Properties of Portfolios Formed on VaR and Pre-ranking β

5. Empirical Results

5.4 Properties of Portfolios Formed on VaR and Pre-ranking β

[Insert Table 5 here]

Table 5 of Panel A reports that when common stock portfolios are formed on 5%

VaR, the average stock returns are positively related to VaR. Going from the lowest 5% VaR quintile to the highest 5% VaR quintile, the average stock returns from VaR portfolios increase from 0.55% per month to 1.27% per month monotonically. This result supports our argument to the effect that if investors are more averse to the risk

of losses on the downside than of gains on the upside, i.e. a higher VaR, investors ought to demand greater compensation. Furthermore, we can see that the greatest average monthly post-formation return is about 1.92% and not surprisingly is apparent in the highest VaR-BE/ME group. However, the average monthly post-formation returns are not similar within the sameβ quintile. For the smallest 5% VaR quintile, the highest β does not have the largest stock returns. Beta seems to have much less power to explain the average stock returns after controlling for the 5% VaR and book-to-market effects. These results inform us that the more a stock can potentially fall in value, the higher should be the expected return.

5.5 Main Model Results: Factor Models

[Insert Table 6 here]

Table 6 shows, not surprisingly, the excess return on the market portfolio of stocks. RMRF captures a more common variation in stock returns than SMB, HML, and HVARL. As presented in Panel A of Table 6, the coefficients of RMRF are in the range of 0.78 to 1.17, and the t statistics are in the range of 8.77 to 19.46. The R values are extremely high, but the important fact is that the market leaves much 2

variation in stock returns that might be explained by other factors. The only R ² value near 0.8 is related to the big-stock high-BE/ME portfolios. For small-stock and low-BE/ME portfolios, the R are less than 0.6 or 0.5, respectively. Panel B of ² Table 6 indicates that HVARL, even if used alone, captures substantial time-series variation in stock returns. The slopes on HVARL range from 0.45 to 1.38, and their t-statistics are in the range of 2.81 to 7.69. We should note that 20 of the 25 R ² values are above 0.20. Panel C of Table 6 shows that SMB, the mimicking return for the size factor, has less power than HVARL in terms of explaining stock returns.

The R values in Panel B are greater than those in Panel C. It should be noted that ² both HVARL and SMB have little power for the portfolios in the big-size quintile.

Specifically, the R values for HVARL are in the range of 0.08 to 0.23, whereas the ² corresponding figures for SMB range from 0.00 to 0.11. As expected, on average, the slopes for SMB are related to size. In every BE/ME quintile in Panel C, the slopes for SMB decrease monotonically from smaller- to bigger-size quintiles. We can see an interesting result in that smaller-size quintiles seem to capture more variations in terms of R values. Panel D of Table 6 points out that for HML, ² when used alone, the slopes in relation to HML increase monotonically from the strong negative values for the smaller- to bigger-size quintiles. Not surprisingly, the slopes for HML are systematically related to BE/ME. The R values for the ² small-stock small-BE/ME portfolios capture more of the variations in stock returns and range from 0.22 to 0.38. This result accords with the intuition that the stocks with lower BE/ME ratios are less risky and so lower stock returns are required.

[Insert Table 7 here]

Table 7 shows two-factor models in which monthly returns on 25 portfolios are regressed on RMRF along with SMB, HML and HVARL. Panel A of Table 7 displays the slope coefficients for RMRF and HVARL, their t-statistics, R values ² and the standard error values of estimates (SEE). All of the slopes of RMRF are statistically significant at the 5% level. The R values are in the range of 0.50 to ² 0.78. Panel B of Table 7 presents very similar results for RMRF and SMB. The market βs for stocks are all significant according to the t-statistics. On average, 22 of the 25 slope coefficients for HVARL are statistically different from 0. The R ² values fall within the range of 0.66 to 0.85. Interestingly, SMB and HML, when used

along with RMRF, capture substantial time-series variation in stock returns. Panel C of Table 7 indicates that only 3 of the 25 coefficients for HML are statistically insignificant, and the R values range from 0.54 to 0.90. Similar to Table 6, the ² slope coefficients for SMB and HML are related to the size and BE/ME factors, respectively. In every BE/ME quintile, on average, the SMB slopes decrease monotonically from small- to big-size quintiles. For every size quintile for stocks, the HML slopes increase monotonically from strong negative values for the lowest-BE/ME quintile to strong positive values for the highest-BE/ME quintile.

[Insert Table 8 here]

Table 8 presents estimates from the three-factor model in which the excess returns on 25 portfolios are regressed on RMRF, SMB and HML. Table 8 demonstrates that most of the coefficients for the three Fama-French factors (RMRF, SMB and HML) are highly significant. The lower BE/ME quintile and bigger size quintile portfolios capture between 70% and 90% of the variations in terms of the R ² values. However, the higher BE/ME quintile and smaller size quintile seem to leave 30%-40% of variations that cannot be explained by Fama and French’s three-factor model. Furthermore, the results indicate that, when controlling for the BE/ME effect, the SMB factor loading is highly significant. What is initially surprising, however, is the fact that SMB seems to work in a reverse manner than what would be expected, i.e. small firms have on average higher returns than big firms. This can be seen by looking at the coefficients for SMB, which go from positive to negative when moving from small stock portfolios to big stock portfolios and after taking into account the fact that the size premium is negative during our sample period. On the other hand, when controlling for size, the HML factor clearly captures the higher returns for the

high BE/ME portfolios as compared to the low BE/ME stocks. Subsequently, we will continue to see if another factor — the VaR — can enhance and capture the variations.

[Insert Table 9 here]

Table 9 presents the parameter estimates, t-statistics, R values, and standard ² errors of estimate (S.E.E) from the time series regressions of excess stock returns on RMRF, SMB, HML and HVARL. As shown in Table 9, the slope coefficients for the market factor, RMRF, are highly significant. Most of the slope coefficients for SMB and HML factor are also significant. A notable point is that, for the lowest size-quintile, none of HVARL slopes are significant. Only 8 of 25 HVARL slopes are significant. The R values of the four-factor model are greater than those of ² the three-factor model. When viewed at the portfolio level, these empirical results show that the VaR factor plays an important role in firms especially with larger capitalization. This could be the reason why either the concept of VaR is not very familiar to individual investors since they are the major participants in Taiwan’s stock market or else larger companies always pay much attention to VaR in order to control for downside risk. However, the New Basle II Accord will be implemented at the end of 2006, and so we think VaR will play an increasingly important role in the future. Therefore, this could perhaps be tested and verified by further research.

6. Conclusions and Comments

By focusing on downside risk as an alternative measure of risk measured by VaR, this paper investigates whether the new VaR factor plays an important role in explaining Taiwan’s stock returns from January 1996 to December 2004. The empirical results

do not support the central prediction of the CAPM because average stock returns are not positively related to the market beta at the portfolio level. From the cross-sectional regressions in a Fama and French (1992) asset pricing framework, we can find that, in addition to market betas, idiosyncratic factors, such as firm size, book value of equity to market value of equity, 1% VaR and 5% VaR, are related to the return at the individual stock level. In particular, the BE/ME factor captures most of the variations in average realized stock returns in terms of R . From the time series ² regressions we investigate models with factors ranging from one to four to test the empirical performance at the portfolio level. From the results, which are based on 25 size/book-to-market portfolios of Fama and French (1993) and follow Bali and Cakici (2004), we find that the HVARL factor can also help to explain the variation in the stock market, especially for the larger companies in Taiwan’s stock market. One direction for future research could explore whether expected returns are related to a stock’s sensitivities to fluctuations in other aspects of VaR. Another point is that since expected average returns seem to be explained by the four-factor risk return relationship, it would be interesting to analyze whether it is the time variation in expected premiums or the time variation in the factor sensitivities that capture most of the predicted variation in the expected returns.

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Table 1: Cross-Sectional Regressions of Stock Returns on Beta, Size, BE/ME, and VaR

This table reports the time-series average of the month-by-month regression slopes from January 1996 to December 2004. The dependent variables are the monthly average returns on individual stocks.

The independent variables include beta, firm size, the book-to-market ratio (BE/ME), and VaR(α), where α=1%, 5%, and 10%. The betas that correspond to the portfolio they belong to are assigned to individual stocks. The size is the natural log of the market value. The BE/ME is the natural log of the book-to-market value. The VaR is calculated using the historical simulation method. The t-statistic reported in the parentheses is the average slope divided by its time-series standard error.

Monthly Regression (n=108) Average value of ω

Note: ***, **, * denotes significantly different from zero at the 0.01, 0.05, and 0.10-levels, respectively.

Table 2: Time Series Regressions -- Simple Statistics

This table presents simple summary statistics for the stocks in the sample. The six size-PB portfolios (S/L, S/M, S/H, B/L, B/M, and B/H) are formed in December of each year t-1 and value-weighted monthly returns are calculated from January to December of year t. Panel A presents the basic statistics of the four factors. Panel B presents the Pearson correlation coefficients that are calculated based on monthly returns for each of the factors: RMRF, SMB, HML and HVARL. The sample period extends from January 1996 to December 2004, there being 108 monthly observations.

Panel A: Simple Statistics

Variable N Mean Std Dev Sum Minimum Maximum

RMRF 108 1.2801 9.0447 138.251 -20.345 24.2122

SMB 108 -0.6058 4.6631 -65.431 -14.162 10.5153

HML 108 3.0023 6.2115 324.246 -19.486 21.4384

HVARL 108 0.4437 5.6877 47.9199 -16.046 20.1611

Panel B Pearson Correlation Coefficients, N = 108 Prob > |r| under H0: Rho=0

RMRF SMB HML HVARL

RMRF 1

SMB -0.0624 1

HML -0.074 -0.5955^* 1

HVARL 0.5066^* 0.336^* -0.2758^* 1

Note: This table gives the correlation coefficients calculated from the sample. An asterisk indicates that the correlation coefficient is significant (i.e. the p-value is less than 0.05).

Table 3: Correlations of 25 Portfolio Returns with RMRF, SMB, HML and HVARL

Correlations RMRF SMB HML HVARL

S1B1 0.6720 0.5045 -0.5785 0.5319

S1B2 0.7308 0.4740 -0.5268 0.5445

S1B3 0.6921 0.5509 -0.5088 0.5662

S1B4 0.6485 0.4840 -0.5115 0.5005

S1B5 0.6949 0.4243 -0.3128 0.4982

S2B1 0.7486 0.4834 -0.5887 0.5985

S2B2 0.7446 0.4344 -0.5218 0.4912

S2B3 0.7574 0.4624 -0.4791 0.5669

S2B4 0.6924 0.4122 -0.4994 0.4480

S2B5 0.7434 0.3502 -0.1908 0.4613

S3B1 0.7485 0.4520 -0.6137 0.5626

S3B2 0.7982 0.4131 -0.5313 0.5376

S3B3 0.7321 0.3779 -0.4187 0.4742

S3B4 0.7650 0.3576 -0.3484 0.4452

S3B5 0.7701 0.2133 -0.1495 0.4589

S4B1 0.7634 0.3700 -0.6180 0.5845

S4B2 0.7711 0.3215 -0.5371 0.5410

S4B3 0.7913 0.3034 -0.4563 0.4607

S4B4 0.8079 0.2035 -0.3390 0.3994

S4B5 0.8115 0.0823 -0.0692 0.5459

S5B1 0.8282 0.1693 -0.4647 0.4519

S5B2 0.8526 0.0552 -0.2845 0.3205

S5B3 0.8288 0.0112 -0.2246 0.2636

S5B4 0.8602 -0.1077 -0.0284 0.2860

S5B5 0.8839 -0.3281 0.2362 0.4774

Average 0.7655 0.2990 -0.3826 0.4807

Note: S1B1 (S5B5) denotes a size-BE/ME portfolio that belongs to the smallest (largest) size quintile and lowest (highest) BE/ME quintile.

Table 4: Properties of Portfolios Formed on Size and Pre-ranking β: Stocks Sorted by Size (Down) then Pre-ranking β (Across), 1996-2004

At the end of year t-1, the stocks obtained from the TEJ are assigned to 5 size portfolios. Each size quintile is subdivided into 5 β portfolios using the pre-ranking β of individual stocks estimated with 60 monthly returns ending in December of year t-1. The equal-weighted monthly returns on the resulting 25 portfolios are then calculated for year t. The average returns are the time-series average of the monthly returns, in percent. The post-ranking βs use the full 1996-2004 sample of post-ranking returns for each portfolio. The pre- and post-ranking βs are the sum of the slopes from a regression of monthly returns for the current and prior month’s value-weighted market return. The average size of a portfolio is the time-series average of each month’s average value of ln (Size) for stock within the portfolio. Size is dominated in millions of TWD. There are, on average, about 5 stocks in each size-β portfolio in each month.

Low -β 2 3 4 High-β Average

Panel A: Average Monthly Post-formation Returns (in percent)

Small-size 1.0293 1.3052 0.6207 1.0251 2.5847 1.3130

2 0.4303 0.7127 1.2314 0.6835 1.2962 0.8708

3 0.8353 0.2684 0.2441 1.2928 1.1026 0.7486

4 0.4469 0.6885 0.0076 1.2041 0.6368 0.5968

Big-size -0.1541 0.5779 1.0680 -0.2209 -0.1574 0.2227

Average 0.5175 0.7106 0.6344 0.7969 1.0926

Panel B: Post-ranking β

Small-size 0.7941 0.9160 0.9644 1.2843 1.4599 1.0837

2 0.8132 0.8710 1.0172 1.1230 1.1833 1.0015

3 0.8458 0.9948 1.0100 1.3498 1.3091 1.1019

4 0.8124 1.0384 1.0222 1.4002 1.2299 1.1006

Big-size 0.7715 0.8263 0.8643 1.0182 0.8916 0.8744

Average 0.8074 0.9293 0.9756 1.2351 1.2148

Panel C: Average Ln (Size)

Small-size 7.1450 7.2802 7.2981 7.2590 7.4390 7.2842

2 7.9950 8.0069 8.0009 7.9556 8.0679 8.0053

3 8.5667 8.5161 8.5679 8.6229 8.5625 8.5672

4 9.1994 9.2539 9.2348 9.2685 9.2632 9.2440

Big-size 10.2412 10.7327 10.6171 10.4087 10.7113 10.5422

Average 8.6295 8.7579 8.7438 8.7030 8.8088

Table 5: Properties of Portfolios Formed on VaR and Pre-ranking β: Stocks Sorted by VaR (Down) then Pre-ranking β (Across), 1996-2004

The formation of the VaR-beta portfolios is similar to that of the size-β portfolios. At the end of year t-1, stocks are sorted by their 5% VaR and assigned to 5 portfolios. Each VaR quintile is subdivided into 5 β portfolios using the pre-ranking βending in December of year t-1. The equal-weighted monthly returns on the resulting 25 portfolios are then calculated for year t. The average returns are the time-series average of the monthly returns, in percent. The post-ranking βs use the full 1996-2004 sample of post-ranking returns for each portfolio. The pre- and post-ranking βs are the sum of the slopes from a regression of monthly returns on the current and prior month’s value-weighted market return. The average 5% VaR of a portfolio is the time-series average of each month’s average value of 5% VaR for stock in the portfolio. There are, on average, about 5 stocks in each VaR-β portfolio each month.

Panel A: Average Monthly Post-formation Returns (in percent)

Low -β 2 3 4 High-β Average

Small-VaR -0.1722 0.8005 0.9174 0.4467 0.7515 0.5488

2 0.5899 0.6460 0.9079 0.8104 0.1219 0.6152

3 0.9873 0.5480 0.7447 1.0340 0.2751 0.7178

4 0.6689 0.3862 1.5197 0.0331 0.6422 0.6500

Big-VaR 0.7067 1.2596 1.2077 1.2487 1.9213 1.2688

Average 0.5561 0.7280 1.0595 0.7146 0.7424

Panel B: Post-ranking β

Small-VaR 0.4900 0.7738 0.5932 0.8779 0.8600 0.7190

2 0.9007 0.9186 0.9306 0.8939 0.8637 0.9015

3 0.9327 0.9686 1.1463 1.1416 1.1855 1.0750

4 0.9866 0.9977 1.4168 1.0077 1.2284 1.1274

Big-VaR 1.1235 1.4283 1.3407 1.3202 1.5012 1.3428

Average 0.8867 1.0174 1.0855 1.0483 1.1278

Panel C: Average VaR

Small-VaR 13.6133 14.0500 14.0540 14.5902 14.9116 14.2438

2 16.7515 17.0488 16.7265 16.8485 16.7665 16.8284

3 18.9336 18.8091 18.7304 19.2716 19.5507 19.0591

4 20.9608 21.4593 22.0351 21.5672 21.8481 21.5741

Big-VaR 25.8988 25.6252 25.6738 25.8725 27.3475 26.0836 Average 19.2316 19.3985 19.4440 19.6300 20.0849

Table 6: One-Factor Model: Regression of Excess Stock Returns on the Excess Stock-Market Return, HVARL, SMB and HML (January 1996 to December

2004, n=108)

The formation of the 25 size and BE/ME-sorted portfolios and the slope coefficients b, the t-statistics, values, and the standard errors of estimate (S.E.E) are described in this table. The construction of the SMB (Small-Minus-Big) factor portfolio (RSMB), the HML and HVARL (High-Minus-Low) factor portfolios, and the RM(t) (market factor) portfolio is as follows. We first exclude from the sample all firms with book values of less than zero. We take all TSE stocks in the sample and rank them according to their size and BE/ME, using a 50 percent breakpoint for size. Firms above the 50 percent size breakpoint are designated as B, and the remaining 50 percent as S. The stocks above the 70 percent BE/ME breakpoint are designated as H, the middle 40 percent of firms are designated as M, and the firms below the 30 percent BE/ME breakpoint are designated as L. These two sets of rankings allow us to form the six value-weighted portfolios L/S, M/S, H/S, L/B, M/B, and H/B. From these six portfolio returns, we calculate the SMB and HML factor portfolio returns, which are defined as SMB=

(RHB + RHS – RLB – RLS) /2, and the HML factor portfolio returns, which are defined as HML= (RHS+ RMS + RLS - RHB – RMB –RLB)/3. The HVARL calculation is the same as that of the SML. The estimation model uses ordinary least squares (OLS).

Panel A: R t( ) − RF t( ) = a + b ×[RM t( ) − RF t( )]+ u t( )

BE/ME Quintile

Size Quintiles Low 2 3 4 High Low 2 3 4 High

Slope Coefficient (a) t-statistic(a)

Small -4.1851 -2.2994 -1.5159 -1.4129 -0.0130 -3.9171 -2.8971 -1.8968 -1.7369 -0.0178 2 -3.0201 -1.4946 -0.9216 -0.1979 2.0933 -3.7263 -1.9612 -1.3726 -0.2695 2.8481 3 -2.6750 -1.7270 -0.6195 -0.2426 2.3138 -3.0486 -2.3604 -0.7499 -0.3336 3.0810 4 -2.6597 -1.1091 0.1683 -0.4765 1.8310 -3.3412 -1.5192 0.2324 -0.7999 2.4531 Big -2.0606 -1.0047 0.3085 -0.3497 0.8765 -3.5353 -2.0161 0.5779 -0.7663 1.6166

Slope Coefficient (b) t-statistic(b)

Small 1.0977 0.9620 0.8676 0.7846 0.8001 9.3426 11.0219 9.8720 8.7709 9.9499 2 1.0360 0.9623 0.8818 0.7977 0.9250 11.6231 11.4829 11.9419 9.8795 11.4444 3 1.1214 1.0976 1.0051 0.9782 1.0266 11.6216 13.6407 11.0640 12.2297 12.4304 4 1.0652 1.0008 1.0610 0.9247 1.1736 12.1682 12.4667 13.3263 14.1146 14.2975 Big 0.9754 0.9205 0.8953 0.8716 1.1602 15.2168 16.7963 15.2482 17.3700 19.4592

R2 ^S.E.E

Small 0.4474 0.5304 0.4750 0.4161 0.4790 120.839 66.6843 67.6122 70.0459 56.6047 2 0.5569 0.5510 0.5703 0.4754 0.5493 69.5378 61.4784 47.7262 57.0728 57.1882 3 0.5569 0.6343 0.5324 0.5820 0.5900 81.5043 56.6699 72.2352 55.9961 59.705 4 0.5796 0.5914 0.6233 0.6500 0.6559 67.0823 56.4153 55.4844 37.5687 58.9743 Big 0.6836 0.7248 0.6845 0.7380 0.7796 35.9635 26.2887 30.1744 22.0412 31.1176

(Continued)

Panel B:

R t

( ) −

RF t

( ) =

a

b

HVARL

u t

( )

Slope Coefficient (a) t-statistic(a)

Small -3.1918 -1.3674 -0.7304 -0.6801 0.7827 -2.9103 -1.4553 -0.8861 -0.7826 0.8998 2 -2.0724 -0.5463 -0.0877 0.5892 3.0404 -2.3820 -0.5820 -0.1126 0.6825 3.1919 3 -1.6366 -0.6521 0.3883 0.7403 3.3709 -1.6902 -0.6844 0.3774 0.7834 3.3158 4 -1.6688 -0.1444 1.2435 0.4912 3.0467 -1.8625 -0.1621 1.2560 0.5590 2.7871 Big -1.0498 0.0266 1.3512 0.6735 2.1546 -1.1872 0.0300 1.4734 0.7808 2.0476

Slope Coefficient (b) t-statistic(b)

Small 1.3816 1.1399 1.1288 0.9629 0.9123 6.4667 6.6839 7.073 5.9521 5.9165 2 1.3171 1.0095 1.0496 0.8208 0.9127 7.6908 5.8052 7.0856 5.159 5.3522 3 1.3403 1.1755 1.0353 0.9052 0.9727 7.0058 6.5635 5.5456 5.1185 5.317 4 1.297 1.1166 0.9822 0.727 1.2555 7.4164 6.6219 5.344 4.4859 6.7089 Big 0.8463 0.5503 0.4528 0.4608 0.9965 5.2158 3.4836 2.8136 3.0728 5.5939

R2 ^S.E.E

Small 0.2774 0.2911 0.3154 0.2448 0.2426 158.007 100.677 88.1646 90.6003 82.2953 2 0.3533 0.2354 0.3162 0.1946 0.2068 101.517 104.675 75.9589 87.6242 100.650 3 0.3113 0.2836 0.2190 0.1921 0.2045 126.692 111.025 120.651 108.251 115.841 4 0.3366 0.2872 0.2062 0.1532 0.2927 105.857 98.4182 116.937 90.9179 121.229 Big 0.1981 0.0959 0.0624 0.0748 0.2220 91.1343 86.3676 89.6643 77.8451 109.850

Panel C:

R t

( ) −

RF t

( ) =

a

b

SMB

u t

( )

Small 1.5985 1.2104 1.3396 1.1358 0.9475 6.0163 5.5429 6.7965 5.6943 4.8237 2 1.2976 1.089 1.0442 0.9211 0.8452 5.6852 4.9654 5.3688 4.6576 3.8495 3 1.3136 1.1019 1.0063 0.8869 0.5516 5.2173 4.6706 4.2020 3.9423 2.2482 4 1.0013 0.8095 0.7889 0.4517 0.2309 4.1000 3.4960 3.2779 2.1395 0.8503 Big 0.3867 0.1156 0.0236 -0.2117 -0.8353 1.7683 0.5693 0.1158 -1.1155 -3.5755

(Continued)

R2 ^S.E.E

Small 0.2488 0.2188 0.2982 0.2284 0.1737 164.255 110.950 90.3864 92.5655 89.7672 2 0.2279 0.1825 0.2078 0.1636 0.1159 121.206 111.925 88.0048 91.0021 112.170 3 0.1982 0.1644 0.1363 0.1212 0.0382 147.482 129.496 133.429 117.743 140.058 4 0.1303 0.0966 0.0851 0.0341 -0.0008 138.778 124.748 134.780 103.700 171.534 Big 0.0213 -0.0046 -0.0075 0.0041 0.1008 111.242 95.9618 96.3487 83.7954 126.965

Panel D:

R t

( ) −

RF t

( ) =

a

b

HML

u t

( )

Slope Coefficient (a) t-statistic(a)

Small 1.3514 1.9636 2.3829 2.2969 2.5858 1.0434 1.8052 2.2714 2.2728 2.4325 2 1.8681 2.6855 2.6459 3.3389 4.3155 1.7179 2.5055 2.6635 3.4411 3.6347 3 2.7798 2.8721 3.1804 2.9572 4.4990 2.4175 2.5364 2.6242 2.5383 3.5115 4 2.4736 3.2201 4.2007 2.4035 3.7709 2.3196 3.0255 3.6221 2.2963 2.6889 Big 1.5803 1.5166 2.5152 0.8920 1.0064 1.5590 1.5074 2.4581 0.9060 0.8117

Slope Coefficient (b) t-statistic(b)

Small -1.3760 -1.0097 -0.9287 -0.9011 -0.5245 -7.3022 -6.3802 -6.0842 -6.1284 -3.391 2 -1.1865 -0.982 -0.8123 -0.8379 -0.3457 -7.499 -6.2968 -5.6201 -5.9352 -2.0014 3 -1.3388 -1.0639 -0.8371 -0.6487 -0.2901 -8.0021 -6.4574 -4.7475 -3.8272 -1.5564 4 -1.2556 -1.0152 -0.8907 -0.5650 -0.1458 -8.0927 -6.5561 -5.2789 -3.71 -0.7145 Big -0.7968 -0.4473 -0.3533 -0.0419 0.4514 -5.4029 -3.0558 -2.3729 -0.2927 2.5023

R2 ^S.E.E

Small 0.3296 0.2720 0.2531 0.2560 0.0910 146.598 103.400 96.185 89.2556 98.7588 2 0.3416 0.2666 0.2237 0.2437 0.0290 103.340 100.399 86.2387 82.2813 123.195 3 0.3718 0.2768 0.1690 0.1147 0.0148 115.551 112.063 128.362 118.616 143.458 4 0.3772 0.2831 0.2022 0.1081 -0.0028 99.3824 98.9915 117.541 95.7451 171.877 Big 0.2099 0.0740 0.0432 -0.0068 0.0486 89.7947 88.4625 91.5003 84.7106 134.342

Table 7: Two-Factor Model: Regression of Excess Stock Returns on the Excess Stock-Market Return and HVARL/ SMB / HML (January 1996 to December

2004, n=108)

Panel A: R(t)−RF(t)=a+b×[RM(t)−RF(t)]+c×HVARL+u(t) BE/ME Quintile

Size Quintiles Low 2 3 4 High Low 2 3 4 High

Slope Coefficient (a) t-statistic(a)

Small -4.0373 -2.2140 -1.3993 -1.3235 0.0433 -4.3214 -3.0052 -2.0392 -1.7591 0.0612 2 -2.8880 -1.4206 -0.8287 -0.1373 2.1390 -4.3560 -1.9767 -1.4116 -0.1947 2.9689 3 -2.5410 -1.6378 -0.5547 -0.1811 2.3601 -3.4346 -2.4726 -0.6958 -0.2598 3.2050 4 -2.5357 -1.0166 0.2285 -0.4460 1.8787 -3.8110 -1.5526 0.3287 -0.7575 2.5717 Big -2.0212 -1.0230 0.2623 -0.4005 0.8690 -3.5547 -2.0603 0.5138 -0.9512 1.5965

Slope Coefficient (b) t-statistic(b)

Small 0.7738 0.7748 0.6122 0.5889 0.6768 6.6218 8.4082 7.1326 6.2570 7.6551 2 0.7465 0.8003 0.6781 0.6650 0.8251 9.0010 8.9020 9.2354 7.5367 9.1552 3 0.8278 0.9022 0.8632 0.8433 0.9251 8.9450 10.8883 8.6559 9.6727 10.0435 4 0.7934 0.7983 0.9290 0.8578 1.0691 9.5333 9.7468 10.6871 11.6485 11.6997 Big 0.8890 0.9607 0.9966 0.9829 1.1767 12.5000 15.4673 15.6104 18.6656 17.2832

在文檔中系統風險、公司規模、帳面市值比、風險值和股票報酬的關係:以台灣股票市場為例 (頁 32-59)