ANALYZING TIME-FREQUENCY NEXUS BETWEEN STOCK RETURNS AND BOND YIELDS THROUGH WAVELETS: THE CASE OF TURKEY – PART I

Abstract

This paper reinvestigates the stock-bond nexus using 605 weekly observations of stock index prices and the 2-year benchmark rate of Turkey over a sample period covering April 1, 2005, and December 30, 2016. By conducting a novel approach, wavelet analysis, we aimed to offer a deeper understanding of the relationship considering the investor's heterogeneities on investment periods. The results show weekly positive averages for all stock index returns but negative average for bond yields over time. Wavelets variance analysis reveals that the higher scale the lower volatility, namely, the most of fluctuations in returns is explained by short-term, suggesting that short-term investors should react to every fluctuation in their asset returns. Similarly, the stock market is found to be more volatile than the bond market. As expected, test findings highlight significantly negative stock-bond linkage. Wavelet cross-correlation results show significantly both positive and negative bidirectional causal linkages over higher wavelet-scales. Keywords: Wavelets, lead-lag, wavelet variance, correlation, and cross-correlation.

Keywords

• Wavelets
• lead-lag
• wavelet variance
• correlation
• cross-correlation

ANALYZING TIME-FREQUENCY NEXUS BETWEEN STOCK RETURNS AND BOND YIELDS THROUGH WAVELETS: THE CASE OF TURKEY – PART I

Abstract

This paper reinvestigates the stock-bond nexus using 605 weekly observations of stock index prices and the 2-year benchmark rate of Turkey over a sample period covering April 1, 2005, and December 30, 2016. By conducting a novel approach, wavelet analysis, we aimed to offer a deeper understanding of the relationship considering the investor's heterogeneities on investment periods. The results show weekly positive averages for all stock index returns but negative average for bond yields over time. Wavelets variance analysis reveals that the higher scale the lower volatility, namely, the most of fluctuations in returns is explained by short-term, suggesting that short-term investors should react to every fluctuation in their asset returns. Similarly, the stock market is found to be more volatile than the bond market. As expected, test findings highlight significantly negative stock-bond linkage. Wavelet

Keywords

• Wavelets
• lead-lag
• wavelet variance
• correlation
• cross-correlation

References

1. ABDULLAH, Ahmad M., SAITI, Buerhan, and MASIH, Abul M. M. (2014). Causality between stock market index and macroeconomic variables: a case study for Malaysia. Munich Personal RePEc Archive, Paper No. 56987. Available at https://mpra.ub.uni-muenchen.de/56987/1/MPRA_paper_56987.pdf
2. ABUGRI, Benjamin. A. (2008). Empirical relationship between macroeconomic volatility and stock returns: Evidence from Latin American markets. International Review of Financial Analysis, 17(2): 396-410.
3. ACHARD, Sophie. (2012). R-Package Brainwaver: Basic wavelet analysis of multivariate time series with a visualisation and parametrisation using graph theory. R Package Version, 1.6.
4. ANDERSSON, Magnus, KRYLOVA, Elizaveta, and VÄHÄMAA, Sami. (2008). Why does the correlation between stock and bond returns vary over time?. Journal of Applied Financial Economics, 18(2): 139-151.
5. ANDRIEȘ, Alin M., IHNATOV, Iulian, and TIWARI, Aviral. K. (2014). Analyzing time–frequency relationship between interest rate, stock price and exchange rate through continuous wavelet. Economic Modelling, (41): 227-238.
6. APERGIS, Nicholas and ELEFTHERIOU, Sophia. (2002). Interest rates, inflation, and stock prices: the case of the Athens Stock Exchange. Journal of Policy Modeling, 24(3): 231-236.
7. ASGHARIAN, Hossein, CHRISTIANSEN, Charlotte, and HOU, Ai J. (2015). Macro-finance determinants of the long run stock–bond correlation: The DCC-MIDAS specification. Journal of Financial Econometrics, 14(3): 617-642.
8. BAE, Sung C. (1990). Interest rate changes and common stock returns of financial institutions: Revisited. Journal of Financial Research, 13(1): 71-79.

9. BAELE, Lieven, BEKAERT, Geert, and INGHELBRECHT, Koen. (2010). The determinants of stock and bond return comovements. The Review of Financial Studies, 23(6): 2374-2428.
10. BARAKAT, Mahmoud. R., ELGAZZAR, Sara H., and HANAFY, Khaled M. (2015). Impact of macroeconomic variables on stock markets: Evidence from emerging markets. International Journal of Economics and Finance, 8(1): 195.
11. BARSKY, Robert B. (1989). Why don’t the prices of stocks and bonds move together? American Economy Review, (79): 1132–1145.
12. BAUR, Dirk G., and LUCEY, Brian M. (2009). Flights and contagion – An empirical analysis of stock – bond correlations. Journal of Financial Stability, 5(4): 339-352.
13. BAYRACI, Selcuk, DEMIRALAY, Sercan, and GENCER, Hatice G. (2018). Stock-bond co-movements and flight-to-quality in G7 countries: a time-frequency analysis. Bulletin of Economic Research, 70(1).
14. BOHL, Martin T., SIKLOS, Pierre L., and WERNER, Thomas. (2003). Did the Bundesbank react to stock price movements?. Dt. Bundesbank.
15. BREITUNG, Jörg and CANDELON, Bertrand. (2006). Testing for short-and long run causality: A frequency-domain approach. Journal of Econometrics, 132(2): 363-378.
16. CAMPBELL, John Y. and AMMER, John. (1993). What moves the stock and bond markets? A variance decomposition for long-term asset returns. The Journal of Finance, 48(1): 3–37.
17. CAMPBELL, John Y. (1987). Stock returns and the term structure. Journal of Financial Economics, 18(2): 373-399.
18. CENEDESE, Gino and MALLUCCI, Enrico. (2016). What moves international stock and bond markets?. Journal of International Money and Finance, 60, 94-113.
19. CHEN, Carl R., MOHAN, Nancy J., and STEINER, Thomas L. (1999). Discount rate changes, stock market returns, volatility, and trading volume: Evidence from intraday data and implications for market efficiency. Journal of Banking & Finance, 23(6): 897-924.
20. CHRISTIE, Andrew A. (1982). The stochastic behavior of common stock variances: value, leverage and interest rate effects. Journal of Financial Economics, 10(4): 407-432.
21. ÇIFTER, Atilla and ÖZÜN, Alper. (2007). Multiscale systematic risk: an application on ISE-30. Munich Personal RePEc Archive, Paper No. 4288, available at https://mpra.ub.uni-muenchen.de/4288/1/MPRA_paper_4288.pdf
22. CONNOLLY, Robert, STIVERS, Chris, and Sun, Licheng. (2005). Stock market uncertainty and the stock-bond return relation. Journal of Financial and Quantitative Analysis, 40(1): 161-194.
23. CROWLEY, Patrick M. (2007). A Guide to Wavelets for Economists. Journal of Economic Surveys, 21(2): 207-267.
24. DAJCMAN, Silvo. (2012). Comovement between stock and bond markets and the "flight-to-quality" during financial market turmoil–a case of the Eurozone countries most affected by the sovereign debt crisis of 2010–2011. Applied Economics Letters, 19(17): 1655-1662.
25. DAJCMAN, Silvo. (2013). Interdependence between some major European stock markets -a wavelet lead/lag analysis. Prague Economic Papers, 22(1): 28-49.
26. DAJCMAN, Silvo. (2015). An empirical investigation of the nexus between sovereign bond yields and stock market returns - a multiscale approach. Engineering Economics, 26(2): 108-117.
27. DAUBECHIES, Ingrid. (1992). Ten lectures on wavelets. Philadelphia: Society for Industrial and Applied Mathematics, 61, 198-202.
28. DICKEY, David A. and FULLER, Wayne A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366a): 427-431.
29. DIMIC, Nebojsa, KIVIAHO, Jarno, PILJAK, V., and ÄIJÖ, Janne. (2016). Impact of financial market uncertainty and macroeconomic factors on stock–bond correlation in emerging markets. Research in International Business and Finance, (36): 41-51.
30. DINENIS, Elias and STAIKOURAS, Sotiris K. (1998). Interest rate changes and common stock returns of financial institutions: evidence from the UK. The European Journal of Finance, 4(2): 113-127.,
31. DURAN, Murat, ÖZLÜ, Pınar, and ÜNALMIS, Deren. (2010). TCMB faiz kararlarinin hisse senedi piyasalari üzerine etkisi. Central Bank Review, 10(2): 23.
32. EKINCI, Ramazan, CEYLAN, Fatih, TÜZÜN, Osman, and KAHYAOĞLU, Hakan. (2016). TCMB ağırlıklı ortalama fonlama maliyetinin BİST100 üzerindeki etkisi. Journal of Yaşar University, 11(44): 263-277.
33. ELYASIANI, Elyas and MANSUR, Iqbal. (1998). Sensitivity of the bank stock returns distribution to changes in the level and volatility of interest rate: A GARCH-M model. Journal of Banking & Finance, 22(5): 535-563.
34. ERDEM, Cumhur, ARSLAN, Cem K., and ERDEM, Sema M. (2005). Effects of macroeconomic variables on Istanbul stock exchange indexes. Applied Financial Economics, 15(14): 987-994.
35. FAMA, Eugene. F., and FRENCH, Kenneth R. (1989). Business conditions and expected returns on stocks and bonds. Journal of Financial Economics, 25(1): 23-49.
36. FERNANDEZ, Viviana. (2005). Time-scale decomposition of price transmission in international markets. Emerging Markets Finance and Trade, 41(4): 57-90.
37. FERRER, Roman, BOLÓS, Vicente J., and BENÍTEZ, Rafael. (2016). Interest rate changes and stock returns: A European multi-country study with wavelets. International Review of Economics and Finance, 44, 1-12.
38. FERRER, Roman, GONZÁLEZ, Cristobal, and SOTO, Gloria M. (2010). Linear and nonlinear interest rate exposure in Spain. Managerial Finance, 36(5): 431-451.
39. FLANNERY, Mark J., and JAMES, Christopher M. (1984). The effect of interest rate changes on the common stock returns of financial institutions. The Journal of Finance, 39(4): 1141-1153.
40. FLEMING, Jeff, KIRBY, Chris, and OSTDIEK, Barbara. (1998). Information and volatility linkages in the stock, bond, and money markets. Journal of Financial Economics, (49): 11137.
41. GALLEGATI, Marco. (2008). Wavelet analysis of stock returns and aggregate economic activity. Computational Statistics and Data Analysis, 52(6): 3061-3074.
42. GALLEGATI, Marco, and RAMSEY, James B. (2013). Structural change and phase variation: A re-examination of the q-model using wavelet exploratory analysis. Structural Change and Economic Dynamics, 25, 60-73.
43. GALLEGATI, Marco, GALLEGATI, Marco, RAMSEY, James B., and SEMMLER, Willi. (2017). Long waves in prices: new evidence from wavelet analysis. Cliometrica, 11(1): 127-151.
44. GENCAY, Ramazan, SELÇUK, Faruk, and WHITCHER, Brandon J. (2002). An introduction to wavelets and other filtering methods in finance and economics. Academic Press.
45. GJERDE, Øystein and SÆTTEM, Frode. (1999). Causal relations among stock returns and macroeconomic variables in a small, open economy. Journal of International Finance Markets Institutions and Money, 9, 61–74.
46. GONZÁLEZ, Maria D. L. O., JAREÑO, Francisco, and SKINNER, Frank S. (2017). The financial crisis impact: an industry level analysis of the US stock market. Applied Econometrics and International Development, 17(2): 61-74.
47. GRAPS, Amara. (1995). An introduction to wavelets. IEEE Computational Science and Engineering, 2(2): 50-61.
48. GULKO, Les. (2002). Decoupling. The Journal of Portfolio Management, 28(3): 59-66.
49. HAMRITA, Mohamed E., and TRIFI, Abdelkader. (2011). The relationship between interest rate, exchange rate and stock price: A wavelet analysis. International Journal of Economics and Financial Issues, 1(4): 220-228.
50. HARRISON, Paul, and ZHANG, Harold H. (1999). An investigation of the risk and return relation at long horizons. The Review of Economics and Statistics, 81(3): 399-408.
51. ILMANEN, Antti. (2003). Stock-bond correlations. The Journal of Fixed Income, 13(2): 55-66.
52. IN, Francis and KIM, Sangbae. (2012). An introduction to wavelet theory in finance: a wavelet multiscale approach. World Scientific.
53. ISMAIL, Rizwan, PERVAZ, Asghar, AHMED, Ayaz, and IQBAL, Raees. (2016). Macroeconomic factors and the Pakistani equity market: a relationship analysis. International Journal of Innovation and Applied Studies, 15(1): 122.
54. JAMMAZI, Rania, TIWARI, Aviral K., FERRER, Roman, and MOYA, Pablo. (2015). Time-varying dependence between stock and government bond returns: International evidence with dynamic copulas. The North American Journal of Economics and Finance, 33, 74-93.
55. JAREÑO, Francisco. (2008). Spanish stock market sensitivity to real interest and inflation rates: an extension of the Stone two-factor model with factors of the Fama and French three-factor model. Applied Economics, 40(24): 3159-3171.
56. JAWAID, Syed T. and HAQ, Anwar U. (2012). Effects of interest rate, exchange rate and their volatilities on stock prices: Evidence from banking industry of Pakistan. Theoretical and Applied Economics, 19(8).
57. JOHNSON, Nicholas, NAIK, Vasant, PEDERSEN, Niels, and SAPRA, Steve. (2013). The stock-bond correlation. PIMCO, Quantitative Research (November): 1-12.
58. JOSEPH, Nathan L. (2002). Modeling the impacts of interest rate and exchange rate changes on UK stock returns. Derivatives Use, Trading and Regulation 7(4): 306-323.
59. KASMAN, Saadet, VARDAR, Gülin, and TUNÇ, Gökçe. (2011). The impact of interest rate and exchange rate volatility on banks' stock returns and volatility: Evidence from Turkey. Economic Modelling, 28(3): 1328-1334.
60. KIM, Sangbae and IN, Francis. (2007). On the relationship between changes in stock prices and bond yields in the G7 countries: Wavelet analysis. Journal of International Financial Markets, Institutions and Money, 17(2): 167-179.
61. KONTONIKAS, Alexandros, MACDONALD, Ronald, and SAGGU, Aman. (2013). Stock market reaction to Fed funds rate surprises: State dependence and the financial crisis. Journal of Banking & Finance, 37(11): 4025-4037.
62. KORKEAMÄKI, Timo. (2011). Interest rate sensitivity of the European stock markets before and after the euro introduction. Journal of International Financial Markets, Institutions and Money, 21(5): 811-831.
63. KWIATKOWSKI, Denis, PHILLIPS, Peter C. B., SCHMIDT, Peter, and SHIN, Yongcheol. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root?. Journal of Econometrics, 54(1-3): 159-178.
64. LEE, Hahn S. (2004). Price and volatility spillovers in stock markets: A wavelet analysis. Applied Economic Letters, 11(3): 197-201.
65. LI, Lingheng. (2002). Macroeconomic factors and the correlation of stock and bond returns. Yale ICF Working Paper No. 02-46, available at SSRN: https://ssrn.com/abstract=363641
66. LINDSAY, Ronald W., PERCIVAL, Donald B., and ROTHROCK, Andrew. (1996). The discrete wavelet transform and the scale analysis of the surface properties of sea ice. IEEE Transactions on Geoscience and Remote Sensing, 34(3): 771-787.
67. LIU, Hsiang H. and CHEN, Sheng-Hung. (2016). Nonlinear relationships and volatility spillovers among house prices, interest rates and stock market prices. International Journal of Strategic Property Management, 20(4): 371-383.
68. LIU, Ming-Hua and SHRESTHA, Keshab M. (2008). Analysis of the long-term relationship between macro-economic variables and the Chinese stock market using heteroscedastic cointegration. Managerial Finance, 34(11): 744-755.
69. MALLAT, Stephane G. (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis & Machine Intelligence, 11(7): 674-693.
70. MASSET, Philippe. (2008). Analysis of financial time-series using Fourier and wavelet methods. University of Fribourg (Switzerland), Faculty of Economics and Social Science.
71. MAYSAMI, Ramin C. and Koh, Tiong S. (2000). A vector error correction model of the Singapore stock market. International Review of Economics and Finance, 9(1): 79-96.
72. MOYA-MARTÍNEZ, Pablo, FERRER-LAPEÑA, Roman, and ESCRIBANO-SOTOS, Francisco. (2015). Interest rate changes and stock returns in Spain: A wavelet analysis. BRQ Business Research Quarterly, 18(2): 95-110.
73. MÜLLER, U. A., DACOROGNA, Michel M., DAVÉ, R. D., PICTET, O. V., OLSEN, Richard B., and
74. WARD, J. R. (1993). Fractals and intrinsic time: A challenge to econometricians. Working Paper. Research Institute for Applied Economics, Zürich: Olsen & Associates.
75. OERTMANN, Peter, RENDU, Christel, and ZIMMERMANN, Heinz. (2000). Interest rate risk of European financial corporations. European Financial Management, 6(4): 459-478.
76. ÖZER, Mustafa and KAMISLI, Melik. (2015). Frequency domain causality analysis of interactions between financial markets of Turkey. International Business Research, 9(1): 176. DOI: https://doi.org/10.5539/ibr.v9n1p176
77. PERCIVAL, Donald. P., and Walden, Andrew. T. (2000). Wavelet methods for time series analysis (Volume 4). Cambridge University Press.
78. PERCIVAL, Donald. P. (1995). On estimation of the wavelet variance. Biometrika, 82(3): 619-631.
79. PETERS, Edgar E. (1994). Fractal market analysis: applying chaos theory to investment and economics (24th Edition). New York: John Wiley & Sons.
80. PHILLIPS, Peter C., and PERRON, Pierre. (1988). Testing for a unit root in time series regression. Biometrika, 75(2): 335-346. R Development Core Team, (2006). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0. (http://www.R-project.org)
81. RAMSEY, James. B. (2014). Functional representation, approximation, bases and wavelets. In Wavelet Applications in Economics and Finance (1-20). New York: Springer International Publishing.
82. RANKIN, Ewan and IDIL, Mumamed. S. (2014). A century of stock-bond correlations. RBA Bulletin, 67-74. Available at http://www.rba.gov.au/publications/bulletin/2014/sep/pdf/bu-0914-8.pdf
83. SANCAR, Canan, UĞUR, Ahmet, AKBAŞ, Yusuf E. (2017). Hisse senedi fiyat endeksi ile makroekonomik değişkenler arasındaki ilişkinin analizi: Türkiye Örneği. International Journal of Social Sciences and Education Research, 3(5): 1774-1786.
84. SAPOROSCHENKO, Andrew. (2002). The sensitivity of Japanese bank stock returns to economic factors: An examination of asset/liability differences and main bank status. Global Finance Journal, 13(2): 253-270.
85. SAYILGAN, Güven and SÜSLÜ, Cemil. (2011). Makroekonomik faktörlerin hisse senedi getirilerine etkisi: Türkiye ve gelişmekte olan piyasalar üzerine bir inceleme. Journal of BRSA Banking & Financial Markets, 5(1): 73-96.
86. SCHLEICHER, Christoph. (2002). An introduction to wavelets for economists. Working Paper 2002–3, Bank of Canada, Ottawa, Canada, 1-33.
87. SCHWERT, William. (1989). Why does stock market volatility change over time? The Journal of Finance, 44, 1115–1153.
88. SENSOY, Ahmet and SOBACI, Cihat. (2014). Effects of volatility shocks on the dynamic linkages between exchange rate, interest rate and the stock market: The case of Turkey. Economic Modelling, 43, 448-457.
89. SHILLER, Robert J. and BELTRATTI, Andrea. E. (1992). Stock prices and bond yields: Can their comovements be explained in terms of present value models?. Journal of Monetary Economics, 30(1): 25-46.
90. SOMAN, K. P., RAMACHANDRAN, K. I., and RESMI , N.G. (2010). Insight into wavelets: from theory to practice (3rd Edition). India: PHI Learning Pvt. Ltd.
91. STIVERS, Chris T., and SUN, Licheng. (2002). Stock market uncertainty and the relation between stock and bond returns (No. 2002-3). Federal Reserve Bank of Atlanta.
92. THORBECKE, Willem. (1997). On stock market returns and monetary policy. The Journal of Finance, 52(2): 635-654.
93. TITMAN, Sheridan and WARGA, Arthur. (1989). Stock returns as predictors of interest rates and inflation. Journal of Financial and Quantitative Analysis, 24(1): 47-58.
94. TIWARI, Aviral K. (2012). Decomposing time-frequency relationship between interest rates and share prices in India through wavelets. Munich Personal RePEc Archive, Paper No. 2692, available at http://www.iei1946.it/RePEc/ccg/TIWARI%20515_531.pdf
95. UDEGBUNAM, Raphael I., and OAIKHENAN, Hassan E. (2012). Interest rate risk of stock prices in Nigeria: empirical test of the duration and convexity model. Journal of Emerging Market Finance, 11(1): 93-113.
96. UYAR, Umut, UYAR, Sinem K., and GÖKÇE, Altan. (2016). Gösterge faiz oranı dalgalanmaları ve BIST endeksleri arasındaki ilişkinin eşanlı kantil regresyon ile analizi. Ege Akademik Bakış, 16(4): 587-598.
97. WHITCHER, Brandon. J. (2005). Waveslim: Basic wavelet routines for one-, two-and three-dimensional signal processing. R Package Version, 1(3).
98. WHITCHER, Brandon., GUTTORP, Peter, and PERCIVAL, Donald B. (2000). Wavelet analysis of covariance with application to atmospheric time series. Journal of Geophysical Research: Atmospheres (1984–2012): 105(D11), 14941-14962.