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.
Hinweise
Moinak Maiti and Darko Vuković contributed equally to this work
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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 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.
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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 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 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.
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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:
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.
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.
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.
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
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 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.
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
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.
Fig. 1
Radar graph shows 25 portfolios mean returns based on MC_PB, MC_ROE, MC_TA and MC_TAM crosses
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Details of each portfolio formed from each cross are shown in Table 3 for further discussion.
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
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
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 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.
Fig. 2
Visual 3D surface images for 25 portfolios mean returns formed on MC_PB, MC_ROE, MC_TA and MC_TAM
×
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 three-factor regressions. The study findings are similar to the global findings of Aharoni et al. (2013) and Fama–French (2015).
Table 4
FF three-factor regression results RPt − RFt = a + b (RMt − RFt) + s SMBt + l LMHt + et
Panel A (MC_PB
a
RM
Low
2
3
4
High
Low
2
3
4
High
Small
0.013
0.009
0.009
0.002
− 0.004
1.038
1.093
1.103
1.011
1.096
2
0.001
− 0.001
0.000
− 0.005
0.002
0.804
1.075
0.951
1.021
1.019
3
− 0.006
− 0.003
− 0.003
0.001
0.003
1.118
1.199
0.920
1.139
0.979
4
− 0.003
0.001
0.006
0.002
0.004
1.050
0.952
1.258
1.139
0.866
Big
0.003
0.000
0.002
0.002
0.001
0.994
1.106
1.024
1.139
0.911
S
L
Low
2
3
4
High
Low
2
3
4
High
Small
1.423
1.220
0.967
1.193
1.231
0.631
0.414
0.183
0.062
− 0.165
2
1.464
0.772
0.795
0.893
0.629
1.433
0.427
0.282
0.148
− 0.152
3
0.680
0.575
0.415
0.471
0.358
0.813
0.470
0.295
− 0.064
− 0.115
4
− 0.184
− 0.096
− 0.135
0.270
0.248
1.121
0.666
0.247
− 0.064
− 0.227
Big
− 0.361
− 0.401
− 0.287
0.270
0.181
0.998
0.628
0.303
− 0.064
− 0.270
t(a)
t(RM)
Low
2
3
4
High
Low
2
3
4
High
Small
2.601
1.966
2.262
0.522
− 1.119
15.455
17.404
19.464
21.447
21.491
2
0.135
− 0.113
0.061
− 1.560
0.683
6.286
16.486
18.565
21.907
22.855
3
− 1.979
− 0.774
− 0.763
0.156
0.984
19.763
22.420
18.153
25.087
23.376
4
− 0.821
0.155
1.987
0.611
1.536
19.386
16.925
21.962
23.993
21.939
Big
0.928
− 0.158
1.047
0.611
0.239
21.391
25.439
31.552
23.993
28.252
t(s)
t(l)
Low
2
3
4
High
Low
2
3
4
High
Small
9.517
8.727
7.670
11.378
10.844
6.230
4.366
2.147
0.874
− 2.151
2
5.142
5.321
6.977
8.615
6.335
7.425
4.345
3.651
2.110
− 2.259
3
5.400
4.834
3.679
4.659
3.841
9.533
5.830
3.862
− 0.940
− 1.820
4
− 1.528
− 0.769
− 1.058
2.552
2.820
13.720
7.857
2.861
− 0.889
− 3.813
Big
− 3.496
− 4.147
− 3.978
2.552
2.527
14.238
9.581
6.192
− 0.889
− 5.559
Panel B MC_ROE
a
RM
Low
2
3
4
High
Low
2
3
4
High
Small
0.006
0.007
0.004
0.007
0.008
1.076
0.776
0.998
1.037
1.108
2
− 0.006
− 0.003
− 0.001
− 0.002
0.005
1.091
1.051
1.011
1.073
1.037
3
− 0.007
− 0.002
0.000
− 0.001
0.008
1.106
1.115
1.083
0.991
1.028
4
− 0.009
− 0.002
0.007
0.009
0.010
1.150
0.996
0.957
0.953
0.903
Big
− 0.003
− 0.005
0.002
0.003
0.005
1.136
1.123
1.027
1.013
1.006
S
L
Low
2
3
4
High
Low
2
3
4
High
Small
1.667
1.189
1.094
1.175
1.351
0.617
1.251
0.457
0.210
− 0.110
2
0.858
0.669
0.658
0.925
0.629
0.808
0.562
0.183
− 0.068
0.006
3
0.618
0.232
0.294
0.421
0.197
0.764
0.451
0.244
0.270
− 0.004
4
0.214
− 0.043
− 0.163
− 0.099
0.300
0.611
0.680
0.360
0.130
− 0.200
Big
− 0.222
− 0.220
− 0.158
− 0.018
− 0.003
0.516
0.469
0.220
− 0.028
− 0.209
t(a)
t(RM)
Low
2
3
4
High
Low
2
3
4
High
Small
1.997
0.566
0.979
1.831
1.916
16.349
4.765
16.617
18.954
19.143
2
− 1.330
− 0.620
− 0.151
− 0.660
1.491
16.180
18.117
19.342
20.701
20.755
3
− 1.476
− 0.405
0.051
− 0.308
2.597
16.007
18.809
21.125
19.774
23.729
4
− 1.775
− 0.416
1.968
2.433
3.518
17.190
17.404
18.116
18.402
23.898
Big
− 0.739
− 1.501
0.622
1.103
1.628
23.714
25.233
27.717
25.631
25.179
t(s)
t(l)
Low
2
3
4
High
Low
2
3
4
High
Small
11.381
3.279
8.188
9.654
10.493
6.217
5.091
5.051
2.547
− 1.257
2
5.718
5.185
5.659
8.019
5.660
7.949
6.428
2.322
− 0.872
0.084
3
4.018
1.758
2.575
3.778
2.039
7.330
5.050
3.161
3.566
− 0.057
4
1.436
− 0.338
− 1.390
− 0.862
3.572
6.051
7.871
4.519
1.669
− 3.509
Big
− 2.080
− 2.220
− 1.915
− 0.202
− 0.039
7.136
6.984
3.938
− 0.476
− 3.473
Panel C MC_TA
a
RM
Low
2
3
4
High
Low
2
3
4
High
Small
0.009
0.005
0.001
0.009
0.006
1.051
1.143
1.071
0.788
1.108
2
0.000
− 0.001
− 0.003
0.000
0.000
1.080
1.048
0.969
0.929
1.086
3
− 0.004
− 0.004
− 0.004
0.000
− 0.004
1.099
0.978
1.139
1.119
1.093
4
0.000
0.004
0.006
0.002
0.005
1.049
1.016
0.988
0.984
1.282
Big
0.003
0.002
0.000
0.009
− 0.001
0.971
0.830
1.004
1.031
1.181
S
L
Low
2
3
4
High
Low
2
3
4
High
Small
1.629
1.314
1.073
1.274
1.448
0.262
0.536
0.458
0.920
0.371
2
0.700
0.704
0.667
0.449
0.793
0.556
0.345
0.448
0.403
0.270
3
0.653
0.385
0.349
0.164
0.494
0.478
0.345
0.226
0.200
0.306
4
0.179
0.005
0.027
− 0.009
− 0.011
0.195
0.314
0.333
0.339
0.078
Big
0.052
− 0.131
− 0.120
− 0.304
− 0.042
0.135
0.282
0.070
0.151
0.018
t(a)
t(RM)
Low
2
3
4
High
Low
2
3
4
High
Small
2.029
1.103
0.285
1.975
1.997
16.214
18.425
17.937
5.504
16.419
2
− 0.101
− 0.311
− 0.711
0.017
− 0.090
19.564
17.682
19.469
17.775
17.412
3
− 1.107
− 1.012
− 1.250
− 0.086
− 0.760
22.238
18.320
25.376
22.580
15.654
4
0.055
1.279
1.978
0.669
1.000
17.536
20.961
20.534
22.067
18.501
Big
0.775
0.734
− 0.145
3.479
− 0.417
21.513
22.036
32.640
28.766
26.228
t(s)
t(l)
Low
2
3
4
High
Low
2
3
4
High
Small
10.303
9.518
8.074
4.002
9.649
2.529
5.724
5.086
4.264
3.641
2
5.698
5.337
6.021
3.863
5.717
6.676
3.860
5.969
5.109
2.870
3
5.939
3.239
3.495
1.490
3.180
6.419
4.283
3.337
2.677
2.908
4
1.346
0.048
0.248
− 0.088
− 0.074
2.162
4.299
4.589
5.038
0.748
Big
0.516
− 1.569
− 1.750
− 3.814
− 0.419
1.978
4.961
1.518
2.800
0.270
Panel D MC_TAM
a
RM
Low
2
3
4
High
Low
2
3
4
High
Small
0.003
0.013
0.002
0.003
− 0.001
1.291
0.851
0.819
0.957
0.897
2
0.001
0.002
0.001
0.000
− 0.002
1.192
1.015
0.973
0.923
0.933
3
− 0.006
− 0.001
0.005
− 0.004
0.002
1.224
1.040
1.046
1.124
0.904
4
0.001
− 0.001
0.006
0.003
0.007
1.187
0.834
0.906
0.907
0.914
Big
0.004
0.002
0.002
0.007
0.001
0.987
1.307
1.083
0.965
1.000
S
L
Low
2
3
4
High
Low
2
3
4
High
Small
1.615
0.901
1.457
1.164
0.867
0.125
0.662
0.988
0.355
0.387
2
0.831
0.811
0.443
0.757
0.289
0.579
0.431
0.317
0.449
0.327
3
1.053
0.392
0.305
0.132
0.031
0.185
0.269
0.076
0.405
0.393
4
0.399
0.176
0.090
− 0.261
0.178
0.202
0.371
0.295
0.529
0.003
Big
− 0.171
− 0.043
0.039
− 0.231
0.030
0.133
0.004
0.098
0.177
− 0.130
t(a)
t(RM)
Low
2
3
4
High
Low
2
3
4
High
Small
0.700
2.456
0.241
0.731
− 0.333
19.444
11.308
6.202
15.261
14.943
2
0.238
0.425
0.263
− 0.053
− 0.408
17.029
17.696
17.117
16.392
17.245
3
− 1.294
− 0.377
1.372
− 0.856
0.453
19.507
19.014
19.696
19.405
19.013
4
0.173
− 0.199
1.975
0.804
2.158
19.411
16.829
16.299
19.323
19.951
Big
0.861
0.537
0.718
2.725
0.499
15.506
26.744
23.671
26.202
28.262
t(s)
t(l)
Low
2
3
4
High
Low
2
3
4
High
Small
10.930
5.377
4.962
8.346
6.495
1.250
5.831
4.962
3.751
4.275
2
5.335
6.351
3.503
6.041
2.400
5.484
4.979
3.701
5.285
4.004
3
7.542
3.218
2.580
1.025
0.294
1.955
3.261
0.950
4.638
5.478
4
2.935
1.593
0.729
− 2.495
1.749
2.191
4.967
3.519
7.470
0.046
Big
− 1.207
− 0.394
0.386
− 2.813
0.379
1.389
0.061
1.427
3.185
− 2.429
Panel E R2
MC_PB
MC_ROE
Low
2
3
4
High
Low
2
3
4
High
Small
0.733
0.741
0.749
0.785
0.768
0.757
0.342
0.733
0.754
0.732
2
0.510
0.716
0.750
0.793
0.782
0.755
0.769
0.751
0.755
0.760
3
0.819
0.823
0.745
0.820
0.795
0.743
0.771
0.791
0.771
0.811
4
0.854
0.776
0.812
0.810
0.768
0.754
0.782
0.767
0.747
0.797
Big
0.876
0.884
0.908
0.810
0.847
0.856
0.868
0.876
0.839
0.825
MC_TA
MC_TAM
Low
2
3
4
High
Low
2
3
4
High
Small
0.734
0.774
0.756
0.346
0.719
0.756
0.612
0.415
0.691
0.682
2
0.792
0.734
0.785
0.750
0.718
0.740
0.747
0.722
0.726
0.730
3
0.824
0.752
0.842
0.811
0.678
0.753
0.756
0.752
0.780
0.783
4
0.721
0.803
0.798
0.822
0.737
0.755
0.735
0.710
0.813
0.753
Big
0.795
0.826
0.900
0.884
0.847
0.680
0.852
0.822
0.864
0.858
Microcaps remain the problem for most of the crosses expect MC_TAM cross. Since three-factor model is unable to explain all risk return relationship, this study further estimates five-factor regression with market, size, value, profitability and investment (without human investment).
6.2 Five-factor regressions (without human asset investment)
Five-factor regression results with market, size; value, profitability and investment (without human investment) are shown in Table 5.
Table 5
Regression results of Fama–French five-factor model for 25 portfolios RPt – RFt = a + b (RMt − RFt) + s SMBt + l LMHt + p RMWt + t CMAt + et
Panel A MC_PB
a
b
Low
2
3
4
High
Low
2
3
4
High
Small
0.010
0.011
0.012
0.003
− 0.002
1.063
1.076
1.100
0.993
1.087
2
0.010
0.004
0.002
− 0.004
0.005
0.657
1.050
0.949
0.990
0.988
3
− 0.004
0.000
− 0.001
0.002
0.003
1.122
1.176
0.908
1.104
0.962
4
− 0.002
0.003
0.012
0.005
0.006
1.042
0.936
1.184
1.109
0.838
Big
0.004
0.001
0.003
0.008
0.003
0.991
1.081
1.023
1.104
0.893
S
L
Low
2
3
4
High
Low
2
3
4
High
Small
1.417
1.232
0.925
1.216
1.200
0.921
0.254
− 0.032
− 0.071
− 0.408
2
1.697
0.747
0.761
0.943
0.659
0.578
− 0.001
0.106
− 0.018
− 0.414
3
0.622
0.583
0.415
0.545
0.396
0.617
0.202
0.151
− 0.184
− 0.161
4
− 0.178
− 0.097
− 0.056
0.304
0.291
1.042
0.465
− 0.350
− 0.304
− 0.387
Big
− 0.372
− 0.371
− 0.290
− 0.157
0.184
0.922
0.439
0.278
− 0.215
− 0.484
R
T
Low
2
3
4
High
Low
2
3
4
High
Small
0.384
− 0.221
− 0.241
− 0.196
− 0.288
0.066
− 0.086
0.179
− 0.132
0.120
2
− 1.343
− 0.536
− 0.198
− 0.266
− 0.373
− 1.283
0.064
0.145
− 0.273
− 0.189
3
− 0.201
− 0.359
− 0.189
− 0.228
− 0.097
0.260
− 0.075
− 0.023
− 0.386
− 0.195
4
− 0.110
− 0.263
− 0.857
− 0.348
− 0.251
− 0.044
− 0.025
− 0.478
− 0.207
− 0.240
Big
− 0.089
− 0.276
− 0.029
− 0.230
− 0.282
0.041
− 0.176
0.012
− 0.142
− 0.043
t(a)
t(RM)
Low
2
3
4
High
Low
2
3
4
High
Small
1.908
2.216
2.722
0.875
− 0.414
15.406
16.546
18.995
20.395
20.935
2
1.068
0.816
0.544
− 1.037
1.472
5.273
15.992
18.059
20.855
21.893
3
− 0.935
− 0.058
− 0.341
0.492
1.076
19.494
21.491
17.326
24.189
22.307
4
− 0.584
0.639
3.041
1.281
2.032
18.513
16.143
21.892
22.942
20.902
Big
1.108
0.433
1.099
2.724
1.157
20.565
24.309
30.323
28.350
27.447
t(s)
t(l)
Low
2
3
4
High
Low
2
3
4
High
Small
9.281
8.562
7.217
11.290
10.436
5.204
1.523
− 0.216
− 0.569
− 3.063
2
6.155
5.143
6.547
8.973
6.600
1.807
− 0.006
0.786
− 0.148
− 3.580
3
4.882
4.814
3.580
5.390
4.145
4.178
1.436
1.124
− 1.572
− 1.454
4
− 1.425
− 0.755
− 0.467
2.845
3.280
7.215
3.124
− 2.522
− 2.456
− 3.759
Big
− 3.483
− 3.772
− 3.889
− 1.821
2.555
7.455
3.851
3.215
− 2.151
− 5.798
t(r)
t(T)
Low
2
3
4
High
Low
2
3
4
High
Small
1.958
− 1.195
− 1.466
− 1.418
− 1.949
0.368
− 0.509
1.182
− 1.042
0.884
2
− 3.793
− 2.872
− 1.323
− 1.969
− 2.905
− 3.948
0.376
1.058
− 2.208
− 1.609
3
− 1.228
− 2.306
− 1.267
− 1.757
− 0.788
1.735
− 0.524
− 0.168
− 3.244
− 1.737
4
− 0.689
− 1.595
− 5.574
− 2.535
− 2.201
− 0.301
− 0.163
− 3.391
− 1.640
− 2.291
Big
− 0.649
− 2.183
− 0.306
− 2.082
− 3.049
0.324
− 1.518
0.139
− 1.402
− 0.512
Panel B MC_ROE
a
RM
Low
2
3
4
High
Low
2
3
4
High
Small
0.008
0.019
0.005
0.004
0.005
1.088
0.558
0.995
1.040
1.126
2
− 0.003
0.001
0.002
− 0.003
0.003
1.084
1.027
1.010
1.051
1.042
3
− 0.001
0.005
0.000
− 0.003
0.007
1.068
1.062
1.072
0.975
1.022
4
− 0.001
0.002
0.010
0.009
0.010
1.104
0.944
0.933
0.956
0.893
Big
0.003
0.000
0.005
0.005
0.003
1.107
1.093
1.000
0.980
1.002
S
L
Low
2
3
4
High
Low
2
3
4
High
Small
1.589
1.528
1.093
1.234
1.364
0.433
− 0.035
0.418
0.505
0.179
2
0.796
0.655
0.611
0.991
0.659
0.452
0.204
− 0.028
− 0.061
0.201
3
0.598
0.234
0.320
0.507
0.238
0.190
− 0.208
0.214
0.429
0.093
4
0.177
0.023
− 0.152
− 0.111
0.312
− 0.132
0.297
0.111
0.126
− 0.274
Big
− 0.259
− 0.229
− 0.150
0.034
0.037
− 0.007
0.050
− 0.075
− 0.228
− 0.079
R
T
Low
2
3
4
High
Low
2
3
4
High
Small
− 0.165
− 2.009
− 0.051
0.328
0.365
0.363
− 1.874
− 0.001
− 0.254
− 0.024
2
− 0.407
− 0.455
− 0.231
− 0.055
0.226
0.258
0.019
0.203
− 0.330
− 0.120
3
− 0.732
− 0.863
− 0.065
0.127
0.087
0.019
− 0.102
− 0.133
− 0.404
− 0.193
4
− 0.936
− 0.564
− 0.337
0.006
− 0.108
0.077
− 0.382
− 0.092
0.057
− 0.067
Big
− 0.648
− 0.539
− 0.394
− 0.311
0.131
0.111
− 0.013
− 0.081
− 0.285
− 0.182
t(a)
t(RM)
Low
2
3
4
High
Low
2
3
4
High
Small
1.980
1.718
1.019
1.025
1.159
16.267
3.609
15.935
18.960
19.054
2
− 0.546
0.260
0.430
− 0.681
0.891
15.948
17.504
18.997
19.864
20.367
3
− 0.284
1.228
0.120
− 0.790
2.175
15.628
18.865
20.157
19.533
23.010
4
− 0.189
0.512
2.494
2.326
3.611
17.494
16.547
17.247
17.768
22.802
Big
0.874
− 0.155
1.740
1.767
1.109
24.559
25.196
27.147
24.667
24.622
t(s)
t(l)
Low
2
3
4
High
Low
2
3
4
High
Small
10.731
4.464
7.909
10.165
10.425
2.525
− 0.088
2.610
3.587
1.181
2
5.293
5.045
5.195
8.465
5.815
2.590
1.356
− 0.206
− 0.450
1.528
3
3.955
1.875
2.715
4.588
2.422
1.083
− 1.438
1.566
3.354
0.821
4
1.271
0.179
− 1.269
− 0.931
3.594
− 0.818
2.028
0.796
0.912
− 2.729
Big
− 2.591
− 2.385
− 1.836
0.384
0.407
− 0.061
0.447
− 0.795
− 2.238
− 0.760
t(r)
t(T)
Low
2
3
4
High
Low
2
3
4
High
Small
− 0.868
− 4.569
− 0.285
2.106
2.173
2.082
− 4.645
− 0.007
− 1.772
− 0.154
2
− 2.106
− 2.727
− 1.527
− 0.364
1.550
1.456
0.124
1.467
− 2.393
− 0.899
3
− 3.767
− 5.395
− 0.430
0.893
0.691
0.108
− 0.692
− 0.960
− 3.100
− 1.668
4
− 5.220
− 3.480
− 2.191
0.036
− 0.970
0.469
− 2.569
− 0.650
0.409
− 0.655
Big
− 5.055
− 4.372
− 3.756
− 2.752
1.133
0.942
− 0.117
− 0.848
− 2.751
− 1.716
Panel C MC_TA
a
RM
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
Panel D MC_TAM
a
RM
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
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
MC_PB: Five portfolios found to be significant with average alpha value of 0.0047 and 79.9 average R-square (%). Market and value slopes found to be highly positive, size slopes are positive for small-size stock portfolio but becomes slightly negative toward big-size portfolios. Five factors provide more information than three-factor model on the risk return relationship for the first portfolio with microcaps. In column one with low-value stocks, the coefficient of profitability (RMW) factor has 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. Value (LMH) coefficients are highly positive for low P/B stock portfolio and become negative for high P/B stock portfolios. MC_PB cross is not based on the investment factor but it seems that results are aligned with it as low P/B stock portfolios show lower negative investment (CMA) than high P/B stock portfolios. Theoretically, it justifies as low P/B firms are conservative investment nature whereas high P/B firms have aggressive investment nature.
MC_ROE: Five portfolios found to be significant with average alpha value of 0.0048 and 78.2 average R-square (%). Profitability (RMW) and investment (CMA) coefficient changes its sign on moving from low ROE stock portfolios to the high ROE stock portfolios. 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.
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 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
R
h
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
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
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
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
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
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 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 five-factor 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
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.
Fig. 3
Residual graphs for three-, five- and modified five-factor regressions for first Portfolio (Microcap)
×
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 five-factor 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
Fama–French three-factor
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
* Significant @ 5% level
8 Conclusion
Both size and value effects are dominating in the portfolios average mean excess return patterns in Indian context. The portfolio average mean excess return with microcap stocks outperformed the other portfolios for every cross as similar to Fama–French (1993, 2015) findings in US context. The study also finds that portfolios formed based on MC_ROE, MC_TA and MC_TAM cross show complex return patterns as portfolios as average mean excess return patterns frequently change its slope but in spite of that size effect is consistent for all crosses. For all the crosses except MC_TAM portfolio with microcaps are not captured by the Fama–French (1993) three-factor model, the findings are in line with Aharoni et al. (2013) and Fama–French (2015) studies. Similarly all the crosses except MC_TA & MC_TAM portfolio with microcaps are not captured by the Fama–French (2015) five-factor model. Moreover study results find that there is no much significant difference lying between the results obtained from Fama–French three- and five-factor models. 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 the present study defined a new factor of investment with human asset (CvMAv) instead of Fama–French (2015) investment (CMA) factor which generally do not consider human investment. Then, study performs regressions using modified five-factor model with market (Rm), size (SMB), value (LMH), profitability (RMW), and investment with human asset (CvMAv). The study empirically finds that modified five-factor model is robust than both Fama–French three- and five-factor models. The main problem with the modified five-factor model with human asset is the microcap with conservative investment (including human investment) stocks whose returns behave like that low-value unprofitable firms. Further microcap portfolio’s (first portfolio) regression residuals are plotted using residual graphs to check the ability of various factor models that are used in the study for capturing risk return relationships. The residual graphs show more number of higher peaks in case of Fama–French three- and five-factor models’ regression residuals than modified five-factor model. Residual graphs further confirm modified five-factor model is able to capture more risk return relationship. Finally study uses GRS test, a more model specific test to evaluate the performance of the various factor models. All of the Fama–French (1993) three-factor except MC_TAM cross and three Fama–French (2015) five-factor models are easily rejected by the GRS test. Whereas all modified five-factor model except MC_TA cross and one Fama–French (2015) five-factor models pass the GRS test. Further the lower values of GRS test F-Statistics of modified five-factor model justifies supremacy over both Fama–French three-factor and Fama–French five-factor models.
The study results clearly justify the importance of human asset in firm valuation and ignoring human asset may lead to serious issues. Investors those who are interested to gain from investment premium should consider human asset investment by the firms in making investment decision. Moreover considering human asset investment in valuation of the firms by the investors will have more informational advantages over others. Investors those whose investment patterns are based on size may gain abnormal returns by investing in the microcaps. Study finds that human asset plays a vital role in predicting returns and this has significant implications on public policy content.
Acknowledgements
Not applicable.
Competing interests
The authors declare that they have no competing interests.
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