0.802 Big 0.876 0.886 0.908 0.880 0.857 0.883 0.885 0.886 0.844 0.830 MC_TA MC_TAM Low 2 3 4 High Low 2 3 4 High Small 0.785 0.798 0.766 0.370 0.732 0.806 0.677 0.448 0.699 0.719 2 0.801 0.750 0.797 0.753 0.719 0.790 0.769 0.724 0.732 0.732 3 0.841 0.761 0.843 0.819 0.680 0.798 0.766 0.762 0.781 0.784 4 0.740 0.821 0.803 0.823 0.777 0.788 0.740 0.714 0.815 0.770 Big 0.822 0.839 0.902 0.890 0.868 0.730 0.872 0.826 0.866 0.866 Page 23 of 27 Maitiand Vuković Economic Structures (2020) 9:47 stocks behave like unprofitable firms with aggressive investment and microcap not captured by the model. MC_TAM: Three portfolios found to be significant with average alpha value of 0.0041 and 75.9 average R-square (%). Similar to Fama–French three factors (1993) and Fama–French five factors (2015), microcap is well captured by the modified fivefactor model with human asset. Study results find that modified five-factor model with human asset is robust than both Fama–French three- and five-factor models as it able to capture most of the portfolios risk return relationship. The detailed summary of all the regressions: Fama–French three-factor, Fama–French five-factor and Modified five-factor with human asset are shown in Table7. Table 7 Summary ofthefactor regressions Model No ofsignificant intercepts R-Square (%) MC_PB MC_ROE MC_TA MC_TAM MC_PB MC_ROE MC_TA MC_TAM 3 Factor 5 5 5 4 78.7 76.4 76.6 73.9 5 Factor 5 5 6 4 79.9 78.2 78.9 74.9 5 Factor (Human Asset) 2 3 3 3 80.1 77.9 78 75.9 Fig. 3 Residual graphs for three-, five- and modified five-factor regressions for first Portfolio (Microcap) Page 24 of 27 Maitiand Vuković Economic Structures (2020) 9:47 7 Residual graphs Then residual graphs of first Portfolio with microcaps of all regressions: Fama–French three-factor, Fama–French five-factor and Modified five-factor with human asset are shown in Fig.3. Residual more closer to zero said to be the best model fit or model is able to capture maximum risk return relationship. Residual graphs of Fama–French three-factor and Fama–French five-factor do not show much of difference but high peaks are reduced in case of Modified five-factor with human asset that justifies superiority of the later. Though asset pricing results and residual graphs confirm the superiority of Modified five-factor with human asset over both Fama–French three-factor and Fama–French five-factor models but it will be well justified if it passes model performance test. 7.1 Model performance test The study uses very prominent asset pricing model test designed by Gibbons etal. (1989). The GRS test results are shown in Table8 for all the factor models used in the study. GRS test rejects all the Fama–French three-factor regressions except for MC_ TAM and study findings are in line with Fama–French (2015) findings and do not support Connor and Sehgal (2003) findings in Indian context. GRS test also rejects three of the Fama–French five-factor model (2015) for MC_PB, MC_ROE & MC_TA crosses as similar to Fama–French (2015) findings in US context. All of the Modified five-factor models with human asset except MC_TA cross and one Fama–French fivefactor model for MC_TAM crosses pass the GRS test. Further, lower value of GRS test F-Statistics once again confirms the superiority of Modified five-factor model with human asset over both Fama–French three-factor and Fama–French five-factor models. Table 8 Summary ofGRS test results forall theFactor models * Significant @ 5% level Fama–French threefactor GRS F-statistics p value Average absolute alpha value Average R2 (%) MC_PB* 1.754 0.026 0.003 78.7 MC_ROE* 2.303 0.001 0.004 76.4 MC_TA* 1.673 0.045 0.003 76.6 MC_TAM 1.227 0.228 0.003 73.9 Fama–French five-factor MC_PB* 1.640 0.039 0.004 79.9 MC_ROE* 1.766 0.021 0.004 78.2 MC_TA* 1.594 0.050 0.004 78.9 MC_TAM 1.475 0.084 0.004 74.9 Modified five-factor with human asset MC_PB 1.514 0.054 0.004 80.1 MC_ROE 1.532 0.052 0.004 77.9 MC_TA* 1.589 0.050 0.004 78 MC_TAM 1.497 0.076 0.004 75.9