Faculty of Business and Law School of Accounting, Economics and Finance Financial Econometrics Series SWP 2013/06 Determinants of Stock Price Bubbles P.K. Narayan, S. Mishra, S.S. Sharma, and L. Ruipeng The working papers are a series of manuscripts in their draft form. Please do not quote without obtaining the author s consent as these works are in their draft form. The views expressed in this paper are those of the author and not necessarily endorsed by the School or IBISWorld Pty Ltd.
Determinants of Stock Price Bubbles Paresh Kumar Narayan, Sagarika Mishra, Susan Sunila Sharma, Ruipeng Liu Mailing address: Professor Paresh Kumar Narayan Centre for Financial Economietrics School of Accounting, Economics and Finance Faculty of Business and Law Deakin University, 221 Burwood Highway, Burwood, Victoria 3125 Australia. Email: paresh.narayan@deakin.edu.au
Determinants of Stock Price Bubbles ABSTRACT In this paper we propose a cross-sectional model of the determinants of asset price bubbles. Using 589 firms listed on the NYSE, we find conclusive evidence that trading volume and share price volatility have statistically significant effects on asset price bubbles. However, evidence from sector-based stocks is mixed. We find that for firms belonging to electricity, energy, financial, and banking sectors, and for the smallest size firms, trading volume has a statistically significant and positive effect on bubbles. We do not discover any robust evidence of a statistically significant effect of share price volatility on bubbles at the sector-level. Keywords: Asset Price; Bubbles; Cross-section; Trading Volume; Volatility. 1
1. Introduction A large literature has shown that asset prices are characterized by bubbles (see Garber, 1989; Ofek and Richardson, 2003). The existence of bubbles in asset prices has had a profound impact on financial models and hypotheses. For example, the presence of bubbles in asset prices is one of the well-argued reasons for market inefficiencies. Motivated by the importance of asset price bubbles for market inefficiencies, Scheinkman and Xiong (SX, 2003) develop a theoretical model that shows how trading volume and share price volatility impact asset price bubbles. The main outcome of the SX (2003) model is that in equilibrium, bubbles, trading volume, and price volatility co-move, and that both trading volume and price volatility have a positive effect on asset price bubbles. While the SX study represents the first comprehensive analysis of the determinants of bubbles, albeit from a purely theoretical point of view, despite the relevance of asset price bubbles on the functioning of financial markets, no empirical analysis of the determinants of bubbles exists. Generally, the literature considers two types of bubbles: rational bubbles and intrinsic bubbles. In this paper, we define asset price bubbles as the difference between the fundamental and market value of assets, and thus follow the work of Scheinkman and Xiong (2003), Abreu and Brunnermeier (2003), among others. The key motivation for our study is as follows. While there are some theoretical works that establish the relationship between bubbles, trading volume, and share price volatility, there is no empirical analysis of these relationships. The main motivation for this paper is rooted in the fact that there is no empirical evidence on how trading volume and price volatility impact asset price bubbles. Our goal in this paper is to fill this existing research gap. We, thus, undertaken a rigorous empirical 2
test of the determinants of bubbles for no fewer than 589 firms listed on the NYSE. We use a recent procedure developed by Phillips et al. (2011) to extract the number of days of bubbles in stock prices of 589 firms using time series daily data for the period 1 January 1998 to 31 December 2008. Here is what we find. Based on simple descriptive statistics of the data set, we show that firms are heterogeneous. When we estimate a cross-sectional model of the determinants of bubbles for all 589 firms taken together, we find strong evidence that trading volume and share price volatility have statistically significant effects on bubbles. We then make stocks relatively homogenous by grouping them into nine different sectors. We find that of the nine sectors in only four sectors, namely, electricity, energy, financial and banking, trading volume has a statistically significant and positive effect on bubbles. There is no robust evidence of a statistically significant relationship between share price volatility and bubbles for firms at the sectoral level. We also estimate the cross-sectional regression model for firms categorized into four different sizes and discover a statistically significant and negative relationship between share price volatility and bubbles for only the smallest sized firms. Generally the finding of a negative relationship between bubbles and share price volatility is a puzzle and we alert the literature to this puzzling result; we highlight the need for more theoretical work on this front. The rest of the paper is organized as follows. In the next section, we explain the empirical model and discuss the data and the approaches used to construct variables such as bubbles and volatility. We conclude this section with a discussion of the empirical findings. In the final section, we provide some concluding remarks and identify an agenda for future research in this relatively nascent strand of applied research in financial economics. 3
2. Model and Results 2.1. Empirical Model Motivated by the theoretical work of SX (2003), our empirical model takes the following form: (1) Equation (1) is a cross-sectional model of the determinants of bubbles. In this model, based on the theoretical postulate of SX (2003), bubbles (B) are determined by trading volume (TV) and asset price volatility (PV). SX (2003) show that in equilibrium, an asset owner will only sell his asset when his view of the fundamental exceeds that of an agent. And, as this process repeats infinitely many times in any finite time period, there will be a trading frenzy. The resulting trading frenzy increases average trading volume. An increase in trading volume, thus, contributes to more bubbles. From elsewhere in the literature, the evidence on bubbles and trading volume can be summarised as follows. Hong and Stein (2007) claim that classic equity bubbles are loud - high prices and are accompanied by large trading volume as investors purchase in anticipation of capital gains. Carlos et al. (2006) suggest that in the South Sea Bubble of 1720, transactions in the Bank of England stock (one of the three bubble stocks) were three times larger than in the prior three years. Furthermore, Ofek and Richardson (2003) document that the stock share turnover during the years before the Crash of 1929 in the US were abnormally high by historical standards. In addition, in the dot-com bubble years of the late nineties, interest stocks accounted for nearly 20% of the trading volume in the stock market. It was found that at the peak of the dotcom bubble, internet stocks had three times the turnover of similar non-dotcom stocks. Ofek and Richardson (2003), for instance, state that in February 2000, internet firms represented 6% of the public equity market and 19% of the trading volume. 4
SX (2003) also show that asset price volatility will have a positive effect on asset price bubbles. They show, using a framework of two groups of agents, that when the variance in beliefs of agents in the two groups varies, it gives rise to price volatility. This changing variance in beliefs, and as a result in asset prices, is a source of large bubbles in the SX model. 1 We use four measures of price volatility. The first measure of price volatility (PV1) is simply the logarithmic difference between high and low prices, which is proposed by Gallant et al. (1999) and Alizadeh et al. (2002): 1 ln ln (2) The second measure of price volatility (PV2), proposed by Parkinson (1980), has the following form: 2 0.361 / (3) The third measure of price volatility (PV3) is based on the work of German and Klass (1980). It has the following form: 3 0.5 2 2 1 (4) The final measure of price volatility (PV4) owes to the work of Rogers and Satchel (1991). It has the following form: 4 (5) In these models, denotes the natural logarithmic form of the variables; and HP, LP, OP, and CP are high price, low price, opening price, and closing price, respectively. One referee of this journal suggested that we also consider a principal components 1 In related work, Topol (1991) suggests that a bubble is initiated and displays some excess volatility as soon as agents have mimetic contagion behaviour and/or correlated present values. When the bubble blows up, the excess volatility decreases as the behaviour becomes uncorrelated. This drives the stock price away from its present value dynamics. 5
measure of volatility; we do. We generate a principal component from amongst the four measures of volatility and use this as an additional proxy for volatility. We compute bubbles by using the econometric procedure developed by Phillips et al. (2011), which is based on the following regression model: 6 Here, SP is the stock price of a particular firm at time t and the optimal lag length k is chosen by applying the Schwarz Information Criterion. The model is nothing but the augmented Dickey-Fuller (ADF) test for a unit root against the alternative of an explosive root; that is, the null hypothesis is tested as : 1 against the right-tailed alternative hypothesis : 1. Following Phillips et al. (2011), we adopt a recursive regression procedure, whereby the regression model is estimated using subsets of the sample data incremented by one observation recursively. We then match the time series of the recursive test statistic (where subscript r is some fraction of the total sample) against the right-tailed critical values of the asymptotic distribution of the standard Dickey-Fuller t-statistic. The corresponding t-test statistic and their critical values are generated following the procedure outlined in Phillips et al. (2011). We obtain the number of days for which the computed t-statistic is greater than the critical value. When the t-statistic is greater than the critical value, the stock price is above its fundamental value. Similarly, from these t-statistics and critical values, we compute the maximum days for which continuously the t-statistic is greater than the critical value. This gives us the continuous days of bubbles. 6
2.2. Results We search for bubbles using daily data on stock prices for each of the 589 firms listed on the NYSE over the period 1 January 1998 to 31 December 2008. Data on trading volume and share price volatility (based on the four measures outlined in section 2.1) are averaged over the period 1 January 1998 to 31 December 2008 for each of the 589 firms. We consider this relatively recent time period in order to ensure that our sample size does not suffer from the survivorship bias. However, we believe that no sample choice is immune from the survivorship bias; one is almost always going to have to entertain survivorship bias. For example, if we considered a sample after the start date of 1998 we would have more stocks in our sample. We choose the time period we did in order to ensure that we can successfully extract bubbles. Our approach leads to a cross-sectional dataset of the determinants of bubbles. We obtain all data used in this paper from the Centre for Research and Securities Prices (CRSP). In Table 1, we present a summary of our bubbles dataset. In particular, we report the mean number of days of bubbles and their standard deviation for firms in each of the nine sectors. INSERT TABLE 1 We notice that firms in the electricity and energy sectors on average have the most number of days of bubbles compared to firms in the rest of the sectors. The coefficient of variation for firms belonging to these two sectors implies that firms in these sectors experience the least volatile bubbles. By comparison, firms in the banking sector, followed by firms in the medical sector, experience the least number of bubbles. In Figure 1, we plot the mean share price by sector and in Figure 2 we plot the coefficient of variation of share price for each of the nine sectors. Two main features of the data based on share prices are noticeable and which provide further credence that firms belonging to each of these sectors are heterogeneous. First, the 7
mean share price differs by sector. Firms in the medical and energy sectors have the highest share price while firms belonging to supply, food, and financial sectors have the lowest share price. Second, volatility is lowest for firms in the financial and food sectors, while it is highest for firms in the energy and engineering sectors. INSERT FIGURES 1 AND 2 The heterogeneity of sectors is further confirmed by some simple descriptive statistics. In Table 2, we report the descriptive statistics namely, mean, coefficient of variation (CV), skewness, and kurtosis for firm returns, trading volume and volatility (PV1). The descriptive statistics are reported for firms belonging to each of the nine sectors. We only report the descriptive statistics for PV1 as the statistics for the other three proxies of volatility are broadly similar. On all indicators there is strong evidence that sectors are different with respect to bubble activity and its determinants. INSERT TABLE 2 To get a feel of the relationship between asset price bubbles, trading volume, and share price volatility, we also report the unconditional correlation coefficients between bubbles and trading volume (TV), between bubbles and each of the four measures of price volatility (PV1, PV2, PV3, and PV4), and between bubbles and the principal component of volatility (PC1). These are reported in Table 3. Expect for the medical sector and to some extent the supply sector where price volatility has a statistically significant correlation with bubbles in the rest of the sectors the correlations are statistically insignificant. Trading volume meanwhile is statistically significantly correlated with bubbles in three sectors (banking, energy, and electricity). Generally, then, the correlation relationships are weak. INSERT TABLE 3 8
We begin with a cross-sectional model consisting all 589 stocks. The aim here is to get an idea of what to expect of the impact of trading volume and volatility on bubbles when stocks are treated as homogeneous when they are not. The results are reported in Table 4. We find that in all four models, trading volume has a statistically significant positive effect while price volatility has a statistically significant negative effect on bubbles. Therefore, the results on the determinants of bubbles are strong. The key question is: do these results hold for different sectors when we make the stocks relatively more homogenous by considering cross-section of stocks by sector? This is a question we answer next. INSERT TABLE 4 The results on the determinants of bubbles by sector are reported in Table 5, which is divided into several parts to distinguish results by sector. In panel A, we report the results for the banking sector. The organization of the results is as follows. To test the statistical significance of trading volume and volatility, the p-values are reported in parenthesis. In the final column of the table, the adjusted R-squared of the cross-section regression model is reported. Essentially, because we have four measures of volatility, we end up estimating four cross-section regression models per sector. The results for volume are reported in column 2, while results for volatility are reported in columns 3 to 6. INSERT TABLE 5 The findings reveal that volume across all four models has a statistically significant (at the 5% level) effect on bubbles. The effect of volume is robust in that the magnitude of the effect when the number of days of bubbles is the dependent variable ranges from 0.15 to 0.17. The second source of robustness is in terms of statistical significance. We find that all results are statistically significant at the 5% 9
level. With respect to the effect of volatility on bubbles, we find that volatility has a statistically insignificant effect. In Panel B, we present results for the financial sector. We find that across the four models, trading volume has a positive and statistically significant effect on bubbles in two models while the price volatility has a statistically insignificant effect. The results based on firms in the manufacturing sector (Panel D), food sector (Panel F), and engineering sector (Panel I) reveal that neither trading volume nor price volatility have any statistically significant effects on bubbles. Results for the supply and medical sectors are reported in Panels C and E, respectively. We observe that two out of the four proxies for volatility have a statistically significant and positive effect on the number of days of bubbles in the supply sector whereas in the medical sector, one out of the four proxies of volatility has a negative and statistically significant effect on bubbles. However, we do not find any evidence that trading volume has any statistically significant effects on bubbles. Finally, results for the energy and electricity sectors are reported in Panels G and H, respectively. We find that across all four models, volume has a statistically significant and positive effect. However, firms in both sectors do not experience any statistically significant effect of price volatility on bubbles. As suggested by one referee of this journal, we extract the principal component of volatility from amongst the four measures of volatility. This means we run a separate regression model, where instead of price volatility we have a principal component of volatility together with the trading volume variable as determinants of bubbles. The results are reported in Table 6. We find that like with the individual measures of volatility that in the medical sector volatility (its principal components) has a negative and statistically significant effect on bubbles. In addition, there is 10
evidence that volatility has a negative and statistically significant effect on bubbles in the engineering sector. Therefore, while evidence that volatility has a statistically significant effect on bubbles remains weak the evidence with a principal component of volatility is found for additional sector engineering but not for the supply sector for which individual measures of volatility suggested a positive and statistically significant relationship. In terms of the relationship between trading volume and bubbles we find, as we did before, that trading volume has a statistically significant and positive effect on bubbles in three sectors banking, energy, and electricity. While the relationship between trading volume and bubbles and price volatility and bubbles is mixed at the sector-level for the market as a whole (that is, for a cross-section of all 589 stocks) the results suggest that trading volume has a statistically significant positive and volatility has a statistically significant negative effect on bubbles; see last row of table 6. The main implication of the sector versus market results is that sectors are heterogeneous and the strong results at the market level are dictated by a handful of sectors. INSERT TABLE 6 To conclude the results, we undertake a size-based analysis of the determinants of bubbles. Essentially, we divide our sample of 589 firms into four sizes based on market capitalization of firms. Following Narayan and Sharma (2011) we rank each of 589 stocks from highest to lowest based on market capitalisation. The first 147 stocks are the largest sized stock while the bottom 147 stocks are the smallest sized stocks. This leads to four size-based cross-section regression models of the determinants of bubbles. Before we examine the regression results, it is imperative to examine some data properties of each of the four sizes of firms to gauge how firms 11
in each of the size categories behave. Across all variables for different sizes of firms, there are differences in terms of mean, coefficient of variation, skewness, and kurtosis of all variables. To conserve space, we do not report the summary statistics here but they are available upon request. The implication of these descriptive statistics is that firms in each of the four size categories are different. We also plot the data on the number of days of bubbles per each firm size in Figure 3. We find that the smallest size firms have on average the lowest number of days of bubbles compared to large size firms. Firms in size 1 have around 61 days of bubbles and firms in size 2 have around 83 days of bubbles. By comparison, firms in sizes 3 and 4 on average have around 112 days of bubbles. INSERT FIGURE 3 The results for each of the four sizes of firms are reported in Table 7. There are two main features of these results. First, we notice that volume is only statistically significant (with a positive sign) for firms in size 1. For the relatively large size firms (sizes 2-4), volume has a statistically insignificant effect on bubbles. This result suggests that the smallest size firms behave in a manner consistent with the SX (2003) description of the relationship between trading volume and bubbles; however, such a relationship is not seen for the bulk of the firms in our sample. INSERT TABLE 7 Second, we find that inconsistent with theory, for the smallest size firms volatility has a statistically significant and negative effect on bubbles. Moreover, this negative relationship is only found for the smallest sized firms, so effectively for around 25% of firms in our sample. For the rest of the firms, the relationship is statistically insignificant. While we find some evidence, in particular with respect to the trading volume and bubbles nexus, consistent with theory, the results on the 12
relationship between volatility and bubbles is inconsistent with existing theory. There are no acceptable explanations on why volatility should have a statistically significant and negative effect for small sized firms. Our results, thus, present a theoretical challenge for future work. It should be noted that our work here is extremely exploratory in nature ours is actually the first attempt to model the determinants of bubbles following the theoretical guidelines in SX (2003). Given the extremely nascent stage of research on the determinants of bubbles, we wish not to speculate on reasons behind the negative relationship between volatility and bubbles; rather, we declare this as an issue for further theoretical work. 3. Concluding Remarks Our work is the first to empirically examine the impact of trading volume and price volatility on bubbles, and we unravel two key findings. First, when we disaggregate firms and categorize them into sectors, we find that of the nine sectors in only four sectors, namely, electricity, energy, financial and banking, volume has a statistically significant and positive effect on bubbles. This finding takes us back to our motivation for undertaking a firm-level (and hence sector-based) analysis of the determinants of bubbles. We show that sector-based firms were heterogeneous. This means that the strong statistically significant effects of trading volume and volatility on bubbles we obtain from a full-sample (589 stocks) cross-sectional model is dictated by only a fraction of stocks in our sample. The second finding is that when we examine the impact of volatility on bubbles for each of the nine sectors, the evidence is mainly statistically insignificant. We use four proxies for volatility to test whether or not the relationship between 13
volatility and bubbles is dependent on the measure of volatility; we discover robust evidence of a statistically insignificant relationship. Finally, when we form cross-section models based on four different sizes of firms, we find evidence of a statistically significant effect of volume on bubbles for the smallest size firms (size 1). For the smallest size firms, we also discover a statistically significant and negative effect of price volatility on bubbles a finding replicated when considering a model of all 589 stocks and inconsistent with the theoretical model of SX (2003). This finding is a puzzle and future research should consider providing a theoretical basis for the existence of a negative relationship between share price volatility and bubbles for small size firms. To say nothing about the reasons for this relationship will draw criticism. In our view, as much as we leave this issue for further investigation, there are two potential reasons for this conflicting result. First, the results can be attributed to our small sample size; that is, in some sectors we have relatively small number of stocks. Future studies can potentially consider a larger cross-section of stocks. Second, the results may simply be due to our cross-section estimation approach. Further work that examines the relationship between asset price bubbles and their determinants based on time series and panel data models should be in demand. These types of models allow one to capture the dynamics of not only the bubbles but also their determinants therefore offering a richer characterisation of the model. It is here that we conclude. 14
References Abreu, D., and Brunnermeier, M.K., (2003) Bubbles and crashes, Econometrica, 71, 173-204. Alizadeh, S., Brandt, M.W., Diebold, F.X., (2002). Range-based estimation of stochastic volatility models, The Journal of Finance, 57, 1047-1091. Carlos, A., Neal, L., and Wandschneider, K., (2006) Dissecting the anatomy of exchange alley: The dealings of stockjobbers during and after the South Sea bubble, Unpublished paper, University of Illinois. German, M.B., and Klass, M.J., (1980) On the estimation of security price volatilities from historical data, Journal of Business, 53, 67-78. Gallant, A.R., Hsu, C.T., Tauchen, G., (1999) Using daily range data to calibrate volatility diffusions and extract the forward integrated variance. The Review of Economics and Statistics, 81, 617-631. Garber, P., (1989) Tulipmania, Journal of Political Economy, 97, 535-560. Hong, H., and Stein, J.C., (2007) Disagreement and the stock market, Journal of Economic Perspectives, 21, 109-128. Narayan, P.K., and Sharma, S.S., (2011) New evidence on oil price and firm returns, Journal of Banking and Finance, 35, 3253-3262. Ofek, E., and Richardson, M., (2003) Dotcom Mania: The rise and fall of internet stock prices, Journal of Finance, 58, 1113-1137. Parkinson M., (1980) The extreme value method for estimating the variance of the rate of return, Journal of Business, 53, 61-65. 15
Phillips. P.C.B., Wu, Y., and Yu, J., (2011) Explosive behavior in the 1990s NASDAQ: When did exuberance escalate asset values? International Economic Review, 52, 201-226. Rogers, L.C.G., and Satchell, S.E., (1991) Estimating variance from high, low, and closing prices, Analysis of Applied Probability, 1, 500-512. Scheinkman, J.A. and Xiong, W., (2003) Overconfidence and speculative bubbles, Journal of Political Economy, 111, 1183 1219. Topol, R., (1991) Bubbles and volatility of stock prices: Effect of mimetic contagion, The Economic Journal, 101, 786-800. 16
Figure 1: Mean share price by sector 50 45 40 35 30 25 20 15 10 5 0 In this figure, we plot the mean share price for firms in each of the nine sectors. The nine sectors are: electricity, energy, engineering, financial, food, manufacturing, medical, supply, and banking. There are 90 firms in the electricity sector, 44 firms in the energy and engineering sectors, 86 firms in the financial sector, 37 firms in the food sector, 89 firms in the manufacturing sector, 41 firms in the medical sector, 85 firms in the supply sector, and 73 firms in the banking sector. 17
Figure 2: Coefficient of variation by sector 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 In this figure, we plot the coefficient of variation for firms in each of the nine sectors. The nine sectors are: electricity, energy, engineering, financial, food, manufacturing, medical, supply, and banking. There are 90 firms in the electricity sector, 44 firms in the energy and engineering sectors, 86 firms in the financial sector, 37 firms in the food sector, 89 firms in the manufacturing sector, 41 firms in the medical sector, 85 firms in the supply sector, and 73 firms in the banking sector. 18
Figure 3: Number of days of bubbles by firm size SIZE1 SIZE2 280 250 240 200 200 160 150 120 100 80 40 50 0 25 50 75 100 0 25 50 75 100 SIZE3 SIZE4 400 320 280 300 240 200 200 160 120 100 80 40 0 25 50 75 100 0 25 50 75 100 In this figure, we plot the number of days of bubbles for firms belonging to each of the four sizes. Size 1 represents the smallest sized firms while size 4 represents the largest size firms. 19
Table 1: Summary statistics of bubbles data Number of days of bubbles Mean Standard deviation Coefficient of variation Electricity (90) 108 71.6 0.66 Energy (44) 127 71.5 0.56 Banking (73) 56 23.9 0.43 Engineering (44) 89 65.9 0.74 Financial (86) 86 62.9 0.73 Food (37) 80 62.5 0.78 Manufacturing (89) 97 80.2 0.83 Medical (41) 70 50.3 0.72 Supply (85) 88 81.6 0.93 This table reports the mean and the variance of the number of days of bubbles. The mean, standard deviation, and coefficient of variation relating to bubbles are reported in columns 2, 3, and 4, respectively. The number of firms in each sector is reported in parenthesis beside the sector in column 1. The number of days of bubbles is computed based on Equation (6). 20
Table 2: Descriptive statistics by sector Banking Returns Volume PV1 Food Returns Volume PV1 Mean.00006 1.23 0.03 mean -.0001 1.11 0.03 CV 446.76 4.52 0.89 CV -258.96 1.82 0.75 skewness -6.86 19.01 7.66 skewness -6.18 5.79 3.28 Kurtosis 352.54 620.39 334.52 kurtosis 213.26 91.25 27.57 Electricity Returns Volume PV1 Manufacturing Returns Volume PV1 Mean -.0001 1.86 0.03 mean -.00006 1.97 0.03 CV -213.38 4.15 0.79 CV -191.07 3.64 0.88 skewness -7.66 12.43 4.93 skewness -6.31 9.73 72.20 Kurtosis 301.83 277.48 112.30 kurtosis 205.71 153.50 18098.25 Energy Returns Volume PV1 Medical Returns Volume PV1 Mean.0001 2.01 0.03 mean -.0001 2.58 0.03 CV 107.66 1.90 0.73 CV -607.27 2.17 0.77 skewness -7.30 5.53 3.57 skewness -7.35 8.73 3.65 Kurtosis 217.04 59.66 41.76 kurtosis 223.14 201.38 43.22 Engineering Returns Volume PV1 Supply Returns Volume PV1 Mean -.0004 0.89 0.03 mean -.0001 2.39 0.03 CV -228.03 2.05 1.13 CV -203.44 3.48 0.74 skewness -5.62 5.43 136.43 skewness -5.65 10.11 8.29 Kurtosis 192.25 57.25 34494.39 kurtosis 147.60 222.36 627.67 Financial Returns Volume PV1 mean -.0005 0.33 0.02 CV -111.99 3.35 1.07 skewness -10.66 14.24 6.63 kurtosis 485.55 543.88 138.04 In this table, we report the descriptive statistics namely, mean, coefficient of variation (CV), skewness, and kurtosis for firm returns, trading volume and volatility (PV1). The descriptive statistics are reported for firms belonging to each of the nine sectors. We only report the descriptive statistics for PV1 as the statistics for the other three proxies of volatility are broadly similar. 21
Table 3: Correlation coefficients between bubbles and trading volume and bubbles and price volatility Bankin g Finance Supply Manufactu re Medical Food Energy Electricit y Engineerin g Full Sample TV 0.25* 0.05 0.03 0.11-0.13-0.05 0.37* 0.36* 0.05 0.14* PV1 0.05-0.13 0.18 0.01-0.29* 0.06 0.10-0.01-0.10-0.03 PV2-0.02-0.14 0.26* 0.01-0.30* 0.06 0.15 0.03-0.14-0.05 PV3 0.04-0.15 0.21* 0.02-0.32* 0.02 0.14 0.05-0.17-0.04 PV4-0.05 0.02-0.13-0.01-0.34* -0.04 0.15-0.05-0.35* -0.06 PC1 0.01-0.13 0.15 0.01-0.31* 0.04 0.15 0.01-0.21-0.05 This table reports simple unconditional correlations between bubbles and trading volume (TV), between bubbles and each of the four measures of price volatility (PV1, PV2, PV3, and PV4), and between bubbles and the principal component of volatility (PC1). * denotes significant at 10%. 22
Table 4: Determinants of bubbles for a cross-section of all 589 stocks Intercept Log TV Log PV1 Log PV2 Log PV3 Log PV4 1.69** 0.10*** -0.29** 2% (0.02) (0.00) (0.04) 1.57** 0.10*** -0.16** 2% (0.03) (0.00) (0.03) 1.67** 0.10*** -0.14** 2% (0.02) (0.00) (0.05) 2.31 (0.00) 0.09*** (0.00) -0.07** (0.05) 2% In this table, we report the determinants of the number of days of bubbles for a cross-section of all 598 firms based on the following cross-section regression model: Here, B represents bubbles, computed based on Equation (6), and is the number of days of bubbles; TV is the trading volume; and PV is price volatility. We use four proxies for price volatility. Hence, we have four cross-section regression models. 23
Table 5: Determinants of bubbles for each sector Panel A: Results for the banking sector Intercept Log TV Log PV1 Log PV2 Log PV3 Log PV4 1.11 0.15** -0.14 4% (0.70) (0.03) (0.83) -1.44 0.17** -0.38 5% (0.67) (0.02) (0.35) 0.76 0.16** -0.11 4% (0.80) (0.03) (0.75) 1.07 (0.44) 0.15** (0.03) -0.08 (0.57) 4% Panel B: Results for the financial sector Intercept Log TV Log PV1 Log PV2 Log PV3 Log PV4 2.61** 0.02** -0.31 2% (0.04) (0.03) (0.26) 2.29* 0.02** -0.19 2% (0.10) (0.02) (0.21) 2.21 0.01-0.20 2% (0.11) (0.83) (0.18) 3.87*** (0.00) 0.03 (0.63) 0.15 (0.85) 0.2% Panel C: Results for the supply sector Intercept Log TV Log PV1 Log PV2 Log PV3 Log PV4 8.67*** -0.05 1.16 4% (0.00) (0.61) (0.09) 9.56*** -0.03 0.67** 5% (0.00) (0.669) (0.05) 9.55*** -0.04 0.65** 5% (0.00) (0.63) (0.05) 1.58 (0.40) 0.06 (0.51) -0.21 (0.17) 2% Panel D: Results for the manufacturing sector Intercept Log TV Log PV1 Log PV2 Log PV3 Log PV4 2.54 0.09-0.12 1% (0.31) (0.28) (0.83) 2.98 0.08-0.01 1% (0.16) (0.29) (0.98) 3.25 0.08 0.03 1% (0.12) (0.30) (0.90) 2.86 (0.07) 0.08 (0.29) -0.02 (0.89) 1% Panel E: Results for the medical sector Intercept Log TV Log PV1 Log PV2 Log PV3 Log PV4-0.20-0.10-1.17 3% (0.96) (0.93) (0.12) -0.84-0.00-0.61 4% (0.83) (0.99) (0.09) -1.19 (0.75) -0.00 (0.99) -0.65 (0.07) 5% 24
-1.51 (0.68) 0.00 (0.99) -0.69** (0.05) 7% Panel F: Results for the food sector Intercept Log TV Log PV1 Log PV2 Log PV3 Log PV4 5.13** -0.03 0.19 5% (0.05) (0.80) (0.75) 5.12-0.03 0.09 6% (0.06) (0.81) (0.77) 4.69-0.03 0.03 6% (0.06) (0.79) (0.91) 4.32*** (0.00) -0.03 (0.77) -0.02 (0.80) 6% Panel G: Results for the energy sector Intercept Log TV Log PV1 Log PV2 Log PV3 Log PV4 3.71* 0.20*** 0.51 11% (0.08) (0.01) (0.34) 4.66* 0.20*** 0.35 13% (0.05) (0.01) (0.21) 4.57* 0.20*** 0.34 13% (0.06) (0.01) (0.23) 2.76** (0.03) 0.19*** (0.01) 0.09 (0.34) 11% Panel H: Results for the electricity sector Intercept Log TV Log PV1 Log PV2 Log PV3 Log PV4 0.84 0.22*** -0.16 12% (0.61) (0.00) (0.66) 1.51 0.22*** 0.003 11% (0.38) (0.00) (0.98) 1.53 0.22*** 0.005 11% (0.38) (0.00) (0.97) 1.29 (0.16) 0.22*** (0.00) -0.03 (0.67) 12% Panel I: Results for the engineering sector Intercept Log TV Log PV1 Log PV2 Log PV3 Log PV4 0.65 0.10-0.67 3% (0.86) (0.46) (0.35) 0.25 0.08-0.38 3% (0.07) (0.49) (0.28) -0.18 0.09-0.42 5% (0.96) (0.43) (0.20) -0.06 (0.98) 0.11 (0.31) -0.38 (0.10) 5% In this table, we report the determinants of the number of days of bubbles for firms in each of the nine sectors based on the cross-section regression model: Here, B represents bubbles, computed based on Equation (6), and is the number of days of bubbles; TV is the trading volume; and PV is price volatility. We use four proxies for price volatility. Hence, we have four cross-section regression models. 25
Table 6: Cross-section results when principal components of volatility is used as a determinant Intercept Log TV Principal Component of 4 measures of volatility Banking 1.51* 0.16** -0.04 4% (0.08) (0.02) (0.50) Finance 3.89*** 0.02-0.06 1% (0.00) (0.78) (0.27) Supply 4.28*** -0.02 0.12 1% (0.00) (0.75) (0.17) Manufacture 3.02*** 0.08-0.01 1% (0.00) (0.29) (0.95) Medical 3.88** -0.001-0.18* 4% (0.02) (0.98) (0.07) Food 4.44*** -0.02 0.02 1% (0.00) (0.79) (0.82) Energy 1.91** 0.19*** 0.08 12% (0.06) (0.01) (0.23) Electricity 1.47* 0.22*** -0.01 11% (0.07) (0.00) (0.84) Engineering 2.68* 0.11-0.17* 2% (0.08) (0.31) (0.10) Full sample 2.77*** (0.00) 0.10*** (0.00) -0.05** (0.02) 2% In this table, we report the determinants of the number of days of bubbles for cross-sections representing different sectors and a cross-section containing all 598 firms (full-sample) based on the following cross-section regression model: Here, B represents asset price bubbles, computed based on Equation (6), and is simply the number of days of bubbles; TV is the trading volume; and PV is price volatility. The price volatility is proxied by a principal component of the four specific measures of price volatility. Hence, we have four crosssection regression models. 26
Table 7: Results for cross-sections of size-based firms Panel A: Size 1, Dependent variable = Log of the number of days t>cv Intercept Log TV Log PV1 Log PV2 Log PV3 Log PV4-4.16 0.46*** -0.84 - - - 7.5 (0.082) (0.007) (0.10) -3.74 0.43*** - -0.38** 6.2 (0.13) (0.01) (0.02) -3.64 0.43*** - - -0.37** - 6 (0.14) (0.01) (0.03) -1.28 (0.53) 0.37** (0.03) - - - -0.10 (0.35) 3.3 Panel B: Size 2, Dependent variable = Log of the number of days t>cv Intercept Log TV Log PV1 Log PV2 Log PV3 Log PV4 2.43 0.02-0.36 - - - -0.7 (0.46) (0.93) (0.27) 1.88 0.02 - -0.24 - - 0.04 (0.57) (0.94) (0.16) 2.29 0.02 - - -0.19 - -0.6 (0.49) (0.94) (0.26) 2.89 (0.36) 0.03 (0.91) - - - -0.10 (0.20) -0.26 Panel C: Size 3, Dependent variable = Log of the number of days t>cv Intercept Log TV Log PV1 Log PV2 Log PV3 Log PV4 4.49-0.01-0.008 - - - -1.7 (0.36) (0.97) (0.98) 5.17-0.02-0.06 - - -1.6 (0.30) (0.95) (0.68) 4.98-0.02 - - 0.04 - -1.7 (0.31) (0.96) (0.77) 5.62 (0.24) -0.04 (0.91) - - - 0.09 (0.26) -0.61 Panel D: Size 4, Dependent variable = Log of the number of days t>cv Intercept Log TV Log PV1 Log PV2 Log PV3 Log PV4 0.82 0.23-0.09 - - - -1.1 (0.85) (0.47) (0.74) 0.87 0.24 - -0.02 - - -1.2 (0.85) (0.45) (0.90) 0.82 0.24 - - -0.02 - -1.2 (0.86) (0.45) (0.86) 1.07 (0.81) 0.23 (0.49) - - - -0.02 (0.73) -1.1 In this table, we report the determinants of the number of days of bubbles for firms in the largest size category (size 4). The cross-section regression model is of the following form: Here, B represents bubbles, computed based on Equation (6), and is the number of days of bubbles; TV is the trading volume; and PV is price volatility. We use four proxies for price volatility. Hence, we have four cross-sectional regression models. 27