Dependence of Stock Returns in Bull and Bear Markets

Jadran Dobric; Gabriel Frahm; Friedrich Schmid

Dependence Modeling (2013)

  • Volume: 1, page 94-110
  • ISSN: 2300-2298

Abstract

top
Despite of its many shortcomings, Pearson’s rho is often used as an association measure for stock returns. A conditional version of Spearman’s rho is suggested as an alternative measure of association. This approach is purely nonparametric and avoids any kind of model misspecification. We derive hypothesis tests for the conditional rank-correlation coefficients particularly arising in bull and bear markets and study their finite-sample performance by Monte Carlo simulation. Further, the daily returns on stocks contained in the German stock index DAX 30 are analyzed. The empirical study reveals significant differences in the dependence of stock returns in bull and bear markets.

How to cite

top

Jadran Dobric, Gabriel Frahm, and Friedrich Schmid. "Dependence of Stock Returns in Bull and Bear Markets." Dependence Modeling 1 (2013): 94-110. <http://eudml.org/doc/266776>.

@article{JadranDobric2013,
abstract = {Despite of its many shortcomings, Pearson’s rho is often used as an association measure for stock returns. A conditional version of Spearman’s rho is suggested as an alternative measure of association. This approach is purely nonparametric and avoids any kind of model misspecification. We derive hypothesis tests for the conditional rank-correlation coefficients particularly arising in bull and bear markets and study their finite-sample performance by Monte Carlo simulation. Further, the daily returns on stocks contained in the German stock index DAX 30 are analyzed. The empirical study reveals significant differences in the dependence of stock returns in bull and bear markets.},
author = {Jadran Dobric, Gabriel Frahm, Friedrich Schmid},
journal = {Dependence Modeling},
keywords = {Bear market; bootstrapping; bull market; conditional Spearman’s rho; copulas; Monte Carlo simulation; Pearson’s rho; stock returns; bear market; conditional Spearman's rho; Pearson's rho},
language = {eng},
pages = {94-110},
title = {Dependence of Stock Returns in Bull and Bear Markets},
url = {http://eudml.org/doc/266776},
volume = {1},
year = {2013},
}

TY - JOUR
AU - Jadran Dobric
AU - Gabriel Frahm
AU - Friedrich Schmid
TI - Dependence of Stock Returns in Bull and Bear Markets
JO - Dependence Modeling
PY - 2013
VL - 1
SP - 94
EP - 110
AB - Despite of its many shortcomings, Pearson’s rho is often used as an association measure for stock returns. A conditional version of Spearman’s rho is suggested as an alternative measure of association. This approach is purely nonparametric and avoids any kind of model misspecification. We derive hypothesis tests for the conditional rank-correlation coefficients particularly arising in bull and bear markets and study their finite-sample performance by Monte Carlo simulation. Further, the daily returns on stocks contained in the German stock index DAX 30 are analyzed. The empirical study reveals significant differences in the dependence of stock returns in bull and bear markets.
LA - eng
KW - Bear market; bootstrapping; bull market; conditional Spearman’s rho; copulas; Monte Carlo simulation; Pearson’s rho; stock returns; bear market; conditional Spearman's rho; Pearson's rho
UR - http://eudml.org/doc/266776
ER -

References

top
  1. [1] A. Ang and J. Chen (2002), ‘Asymmetric correlations of equity portfolios’, J. Financ. Econ. 63, pp. 443–494. [Crossref] 
  2. [2] U. Cherubini, E. Luciano, and W. Vecchiato (2004), Copula Methods in Finance, John Wiley. Zbl1163.62081
  3. [3] J. Dobric and F. Schmid (2005), ‘Nonparametric estimation of the lower tail dependence λL in bivariate copulas’, J. Appl. Stat. 32, pp. 387–407. [Crossref] Zbl1121.62364
  4. [4] P. Doukhan, J.D. Fermanian, and G. Lang (2009), ‘An empirical central limit theorem with applications to copulas under weak dependence’, Stat. Inference Stoch. Process. 12, pp. 65–87. [Crossref] Zbl1333.62207
  5. [5] P. Embrechts, A.J. McNeil, and D. Straumann (2002), ‘Correlation and dependence in risk management: properties and pitfalls’, in: M. Dempster, ed., ‘Risk Management: Value at Risk and Beyond’, Cambridge University Press. 
  6. [6] C.B. Erb, C.R. Harvey, and T.E. Viskanta (1994), ‘Forecasting international equity correlations’, Financ. Anal. J. 50, pp. 32–45. [Crossref] 
  7. [7] I. Fortin and C. Kuzmics (2002), ‘Tail-dependence in stock return pairs’, Int. J. Intell. Syst. Account. Finance Manag. 11, pp. 89–107. [Crossref] 
  8. [8] G. Frahm, M. Junker, and R. Schmidt (2005), ‘Estimating the tail-dependence coefficient: properties and pitfalls’, Insurance Math. Econom. 37, pp. 80–100. [Crossref] Zbl1101.62012
  9. [9] P. Hall, J.L. Horowitz, and J. Bing-Yi (1995), ‘On blocking rules for the bootstrap with dependent data’, Biometrika 82, pp. 561–574. Zbl0830.62082
  10. [10] Y. Hong, J. Tu, and G. Zhou (2007), ‘Asymmetries in stock returns: statistical tests and economic evaluation’, Rev. Financ. Stud. 20, pp. 1547–1581. [Crossref] 
  11. [11] H. Hult and F. Lindskog (2002), ‘Multivariate extremes, aggregation and dependence in elliptical distributions’, Adv. in Appl. Probab. 34, pp. 587–608. Zbl1023.60021
  12. [12] P. Jaworski and M. Pitera (2013), ‘On spatial contagion and multivariate GARCH models’, Appl. Stoch. Models Bus. Ind. DOI: 10.1002/asmb.1977. [Crossref] 
  13. [13] H. Joe (1997), Multivariate Models and Dependence Concepts, Chapman & Hall. Zbl0990.62517
  14. [14] M. Junker and A. May (2005), ‘Measurement of aggregate risk with copulas’, Econom. J. 8, pp. 428–454. Zbl1125.91351
  15. [15] A. Juri and M. Wüthrich (2002), ‘Copula convergence theorems for tail events’, Insurance Math. Econom. 30, pp. 405–420. [Crossref] Zbl1039.62043
  16. [16] H.R. Künsch (1989), ‘The jackknife and the bootstrap for general stationary observations’, Ann. Statist. 17, pp. 1217–1241. [Crossref] Zbl0684.62035
  17. [17] A.J. McNeil, R. Frey, and P. Embrechts (2005), Quantitative Risk Management, Princeton University Press. Zbl1089.91037
  18. [18] R.B. Nelsen (2006), An Introduction to Copulas, Springer, second edition. Zbl1152.62030
  19. [19] A.J. Patton (2004), ‘On the out-of-sample importance of skewness and asymmetric dependence for asset allocation’, J. Financ. Econometrics 2, pp. 130–168. [Crossref] 
  20. [20] D.N. Politis (2003), ‘The impact of bootstrap methods on time series analysis’, Statist. Sci. 18, pp. 219–230. [Crossref] Zbl1332.62340
  21. [21] J.P. Romano and M. Wolf (2005), ‘Stepwise multiple testing as formalized data snooping’, Econometrica 73, pp. 1237–1282. Zbl1153.62310
  22. [22] F. Schmid and R. Schmidt (2006), ‘Multivariate extensions of Spearman’s rho and related statistics’, Statist. Probab. Lett. 77, pp. 407–416. [WoS] Zbl1108.62056
  23. [23] P. Silvapulle and C.W.J. Granger (2001), ‘Large returns, conditional correlation and portfolio diversification: a value-at-risk approach’, Quant. Finance 1, pp. 542–551. [Crossref] 
  24. [24] A. Sklar (1959), ‘Fonctions de répartition à n dimensions et leurs marges’, Publ. Inst. Statist. Univ. Paris 8, 229–231. 
  25. [25] A.W. van der Vaart (1998), Asymptotic Statistics, Cambridge University Press. Zbl0910.62001
  26. [26] B. Vaz de Melo Mendes (2005), ‘Asymmetric extreme interdependence in emerging equity markets’, Appl. Stoch. Models Bus. Ind. 21, pp. 483–498. Zbl1101.91330

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.