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A wavelet-based assessment of market risk: The emerging markets case

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  • António Rua
  • Luís Catela Nunes

Abstract

The measurement of market risk poses major challenges to researchers and different economic agents. On one hand, it is by now widely recognized that risk varies over time. On the other hand, the risk profile of an investor, in terms of investment horizon, makes it crucial to also assess risk at the frequency level. We propose a novel approach to measuring market risk based on the continuous wavelet transform. Risk is allowed to vary both through time and at the frequency level within a unified framework. In particular, we derive the wavelet counterparts of well-known measures of risk. One is thereby able to assess total risk, systematic risk and the importance of systematic risk to total risk in the time-frequency space. To illustrate the method we consider the emerging markets case over the last twenty years, finding noteworthy heterogeneity across frequencies and over time, which highlights the usefulness of the wavelet approach.

Suggested Citation

  • António Rua & Luís Catela Nunes, 2012. "A wavelet-based assessment of market risk: The emerging markets case," Working Papers w201203, Banco de Portugal, Economics and Research Department.
  • Handle: RePEc:ptu:wpaper:w201203
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    as
    1. Geert Bekaert & Campbell R. Harvey, 2000. "Foreign Speculators and Emerging Equity Markets," Journal of Finance, American Finance Association, vol. 55(2), pages 565-613, April.
    2. Ramsey James B. & Lampart Camille, 1998. "The Decomposition of Economic Relationships by Time Scale Using Wavelets: Expenditure and Income," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(1), pages 1-22, April.
    3. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    4. Garcia, Rene & Ghysels, Eric, 1998. "Structural change and asset pricing in emerging markets," Journal of International Money and Finance, Elsevier, vol. 17(3), pages 455-473, June.
    5. Luís Aguiar-Conraria & Maria Soares, 2011. "Oil and the macroeconomy: using wavelets to analyze old issues," Empirical Economics, Springer, vol. 40(3), pages 645-655, May.
    6. Yogo, Motohiro, 2008. "Measuring business cycles: A wavelet analysis of economic time series," Economics Letters, Elsevier, vol. 100(2), pages 208-212, August.
    7. Ramsey, James B. & Zhang, Zhifeng, 1997. "The analysis of foreign exchange data using waveform dictionaries," Journal of Empirical Finance, Elsevier, vol. 4(4), pages 341-372, December.
    8. Dimitrakopoulos, Dimitris N. & Kavussanos, Manolis G. & Spyrou, Spyros I., 2010. "Value at risk models for volatile emerging markets equity portfolios," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(4), pages 515-526, November.
    9. Harvey, Campbell R, 1995. "Predictable Risk and Returns in Emerging Markets," Review of Financial Studies, Society for Financial Studies, vol. 8(3), pages 773-816.
    10. Eric Ghysels, 1998. "On Stable Factor Structures in the Pricing of Risk: Do Time-Varying Betas Help or Hurt?," Journal of Finance, American Finance Association, vol. 53(2), pages 549-573, April.
    11. Blume, Marshall E, 1975. "Betas and Their Regression Tendencies," Journal of Finance, American Finance Association, vol. 30(3), pages 785-795, June.
    12. Dirk Tasche, 2002. "Expected Shortfall and Beyond," Papers cond-mat/0203558, arXiv.org, revised Oct 2002.
    13. Ramazan Genay & Faruk Seļuk & Brandon Whitcher, 2003. "Systematic risk and timescales," Quantitative Finance, Taylor & Francis Journals, vol. 3(2), pages 108-116.
    14. Bekaert, Geert & Harvey, Campbell R, 1995. "Time-Varying World Market Integration," Journal of Finance, American Finance Association, vol. 50(2), pages 403-444, June.
    15. Aguiar-Conraria, LuI´s & Joana Soares, Maria, 2011. "Business cycle synchronization and the Euro: A wavelet analysis," Journal of Macroeconomics, Elsevier, vol. 33(3), pages 477-489, September.
    16. Ferson, Wayne E & Harvey, Campbell R, 1991. "The Variation of Economic Risk Premiums," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 385-415, April.
    17. Kim, Sangbae & In, Francis, 2005. "The relationship between stock returns and inflation: new evidence from wavelet analysis," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 435-444, June.
    18. Rua, António, 2010. "Measuring comovement in the time-frequency space," Journal of Macroeconomics, Elsevier, vol. 32(2), pages 685-691, June.
    19. Fabozzi, Frank J. & Francis, Jack Clark, 1978. "Beta as a Random Coefficient," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(1), pages 101-116, March.
    20. Bekaert, Geert & Harvey, Campbell R., 1997. "Emerging equity market volatility," Journal of Financial Economics, Elsevier, vol. 43(1), pages 29-77, January.
    21. Ramsey, James B. & Lampart, Camille, 1998. "Decomposition Of Economic Relationships By Timescale Using Wavelets," Macroeconomic Dynamics, Cambridge University Press, vol. 2(1), pages 49-71, March.
    22. Fabozzi, Frank J & Francis, Jack Clark, 1977. "Stability Tests for Alphas and Betas over Bull and Bear Market Conditions," Journal of Finance, American Finance Association, vol. 32(4), pages 1093-1099, September.
    23. De Santis, Giorgio & imrohoroglu, Selahattin, 1997. "Stock returns and volatility in emerging financial markets," Journal of International Money and Finance, Elsevier, vol. 16(4), pages 561-579, August.
    24. António Rua, 2011. "A wavelet approach for factor‐augmented forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(7), pages 666-678, November.
    25. António Rua, 2012. "Money Growth and Inflation in the Euro Area: A Time-Frequency View," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(6), pages 875-885, December.
    26. Rua, António & Nunes, Luís C., 2009. "International comovement of stock market returns: A wavelet analysis," Journal of Empirical Finance, Elsevier, vol. 16(4), pages 632-639, September.
    27. de Jong, Frank & de Roon, Frans A., 2005. "Time-varying market integration and expected returns in emerging markets," Journal of Financial Economics, Elsevier, vol. 78(3), pages 583-613, December.
    28. Sunder, Shyam, 1980. "Stationarity of Market Risk: Random Coefficients Tests for Individual Stocks," Journal of Finance, American Finance Association, vol. 35(4), pages 883-896, September.
    29. Bekaert, Geert & Harvey, Campbell R., 2002. "Research in emerging markets finance: looking to the future," Emerging Markets Review, Elsevier, vol. 3(4), pages 429-448, December.
    30. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
    31. Luís Francisco Aguiar & Maria Joana Soares, 2010. "The Continuous Wavelet Transform: A Primer," NIPE Working Papers 23/2010, NIPE - Universidade do Minho.
    32. Fernandez Viviana P, 2005. "The International CAPM and a Wavelet-Based Decomposition of Value at Risk," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(4), pages 1-37, December.
    33. Patrick M. Crowley & David G. Mayes, 2009. "How fused is the euro area core?: An evaluation of growth cycle co-movement and synchronization using wavelet analysis," OECD Journal: Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2008(1), pages 63-95.
    34. Gencay, Ramazan & Selcuk, Faruk & Whitcher, Brandon, 2005. "Multiscale systematic risk," Journal of International Money and Finance, Elsevier, vol. 24(1), pages 55-70, February.
    35. Connor Jeff & Rossiter Rosemary, 2005. "Wavelet Transforms and Commodity Prices," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(1), pages 1-22, March.
    36. Bekaert, Geert & Harvey, Campbell R., 2003. "Emerging markets finance," Journal of Empirical Finance, Elsevier, vol. 10(1-2), pages 3-56, February.
    37. Francis In & Sangbae Kim, 2006. "The Hedge Ratio and the Empirical Relationship between the Stock and Futures Markets: A New Approach Using Wavelet Analysis," The Journal of Business, University of Chicago Press, vol. 79(2), pages 799-820, March.
    38. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    39. Candelon, Bertrand & Piplack, Jan & Straetmans, Stefan, 2008. "On measuring synchronization of bulls and bears: The case of East Asia," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 1022-1035, June.
    40. Kim Sangbae & In Francis Haeuck, 2003. "The Relationship Between Financial Variables and Real Economic Activity: Evidence From Spectral and Wavelet Analyses," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(4), pages 1-18, December.
    41. John Lintner, 1965. "Security Prices, Risk, And Maximal Gains From Diversification," Journal of Finance, American Finance Association, vol. 20(4), pages 587-615, December.
    42. Gallegati Marco & Gallegati Mauro, 2007. "Wavelet Variance Analysis of Output in G-7 Countries," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 11(3), pages 1-25, September.
    43. Tonn, Victor Lux & Li, H.C. & McCarthy, Joseph, 2010. "Wavelet domain correlation between the futures prices of natural gas and oil," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(4), pages 408-414, November.
    44. Patrick M. Crowley, 2007. "A Guide To Wavelets For Economists ," Journal of Economic Surveys, Wiley Blackwell, vol. 21(2), pages 207-267, April.
    45. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    46. Sharif Md. Raihan & Yi Wen & Bing Zeng, 2005. "Wavelet: a new tool for business cycle analysis," Working Papers 2005-050, Federal Reserve Bank of St. Louis.
    47. Chambet, Anthony & Gibson, Rajna, 2008. "Financial integration, economic instability and trade structure in emerging markets," Journal of International Money and Finance, Elsevier, vol. 27(4), pages 654-675, June.
    48. Harvey, Campbell R, 1991. "The World Price of Covariance Risk," Journal of Finance, American Finance Association, vol. 46(1), pages 111-157, March.
    49. Collins, Daniel W & Ledolter, Johannes & Rayburn, Judy Dawson, 1987. "Some Further Evidence on the Stochastic Properties of Systematic Risk," The Journal of Business, University of Chicago Press, vol. 60(3), pages 425-448, July.
    50. Clive W. J. Granger, 2002. "Some comments on risk," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 447-456.
    51. Alexander, Gordon J. & Benson, P. George, 1982. "More on Beta as a Random Coefficient," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(1), pages 27-36, March.
    52. Harvey, Campbell R., 1989. "Time-varying conditional covariances in tests of asset pricing models," Journal of Financial Economics, Elsevier, vol. 24(2), pages 289-317.
    53. Blume, Marshall E, 1971. "On the Assessment of Risk," Journal of Finance, American Finance Association, vol. 26(1), pages 1-10, March.
    54. Fernandez, Viviana, 2006. "The CAPM and value at risk at different time-scales," International Review of Financial Analysis, Elsevier, vol. 15(3), pages 203-219.
    55. Ferson, Wayne E & Harvey, Campbell R, 1993. "The Risk and Predictability of International Equity Returns," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 527-566.
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    2. António Rua, 2012. "Wavelets in economics," Economic Bulletin and Financial Stability Report Articles and Banco de Portugal Economic Studies, Banco de Portugal, Economics and Research Department.
    3. Gazi Salah Uddin & Mohamed Arouri & Aviral Kumar Tiwari, 2014. "Co-movements between Germany and International Stock Markets: Some New Evidence from DCC-GARCH and Wavelet Approaches," Working Papers 2014-143, Department of Research, Ipag Business School.
    4. Özmen, M. Utku & Yılmaz, Erdal, 2017. "Co-movement of exchange rates with interest rate differential, risk premium and FED policy in “fragile economies”," Emerging Markets Review, Elsevier, vol. 33(C), pages 173-188.
    5. Aasif Shah & Arif Tali & Qaiser Farooq, 2018. "Beta through the prism of wavelets," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 4(1), pages 1-17, December.
    6. William Barnett & Zied Ftiti & Fredj Jawadi, 2018. "The Causal Relationships between Inflation and Inflation Uncertainty," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201803, University of Kansas, Department of Economics, revised Mar 2018.
    7. Uddin, Gazi Salah & Hernandez, Jose Areola & Shahzad, Syed Jawad Hussain & Yoon, Seong-Min, 2018. "Time-varying evidence of efficiency, decoupling, and diversification of conventional and Islamic stocks," International Review of Financial Analysis, Elsevier, vol. 56(C), pages 167-180.
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    9. Chakrabarty, Anindya & De, Anupam & Gunasekaran, Angappa & Dubey, Rameshwar, 2015. "Investment horizon heterogeneity and wavelet: Overview and further research directions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 45-61.
    10. Aloui, Chaker & Hkiri, Besma & Lau, Marco Chi Keung & Yarovaya, Larisa, 2018. "Information transmission across stock indices and stock index futures: International evidence using wavelet framework," Research in International Business and Finance, Elsevier, vol. 44(C), pages 411-421.
    11. Kang, Sang Hoon & Lahmiri, Salim & Uddin, Gazi Salah & Arreola Hernandez, Jose & Yoon, Seong-Min, 2020. "Inflation cycle synchronization in ASEAN countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    12. Akoum, Ibrahim & Graham, Michael & Kivihaho, Jarno & Nikkinen, Jussi & Omran, Mohammed, 2012. "Co-movement of oil and stock prices in the GCC region: A wavelet analysis," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(4), pages 385-394.
    13. Anindya Chakrabarty & Anupam De & Gautam Bandyopadhyay, 2016. "Horizon heterogeneity, institutional constraint and managerial myopia: a multi-frequency perspective on ELSS," International Journal of Business Excellence, Inderscience Enterprises Ltd, vol. 9(1), pages 18-47.
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    15. Bruzda, Joanna, 2019. "Complex analytic wavelets in the measurement of macroeconomic risks," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
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    17. M. Utku Ozmen & Erdal Yilmaz, 2016. "Co-movement of Exchange Rates with Interest Rate Differential, Risk Premium and FED Policy in �Fragile Economies�," Working Papers 1621, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
    18. McNevin, Bruce D. & Nix, Joan, 2018. "The beta heuristic from a time/frequency perspective: A wavelet analysis of the market risk of sectors," Economic Modelling, Elsevier, vol. 68(C), pages 570-585.
    19. Berdiev, Aziz N. & Chang, Chun-Ping, 2015. "Business cycle synchronization in Asia-Pacific: New evidence from wavelet analysis," Journal of Asian Economics, Elsevier, vol. 37(C), pages 20-33.
    20. Xiaojie Xu, 2018. "Causal structure among US corn futures and regional cash prices in the time and frequency domain," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(13), pages 2455-2480, October.
    21. Bruno Milani & Paulo Sérgio Ceretta, 2014. "A multiscale approach to emerging market pricing," Economics Bulletin, AccessEcon, vol. 34(2), pages 784-792.
    22. Rua, António, 2017. "A wavelet-based multivariate multiscale approach for forecasting," International Journal of Forecasting, Elsevier, vol. 33(3), pages 581-590.
    23. Naseri, Marjan & Masih, Mansur, 2014. "Integration and Comovement of Developed and Emerging Islamic Stock Markets: A Case Study of Malaysia," MPRA Paper 58799, University Library of Munich, Germany.

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    JEL classification:

    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • F30 - International Economics - - International Finance - - - General
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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