IDEAS home Printed from https://ideas.repec.org/a/spr/fininn/v9y2023i1d10.1186_s40854-023-00500-7.html
   My bibliography  Save this article

Impact of trading hours extensions on foreign exchange volatility: intraday evidence from the Moscow exchange

Author

Listed:
  • Michael Frömmel

    (Ghent University)

  • Eyup Kadioglu

    (Ghent University
    Capital Markets Board of Turkey, Mustafa Kemal Mahallesi)

Abstract

Using transaction-level tick-by-tick data of same- and next-day settlement of the Russian Ruble versus the US Dollar exchange rate (RUB/USD) traded on the Moscow Exchange Market during the period 2005–2013, we analyze the impact of trading hours extensions on volatility. During the sample period, the Moscow Exchange extended trading hours three times for the same-day settlement and two times for the next-day settlement of the RUB/USD rate. To analyze the effect of the implementations, various measures of historical and realized volatility are calculated for 5- and 15-min intraday intervals spanning a period of three months both prior to and following trading hours extensions. Besides historical volatility measures, we also examine volume and spread. We apply an autoregressive moving average-autoregressive conditional heteroscedasticity (ARMA-GARCH) model utilizing realized volatility and a trade classification rule to estimate the probability of informed trading. The extensions of trading hours cause a significant increase in both volatility and volume for further analyzing the reasons behind volatility changes. Volatility changes mostly occur after the opening of the market. The length of the extension has a significant positive effect on realized volatility. The results indicate that informed trading increased substantially after the opening for the rate of same-day settlement, whereas this is not observed for next-day settlement. Although trading hours extensions raise opportunities for more transactions and liquidity in foreign exchange markets, they may also lead to higher volatility in the market. Furthermore, this distortion is more significant at opening and midday. A potential explanation for the increased volatility mostly at the opening is that the trading hours extension attracts informed traders rather than liquidity providers.

Suggested Citation

  • Michael Frömmel & Eyup Kadioglu, 2023. "Impact of trading hours extensions on foreign exchange volatility: intraday evidence from the Moscow exchange," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-23, December.
    • Handle: RePEc:spr:fininn:v:9:y:2023:i:1:d:10.1186_s40854-023-00500-7
    DOI: 10.1186/s40854-023-00500-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1186/s40854-023-00500-7
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1186/s40854-023-00500-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Biais, Bruno & Glosten, Larry & Spatt, Chester, 2005. "Market microstructure: A survey of microfoundations, empirical results, and policy implications," Journal of Financial Markets, Elsevier, vol. 8(2), pages 217-264, May.
    2. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    3. Tauchen, George & Zhang, Harold & Liu, Ming, 1996. "Volume, volatility, and leverage: A dynamic analysis," Journal of Econometrics, Elsevier, vol. 74(1), pages 177-208, September.
    4. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January.
    5. Krohn, Ingomar & Sushko, Vladyslav, 2022. "FX spot and swap market liquidity spillovers," Journal of International Money and Finance, Elsevier, vol. 120(C).
    6. Laurent, Sébastien & Lecourt, Christelle & Palm, Franz C., 2016. "Testing for jumps in conditionally Gaussian ARMA–GARCH models, a robust approach," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 383-400.
    7. Andrew J. Patton & Kevin Sheppard, 2015. "Good Volatility, Bad Volatility: Signed Jumps and The Persistence of Volatility," The Review of Economics and Statistics, MIT Press, vol. 97(3), pages 683-697, July.
    8. Savickas, Robert & Wilson, Arthur J., 2003. "On Inferring the Direction of Option Trades," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(4), pages 881-902, December.
    9. Donglian Ma & Hisashi Tanizaki, 2022. "Intraday patterns of price clustering in Bitcoin," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-25, December.
    10. Andersen, Torben G & Bollerslev, Tim, 1997. "Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, American Finance Association, vol. 52(3), pages 975-1005, July.
    11. Kotaro Miwa & Kazuhiro Ueda, 2017. "Is the Extension of Trading Hours Always Beneficial? An Artificial Agent-Based Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 50(4), pages 595-627, December.
    12. Koubaa, Yosra & Slim, Skander, 2019. "The relationship between trading activity and stock market volatility: Does the volume threshold matter?," Economic Modelling, Elsevier, vol. 82(C), pages 168-184.
    13. Francesco Audrino & Simon D. Knaus, 2016. "Lassoing the HAR Model: A Model Selection Perspective on Realized Volatility Dynamics," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1485-1521, December.
    14. Kočenda, Evžen & Moravcová, Michala, 2019. "Exchange rate comovements, hedging and volatility spillovers on new EU forex markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 58(C), pages 42-64.
    15. repec:bla:jfinan:v:44:y:1989:i:4:p:827-48 is not listed on IDEAS
    16. Park, Seongkyu “Gilbert” & Suen, Wing & Wan, Kam-Ming, 2022. "Call auction design and closing price manipulation: Evidence from the Hong Kong stock exchange," Journal of Financial Markets, Elsevier, vol. 58(C).
    17. Frömmel, Michael & Mende, Alexander & Menkhoff, Lukas, 2008. "Order flows, news, and exchange rate volatility," Journal of International Money and Finance, Elsevier, vol. 27(6), pages 994-1012, October.
    18. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    19. Panayides, Marios A. & Shohfi, Thomas D. & Smith, Jared D., 2019. "Bulk volume classification and information detection," Journal of Banking & Finance, Elsevier, vol. 103(C), pages 113-129.
    20. Yung, Chris, 2005. "Insider trading with private information and moral hazard," Finance Research Letters, Elsevier, vol. 2(2), pages 51-57, June.
    21. repec:bla:jecsur:v:16:y:2002:i:3:p:245-69 is not listed on IDEAS
    22. Luc Bauwens & Dagfinn Rime & Genaro Sucarrat, 2008. "Exchange rate volatility and the mixture of distribution hypothesis," Studies in Empirical Economics, in: Luc Bauwens & Winfried Pohlmeier & David Veredas (ed.), High Frequency Financial Econometrics, pages 7-29, Springer.
    23. Michael J. Barclay, 2003. "Price Discovery and Trading After Hours," The Review of Financial Studies, Society for Financial Studies, vol. 16(4), pages 1041-1073.
    24. Lyons, Richard K., 1995. "Tests of microstructural hypotheses in the foreign exchange market," Journal of Financial Economics, Elsevier, vol. 39(2-3), pages 321-351.
    25. W. K. Li & Shiqing Ling & Michael McAleer, 2002. "Recent Theoretical Results for Time Series Models with GARCH Errors," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 245-269, July.
    26. Seemann, Lars & McCauley, Joseph L. & Gunaratne, Gemunu H., 2011. "Intraday volatility and scaling in high frequency foreign exchange markets," International Review of Financial Analysis, Elsevier, vol. 20(3), pages 121-126, June.
    27. Du, Ding & Hu, Ou, 2012. "Foreign exchange volatility and stock returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 22(5), pages 1202-1216.
    28. Gau, Yin-Feng, 2005. "Intraday volatility in the Taipei FX market," Pacific-Basin Finance Journal, Elsevier, vol. 13(4), pages 471-487, September.
    29. Lee, Charles M C & Ready, Mark J, 1991. "Inferring Trade Direction from Intraday Data," Journal of Finance, American Finance Association, vol. 46(2), pages 733-746, June.
    30. Anat R. Admati, Paul Pfleiderer, 1988. "A Theory of Intraday Patterns: Volume and Price Variability," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 3-40.
    31. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    32. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects," Journal of Finance, American Finance Association, vol. 45(1), pages 221-229, March.
    33. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    34. Hasbrouck, Joel, 1988. "Trades, quotes, inventories, and information," Journal of Financial Economics, Elsevier, vol. 22(2), pages 229-252, December.
    35. Sévi, Benoît, 2014. "Forecasting the volatility of crude oil futures using intraday data," European Journal of Operational Research, Elsevier, vol. 235(3), pages 643-659.
    36. Pöppe, T. & Moos, S. & Schiereck, D., 2016. "The sensitivity of VPIN to the choice of trade classification algorithm," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 83467, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    37. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    38. Viola, Alessandra Pasqualina & Klotzle, Marcelo Cabus & Pinto, Antonio Carlos Figueiredo & da Silveira Barbedo, Claudio Henrique, 2019. "Foreign exchange interventions in Brazil and their impact on volatility: A quantile regression approach," Research in International Business and Finance, Elsevier, vol. 47(C), pages 251-263.
    39. Chakrabarty, Bidisha & Li, Bingguang & Nguyen, Vanthuan & Van Ness, Robert A., 2007. "Trade classification algorithms for electronic communications network trades," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3806-3821, December.
    40. Dunis, Christian & Kellard, Neil M. & Snaith, Stuart, 2013. "Forecasting EUR–USD implied volatility: The case of intraday data," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4943-4957.
    41. Doron Avramov & Tarun Chordia & Amit Goyal, 2006. "The Impact of Trades on Daily Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 19(4), pages 1241-1277.
    42. Su, Fei, 2021. "Conditional volatility persistence and volatility spillovers in the foreign exchange market," Research in International Business and Finance, Elsevier, vol. 55(C).
    43. Eyup Kadioglu, 2021. "Intraday analysis of regulation change in microstructure: evidence from an emerging market," International Journal of Emerging Markets, Emerald Group Publishing Limited, vol. 18(5), pages 1216-1235, June.
    44. Sensoy, Ahmet & Serdengeçti, Süleyman, 2019. "Intraday volume-volatility nexus in the FX markets: Evidence from an emerging market," International Review of Financial Analysis, Elsevier, vol. 64(C), pages 1-12.
    45. David Easley & Marcos M. López de Prado & Maureen O'Hara, 2012. "Flow Toxicity and Liquidity in a High-frequency World," The Review of Financial Studies, Society for Financial Studies, vol. 25(5), pages 1457-1493.
    46. S. M. Abdullah & Salina Siddiqua & Muhammad Shahadat Hossain Siddiquee & Nazmul Hossain, 2017. "Modeling and forecasting exchange rate volatility in Bangladesh using GARCH models: a comparison based on normal and Student’s t-error distribution," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 3(1), pages 1-19, December.
    47. Khademalomoom, Siroos & Narayan, Paresh Kumar, 2019. "Intraday effects of the currency market," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 58(C), pages 65-77.
    48. Ellis, Katrina & Michaely, Roni & O'Hara, Maureen, 2000. "The Accuracy of Trade Classification Rules: Evidence from Nasdaq," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 35(4), pages 529-551, December.
    49. Zhang, Hao, 2018. "Intraday patterns in foreign exchange returns and realized volatility," Finance Research Letters, Elsevier, vol. 27(C), pages 99-104.
    50. Julija Cerović Smolović & Milena Lipovina-Božović & Saša Vujošević, 2017. "GARCH models in value at risk estimation: empirical evidence from the Montenegrin stock exchange," Economic Research-Ekonomska Istraživanja, Taylor & Francis Journals, vol. 30(1), pages 477-498, January.
    51. Gerety, Mason S & Mulherin, J Harold, 1992. "Trading Halts and Market Activity: An Analysis of Volume at the Open and the Close," Journal of Finance, American Finance Association, vol. 47(5), pages 1765-1784, December.
    52. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    53. Wei Zhang & Kai Yan & Dehua Shen, 2021. "Can the Baidu Index predict realized volatility in the Chinese stock market?," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-31, December.
    54. Takahiro Hattori, 2020. "A forecast comparison of volatility models using realized volatility: evidence from the Bitcoin market," Applied Economics Letters, Taylor & Francis Journals, vol. 27(7), pages 591-595, April.
    55. Wang, Yudong & Wei, Yu & Wu, Chongfeng & Yin, Libo, 2018. "Oil and the short-term predictability of stock return volatility," Journal of Empirical Finance, Elsevier, vol. 47(C), pages 90-104.
    56. Pan, Qunxing & Mei, Xiaowen & Gao, Tianqing, 2022. "Modeling dynamic conditional correlations with leverage effects and volatility spillover effects: Evidence from the Chinese and US stock markets affected by the recent trade friction," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    57. Pöppe, Thomas & Moos, Sebastian & Schiereck, Dirk, 2016. "The sensitivity of VPIN to the choice of trade classification algorithm," Journal of Banking & Finance, Elsevier, vol. 73(C), pages 165-181.
    58. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    59. Chang, Sanders S. & Chang, Lenisa V. & Wang, F. Albert, 2014. "A dynamic intraday measure of the probability of informed trading and firm-specific return variation," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 80-94.
    60. Wang, Yudong & Ma, Feng & Wei, Yu & Wu, Chongfeng, 2016. "Forecasting realized volatility in a changing world: A dynamic model averaging approach," Journal of Banking & Finance, Elsevier, vol. 64(C), pages 136-149.
    61. Elaut, Gert & Frömmel, Michael & Lampaert, Kevin, 2018. "Intraday momentum in FX markets: Disentangling informed trading from liquidity provision," Journal of Financial Markets, Elsevier, vol. 37(C), pages 35-51.
    62. Inci, A. Can & Ozenbas, Deniz, 2017. "Intraday volatility and the implementation of a closing call auction at Borsa Istanbul," Emerging Markets Review, Elsevier, vol. 33(C), pages 79-89.
    63. Dai, Zhifeng & Zhu, Huan & Dong, Xiaodi, 2020. "Forecasting Chinese industry return volatilities with RMB/USD exchange rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    64. Joel F. Houston & Michael D. Ryngaert, 1992. "The Links Between Trading Time And Market Volatility," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 15(2), pages 91-100, June.
    65. Andersen, Torben G, 1996. "Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility," Journal of Finance, American Finance Association, vol. 51(1), pages 169-204, March.
    66. Todorova, Neda & Souček, Michael, 2014. "Overnight information flow and realized volatility forecasting," Finance Research Letters, Elsevier, vol. 11(4), pages 420-428.
    67. Ben Omrane, Walid & Welch, Robert, 2016. "Tick test accuracy in foreign exchange ECN markets," Research in International Business and Finance, Elsevier, vol. 37(C), pages 135-152.
    68. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Frömmel, Michael & D'Hoore, Dick & Lampaert, Kevin, 2021. "The Accuracy of Trade Classification Systems on the Foreign Exchange Market: Evidence from the RUB/USD Market," Finance Research Letters, Elsevier, vol. 42(C).
    2. repec:uts:finphd:39 is not listed on IDEAS
    3. repec:uts:finphd:38 is not listed on IDEAS
    4. Fei Su, 2018. "Essays on Price Discovery and Volatility Dynamics in the Foreign Exchange Market," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2018, January-A.
    5. Hussain, Syed Mujahid & Ahmad, Nisar & Ahmed, Sheraz, 2023. "Applications of high-frequency data in finance: A bibliometric literature review," International Review of Financial Analysis, Elsevier, vol. 89(C).
    6. Fei Su & Lei Wang, 2020. "Conditional Volatility Persistence and Realized Volatility Asymmetry: Evidence from the Chinese Stock Markets," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 56(14), pages 3252-3269, November.
    7. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    8. Aris Kartsaklas, 2018. "Trader Type Effects On The Volatility‐Volume Relationship Evidence From The Kospi 200 Index Futures Market," Bulletin of Economic Research, Wiley Blackwell, vol. 70(3), pages 226-250, July.
    9. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    10. Yamani, Ehab, 2023. "Return–volume nexus in financial markets: A survey of research," Research in International Business and Finance, Elsevier, vol. 65(C).
    11. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    12. Rzayev, Khaladdin & Ibikunle, Gbenga, 2019. "A state-space modeling of the information content of trading volume," Journal of Financial Markets, Elsevier, vol. 46(C).
    13. Yadav, Pradeep K., 1992. "Event studies based on volatility of returns and trading volume: A review," The British Accounting Review, Elsevier, vol. 24(2), pages 157-184.
    14. Ho, Kin-Yip & Shi, Yanlin & Zhang, Zhaoyong, 2013. "How does news sentiment impact asset volatility? Evidence from long memory and regime-switching approaches," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 436-456.
    15. Lyócsa, Štefan & Todorova, Neda & Výrost, Tomáš, 2021. "Predicting risk in energy markets: Low-frequency data still matter," Applied Energy, Elsevier, vol. 282(PA).
    16. Ran Xiao, 2019. "Essays on Price Discovery and Volatility Dynamics in Emerging Market Currencies," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5-2019, January-A.
    17. Lyócsa, Štefan & Molnár, Peter & Výrost, Tomáš, 2021. "Stock market volatility forecasting: Do we need high-frequency data?," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1092-1110.
    18. Chang, Sanders S. & Wang, F. Albert, 2015. "Adverse selection and the presence of informed trading," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 19-33.
    19. Loredana Ureche-Rangau & Quiterie de Rorthays, 2009. "More on the volatility-trading volume relationship in emerging markets: The Chinese stock market," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(7), pages 779-799.
    20. Beum-Jo Park, 2011. "Forecasting Volatility in Financial Markets Using a Bivariate Stochastic Volatility Model with Surprising Information," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(3), pages 37-58, September.
    21. Chang, Sanders S. & Albert Wang, F., 2019. "Informed contrarian trades and stock returns," Journal of Financial Markets, Elsevier, vol. 42(C), pages 75-93.
    22. Park, Beum-Jo, 2010. "Surprising information, the MDH, and the relationship between volatility and trading volume," Journal of Financial Markets, Elsevier, vol. 13(3), pages 344-366, August.

    More about this item

    Keywords

    Volatility; Trading hours extension; Foreign exchange market; Informed trading; Volume; Spread; Market overlap; Information flow;
    All these keywords.

    JEL classification:

    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:fininn:v:9:y:2023:i:1:d:10.1186_s40854-023-00500-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.