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128 nificance of the mean component while the order of magnitude of the volatility component remains approximately constant. In other words, market risk compared to liquidity risk becomes more important at longer horizons. 5 Conclusion and outlook P. Giot, J. Grammig This paper quantified liquidity risk in an automated auction market by employing a new empirical technique which extends the classical frictionless VaR methodology. The notion of an Actual VaR measure was introduced which takes into account the potential price impact of liquidating a portfolio. This Actual VaR measure is particularly relevant for impatient investors who submit market orders. Indeed it provides one number that summarizes the expected cost of immediacy and the volatility cost due to the market risk. This duality is central to our methodology as it stresses that the liquidity risk for impatient investors over short time periods involves both a spread dependent expected cost and a second cost that is related to the variance of the price process (for the given traded volume) over the short time interval being studied. Relative liquidity risk measures were also put forward that are defined on the difference and ratio of Actual and standard (frictionless) VaR. It was argued that automated auction markets, in which a computer manages order entry and matching, provide suitable and accurate data for the task of estimating the Actual VaR. In order to measure the liquidity risk using the methodology pursued in this paper one has to provide a real time limit order book reconstruction from which price impacts of trading a given volume can be computed. Using data from the automated auction system Xetra, liquidity risk was quantified both for portfolios and for individual stocks. The dependence of liquidity risk premiums on time-of-day, trade volume and VaR time horizon was outlined. The analysis revealed a pronounced diurnal variation of the liquidity risk premium. The peak of the liquidity risk premium at the open and its subsequent decrease is consistent with the predictions of the microstructure information models considered by Madhavan (1992) and Foster and Viswanathan (1994). The results show that when assuming a trader’s perspective, accounting for liquidity risk becomes a crucial factor: the traditional (frictionless) measures severely underestimate the risk faced by impatient investors who are committed to trade. This result is the more pronounced the bigger the portfolio size and the shorter the time horizon. Avenues for further research stretch in several directions. In the classification of Dowd (1998), this paper has focused on the normal liquidity risk in contrast to crisis liquidity risk. The latter refers to situations where “a market can be very liquid most of the time, but lose its liquidity in a major crisis” (Dowd 1998). The methodology applied in this paper could be readily used to evaluate crisis liquidity risk using intraday data specific to such crisis periods where liquidity dried up for a few days/weeks (for example during the Asian crisis of the summer months of 1997 or close to the LTCM debacle in September 1998). Second, in a cross section study for a larger collection of stocks one could relate liquidity risk premiums to firmspecific characteristics like e.g. the equity–debt ratio. This would facilitate investigating the question whether corporate financing decisions or ownership structure affect firm specific liquidity risk. Thirdly, it would be interesting to look at how investors adapt to the prevailing liquidity risk. Indeed, traders could decide to split
How large is liquidity risk in an automated auction market? 129 their orders into smaller chunks to avoid prohibitive trading costs. This paves the way for dynamic strategies where market participants are interested in dynamic risk measures which take into account the fact that large orders can be split into smaller orders. To our knowledge, this however asks for much more complicated models that are quite different from the literature on high-frequency volatility models such as considered in this paper. Acknowledgements We are grateful to Deutsche Börse AG for providing access to the limit order data and to Kai-Oliver Maurer and Uwe Schweickert who offered invaluable experise regarding the Xetra trading system. Helpful comments and suggestions were offered by Erik Theissen, Michael Genser, Rico von Wyss and seminar participants at the Sfb 386 workshop on stochastic volatility and risk management at Munich University, December 2002, the 2003 EEA/ ESEM congress in Stockholm, the 54th ISI session in Berlin 2003 and at the CREST finance seminar in October 2003. We thank Helena Beltran-Lopez for her cooperation in the preparation of the datasets and Bogdan Manescu for research assistance. Finally we thank the two anonymous referees for useful suggestions and comments. 1 Appendix 1.1 Additional tables 1.1.1 Table 4 Estimation results at the 30-min frequency Frictionless v=5,000 v=20,000 v=40,000 EVS portfolios δ0 1.2E−04 (9.3E−05) −3.0E−06 (9.2E−05) −3.0E−06 (9.0E−05) −2.0E−06 (9.0E−05) δ1 0.052 (0.031) 0.065 (0.031) 0.067 (0.031) 0.081 (0.031) ω 0.029 (0.019) 0.038 (0.024) 0.035 (0.021) 0.045 (0.026) α1 0.029 (0.013) 0.031 (0.014) 0.030 (0.013) 0.027 (0.013) β1 0.935 (0.031) 0.923 (0.037) 0.926 (0.033) 0.916 (0.039) ν 9.386 (10.048) 20.167 (10.548) 16.230 (7.030) 13.687 (5.048) Q 0.20 [3.46] 0.20 [4.45] 0.19 [4.87] 0.32 [7.69] Q 2 0.26 [4.99] 0.66 [1.13] 0.66 [1.62] 0.81 [2.34] DCX δ0 2.9E−02 (1.9E−02) −7.0E−06 (1.1E−04) −6.0E−06 (1.1E−04) −7.0E−06 (1.1E−04) δ1 0.029 (0.013) 0.012 (0.031) 0.021 (0.031) 0.061 (0.031) ω 0.122 (0.071) 0.129 (0.073) 0.194 (0.141) 0.274 (0.185) α1 0.060 (0.024) 0.058 (0.023) 0.069 (0.031) 0.087 (0.037) β1 0.744 (0.123) 0.744 (0.121) 0.647 (0.220) 0.535 (0.271) ν 6.590 (1.396) 7.058 (1.585) 7.536 (1.756) 8.666 (2.159) Q 2.94 [3.14] 3.03 [3.13] 2.40 [1.86] 1.96 [3.70] Q 2 0.60 [16.69] 0.09 [13.30] 0.12 [10.11] 0.14 [6.93] DTE δ 0 2.3E−04 (1.5E−04) −2.0E−06 (1.5E−04) −1.0E−06 (1.5E−04) 3.0E−06 (1.5E−04) δ1 0.036 (0.031) 0.042 (0.031) 0.054 (0.031) 0.070 (0.031) ω 0.051 (0.023) 0.053 (0.024) 0.054 (0.025) 0.058 (0.027) α 1 0.029 (0.012) 0.030 (0.012) 0.029 (0.012) 0.028 (0.013) β1 0.881 (0.042) 0.877 (0.042) 0.876 (0.045) 0.872 (0.049) ν 5.889 (1.156) 5.944 (1.171) 5.631 (1.072) 5.766 (1.107)
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High Frequency Financial Econometri
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Prof. Luc Bauwens CORE Voie du Roma
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vi Contents Intraday stock prices,
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2 L. Bauwens et al. component nicel
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4 L. Bauwens et al. but provides al
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Luc Bauwens . Dagfinn Rime . Genaro
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Exchange rate volatility and the mi
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32 K. Bien et al. Although economet
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34 K. Bien et al. 2.1 Copula functi
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36 K. Bien et al. and x k t ≡ (xk
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38 K. Bien et al. Fig. 3 Multivaria
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40 K. Bien et al. Bivariate model s
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42 K. Bien et al. deviation 0.0099,
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44 K. Bien et al. - Set ˆzt = Âxt
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46 K. Bien et al. % Frequency −0.
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48 K. Bien et al. References Amilon
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50 1 Introduction A. Escribano and
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52 A. Escribano and R. Pascual Jang
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54 A. Escribano and R. Pascual the
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56 The generating processes of mark
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58 with AtðLÞ ¼ 0 B @ 1 ð ÞAab
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60 A. Escribano and R. Pascual cros
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62 Hasbrouck (1991). The system is
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64 unitary seller-initiated shock (
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66 6.1 Estimation of the baseline m
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Table 2 The base-line VEC model for
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70 Table 3 Simulation of the base-l
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72 revert towards narrow levels. As
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Table 5 Impulse-response functions
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76 We also show that NYSE buyer-ini
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Page 86 and 87: 80 NYSE 2000 Stocks AOL America Onl
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Page 90 and 91: 84 1 Introduction S. Frey, J. Gramm
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Page 94 and 95: Table 1 Sample descriptives Company
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Page 100 and 101: 94 market order distribution that c
Page 102 and 103: 96 Table 2 First stage GMM results
Page 104 and 105: Table 4 First stage GMM results bas
Page 106 and 107: 100 S. Frey, J. Grammig quotes on e
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Page 112 and 113: 106 Hence, using the liquidity stat
Page 114 and 115: 108 In the main text we discuss the
Page 117 and 118: Pierre Giot . Joachim Grammig How l
Page 119 and 120: How large is liquidity risk in an a
Page 133: How large is liquidity risk in an a
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Page 140 and 141: 134 A. D. Hall, N. Hautsch In this
Page 142 and 143: 136 includes order book variables,
Page 144 and 145: 138 An important determinant of liq
Page 146 and 147: 140 The innovation term ei is compu
Page 148 and 149: Table 1 Order book characteristics
Page 150 and 151: 144 data covering the normal tradin
Page 152 and 153: 146 Table 3 Descriptive statistics
Page 154 and 155: Table 4 Fully specified ACI models
Page 156 and 157: Table 4 (continued) BHP NAB NCP TLS
Page 158 and 159: Table 5 ACI models without dynamics
Page 162 and 163: Table 6 ACI models without covariat
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Page 168 and 169: 162 5.2.5 The impact of the bid-ask
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Modelling financial transaction pri
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200 W. B. Omrane, H. V. Oppens anal
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202 W. B. Omrane, H. V. Oppens of s
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204 The extrema detection method ba
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206 price 0.8565 0.8575 0.8585 0.85
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208 We distinguish three possible c
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210 originates. The most active tra
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212 Table 2 Predictability of the c
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214 6 Conclusion Using 5-min euro/d
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216 where σk is the standard devia
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218 If we meet a particular case su
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220 C.5. Triple bottom (TB) TB is c
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222 References W. B. Omrane, H. V.
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Juan M. Rodríguez-Poo · David Ver
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Semiparametric estimation for finan
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254 between price changes and durat
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256 simply aggregated. Even after a
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258 is to make use of the fact that
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260 together with the restrictions
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Table 3 Estimated probabilities of
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264 A. S. Tay, C. Ting More interes
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Table 4 Estimated probabilities of
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268 Acknowledgements Tay gratefully
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270 This paper explores the effect
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272 contrast, price responses to po
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274 Fig. 1 Continuous line is the T
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276 the β’s can form a convex sh
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278 fixing some intervals around th
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280 . That is for a given absolute
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282 30 25 20 15 10 5 CC UNEMW ISM U
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Appendix Table A1 Consumer confiden
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Table A3 Non-farm payrolls • ✓
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Table A5 Weekly unemployment claims
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290 Table A8 Retail sales • ✓ 1
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292 Table A12 GDP, BI, TB and PI Re
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294 V. Voev with the problem of how
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296 V. Voev 2.1 A sample covariance
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298 V. Voev Using the equicorrelate
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300 V. Voev where �kl(t) is the (
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302 V. Voev where hkl,k ′ l ′ i
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304 V. Voev is 1.9%. From the daily
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306 V. Voev ACF ACF ACF 0.5 0.5 0.5
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308 V. Voev autocorrelated. Indeed,
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310 V. Voev 5 Conclusion Table 2 Ro
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312 V. Voev Engle R (1982) Autoregr
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