1. R&D, Risks and Overreaction in a Market where the Book-to-Market Effect is Reputedly Absent
Weifeng Hung,
Feng Chia Universty, Taiwan
Chaoshin Chiao,
National Dong Hwa University, Taiwan
Tung-Liang Liao,
Presenter: Sheng-Tang Huang,
Nanya Institute of Technology, Taiwan

2. Motivation
The absence of the book-to-market effect in the Taiwan stock market has been widely documented in a considerable number of the prior studies.
Is there really the absence of the book-to-market effect in the Taiwan Stock Market?

3. Main idea and finding
After purging the influences of size and risk, we first of all show that the BM effect does indeed exist, but only in those stocks with lower R&D-to-sales ratio.
Secondly, consistent with the behavioral explanation of Lakonishok et al. (1994), the BM premium arises mainly as a result of investors extrapolating prior performance too far into the future.

4. Main idea and finding
Finally, we find that LBM_HRDS firms tend to perform better than LBM_LRDS firms,
whilst HBM_LRDS firms tend to perform worse than HBM_HRDS firms.

5. INTRODUCTION
It is argued in many of the prior studies (such as Fama and French, 1992 and Kothari and Shanken, 1997), that although firms with a high book-to-market (BM) ratio invariably tend to exhibit poor prior performance, they also exhibit high future returns.

6. INTRODUCTION
Empirical evidence on this positive BM-returns relationship has been widely documented; Examples include Chan et al. (1991), Daniel and Titman (1997), Fama and French (1998), Elfakhani, Lockwoord and Zaher (1998) and Chiao and Hueng (2005).
however, there are some who challenge this accepted theory.

7. INTRODUCTION
Chui and Wei (1998), for example, observe that the BM ratio fails to explain the cross-sectional stock returns in the markets of both Thailand and Taiwan
Chen and Zhang (1998) conclude that the high average returns which tend to persist for either value or high-BM stocks in the well-established market of the US, are less persistent in the growth markets of Japan, Hong Kong and Malaysia,

8. INTRODUCTION
and virtually non-existent in the high-growth markets of Thailand and Taiwan. They argue that in Thailand and Taiwan, value stocks do not behave like ‘fallen angels’ at all, but rather, that they yield both prior and future positive excess returns.

9. The interpretations of the positive BM-returns relationship in the extant literature can be roughly divided into three schools.
the first of which provides support for the risk-based explanation; that is, firms with a high BM ratio tend to have high underlying risks. Examples include Fama and French (1993).

10. The second school is based on stock characteristics, with Daniel and Titman (1997) noting that expected stock returns are directly related to stock characteristics, such as the BM ratio and firm size, as opposed to the associated risks (Fama and French, 1992).

11. The third school relates to overreaction or excess expectations with regard to the performance of a firm. Lakonishok, Shleifer and Vishny (1994) argue that firms with a high (low) BM ratio may yield higher (lower) returns;

12. however, this runs contrary to the argument that naïve investors extrapolate prior earnings growth rates too far into the future, with the result that the market undervalues distressed stocks whilst overvaluing growth stocks.
When these pricing errors are corrected, distressed (or value) stocks have high returns, whilst growth stocks have low returns. Subsequent overreaction then leads to the BM effect.

13. The prior studies often examine the source of the BM effect by applying datasets in which the BM premium has been justified;
however, to the best of our knowledge, no study has yet provided any in-depth exploration of how and why the BM effect may be absent. We therefore set out to examine this issue in the present study using the same data which has already been widely used to demonstrate the non-existence of the BM effect in the Taiwan stock market.

14. Why not Thailand stock market?
We are unable to examine value premiums conditional on R&D intensity in Thailand since most Thai firms do not produce data on R&D expenditure.

15. DATA
Accounting data and monthly stock returns were obtained from the Taiwan Economic Journal (TEJ) databank on all non-financial listed firms.
The annual accounting data, covering the years 1991 to 2006, provides a total of 6,494 firm-year observations, whilst the monthly stock returns, which are available from July 1992 to June 2008, provide a maximum of 192 monthly observations for each stock.

16. Table 1 Summary statistics of the sample firms, 1991-2006
Year
Total No of Firms
Total No. of Firms with Positive R&D
Positive R&D Ratio (%)
Average BM for All Firms
Average RDS for All Firms (%)
1991
149 80 54
0.361
0.64
1992
174
104 60
0.513
0.70
1993
194
117
0.362
0.71
1994
214
132 62
0.352
0.75
1995
247
162 66
0.544
0.93
1996
283
151 53
0.466
1.10
1997
315
169
0.479
1.33
1998
362
204 56
0.646
1.34
1999
428
253 59
0.837
1.53
2000
483
296 61
1.546
1.60
2001
526
338 64
1.498
2.08
2002
586
400 68
1.153
2.22
2003
617
430 70
0.879
2.23
2004
627
435 69
0.964
2.13
2005
638
449
1.045
2006
650
466 72
0.769
Table 1, during the sample period, the number of sample firms increases from 149 to 650, while the proportion (number) of firms with positive R&D expenditures raise from 54% (80) to 72% (466) and the average R&D-to-sales ratio (RDS) increases from 0.6% to 2.2%. The increasing R&D intensity emphasizes the rising importance of R&D investments. Also, the BM ratio is increasing for all firms over time.

17. Table 1 Summary statistics of the sample firms, 1991-2006
Year
Total No of Firms
Total No. of Firms with Positive R&D
Positive R&D Ratio (%)
Average BM for All Firms
Average RDS for All Firms (%)
1991
149 80 54
0.361
0.64
1992
174
104 60
0.513
0.70
1993
194
117
0.362
0.71
1994
214
132 62
0.352
0.75
1995
247
162 66
0.544
0.93
1996
283
151 53
0.466
1.10
1997
315
169
0.479
1.33
1998
362
204 56
0.646
1.34
1999
428
253 59
0.837
1.53
2000
483
296 61
1.546
1.60
2001
526
338 64
1.498
2.08
2002
586
400 68
1.153
2.22
2003
617
430 70
0.879
2.23
2004
627
435 69
0.964
2.13
2005
638
449
1.045
2006
650
466 72
0.769
The increasing R&D intensity emphasizes the rising importance of R&D investments. Also, the BM ratio is increasing for all firms over time.
Table 1, during the sample period, the number of sample firms increases from 149 to 650, while the proportion (number) of firms with positive R&D expenditures raise from 54% (80) to 72% (466) and the average R&D-to-sales ratio (RDS) increases from 0.6% to 2.2%. The increasing R&D intensity emphasizes the rising importance of R&D investments. Also, the BM ratio is increasing for all firms over time.

18. 2.2 Portfolio Analysis
We carry out portfolio analyses of the full sample and sub-samples of firms to closely examine the existence of the BM effect in the Taiwan stock market, with the BM-based portfolios.
At the beginning of each July from 1992 to 2008, each stock in a given sample is assigned to one of five portfolios based on its BM ratio. Stocks with a non-positive book value are excluded for the formation date in that year.

19. Portfolio ‘Low’ (‘High’) refers to the portfolio with the lowest (highest) BM ratio. ‘H-L’ denotes a zero-investment portfolio formed by buying the portfolio with the highest BM ratio and short-selling the portfolio with the lowest BM ratio. We then calculate the equally-weighted monthly returns.

20. In order to control for the potential interference of R&D in the BM effect, a two-dimensional dependent sorting portfolio is formed as follows. Firstly, we separate the stocks into three groups on the basis of the R&D-to-sales (RDS) ratio of each stock. Secondly, within each RDS-classified group, we further divide firms into five groups on the basis of their BM ratio.

21. 2.3 Size-adjusted Returns
The return spread between firms with the highest and lowest BM ratio may be partly explained by the difference in their size spread. In order to ease this concern, we derive the size-adjusted returns on the BM-based portfolios which can be interpreted as the net BM effect independent of the potentially correlated size effect.
We follow Lakonishok et al. (1994) to calculate the size-adjusted returns

22. 2.4 Risk-adjusted Returns
The observed anomaly may reflect certain risk factors that are not accounted for by the size effect. Fama and French (1993) argue that since past performance is likely to be negatively associated with changes in systematic risk, high-BM firms are likely to be riskier, and hence require higher expected returns.

23. More specifically, they argue that the observed poor prior performance of high-BM firms indicates that they are more likely to be distressed, and hence, more likely to be exposed to a priced systematic risk factor. In order to address this, we use the well-known CAPM to examine whether the BM premium is explained by the risk model.
The alpha term (p) : the measure for the abnormal return on portfolio p after controlling for systematic risk.

24. 2.5 Reversal Coefficient
Lakonishok et al. (1994) argue that investors will often tend to extrapolate the prior performance of a firm to assess its future performance, since they tend to overestimate the performance of growth (low-BM) stocks which have done well in the past, and underestimate the performance of value (high-BM) stocks that have done poorly.

25. Thus, they are invariably disappointed (positively surprised) by the growth (value) stocks, as compared to their initial expectations. The BM effect may therefore reflect the overreaction of investors to prior performance. In order to precisely measure the observed magnitude of fundamental reversals, we construct the following simple ex-post index:

26. Reversal Coefficient (RCi,t) = (2)
where O, R and Z are the respective growth rates at time t = –2, +2 and 0. The potential behavior of the reversal coefficient

27. We use the return on assets (ROA) and the return on equity (ROE) in this study as proxies for the profitability of the firm, which is assumed to follow a mean-reversion process. The reversal coefficient (RCi,t) for firm i at time t can therefore be interpreted as follows

28. RCi,t = 1: The fundamental growth rate of the firm has reverted to its long-term growth rate.
0 < RCi,t < 1: The fundamental growth rate of the firm has reverted, but it has not yet regained its long-term growth rate.
RCi,t > 1: The fundamental growth rate of the firm has reverted, and has regained and exceeded its long-term growth rate.
RCi,t ≤ 0: The fundamental growth rate of the firm has not reverted

29. 2.5 Idiosyncratic and Systematic Risks
Idiosyncratic risk cannot be directly observed by investors; we therefore use the market model to construct a measure of idiosyncratic volatility. Idiosyncratic and systematic risk for each firm and year are estimated by Equation (1), using daily excess returns. Following Sias (1996) and Xu and Malkiel (2003), we take the natural logarithm of the idiosyncratic volatility (IV) measure to reduce the impact of heteroskedasticity on our results.

30. The measure of idiosyncratic volatility of firm i during fiscal year n is defined as Eqution 1:
where εi,t is the regression residuals of Equation (1) and Mn is the number of return observations in fiscal year n. We also calculate the equally-weighted systematic risk ( in Equation (1)) and idiosyncratic risk for each portfolio.

31. Table 2 Average monthly returns on the book-to-market based portfolios
the BM effect is generally absent in the Taiwan stock market
Table 2 Average monthly returns on the book-to-market based portfolios
Variables
Book-to-market portfolios
Low 2 3 4
High
H-L
Panel A: Average Raw Monthly Returns (%)
Returns
0.49
0.73
0.75
0.92
1.49*
1.00
t-value
1.21
1.28
1.45
1.86
1.50
Panel B: Size-adjusted Monthly Returns (%)
–0.22
–0.04
–0.13
–0.07
0.44
0.67
–0.97
–0.28
–1.21
–0.49
1.59
1.43
Panel C: CAPM Risk-adjusted Returns (%)
Jensen’s 
–0.16
0.07
0.13
0.34
0.77
0.93
0.24
0.43
1.26
1.40
Panel D: Characteristics BM
0.298
0.487
0.687
0.953
1.550
1.252
RDS
0.026
0.020
0.014
0.007
0.005
–0.021
ln(ME)
7.141
7.253
6.979
7.029
6.723
–0.417
Beta
0.943
0.885
0.844
0.863
0.983
0.040
S.D.
8.963
8.374
8.137
8.803
11.079
2.116

32. Book-to-market portfolios
Table 3 Average monthly returns of the BM-based portfolios under different RDS regimes
Book-to-market portfolios
Low 2
Medium 4
High
H-L
Panel A: Raw Monthly Returns (%)
Low RDS
Returns
0.40
0.64
0.72
1.03
1.96**
1.56***
t-value
0.66
1.06
1.15
1.43
2.14
2.54
Med. RDS
0.16
0.18
0.63
0.68
1.19
0.27
0.30
1.07
1.09
1.58
1.63
High RDS
0.83
0.96
1.56**
1.44*
0.61
1.02
1.38
2.33
1.94
1.11
Panel B: Size-adjusted Monthly Returns (%)
–0.35
–0.22
–0.32
0.08
0.88**
1.22**
–1.52
–0.88
–1.36
0.31
2.03
2.30
–0.52**
–0.59***
–0.26
–0.29
0.17
0.70
–2.45
–3.26
–1.53
–1.63
0.62
1.64
0.10
0.00
0.20
0.62***
0.40*
0.28
0.01
0.71
2.60
1.67
Panel C: CAPM Risk-adjusted Returns (%)
Jensen’s 
–0.15
0.11
0.46
1.35**
1.51**
–0.46
0.44
2.02
2.49
–0.38
–0.43
–0.06
–0.02
0.67
–1.26
–1.37
–0.18
–0.04
1.05
1.59
0.24
0.13
0.37
0.98
0.84*
0.59
0.34
0.99
2.61
1.95
1.10

33. Book-to-market portfolios
Table 3 Average monthly returns of the BM-based portfolios under different RDS regimes
Book-to-market portfolios
Low 2
Medium 4
High
H-L
Panel A: Raw Monthly Returns (%)
Low RDS
Returns
0.40
0.64
0.72
1.03
1.96**
1.56***
t-value
0.66
1.06
1.15
1.43
2.14
2.54
Med. RDS
0.16
0.18
0.63
0.68
1.19
0.27
0.30
1.07
1.09
1.58
1.63
High RDS
0.83
0.96
1.56**
1.44*
0.61
1.02
1.38
2.33
1.94
1.11
Panel B: Size-adjusted Monthly Returns (%)
–0.35
–0.22
–0.32
0.08
0.88**
1.22**
–1.52
–0.88
–1.36
0.31
2.03
2.30
–0.52**
–0.59***
–0.26
–0.29
0.17
0.70
–2.45
–3.26
–1.53
–1.63
0.62
1.64
0.10
0.00
0.20
0.62***
0.40*
0.28
0.01
0.71
2.60
1.67
Panel C: CAPM Risk-adjusted Returns (%)
Jensen’s 
–0.15
0.11
0.46
1.35**
1.51**
–0.46
0.44
2.02
2.49
–0.38
–0.43
–0.06
–0.02
0.67
–1.26
–1.37
–0.18
–0.04
1.05
1.59
0.24
0.13
0.37
0.98
0.84*
0.59
0.34
0.99
2.61
1.95
1.10
Thus, our results indicate that the BM premium in the low-RDS group is driven primarily by the underperformance of the low-BM stocks and the out-performance of the high-BM stocks.

34. Table 3 Average monthly returns of the BM-based portfolios under different RDS regimes
Book-to-market portfolios
Low 2
Medium 4
High
H-L
Panel A: Raw Monthly Returns (%)
Low RDS
Returns
0.40
0.64
0.72
1.03
1.96**
1.56***
t-value
0.66
1.06
1.15
1.43
2.14
2.54
Med. RDS
0.16
0.18
0.63
0.68
1.19
0.27
0.30
1.07
1.09
1.58
1.63
High RDS
0.83
0.96
1.56**
1.44*
0.61
1.02
1.38
2.33
1.94
1.11
Panel B: Size-adjusted Monthly Returns (%)
–0.35
–0.22
–0.32
0.08
0.88**
1.22**
–1.52
–0.88
–1.36
0.31
2.03
2.30
–0.52**
–0.59***
–0.26
–0.29
0.17
0.70
–2.45
–3.26
–1.53
–1.63
0.62
1.64
0.10
0.00
0.20
0.62***
0.40*
0.28
0.01
0.71
2.60
1.67
Panel C: CAPM Risk-adjusted Returns (%)
Jensen’s 
–0.15
0.11
0.46
1.35**
1.51**
–0.46
0.44
2.02
2.49
–0.38
–0.43
–0.06
–0.02
0.67
–1.26
–1.37
–0.18
–0.04
1.05
1.59
0.24
0.13
0.37
0.98
0.84*
0.59
0.34
0.99
2.61
1.95
1.10
BM effect is not subsumed by the size effect.

35. Table 3 Average monthly returns of the BM-based portfolios under different RDS regimes
Book-to-market portfolios
Low 2
Medium 4
High
H-L
Panel A: Raw Monthly Returns (%)
Low RDS
Returns
0.40
0.64
0.72
1.03
1.96**
1.56***
t-value
0.66
1.06
1.15
1.43
2.14
2.54
Med. RDS
0.16
0.18
0.63
0.68
1.19
0.27
0.30
1.07
1.09
1.58
1.63
High RDS
0.83
0.96
1.56**
1.44*
0.61
1.02
1.38
2.33
1.94
1.11
Panel B: Size-adjusted Monthly Returns (%)
–0.35
–0.22
–0.32
0.08
0.88**
1.22**
–1.52
–0.88
–1.36
0.31
2.03
2.30
–0.52**
–0.59***
–0.26
–0.29
0.17
0.70
–2.45
–3.26
–1.53
–1.63
0.62
1.64
0.10
0.00
0.20
0.62***
0.40*
0.28
0.01
0.71
2.60
1.67
Panel C: CAPM Risk-adjusted Returns (%)
Jensen’s 
–0.15
0.11
0.46
1.35**
1.51**
–0.46
0.44
2.02
2.49
–0.38
–0.43
–0.06
–0.02
0.67
–1.26
–1.37
–0.18
–0.04
1.05
1.59
0.24
0.13
0.37
0.98
0.84*
0.59
0.34
0.99
2.61
1.95
1.10
BM premium cannot be explained by systematic risk.

36. Book-to-market portfolios
Variables
Book-to-market portfolios
Low 2
Medium 4
High
H-L
Panel D: Characteristics BM
Low RDS
0.432
0.697
0.922
1.196
1.892
1.460
Med. RDS
0.326
0.507
0.707
0.948
1.469
1.143
High RDS
0.245
0.374
0.498
0.661
1.076
0.831
RDS
0.000
0.005
0.004
–0.001
0.055
0.047
0.045
0.028
–0.026
ln(ME)
7.134
7.192
7.150
7.153
6.955
–0.179
7.516
7.412
7.083
7.011
6.881
–0.635
8.202
8.021
7.932
7.903
7.431
–0.771
Beta
0.842
0.788
0.796
0.899
1.019
0.177
0.858
0.802
0.816
0.683
–0.159
1.004
0.992
0.979
1.009
S.D.
8.407
8.494
8.743
10.031
12.749
4.342
8.221
8.432
8.183
8.642
10.502
2.281
10.014
9.759
9.653
9.288
10.297
0.283

37. Figure 2 Cumulative returns on portfolios sorted by book-to-market ratio under high- and low-RDS regimes

38. Figure 3 Evolution of average monthly stock returns for book-to-market based portfolios under high- and low-RDS regimes

39. Figure 3 Evolution of average monthly stock returns for book-to-market based portfolios under high- and low-RDS regimes
over the pre-formation periods, higher return spreads between the high- and low-BM portfolios do not necessarily indicate a higher subsequent BM premium.

40. Figure 3 Evolution of average monthly stock returns for book-to-market based portfolios under high- and low-RDS regimes
there is a tendency for LBM_HRDS firms to consistently outperform LBM_LRDS firms over both the pre- and post-formation periods

41. Figure 4a Evolution of ROA for book-to-market based portfolios under high- and low-RDS regimes

42. Figure 4b Evolution of ROE for book-to-market based portfolios under high- and low-RDS regimes

43. Figure 4b Evolution of ROE for book-to-market based portfolios under high- and low-RDS regimes
the profitability levels of LBM_HRDS (HBM_HRDS) firms consistently outperforms those of LBM_LRDS (HBM_LRDS) firms during both the pre- and post-formation periods

44. Table 4 Average reversal coefficients
Low RDS
High RDS
ROA
ROE
L (Low)
0.347
***
0.351
0.327
0.302 P2
0.162 *
0.218
0.063
0.102 P3
0.121
0.156
0.277
0.216 ** P4
0.234
0.293
0.087
0.181
H (High)
0.320
0.398
0.281
0.363

45. Table 5 Fama-MacBeth regressions
Variables
Model (1)
Model (2)
Model (3)
Model (4)
(Purging risk)
Model (5)
(Purging reversals)
Model (6)
Model (7)
Coeff.
t-ratio
Panel A: Low RDS
Intercept
2.33
1.07
1.57**
2.20
0.99
0.52
2.32
1.11
1.19
0.62
0.21
0.10
ln(ME)
–0.10
–0.48 –
0.06
0.30
–0.04
–0.18
0.03
0.16
0.14
0.75
ln(BM)
0.95**
2.10
0.82**
1.99
ln(BM)′
0.79**
1.98
0.58
1.36
0.67
1.51
Beta
–0.68
–0.50
–0.49 IV
0.68
1.37
0.42
1.04
RCROA
–0.40***
–3.73
–0.45***
–4.26
RCROA × DumRC_ROA
0.81***
5.15
0.91***
5.76
Adj. R2
0.05
0.09
0.08
0.18
Panel B: High RDS
1.66**
2.09
1.32
0.69
0.70
1.48
0.78
0.32
0.01
–0.02
–0.12
0.12
0.56
–0.22
–0.46
0.00
–0.44
–0.95
0.13
–0.36
–0.40
–0.37
-0.44
0.47
0.93
0.48
1.03
–0.54***
–5.20
– 0.56* **
-5.22
0.99***
5.83
1.06* **
5.91
0.11

46. Table 5 Fama-MacBeth regressions
Variables
Model (1)
Model (2)
Model (3)
Model (4)
(Purging risk)
Model (5)
(Purging reversals)
Model (6)
Model (7)
Coeff.
t-ratio
Panel A: Low RDS
Intercept
2.33
1.07
1.57**
2.20
0.99
0.52
2.32
1.11
1.19
0.62
0.21
0.10
ln(ME)
–0.10
–0.48 –
0.06
0.30
–0.04
–0.18
0.03
0.16
0.14
0.75
ln(BM)
0.95**
2.10
0.82**
1.99
ln(BM)′
0.79**
1.98
0.58
1.36
0.67
1.51
Beta
–0.68
–0.50
–0.49 IV
0.68
1.37
0.42
1.04
RCROA
–0.40***
–3.73
–0.45***
–4.26
RCROA × DumRC_ROA
0.81***
5.15
0.91***
5.76
Adj. R2
0.05
0.09
0.08
0.18
Panel B: High RDS
1.66**
2.09
1.32
0.69
0.70
1.48
0.78
0.32
0.01
–0.02
–0.12
0.12
0.56
–0.22
–0.46
0.00
–0.44
–0.95
0.13
–0.36
–0.40
–0.37
-0.44
0.47
0.93
0.48
1.03
–0.54***
–5.20
– 0.56* **
-5.22
0.99***
5.83
1.06* **
5.91
0.11
The results presented in Table 5 are the average coefficients. Firstly, as reported in Model (1) of Panels A and B, when ln(ME) is taken as the sole explanatory variable, the average coefficients on ln(ME) is insignificant, suggesting that no size premium exists for either the low- or high-RDS samples.

47. Table 5 Fama-MacBeth regressions
Secondly, as expected, BM has explanatory power on stock returns only for those firms with a low RDS; for example, the average coefficients on BM in Models (2) and (3) are significant, indicating that, consistent with the previous sections, the BM effect exists only for stocks with a low RDS.
Table 5 Fama-MacBeth regressions
Variables
Model (1)
Model (2)
Model (3)
Model (4)
(Purging risk)
Model (5)
(Purging reversals)
Model (6)
Model (7)
Coeff.
t-ratio
Panel A: Low RDS
Intercept
2.33
1.07
1.57**
2.20
0.99
0.52
2.32
1.11
1.19
0.62
0.21
0.10
ln(ME)
–0.10
–0.48 –
0.06
0.30
–0.04
–0.18
0.03
0.16
0.14
0.75
ln(BM)
0.95**
2.10
0.82**
1.99
ln(BM)′
0.79**
1.98
0.58
1.36
0.67
1.51
Beta
–0.68
–0.50
–0.49 IV
0.68
1.37
0.42
1.04
RCROA
–0.40***
–3.73
–0.45***
–4.26
RCROA × DumRC_ROA
0.81***
5.15
0.91***
5.76
Adj. R2
0.05
0.09
0.08
0.18
Panel B: High RDS
1.66**
2.09
1.32
0.69
0.70
1.48
0.78
0.32
0.01
–0.02
–0.12
0.12
0.56
–0.22
–0.46
0.00
–0.44
–0.95
0.13
–0.36
–0.40
–0.37
-0.44
0.47
0.93
0.48
1.03
–0.54***
–5.20
– 0.56* **
-5.22
0.99***
5.83
1.06* **
5.91
0.11
Secondly, as expected, BM has explanatory power on stock returns only for those firms with a low RDS; for example, the average coefficients on BM in Models (2) and (3) are significant, indicating that, consistent with the previous sections, the BM effect exists only for stocks with a low RDS.

48. Table 5 Fama-MacBeth regressions
Thirdly, and more importantly, we further investigate whether the source of the BM premium results from risks and/or fundamental reversals (i.e., overreaction). The results shown in Models (4) and (5) of Panel A indicate that after purging the risks, the BM effect does have significant predictive power with regard to stock returns. On the other hand, however, the BM effect disappears after purging the reversals, which suggests that the BM effect in Taiwan arises mainly from overreaction, as opposed to risks, a finding which is in line with that of Lakonishok et al. (1994).
Variables
Model (1)
Model (2)
Model (3)
Model (4)
(Purging risk)
Model (5)
(Purging reversals)
Model (6)
Model (7)
Coeff.
t-ratio
Panel A: Low RDS
Intercept
2.33
1.07
1.57**
2.20
0.99
0.52
2.32
1.11
1.19
0.62
0.21
0.10
ln(ME)
–0.10
–0.48 –
0.06
0.30
–0.04
–0.18
0.03
0.16
0.14
0.75
ln(BM)
0.95**
2.10
0.82**
1.99
ln(BM)′
0.79**
1.98
0.58
1.36
0.67
1.51
Beta
–0.68
–0.50
–0.49 IV
0.68
1.37
0.42
1.04
RCROA
–0.40***
–3.73
–0.45***
–4.26
RCROA × DumRC_ROA
0.81***
5.15
0.91***
5.76
Adj. R2
0.05
0.09
0.08
0.18
Panel B: High RDS
1.66**
2.09
1.32
0.69
0.70
1.48
0.78
0.32
0.01
–0.02
–0.12
0.12
0.56
–0.22
–0.46
0.00
–0.44
–0.95
0.13
–0.36
–0.40
–0.37
-0.44
0.47
0.93
0.48
1.03
–0.54***
–5.20
– 0.56* **
-5.22
0.99***
5.83
1.06* **
5.91
0.11

49. Table 5 Fama-MacBeth regressions
Variables
Model (1)
Model (2)
Model (3)
Model (4)
(Purging risk)
Model (5)
(Purging reversals)
Model (6)
Model (7)
Coeff.
t-ratio
Panel A: Low RDS
Intercept
2.33
1.07
1.57**
2.20
0.99
0.52
2.32
1.11
1.19
0.62
0.21
0.10
ln(ME)
–0.10
–0.48 –
0.06
0.30
–0.04
–0.18
0.03
0.16
0.14
0.75
ln(BM)
0.95**
2.10
0.82**
1.99
ln(BM)′
0.79**
1.98
0.58
1.36
0.67
1.51
Beta
–0.68
–0.50
–0.49 IV
0.68
1.37
0.42
1.04
RCROA
–0.40***
–3.73
–0.45***
–4.26
RCROA× DumRC_ROA
0.81***
5.15
0.91***
5.76
Adj. R2
0.05
0.09
0.08
0.18
Panel B: High RDS
1.66**
2.09
1.32
0.69
0.70
1.48
0.78
0.32
0.01
–0.02
–0.12
0.12
0.56
–0.22
–0.46
0.00
–0.44
–0.95
0.13
–0.36
–0.40
–0.37
-0.44
0.47
0.93
0.48
1.03
–0.54***
–5.20
–0.56***
-5.22
0.99***
5.83
1.06***
5.91
0.11
Finally, Models (6) and (7) of Table 5 show that for both the low- and high-RDS samples, all of the average coefficients on fundamental reversals are significant at the 1 per cent level, which indicates that the stock returns are significantly associated with fundamental reversals, albeit insignificantly associated with risks. More specifically, all of the average coefficients on RCROA are negative and significant at the 1 per cent level, whilst those on RCROA DUMROA are positive and significant at the 1 per cent level. It therefore follows that investors will react positively (negatively) to upward (downward) reversals in fundamentals.

50. Thanks for your listening!