4. EMPIRICAL RESULTS

Transcription

1 4. EMPIRICAL RESULTS 4 DECRIPTIVE STATISTICS Table 4-1 provides descriptive statistics on the explanatory variables from regressions in which the dependent variable is the excess stock return. We report the mean, standard deviation, skewness, kurtosis, and correlation matrix. The six stock portfolios formed on size and book-to-market equity produce a wide range of average excess returns, from 1.1% to 1.6% per month. Kurtosis refers to the peakedness of the distribution. For a normal distribution the kurtosis value is 3. Skewness refers to how symmetric the distribution of data is, and perfectly symmetric distribution will have a skewness of 0. If the value of skewness is positive, called right-skewed, it means the mean exceeds the median. On the other hand, if the median exceeds the mean, these data can be negative, or left-skewed. All the distributions of variables are right-skewed, and we can learn that means the variables are increased by some usually high values. We could find in Panel B That some variables are far away from the normal standard of skewness and kurtosis, such as SMB(kurtosis is 5.328), HML(kurtosis is 7.567) and excess stock returns in the big size and high book-to-market equity(skewness is and kurtosis is ). When referred to correlation matrix, taking RDEXP for example, it is positive related to RM-RF (the correlation is 0.24), HML (the correlation is 0.05and RDASSET (the correlation is 0.54), whereas RDEXP is negatively related to SMB (the correlation is -0.08). We find that in Panel A the average excess returns in big-size groups are higher than small ones (1.3%, 1.3%, 1.6% compared to 1.3%, 1.2% 1.4%). 43

2 Table 4-1 Summary statistics for the monthly dependent and explanatory returns: January 1983 to December 2004, 264 observations Panel A Dependent variables: Excess returns on 6 portfolios formed on ME and BE/ME Means Standard deviations t-statistics for means Skewness Kurtosis Book-to Market Ratio Size Low Medium High Low Medium High Low Medium High Low Medium High Low Medium High Small Big Panel B Correlations Name Mean Std. t(mean) Skewness Kurtosis RM-RF SMB HML RDEXP RDASSET PATENT PATENTSTOCK RM RM-RF SMB HML RDEXP RDASSET PATENT PATENTSTOCK is statistically significant at 1% level. is statistically significant at 5% level. is statistically significant at 10% level. 44

3 4 REGRESSION RESULTS In our regressions, we employ the test known as the variance inflation factor (VIF) to help determine whether a coefficient is insignificant due to collinearity or due to lack of explanatory power in the associated variable. The highest VIF (in any of our regressions) is 1.21, below the level of generally viewed as indicating a significant collinearity problem. Overall, collinearity does not appear to be a serious problem in regressions. We report the coefficient estimates and significance levels, as well as adjusted R 2 values. Moreover, we also provide values about coefficients of partial determination. A coefficient of partial determination measures the marginal contribution of one X variable, when all others are already included in the model. Thus, the coefficient of partial correlation has similar function as the coefficient of partial determination. Here, we employ this indicator to find whether the specific explanatory variable has incremental contribution to the model. Excess Stock Returns with R&D-Expense Premiums Table 4-2a presents the estimates of the factors for R&D expenses and excess stock returns regressions. Overall, all the values of R 2 are above 0.9, and it has the level of 0.92 at least, implying that the model has high degree of goodness of fit. Adding RDEXP to the regressions has an interesting effect on the market for stocks. In the Fama and French (1993) three-factor model shown in Table 4-2b, the are , and for small-size stocks from low to high BE/ME 45

4 portfolios, and they are , , and for big-size stocks from low to high BE/ME portfolios. In the four-factor model presented in Table 4-2a, these for small-size stocks are , and , and they are , and for big-size stocks. In general, adding RDEXP to the regressions collapses the for stocks towards 1.0. This is due to the correlation between the market and RDEXP, and the correlation between RM-RF and RDEXP returns is Finally, Most coefficients of RDEXP are significantly positive related to excess stock returns. Only RDEXP in the big-stock, medium book-to-market portfolio is negatively related to the dependent variable, though it is not statistically significant. It is interesting to note that the values of partial determination of RDEXP, in average, are much larger in the big-size stock portfolios than small-size groups (1.96%, 0.00%, 1.21% compared to 0.43%, 0.48%, 0.67%). Overall, for the big-stock, high-be/me-stock portfolios have highest coefficients partial determination in the six portfolios. In general, these results from Table 4-2a support Hypothesis 1, which R&D expenses are positively related to the rate of stock return and they are consistent with our expectation. That is, not only could the R&D-expenses premiums explain the cross-sectional stock returns, but they are positively associated with excess stock returns as well. 46

5 Table4-2a Extension of FF three-factor model with the R&D expenses [RDEXP] factor: from January 1983 to December 2004, 264 months R ( ] + ssmb + hhml + rrdexp + ε Book-to market equity (BE/ME) Size Low Medium High Low Medium High b P-Value(b) Small Big s P-Value(s) Small Big h P-Value(h) Small Big r P-Value(r) Small Big Partial Determination%(r ) Small Big Table4-2b Results of FF three-factor model from January 1983 to December 2004, 264 months R ( ] + ssmb + hhml + ε Book-to market equity (BE/ME) Size Low Medium High Low Medium High b P-Value(b) Small Big s P-Value(s) Small Big h P-Value(h) Small Big Small Big

6 Excess Stock Return with Capitalized-R&D Premiums As Table4-3a indicates, half of coefficients of RDASSET, mimicking the return factors for capitalization of R&D, are significantly positively related to excess stock returns. The other three coefficients about RDASSET in the groups of medium- B/M equity and the small-size with high-be/me equity are negatively related to the dependent variable, though it is not significant in statistics. Moreover, all the values of R 2 are above 0.9, and it has the level of 0.92 at least, indicating that the model has high degree of goodness of fit. Also, adding RDASSET to the regressions generally shows the effect of collapsing the for stocks towards 1.0. In the Fama and French (1993) three-factor model shown in Table 4-3b, the are , and for small-size stocks from low to high BE/ME portfolios, and they are , , and for big-size stocks from low to high BE/ME portfolios. In the four-factor model presented in Table 4-5a, these for small-size stocks are1.0145, and , and they are , and for big-size stocks. However, the values of partial determination are much smaller in RDASSET than in RDEXP. It implies that the marginal contribution of the RDASSET is not as much as that of RDEXP in the extension of Fama and French three-factor-model. In conclusion, the results from the Table 4-3a support our Hypothesis 2. They are also consistent with Lev and Sougiannis (1996) who suggest that the capitalization of R&D, referred to R&D capital, was found to be strongly associated with stock prices and returns. That is, FF three-factor model added with the R&D capital factor could capture and explain stock returns better than the only three-factor model. 48

7 Table4-3a Extension of FF three-factor model with the R&D asset [RDASSET] factor: January 1983 to December 2004, 264 months R ( ] + ssmb + hhml + drdasset + ε Book-to market equity (BE/ME) Size Low Medium High Low Medium High b P-Value(b) Small Big s P-Value(s) Small Big h P-Value(h) Small Big d P-Value(d) Small Big Partial Determination% (d) Small Big Table4-3b Results of FF three-factor model from January 1983 to December 2004, 264 months R ( ] + ssmb + hhml + ε Book-to market equity (BE/ME) Size Low Medium High Low Medium High b P-Value(b) Small Big s P-Value(s) Small Big h P-Value(h) Small Big Small Big

8 Excess Stock Returns with Patent-Count Premiums Table 4-4 indicates the relation between the excess stock returns and returns for the amount of patents. Surprisingly, we see from Table 4-4 that, in small-size groups, excess stock returns are significantly negatively related with the independent variables of PATENT, mimicking the return for the amount of patents. Furthermore, the values of partial determination are much higher in small-stock portfolios than big stock portfolios. On average, they are more than 5% and the highest one is 40.48%. Nevertheless, the value of partial determination in big stocks is 0.02% at best. That is, the factor for the amount of patents has more marginal determination in small-size stocks than in big-size stocks. Contrary to our expectation, results from Table 4-4 show that there is a strong negative relation between excess stock returns and patent-count premiums. Thus, these findings reject Hypothesis 3, which predicts the number of patents granted is positively related with the market excess rate of return. Table 4-4 Extension of FF three-factor model with the number of patent [PATENT] factor: January 1983 to December 2004, 264 months R ( ] + ssmb + hhml + ppatent + ε Book-to market equity (BE/ME) Size Low Medium High Low Medium High b P-Value(b) Small Big s P-Value(s) Small Big h P-Value(h) Small Big p P-Value(p) Small Big Partial Determination% (p) Small Big

9 Excess Stock Returns with Accumulative Patent-Count Premiums Table 4-5 shows the relation between the excess stock returns and returns for accumulated amount of patents. Beyond our expectation, we could find from Table 4-5 that, in small-size groups, excess stock returns are significantly negatively related with the independent variables of PATENTSTOCK, mimicking the return for the cumulated amount of patents. Besides, the values of partial determination are apparently much larger in small-size stocks than in big-size stocks (5.1%, 10.75%, 42.13% compared to 0.04%, 0.02%, 0.02%). Moreover, in small-size stocks, from low to high-be/me-equity portfolios, there is a marked increasing in values of partial determination. Although a few coefficients of PATENTSTOCK are positive in some portfolios and at significant level, which are in the same direction with our prediction, their values of partial determination are much smaller than the others with negative values (0.02% compared to 42.13%). Therefore, there is no conclusive proof that the strong positive association between the cumulated patent-count factor and excess stock returns appears, and the Hypothesis 4 is rejected. Overall, beyond of our intuition and expectation, we find that it is the negative relationship between patents and stock returns. Therefore, in the following parts of this chapter, we will take a close look and go further to check the reasons for this phenomenon and try to find reasonably explanations. 51

10 Table 4-5a Extension of FF three-factor model with accumulative number of patents [PATENTSTOCK] factor: January 1983 to December 2004, 264 months R ( ] + ssmb + hhml + kpatentstock + ε Book-to market equity (BE/ME) Size Low Medium High Low Medium High b P-Value(b) Small Big s P-Value(s) Small Big h P-Value(h) Small Big k P-Value(k) Small Big Partial Determination% (k) Small Big Does the Industry Effect Exist? Table 4-6 shows the top 20 companies ranked by the patent count in Taiwan, and we also calculate the proportion of all the patents they have. Nineteen of them are belonged to the Electron industry, and only one company is from the Rubber industry. It adds up to 56.37% of all the amounts of patents among the top 20 firms. Table 4-6 reveals that almost sixty percent of patents are concentrated on 20 corporations and especially in the Electron industry. In addition, the top 3 companies, Taiwan Semiconductor Mfg. Co., Ltd., Hon Hai Precision Ind Co., Ltd., and United Microelectronics Corp., whose patent count is of nearly 30% of all the patent count. Therefore, it implies that the distribution of patents is so skewed and most patents in top 20 are gathered in Electron industry. 52

11 Table 4-6 top 20 corporations with the amount of patents Top20 Code Corporate Amounts of patent ratio of all the patents Cumulative Proportion Of all the patents (1) Taiwan Semiconductor Mfg. Co., Ltd Hon Hai Precision Ind Co., Ltd United Microelectronics Corp Tatung Co., Ltd Inventec Corp Winbond Electronics Corp Cheng Shin Rubber Ind. Co., Ltd Macronix International Co., Ltd MiTac Technology Corp Mosel Vitelic Inc VIA Technologies, Inc Hannstar Display Corp Nan Ya Plastics Corp Advanced Semiconductor Engineering, Inc Sysware Corp Quanta Computer Inc Enlight Corp Chunghwa Telecom Co., Ltd Chunghwa Picture Tubes Ltd Nanya Technology Corp. 328 Total (2) (3) 9.40% 9.40% 9.18% 18.59% 8.99% 27.57% 8.62% 36.20% 2.77% 38.97% 2.10% 41.07% 1.77% 42.84% 1.67% 44.51% 1.62% 46.13% 1.46% 47.58% 1.27% 48.85% 0.98% 49.83% 0.95% 50.78% 0.90% 51.68% 0.88% 52.56% 0.81% 53.37% 0.79% 54.16% 0.77% 54.93% 0.72% 55.66% 0.72% 56.37% 56.37% The total amount of patents for the entire sample is And the mathematic relations among (1) (2) and (3) are following: (2) = (1) / (3) = summation of (2) 53

12 Let us take a closer look at the distribution of patents for our selected sample. Table 4-7 divides the sample into two groups in every industry according to the amount of cumulative patent-count. Similarly, Table 4-8 partitions the sample into two groups in every industry according to the amount of patent-count instead of cumulated amounts. Table 4-6 indicates that most patents in top 20 are gathered in Electron industry (53.65% = 56.37% % %). But it does not equal that most of electron firms are equipped with patents inside. As the Table 4-7 shows, in the Electron industry, 36% of firms have ever owned one patent at least during , whereas 64% of them have never possessed any patent yet. Compared with the entire sample, electron companies without any patent are on the proportion of 29.03% (6305/21717) in all the observations whatever having patents or not. Likewise, As the Table 4-8 shows, in the Electron industry, 25% of firms have ever owned one patent at least in one year during , whereas 75% of them have never possessed any patent yet in one year from 1982 to In comparison with the entire sample, electron companies without any patent are on the proportion of 34.01% (7386/21717) in all the observations whatever having patents or not. The Electron industry has not only the highest ratio but the number of observations, which are with no patents, in the entire sample as well. As a consequence, the evidence from Table 4-7 and Table 4-8 does not support that there is industry effect in our selected sample for the patent data. 54

13 Table4-7 Industry analysis for the distribution of cumulative patent-count Industry Numbers Numbers Proportion Numbers Proportion Proportion of Sample (firmyear) (1) of Sample with one Patent at least in (2) Of The Industry (3) of Sample without any Patent in (4) Of The Industry (5) Of All The Sample (6) Cement % % 0.75% Food % % 2.09% Plastics % % 1.31% Textiles % % 5.84% Electric & Machinery % % 2.99% Appliance & Cable % % 0.97% Chemical % % 3.65% Glass & Ceramics % % 0.64% Paper & Pulp % % 0.50% Steel & Iron % % 2.81% Rubber % 99 41% 0.46% Automobile % 40 37% 0.18% Electron % % 29.03% Construction % % 5.30% Transportation % % 2.20% Tourism % % 0.96% Banking & Insurance % % 3.48% Department stores % % 1.17% Telecom & Communication % 60 71% 0.28% Software % 94 65% 0.43% Supervised Stocks % % 1.86% Others % % 4.29% Total % The mathematic relations among (1) (2) (3) (4) and (5) are following: (1) = (2) + (4) (2) + (5) = 100% (6) = (4) /

14 Table4-8 Industry analysis for the distribution of patent-count Industry Numbers Numbers Proportion Numbers Proportion Proportion of Sample (firmyear) (1) of Sample with one Patent at least in one year (2) Of The Industry (3) of Sample without Patent in one year (4) Of The Industry (5) Of All The Sample (6) Cement % % 0.88% Food % % 2.81% Plastics % % 2.26% Textiles % % 6.14% Electric & Machinery % % 3.57% Appliance & Cable % % 1.22% Chemical % % 4.54% Glass & Ceramics % % 0.76% Paper & Pulp % % 0.70% Steel & Iron % % 3.23% Rubber % % 0.62% Automobile % 68 64% 0.31% Electron % % 34.01% Construction % % 5.44% Transportation % % 2.20% Tourism % % 0.96% Banking & Insurance % % 3.48% Department stores % % 1.46% Telecom & Communication % 66 78% 0.30% Software % % 0.54% Supervised Stocks % % 1.86% Others % % 4.92% Total % The mathematic relations among (1) (2) (3) (4) and (5) are following: (3) = (2) + (4) (4) + (5) = 100% (6) = (4) /

15 As a result of the information in Table 4-7 and Table 4-8, we exclude the industry effect on the negative relation between patents and stock returns. Next, we draw Figure 4-1 to see the patterns of average stock returns for the sample based on whether they have patents or not. As the Figure 4-1 indicates, the blue line stands for the average stock returns for the sample without patents, whereas the green line represents those for the sample with patents. However, from Figure 4-1, the two lines mix and cross together from time to time, and it does not provide a clear trend between these two lines. Although Figure 4-1 is confusing and noisy, still, we could see that there are some dramatic fluctuations in 1987, 1990, 1993, 2001 and Maybe they are kind of outliers for our data. In turn, we drop 5% of outliers for the negative values of PATENT and PATENTSOTCK to check the relation between patents and excess stock returns again. We are curious that whether the relationship between patents and excess stock returns are changed to positive rather than negative after dropping 5% of outliers. 57

16 Figure 4-1 The weighted-average returns for our selected sample partitioned by the amount of patents Stock return (%) Date weighted-average stock returns for the sample with patents weighted-average stock returns for the sample without patents 58

17 Excess Stock Returns with Patent Count & Dropping 5%of Outliers As the table 4-9a presents, the absolute values of coefficient PATENT are much smaller than those in the Table 4-8b, especially for small-size stocks (0.0739, and compared to , and ). Similarly, values of partial correlation, which imply the marginal determination of PATENT, are also much smaller than those in the Table 4-8b for small-size stocks (0.01%, 0.00% and 0.29% compared to 8.9%, 18.13% and 40.48%). It implies that dropping 5% of outliers would decrease the marginal contribution of the explanatory variable of RDEXP in the extension of Fama and French three-factor-model regression. Still, as for PATENT, it yields a coefficient of for small-size, high-be/me stocks and a coefficient of for big-size, low-be/me stocks, which both have p-values of 5%. Though the other coefficients are positive, they are not at the 90% significance level. In other words, Patent-count premiums are still negative associated with excess stock returns even dropping outliers. 59

18 Table4-9a Extension of FF three-factor model with the number of patent [PATENT] factor after dropping 5% of outliers with negative values of PATENT R ( ] + ssmb + hhml + Book-to market equity (BE/ME) ppatent + ε Size Low Medium High Low Medium High b P-Value(b) Small Big s P-Value(s) Small Big h P-Value(h) Small Big p P-Value(p) Small Big Partial Determination% (p) Small Big Table4-9b Results before dropping 5% of outliers with negative values of PATENT R ( ] + ssmb + hhml + ppatent + ε Book-to market equity (BE/ME) Size Low Medium High Low Medium High b P-Value(b) Small Big s P-Value(s) Small Big h P-Value(h) Small Big p P-Value(p) Small Big Partial Determination% (p) Small Big

19 Excess Stock Returns with Cumulated Patent Count & Dropping 5%of Outliers For the variable PATENTSTOCK, as the table 4-10a indicates, the absolute values of coefficient PATENTSTOCK are much smaller than those in the Table 4-10b, especially for small-size stocks (0.1355, and compared to , and ). Moreover, values of partial determination, which represent the marginal contribution of PATENT, are also far smaller than those in the Table 4-8b for small-size stocks (0.08%, 0.00%, and 0.29% compared to 5.1%, 10.75% and 42.13%). It indicates that dropping 5% of outliers would lower the incremental contribution of the explanatory variable in the original regressions. There is one point different from Table 4-9a, two of six portfolios have significantly positive values of coefficient PATENTSTOCK, which are for small-size, low-be/me at 99% significance level and for big-size, high-be/me stocks at 95% significance level. Furthermore, the number of positive values of PATENTSTOCK is greater than that of negative values (4 compared to 2). In general, Cumulated Patent-Count premiums show positive relation with excess stock returns, after dropping extreme values. 61

20 Table4-10a Extension of FF three-factor model with accumulative number of patents [PATENTSTOCK] after dropping 5% of outliers with negative values of PATENTSTOCK R ( ] + ssmb + hhml + kpatentstock + ε Book-to market equity (BE/ME) Size Low Medium High Low Medium High b P-Value(b) Small Big s P-Value(s) Small Big h P-Value(h) Small Big k P-Value(k) Small Big Partial Determination% (k) Small Big Table4-10b before dropping 5% of outliers with negative values of PATENTSTOCK R ( ] + ssmb + hhml + kpatentstock + ε Book-to market equity (BE/ME) Size Low Medium High Low Medium High b P-Value(b) Small Big s P-Value(s) Small Big h P-Value(h) Small Big k P-Value(k) Small Big Partial Determination% (k) Small Big

21 4 WALD TEST Our concern in this section is to test the Hypotheses 5, 6, and 7 with the Wald test. Although the Wald test uses the coefficient estimates from the regressions, our focus is not on the coefficient estimates. Thus, we do not discuss these values. When a Wald statistic is statistically significant, it means that the explanatory variable 1 and the explanatory variable 2 have distinctive impact on the dependent variable. The degree of impact depends on the absolute values of coefficients. Discussion is divided into three sections according to the results of Wald test for testing Hypotheses 5, 6 and 7 respectively. Do R&D-expenses Premiums Have Distinctive Impact on Stock Returns from Capitalized-R&D Premiums? First, compared RDEXP with RDASSET, the indicator of RDASSET has more significant explanatory power than RDEXP for the big-size groups. The results are supporting our hypothesis 5, in which the indicator of capitalization of R&D has distinctive impact on stock returns from the measurement of R&D expenditures. In particular, for big-size stocks from high to low BE/ME portfolios, Wald test yields F-statistics of 4.52, 4.05 and 13.10, whose p-values are all lower than 5%. So, we accept Hypothesis 5 at 95% significance. However, in the small-size stock, medium and low-b/m equity stock portfolios, there is no evidence to support the Hypothesis 5. 63

22 Since the degree of impact depends on the absolute values of coefficients, taking big-size and low-be/me stocks for example, we could conclude that RDEXP has greater impact on excess stock returns than RDASSET due to their absolute values of coefficient ( compared to ). Table 4-11 Results of Wald test for R&D-related premiums Size B/M B B B S S S Estimate Of RDEXP of the regression with RDEXP Estimate of RDASSET of the regression with RDASSET Wald- Statistic(F) p-value(f) H M L H M L Note: is statistically significant at 1% level. is statistically significant at 5% level. is statistically significant at 10% level. R( ] + ssmb + hhml( + rrdexp( + ε R ( ] + ssmb + hhml( + drdasset( + ε Do Patent-count Premiums Have Distinctive Impact on Stock Returns from Cumulative Patent-Count Premiums? When in comparison PATETN with PATENTSTOCK, it doesn t reach the statistical significance in all the six portfolios. In Table 4-12, all the 6 portfolios yield values of F-statistics, which have p-value greater than 10%. We reject our Hypothesis 6 at the 90% significance. One possible explanation is that patents are highly concentrated on small proportion of companies. It means that most of corporations have no patents at all (82.19% in Table 4-8). That is, we could not tell the difference in explanatory power in stock returns between the two variables. 64

23 Table 4-12 Results of Wald test for patent-related premiums Size B/M B B B S S S Estimate of PATENT of the regression with PATENT Estimate of PATENTSTOCK of the regression with PATENTSOTCK Wald- Statistic(F) p-value(f) H M L H M L Note: is statistically significant at 1% level. is statistically significant at 5% level. is statistically significant at 10% level. R( ] + ssmb + hhml( + ppatent( + ε R ( ] + ssmb + hhml( + kpatentstock( + ε Is There Any Difference Between Indicators of R&D and Patents in Explaining the Rate of Stock Returns? First, we take PATENT and two R&D-related premiums in comparison. In general, the results of Wald test reach statistic significance except for B/M, S/M and S/L groups for comparing RDASSET and PATENT. In addition, one of the notable features of Table 4-13 is that for small-size stocks the absolute values of PATENT are generally larger than those of RDEXP and RDASSET. On the contrary, for big-size stocks, most of absolute values of RDEXP and RDASSET are greater than those of PATENT. In a consequence, it infers that both R&D-related premiums have more impact on excess stock returns than Patent-Count premiums in big-size stocks. Nevertheless, Patent-Count premiums have larger impact on excess stock returns than both R&D-related premiums in small-size stocks. 65

24 Size B/M Ratio Table 4-13 Results of Wald test across R&D and patent-related premiums Variable1 Variable 2 Estimate of Variable 1 of the regression with Variable 1 Estimate of Variable 2 of the regression with Variable 2 Wald- Statistic (F) p-value(f) B H RDEXP PATENT B H RDASSET PATENT B M RDEXP PATENT B M RDASSET PATENT B L RDEXP PATENT B L RDASSET PATENT S H RDEXP PATENT S H RDASSET PATENT S M RDEXP PATENT S M RDASSET PATENT S L RDEXP PATENT S L RDASSET PATENT Note: is statistically significant at 1% level. is statistically significant at 5% level. is statistically significant at 10% level. R( ] + ssmb + hhml( + rrdexp( + ε R( ] + ssmb + hhml( + drdasset( + ε R ( ] + ssmb + hhml( + ppatent( + ε Second, we adopt PATENTSTOCK and two R&D-related premiums in comparison. There is enough evidence to show that R&D-related premiums and PATENTSTOCK have distinctive influence on stock returns. Similarly, we find that, for small-size stocks, the absolute values of PATENTSTOCK are generally larger than those of RDEXP and RDASSET; while most of absolute values of RDEXP and RDASSET are greater than those of PATENT for big-size stocks. All in all, we could conclude that both R&D-related premiums have more impact on excess stock returns than Cumulated Patent-Count premiums in big-size stocks. However, Cumulated Patent-Count premiums have more impact on excess stock returns than both R&D-related premiums in small-size stocks. 66

25 Size B/M Ratio Table 4-14 Results of Wald test across R&D and patent-related premiums Variable1 Variable 2 Estimate of Variable 1 of the regression with Variable 1 Estimate of Variable 2 of the regression with Variable 2 Wald- Statistic (F) p-value (F) B H RDEXP PATENTSTOCK B H RDASSET PATENTSTOCK B M RDEXP PATENTSTOCK B M RDASSET PATENTSTOCK B L RDEXP PATENTSTOCK B L RDASSET PATENTSTOCK S H RDEXP PATENTSTOCK S H RDASSET PATENTSTOCK S M RDEXP PATENTSTOCK S M RDASSET PATENTSTOCK S L RDEXP PATENTSTOCK S L RDASSET PATENTSTOCK Note: is statistically significant at 1% level. is statistically significant at 5% level. is statistically significant at 10% level. R( ] + ssmb + hhml( + rrdexp( + ε R( ] + ssmb + hhml( + drdasset( + ε R ( ] + ssmb + hhml( + kpatentstock( + ε Do These Premiums Have Lag Effect on Stock Returns? In this section we investigate whether R&D and Patent-related premiums have time lag effect on excess stock returns, and add from the 1 year-time lag to 5 years-time lag at most. Based on AIC (Akaike's Information Criterion) which is a criterion for selecting among econometric models, we decide how many years of lag for RDEXP, RDASSET, PATENT and PATENTSTOCK are on excess stock returns. First, we focus the lag effect of R&D-related variables. As the Table 4-15, R&D 67

26 Expense premiums could have 3 year-lag on stock returns, and Capitalized-R&D also have 3 year-lag on stock returns, which is consistent with Chan, Lakonishok and Sougiannis (1999) and Lev and Narin (1999). Consequently, it seems reasonable to conclude that, on average, R&D-related premiums could last 3 year-lag effect on excess stock returns. Table4-15 The lag effect of R&D-related premiums on stock returns RDEXP RDASSET AIC BIC AIC BIC B/H 3 3 B/H 3 3 B/M 0 0 B/M 1 1 B/L 0 0 B/L 3 3 S/H 0 0 S/H 3 3 S/M 0 0 S/M 2 2 S/L 3 1 S/L 2 2 R( RF ( RM ( RF ( ] + ssmb + hhml ( + rrdexp ( + r1rdexp ( t 1) + r2rdexp ( t 2) + r3rdexp ( t 3) + r4rdexp ( t 4) + r5rdexp ( t 5) + ε R( RF ( RM ( RF ( ] + ssmb + hhml( + drdasset ( + d1rdasset ( t 1) + d 2RDASSET ( t 2) + d3rdasset ( t 3) + d 4RDASSET ( t 4) + d5rdasset ( t 5) + ε Akaike's Information Criterion (AIC) Sawa s Bayesian Information Criterion (BIC) Both Akaike's Information Criterion (AIC) and Sawa s Bayesian Information Criterion (BIC) are criterions for selecting among econometric models, to determine the optimum time lag for stock returns. Next, we examine the lag effect of patent-related variables on excess stock returns. As the Table 4-16 presents, Patent-Count premiums could have 5 year-lag on stock returns at least, and Cumulated Patent-Count also have 5 year-lag on stock returns. Not only is that consistent with Lev and Narin (1999) which show patent 68

27 indicators are statistically associated with subsequent stock returns, but, in particular, we find patent-related premiums at least could have 5 year-lag on excess stock returns. Table4-16 The lag effect of patent-related premiums on stock returns PATENT PATENTSTOCK AIC BIC AIC BIC B/H 5 5 B/H 5 5 B/M 3 3 B/M 5 5 B/L 2 2 B/L 0 0 S/H 3 3 S/H 0 0 S/M 0 0 S/M 5 5 S/L 5 5 S/L 5 5 R( RF ( RM ( RF ( ] + ssmb + hhml( + ppatent ( + p1patent ( t 1) + p2patent ( t 2) + p3patent ( t 3) + p4patetn ( t 4) + p5patent ( t 5) + ε R( RF ( RM ( RF ( ] + ssmb + hhml( + kpatentsto CK ( + k1patentstoc K ( t 1) + k2patentstoc K ( t 2) + k3patentstoc K ( t 3) + k4patentstoc K ( t 4) + k5patentstoc K ( t 5) + ε Akaike's Information Criterion (AIC) Sawa s Bayesian Information Criterion (BIC) Both Akaike's Information Criterion (AIC) and Sawa s Bayesian Information Criterion (BIC) are criterions for selecting among econometric models, to determine the optimum time lag for stock returns. 69