Commonality in Returns, Order Flows, and Liquidity in the ...

552 views

Published on

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
552
On SlideShare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
7
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Commonality in Returns, Order Flows, and Liquidity in the ...

  1. 1. Commonality in Returns, Order Flows, and Liquidity in the Greek Stock Market Peter G. Dunnea Central Bank & Financial Services Authority of Ireland Michael J. Mooreb,* Queen’s University, Belfast Vasileios G. Papavassiliouc Queen’s University, Belfast This Version 1st April 2010 JEL classification: G10, G14, G15 Keywords: Market Microstructure, Common Factors, Order Flow, Liquidity a Central Bank & Financial Services Authority of Ireland, PO Box 559, Dame Street, Dublin 2, Ireland. Email: peter.dunne@centralbank.ie b School of Management and Economics, Queen’s University, Belfast, BT7 1NN, Northern Ireland, United Kingdom. Email: m.moore@qub.ac.uk c School of Management and Economics, Queen’s University, Belfast, BT7 1NN, Northern Ireland, United Kingdom. Email: vpapavassiliou01@qub.ac.uk *Corresponding author. Tel/Fax.: (++44) 28 9097 3208/5156 1
  2. 2. Commonality in Returns, Order Flows, and Liquidity in the Greek Stock Market Abstract Using a unique high-frequency data set on a comprehensive sample of Greek blue-chip stocks, spanning from September 2003 through March 2006, this note assesses the extent and role of commonality in returns, order flows, and liquidity. It also formally models aggregate equity returns in terms of aggregate equity order flow, in an effort to clarify order flow’s importance in explaining returns for the Athens Exchange market. Almost a quarter of the daily returns in the FTSE/ATHEX20 index is explained by aggregate own-order flow. In a second step, using principal components and canonical correlation analyses, we document substantial common movements in returns, order flows, and liquidity, both on a market-wide basis as well as on an individual security basis. These results emphasise that asset pricing and liquidity cannot be analyzed in isolation from each other. 2
  3. 3. 1. Introduction A prominent field of research in the market microstructure area is the subject of commonality in returns, order flows, and liquidity. The seminal empirical papers in this area are those of Chordia et al. (2000), Huberman and Halka (2001), and Hasbrouck and Seppi (2001). All three studies find evidence of commonality in liquidity for U.S. listed stocks. Hasbrouck and Seppi (2001) also find that common factors exist in signed order flows and returns of the 30 Dow stocks. Evidence of commonality has also been found in non-U.S. markets (see Brockman and Chung, 2002 (Hong Kong); Fabre and Frino, 2004; Domowitz et al., 2005 (Australia); Kempf and Mayston, 2005 (Germany)). The objective of this case study is to provide fresh results on this topic for the Athens Stock Market. To the best of our knowledge, no previous similar research has ever been performed for the Athens Exchange. Our high-frequency data set constitutes a much larger sample than the majority of related literature and therefore, can provide more robust evidence regarding commonality. The Athens Exchange is Southeastern Europe’s largest stock market and it plays a prominent role in the region, thus, the findings of this study may be viewed as a benchmark for Eastern Europe and other markets of similar size and structure such as those in the Middle East and Africa. Since the structural form of equity markets varies considerably (hybrid markets; quote-driven markets; order-driven markets), the extent to which the empirical findings, especially those of larger and more liquid markets, can be generalized to other smaller ones with different market structures, needs to be explored. First we show that almost a quarter of the daily aggregate equity index variation can be explained by aggregate own-order flows. Next, we analyze the presence of 3
  4. 4. commonality in the returns, order flows and liquidity, both on a market-wide basis as well as on an individual security basis. Our results suggest that common factors have a significant impact on the relationship between returns and order flows. The presence of important commonalities in measures of liquidity is also documented, providing support to the notion that liquidity contributes to systematic risk. Evidence of systematic liquidity highlights the fact that liquidity shocks transmitted across securities can cause market-wide effects, and has important implications for asset pricing since it suggests that liquidity variation is likely to be a source of priced risk (Pastor and Stambaugh, 2003; Acharya and Pedersen, 2005). The remainder of the paper is organized as follows. Section 2 provides some reference to the most important literature in this field of research and particularly the contributions that influence our empirical methods. Section 3 presents the market architecture of the Athens Exchange and describes the data set. Section 4 discusses the estimation results. Finally, section 5 offers some concluding remarks. 2. Microstructure, Order flow and Commonality: A Selective Review Order flow is regarded as a powerful transmission mechanism of information to price, regardless of institutional structure, and provides additional power beyond conventional volume measures in explaining equity returns1. Evans and Lyons (2002) and Rime (2000), show that daily order flow does remain strongly positively related to daily FX price changes. More recently, Dunne et al. (2010), formally model aggregate equity returns in terms of aggregate equity order flow and related cross country differences in 1 Based on Chordia and Subrahmanyam (2004), two of the main reasons why order imbalances are more efficient than volume in explaining returns is (a) returns can be altered by high absolute order imbalances as market makers try to re-adjust their inventory (b) order imbalances might be related to future returns, if the investor interest they signal is autocorrelated. 4
  5. 5. equity order flows to exchange rate movements. Their results suggest that almost 60 percent of the daily return variation in the S&P100 index and 40 percent of the CAC40 return fluctuations are explained jointly by exchange rate returns and macroeconomic order flows. Microstructure studies have given considerable attention to the notion of liquidity and how information transmits to prices (so-called ‘price discovery’). Market microstructure literature already provides explanations for the presence of the bid-ask spread based on asymmetric information (Glosten and Milgrom, 1985; Kyle, 1985) and inventory considerations (Amihud and Mendelson, 1980, 1982; Ho and Stoll, 1981, 1983) of market makers. Theories of depth complement asymmetric information models of the spread and highlight the importance of the quantity dimension in assessing overall market liquidity (see Kavajecz, 1999; Charoenwong and Chung, 2000). However, Huberman and Halka (2001) argue, that the effect of market makers’ presence on spread and depth in actual markets is not obvious particularly at an aggregate level. The aforementioned models say little about systematic variations in liquidity that affect many stocks simultaneously. Chordia et al. (2000) note that co-movements in optimal inventory levels lead to co- movements in individual bid-ask spreads and quoted depth. Also, covariation in liquidity may be induced by asymmetric information, since privileged market information is possessed only by few traders. The studies by Huberman and Halka (2001) and Hasbrouck and Seppi (2001) also provide evidence of co-movement in microstructure characteristics at a market-wide level thereby raising the prospect of a liquidity risk premium. Hasbrouck and Seppi (2001) employ principal component and 5
  6. 6. canonical correlation analyses to measure such effects and this is the approach we take in the following analysis. 3. Market Architecture and the Data The Athens Exchange (ATHEX), formerly known as the Athens Stock Exchange, was established in 1876 and is the only official market for shares in Greece. In May 2001, the Athens Exchange was upgraded by Morgan Stanley from emerging to developed market status. Athens Exchange is an order-driven market, with voluntary market makers participation and provides fully electronic trading and clearing2. Currently, almost 15% of the total of listed firms have designated market makers. In pure order- driven markets there are no designated market makers. The only intermediary on the market is the broker, who transmits client’s orders, but does not take own positions in the assets traded. This is a distinct feature of the Athens Exchange market and indicates that it is less transparent and more fragmented than pure order-driven markets, allowing dealers to offset the risk of excessive inventory positions. Trading hours are set between 10:15 GMT+2 and 17:20 GMT+2 for Big Capitalization shares (effective from March, 2009)3. Table 1 reports transactions statistics for December 2009 in the entire ATHEX market, based on investor type. Domestic investors’ transactions value accounts for almost 50% of the entire market’s transactional activity. Physical persons’ mobility is much larger than that of private financial companies and domestic institutional 2 Liquidity provision in order-driven markets has received relatively little attention in the microstructure literature compared to quote-driven markets, despite their documented significance (see Glosten, 1994; Handa et al., 1998) 3 More information on the Athens Exchange can be obtained from ATHEX Fact Book 2009 (http://www.athex.gr). 6
  7. 7. investors, while public sector’s participation is quite low. Foreign investors’ transactions value is remarkably high and it is mainly driven by the foreign institutional investors’ mobility. This is a very interesting characteristic of the Greek stock market and shows that the regulatory and technological reforms that have taken place in recent years in the Greek capital market, have made it more open to foreign influences. INSERT TABLE 1 AROUND HERE Panel A of Table 2 depicts the percentage upon capitalization for the total of listed equites, while Panel B shows the percentage upon capitalization for equites forming FTSE/ATHEX20 only. Domestic investors’ participation in the total capitalization has decreased from 59.43% in 2005 to 50.22% in 2009, whereas foreign investors’ participation has increased from 40.32% in 2005 to 48.46% in 2009, as shown in Panel A of the table. Greek blue-chips are widely-held firms as illustrated in Panel B of Table 2. Physical persons and the Greek public sector exhibit the highest levels of participation upon capitalization among domestic investors, while foreign institutional investors’ participation rate is 40%, on average. INSERT TABLE 2 AROUND HERE High-frequency data can only be obtained for a small number of countries. As a result, the equity market microstructure field has remained understudied in the Greek market. One of the main contributions of this study, is the acquisition of a recent, detailed, and unique high-frequency data set. At the time we were finishing an earlier draft of this paper, no other study using a similar data set came to our attention. It spans from September 23, 2003 through March 31, 2006, covering 635 trading days in total, 7
  8. 8. and contains high-frequency quotation and trade data, time-stamped to the nearest second. It was obtained from the trades and quotes database of the Athens Exchange. It is concentrated on the 20 firms that comprise the FTSE/ATHEX20 index, a selection motivated by the fact that large capitalization firms constitute a representative sample of the Greek stock market. Additionally, our intention to construct high-frequency order flows, necessitates the use of the most actively traded stocks of the market. Data measures are selected on the basis of a priori distinctions, correlations, and non- stationarity criteria. Unfortunately, commonly available high-frequency databases do not provide information on trade direction, and researchers have to rely on trade classification algorithms to convert unsigned trade data into signed order flow data. Our data set is not different in that sense. We have signed all trades as buyer or seller initiated, based on the Lee and Ready (1991) algorithm, which is standard practice in the literature. For trades exactly at the midpoint of the quote, the classification of trades as buyer (seller) initiated is achieved by the “tick test”, if the prior price change is positive (negative). We derive aggregate and individual raw order flow series (ROF), trading volume series (VOL), and normalized order flow series (OF) similar to Dunne et al. (2010). As an additional order flow measure, the cumulative signed square root of the euro trading volume (SRE volume) is also constructed, as described in Hasbrouck and Seppi (2001). We employ log quote midpoint returns to construct the returns set and rely on conventional spread and depth liquidity proxies to construct the liquidity measures set. At the market-wide level, individual stocks’ liquidity proxies are aggregated in order to obtain an aggregate equally-weighted market-wide liquidity proxy. All pre-sessional quotations, quotations with special settlement conditions, as well as negative spreads are 8
  9. 9. excluded from our data set. The following four liquidity measures are constructed, all averaged on a daily basis: (a) LogSize: log( NT ) + log( NT ) , (b) Quote Slope: A B ( AT − BT ) / (log( NTA ) + log( NTB )) , (c) Spread/price ratio, where price is taken as the midpoint of the bid and ask, (d) Eurodepth, defined as the sum of the euro value of the shares bid and offered, where AT and BT denote the per share bid and ask for quote A B record T, and NT , NT denote the respective number of shares posted at these quotes. 4. Estimation Results 4.1.Aggregate Order Flows: Explaining Equity Returns Our first objective is to identify whether daily aggregate equity return variation can be partly explained by order flow. Index returns are used as the dependent variable and are regressed on daily aggregate normalized order flow (OF), by using OLS. Starting from a general order flow returns model with five lags for both dependent and independent variables, and with the use of the General to Specific methodology, a final model specification is estimated at both 1% ( rt = α + β OF ) and 5% ( rt = α + β1r(t −1) + β 2OF ) levels. The own order flow is significant in both equations with t-statistics of 12.38 at the 1% level and 12.44 at the 5% level, respectively. The models are calculated using White’s heteroskedasticity robust standard errors. Ljung-Box Q tests show that there is no evidence of autocorrelation up to the 5th order (Q(5) takes on a value of 11.69 at the 1% level and 5.30 at the 5% level). R2 in both cases is quite high (0.217 at the 1% level and 0.222 at the 5% level) and shows that approximately a quarter of the daily variation 9
  10. 10. in the FTSE/ATHEX20 index is explained by aggregate order flow. This result confirms order flow’s importance in explaining equity returns via information aggregation. 4.2.Empirical Commonality in Order Flow and Returns Measures In this section we aim at characterizing the extent to which common factors are present in the returns and order flows of the Greek blue-chip stocks. The cumulative proportion of total variation is examined by using principal component analysis (PCA), while the magnitude of correlations between order flows and returns is assessed by using canonical correlation analysis (CCA). Prior to applying PCA we standardize our series to have zero mean and unit variance. One motivation for this is to remove deterministic time-of-day effects. The second motivation lies on the fact that if the series are not standardized, the first principal component will be dominated by the variable with the greatest volatility4. We have chosen to decompose the sample covariance matrix instead of the correlation matrix, similar to Hasbrouck and Seppi (2001). Panel A of Table 3, reports the results for market-wide commonality. It is shown that 98.4% of the total variation is explained with the first three principal components, suggesting the existence of common factors at the market-wide level. To empirically analyze individual securities’ commonality we appropriately filter our data and select 14 continuously listed and traded stocks for the whole period under investigation. They are depicted in Table 4, along with descriptive statistics. The results are shown in Panel B of Table 3. The first eigenvalue of the log midpoint return takes on a value of 4.131, implying that 4.131/14=29.5% of the total variation in average daily returns can be 4 We apply standard unit root tests to make sure that our resulting standardized series are stationary. Additionally, we perform two tests that provide a minimum standard which should be passed before a PCA is conducted, Bartlett’s test of sphericity and Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy. Both measures confirm the quality of our computations. The results are available by the authors upon request. 10
  11. 11. explained by a single common factor. The second and third eigenvalues are small, showing that additional common factors are not so important. The first eigenvalues for signed euro volume, normalized order flow (OF), and SRE volume measures also suggest commonality. These results are in line with the findings of Hasbrouck and Seppi (2001) for the U.S. stock market, however, they are larger in magnitude. INSERT TABLE 3 AROUND HERE Panel A of Table 5 reports the pair-wise canonical correlations along with measures of statistical significance. We focus our attention on normalized order flow (OF), which among all signed measures used, is the most highly correlated with returns at the individual firm level. The first canonical correlation is more important than the others, and the covariate canonical variable explains 45.5% of the variance in the dependent canonical variable, as depicted by the squared canonical correlations. Tests of statistical significance indicate that the two sets of variables are significantly associated by canonical correlation, suggesting that common factors have a profound impact on the relationship between returns and order flows. INSERT TABLE 4 AROUND HERE The results of Canonical Redundancy Analysis are depicted in Panel B of Table 5. The first canonical variate for returns explains 27% of the return variation and 7.2% of the normalized order flow (OF) variation. Respectively, the first canonical variate for OF explains 15.8% of OF variation and 12.3% of the return variation. These findings suggest that the first return and OF canonical variates are functionally equivalent to the first principal components. 11
  12. 12. INSERT TABLE 5 AROUND HERE 4.3. Empirical Commonality in Measures of Liquidity We turn next to investigate the commonality in unexpected liquidity, which constitutes a risk factor to investors, by eliminating time-of-day effects. Panels C and D of Table 3 give the PCA results at the market-wide and individual firm level, respectively. Our results suggest that spread and depth liquidity measures exhibit significant commonalities and that this pattern is higher for spread than it is for depth measures. Thus, even after the removal of time of day effects, commonality in unexpected liquidity exists at a significant level. Hasbrouck and Seppi (2001), provide weaker evidence on liquidity commonality, indicating that the Greek market is more vulnerable to extreme market incidents than the U.S. market. The results on canonical correlation and redundancy analyses are based on the correlation behavior of two sets of pure spread and depth liquidity measures, namely logsize and spread/price ratio, and are presented in Panels C and D of Table 5, respectively. We confirm the findings obtained by PCA and provide evidence that variation in liquidity is not completely idiosyncratic and cannot be eliminated at a market-wide level5. 5. Conclusions With a view toward better understanding order flow’s role in explaining equity market returns, as well as the role of commonality in equity microstructure characteristics, we undertake a case study analysis on Greek blue-chip stocks using high-frequency trade and quote data. It is highly likely that a portion of the documented commonality in order flows can be attributed to foreign institutional investors’ activity. Our findings also 5 Significant canonical correlations are also evidenced for other pairs of liquidity proxies. The results are available by the authors upon request. 12
  13. 13. indicate that the exposure of returns to fluctuations in market-wide liquidity contributes much to the determination of asset prices. The study of the common covariation in unexplored liquidity dimensions could provide interesting additional insights on the workings of equity markets. References 1. Acharya, V., Pedersen, L.H., 2005. Asset pricing with liquidity risk. Journal of Financial Economics 77, 375-410 2. Amihud, Y., Mendelson, H., 1980. Dealership market. Market making with inventory. Journal of Financial Economics 8, 31-53 3. Amihud, Y., Mendelson, H., 1982. Asset price behavior in a dealership market. Financial Analysts Journal 38, 50-59 4. Brockman, P., Chung, D.Y., 2002. Commonality in liquidity: evidence from an order-driven market structure. Journal of Financial Research 25, 521-539 5. Charoenwong, C., Chung, K.H., 2000. An empirical analysis of quoted depths of NYSE and AMEX stocks. Review of Quantitative Finance and Accounting 14, 85-102 6. Chordia, T., Roll, R., Subrahmanyam, A., 2000. Commonality in liquidity. Journal of Financial Economics 56, 3-28 7. Chordia, T., Subrahmanyam, A., 2004. Order imbalance and individual stock returns: theory and evidence. Journal of Financial Economics 72, 485-518 8. Domowitz, I., Hansch, O., Wang, X., 2005. Liquidity commonality and return co-movement. Journal of Financial Markets 8, 351-376 9. Dunne, P.G., Hau, H., Moore, M.J., 2010. International order flows: explaining equity and exchange rate returns. Journal of International Money and Finance 29, 358-386 10. Evans, M., Lyons, R., 2002. Order flow and exchange rate dynamics. Journal of Political Economy 1, 170-180 11. Fabre, J., Frino, A., 2004. Commonality in liquidity: evidence from the Australian Stock Exchange. Accounting and Finance 44, 357-368 12. Glosten, L., 1994. Is the electronic open limit order book inevitable? Journal of Finance 49, 1127-1161 13. Glosten, L., Milgrom, P.R., 1985. Bid, ask and transaction prices in a specialist market with heterogeneously informed agents. Journal of Financial Economics 14, 71-100 13
  14. 14. 14. Handa, P., Schwartz, R., Tiwari, A., 1998. The ecology of an order-driven market. Journal of Portfolio Management 24, 47-55 15. Hasbrouck, J., Seppi, D.J., 2001. Common factors in prices, order flows, and liquidity. Journal of Financial Economics 59, 383-411 16. Ho, T., Stoll, H., 1981. Optimal dealer pricing under transactions and return uncertainty. Journal of Financial Economics 9, 47-73 17. Ho, T., Stoll, H., 1983. The dynamics of dealer markets under competition. Journal of Finance 38, 1053-1074 18. Huberman, G., Halka, D., 2001. Systematic liquidity. Journal of Financial Research 24, 161-178 19. Kavajecz, K.A., 1999. A specialist’s quoted depth and the limit order book. Journal of Finance 54, 747-771 20. Kempf, A., Mayston, D., 2005. Commonalities in liquidity in pure order-driven markets. Working paper, University of Cologne 21. Kyle, A., 1985. Continuous auctions and insider trading. Econometrica 53, 1315-1335 22. Lee, C., Ready, M., 1991. Inferring trade direction from intradaily data. Journal of Finance 46, 733-746 23. Pastor, L., Stambaugh, R.F., 2003. Liquidity risk and expected stock returns. Journal of Political Economy 111, 642-685 24. Rime, D., 2000. Private or public information in foreign exchange markets? an empirical analysis. Typescript, University of Oslo. 14
  15. 15. Table 1. Transaction Statistics The table reports the analysis of investors’ mobility in the ATHEX market based on investor type, for the total of listed equities. Transactions value is reported both in euro value and percentage of participation. Transaction analysis based on investor type (December 2009) Buys Sells Total of Listed Equities Transactions Transactions Transactions Transactions value (mil. €) value (%) value (mil. €) value (%) Domestic Investors 2,384.92 51.20 2,048.60 43.98 Physical Persons 1,561.43 33.52 1,207.30 25.92 Private Financial 773.33 16.60 812.76 17.45 Companies Insurance & Pension Funds 6.12 0.13 6.14 0.13 Investment Companies 6.21 0.13 4.08 0.09 Mutual Funds 137.96 2.96 164.80 3.54 Banks & Investment 621.50 13.34 636.14 13.66 Companies Other Private Financial 1.54 0.03 1.60 0.03 Companies Private Non-Financial 43.49 0.93 18.62 0.40 Companies Companies (SA, Ltd, etc) 42.31 0.91 17.75 0.38 Other Private Non-Financial 1.18 0.03 0.87 0.02 Companies Public Sector 6.67 0.14 9.92 0.21 Foreign Investors 2,211.68 47.48 2,571.64 55.20 Physical Persons 109.69 2.35 109.61 2.35 Legal Entities 205.13 4.40 216.14 4.64 Institutional Investors 1,847.54 39.66 2,164.54 46.46 Other Legal Entities 49.32 1.06 81.35 1.75 Other Not Identified 61.85 1.33 38.21 0.82 Source: Athens Exchange, Monthly Statistics Bulletin, December 2009 15
  16. 16. 16
  17. 17. Table 2. Percentage Upon Capitalization Based on Investor Type Panel A of the table depicts the percentage upon capitalization for the total of listed equities, while Panel B shows the respective statistics for equities forming index FTSE/ATHEX20 only. Dates of data span over a period of five years (Dec 2005 – Dec 2009). Panel A Percentage upon capitalization for the total of listed equites Domestic Investors Foreign Investors Other Private Financial Companies Dates Physical Persons Insurance & Pension Funds Investment Companies Banks & Investment Companies Physical Persons Total of Foreign Investors Other Private Financial Companies Total of Domestic Investors Total Total Cap Mutual Funds Institutional Investors Private Non-Financial Public Sector Legal Entities Other Legal Entities Companies (in millions €) Dec-2005 123,208.52 24.47 0.60 0.18 4.28 4.01 0.34 7.57 17.98 59.43 0.43 9.19 27.96 2.74 40.32 0.24 Dec-2006 158,009.05 22.64 0.40 0.15 3.40 3.34 0.31 8.18 14.65 53.07 0.42 8.81 35.07 2.34 46.64 0.29 Dec-2007 196,390.07 19.35 0.32 0.12 2.35 2.54 0.29 9.98 12.79 47.73 0.44 8.45 39.71 3.18 51.78 0.49 Dec-2008 68,985.30 21.09 0.37 0.11 2.42 3.20 0.48 8.30 15.08 51.07 0.45 11.72 32.39 3.28 47.85 1.08 Dec-2009 84,050.69 21.84 0.37 0.12 2.86 2.62 0.47 8.21 13.73 50.22 0.55 11.33 33.53 3.04 48.46 1.32 Panel B Percentage upon capitalization for equites forming FTSE/ATHEX20 Domestic Investors Foreign Investors Other Private Financial Companies 17
  18. 18. Insurance & Pension Funds Physical Persons Total of Foreign Investors Total of Domestic Investors Dates Total Cap Physical Persons Investment Companies Mutual Funds Banks & Investment Companies Other Private Financial Companies Private Non-Financial Public Sector Legal Entities Institutional Investors Other Legal Entities Total Companies (in millions €) Dec-2005 88,820.66 18.81 0.59 0.11 4.25 1.88 0.33 6.50 22.79 55.28 0.37 8.12 33.18 2.83 44.51 0.21 Dec-2006 113,071.18 17.36 0.36 0.08 3.03 1.69 0.38 5.86 18.60 47.36 0.37 7.90 41.82 2.21 52.31 0.33 Dec-2007 134,078.35 15.91 0.32 0.07 2.17 1.28 0.38 2.75 16.46 39.34 0.47 9.02 47.22 3.37 60.08 0.58 Dec-2008 46,790.79 17.20 0.38 0.08 2.33 2.14 0.61 1.90 19.42 44.06 0.54 11.98 39.59 2.58 54.70 1.24 Dec-2009 58,607.83 18.82 0.41 0.09 2.75 1.54 0.64 2.27 17.10 43.63 0.67 12.01 39.47 2.62 54.78 1.59 Source: Athens Exchange, Monthly Statistics Bulletin, December 2009 18
  19. 19. Table 3: Principal Components Analysis – Order Flow, Returns, and Liquidity Commonality Principal Components Analysis is based on the covariance matrix of the standardized variables. Panel A, reports the results for order flow and returns market-wide commonality. The variables used in the analysis are: returns, euro volume, normalized order flow (OF), and the cumulative square root of the euro volume (SRE volume). It is shown that 98.4% of the total variation is explained with the first three principal components, indicating the existence of common factors. Panel B, refers to order flow and returns commonality of individual securities. For brevity only the first three principal components are reported. It is shown that 29.5% of the total variation in average daily returns can be explained by a single common factor. The results for the rest of measures (euro volume, OF, and SRE volume) are 16.5%, 16.5%, and 31.3% respectively. Panel C shows the results on market-wide liquidity commonality. The variables used are: eurodepth, logsize, spread/price ratio, and quoteslope. The first three principal components are able to explain 96% of the total variation, indicating the existence of common factors. Panel D refers to liquidity commonality of individual securities. It is shown that 23.1% of the total variation in the average eurodepth can be explained by a single common factor. The results for the rest of measures (logsize, spread/price, and quoteslope) are 20.0%, 39.0%, and 25.8%, respectively. Panel A Comp1 Comp2 Comp3 Comp4 Eigenvalue 2.096 1.020 0.822 0.049 Variance 0.524 0.255 0.205 0.012 Prop. Cumulativ 0.524 0.779 0.984 1.000 e Prop. Panel B Returns Euro volume OF SRE volume Comp1 Comp2 Comp3 Comp1 Comp2 Comp3 Comp1 Comp2 Comp3 Comp1 Comp2 Comp3 Eigenvalue 4.131 1.176 1.038 2.316 1.125 1.074 2.305 1.140 1.121 4.380 1.151 1.022 Variance 0.295 0.084 0.074 0.165 0.080 0.077 0.165 0.081 0.080 0.313 0.082 0.073 Prop. Cumulativ 0.295 0.379 0.453 0.165 0.245 0.322 0.165 0.246 0.326 0.313 0.395 0.468 e Prop. Panel C Comp1 Comp2 Comp3 Comp4 Eigenvalue 2.224 1.102 0.512 0.154 Variance 0.556 0.275 0.128 0.038 Prop. 19
  20. 20. Cumulativ 0.556 0.831 0.960 1.000 e Prop. Panel D Eurodepth Logsize Spread/Price Quoteslope Comp1 Comp2 Comp3 Comp1 Comp2 Comp3 Comp1 Comp2 Comp3 Comp1 Comp2 Comp3 Eigenvalue 3.228 1.185 1.063 2.799 1.590 1.378 5.464 1.508 1.145 3.618 1.641 1.054 Variance 0.231 0.085 0.076 0.200 0.113 0.098 0.390 0.108 0.082 0.258 0.117 0.075 Prop. Cumulativ 0.231 0.316 0.392 0.200 0.313 0.411 0.390 0.498 0.580 0.258 0.375 0.450 e Prop. Table 4: Descriptive Statistics The sample is the 14 continuously listed and traded stocks of the FTSE/ATHEX20 index, for the whole period under investigation (September 03-March 06). The daily return is computed as the first difference of the log quote midpoint. Symbol Company name S.D. of daily Mean signed Mean bid-ask return x 100(%) euro volume spread (in millions €) (€/share) ALPHA Alpha Bank 0.001 15.04 0.03 BIOX Viohalko 0.013 0.98 0.03 COSMO Cosmote 0.003 8.34 0.03 20
  21. 21. EEEK Coca-Cola 0.010 4.42 0.05 ELPE Hellenic Petroleum 0.005 1.99 0.03 ETE National Bank of Greece 0.001 20.32 0.03 EUROB EFG Eurobank 0.002 10.74 0.03 HTO Hellenic Telecommunications 0.001 16.47 0.02 INTRK Intracom 0.004 2.07 0.02 MOH Motor Oil Hellas 0.010 2.63 0.04 PPC Public Power Corporation 0.002 11.02 0.03 TEMP Emporiki Bank 0.004 3.78 0.04 TITK Titan Cement 0.009 2.84 0.07 TPEIR Piraeus Bank 0.002 7.12 0.03 Table 5: Canonical Correlation and Redundancy Analysis: Returns, Order Flows, and Liquidity Panel A reports the first three canonical correlations along with measures of statistical significance for the returns and order flows set. The first canonical correlation is more important than the others, and the covariate canonical variable explains 45.5% of the variance in the dependent canonical variable. Panel B presents a canonical redundancy analysis for the returns and order flows set. The upper part of Panel B reports the total variation in returns explained by the return as well as by the order flow canonical variates. The lower part of Panel B reports the total variation in order flows explained by the order flow and return canonical variates. For comparison purposes, variation explained by the principal components is also reported. Panel C shows the first three canonical correlations for the liquidity measures set. The covariate canonical variable explains 60% of the variance in the dependent canonical variable, as depicted in the first squared canonical correlation. Panel D presents a canonical redundancy analysis for the liquidity measures set. The upper part of Panel D reports the total variation in the spread/price ratio explained by the spread/price as well as the logsize canonical variates, while the lower part of Panel D reports the total variation in the logsize liquidity measure explained by the logsize and spread/price canonical variates. Wilks’s lambda distribution is approximated with a Chi-square distribution. 21
  22. 22. Panel A Root No. Canonical Squared Wilk’s F-test P-value Correlations Canonical Lambda Correlations 1 0.675 0.455 0.186 5.681 0.000 2 0.517 0.267 0.342 4.101 0.000 3 0.428 0.183 0.466 3.378 0.000 Panel B Total variation in returns explained by: Return Canonical Variates OF Canonical Variates Return principal comp. Prop. Cum. Prop. Cum. Prop. Cum. 1st 0.270 0.270 0.123 0.123 0.295 0.295 2nd 0.059 0.329 0.016 0.139 0.084 0.379 3rd 0.054 0.383 0.010 0.149 0.074 0.453 Total variation in OF explained by: OF Canonical Variates Return Canonical Variates OF principal comp. Prop. Cum. Prop. Cum. Prop. Cum. 1st 0.158 0.158 0.072 0.072 0.165 0.165 2nd 0.070 0.228 0.019 0.091 0.081 0.246 3rd 0.071 0.299 0.013 0.104 0.080 0.326 Panel C Root No. Canonical Squared Wilk’s F-test P-value Correlations Canonical Lambda Correlations 1 0.774 0.600 0.008 19.035 0.000 2 0.715 0.511 0.021 17.282 0.000 3 0.674 0.454 0.043 16.127 0.000 Panel D Total variation in spread/price ratio explained by: S/P Canonical Variates LS Canonical Variates S/P principal comp. Prop. Cum. Prop. Cum. Prop. Cum. 1st 0.251 0.251 0.151 0.151 0.390 0.390 2nd 0.073 0.324 0.037 0.188 0.108 0.498 3rd 0.138 0.462 0.063 0.251 0.082 0.580 Total variation in Logsize explained by: LS Canonical Variates S/P Canonical Variates LS principal comp. Prop. Cum. Prop. Cum. Prop. Cum. 1st 0.109 0.109 0.066 0.066 0.200 0.200 2nd 0.101 0.210 0.052 0.118 0.113 0.313 3rd 0.119 0.329 0.054 0.172 0.098 0.411 22

×