# 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

## Access Full Article

top## Abstract

top## How to cite

topJadran 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] A. Ang and J. Chen (2002), ‘Asymmetric correlations of equity portfolios’, J. Financ. Econ. 63, pp. 443–494. [Crossref]
- [2] U. Cherubini, E. Luciano, and W. Vecchiato (2004), Copula Methods in Finance, John Wiley. Zbl1163.62081
- [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] 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] 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] C.B. Erb, C.R. Harvey, and T.E. Viskanta (1994), ‘Forecasting international equity correlations’, Financ. Anal. J. 50, pp. 32–45. [Crossref]
- [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] 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] 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] 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] 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] 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] H. Joe (1997), Multivariate Models and Dependence Concepts, Chapman & Hall. Zbl0990.62517
- [14] M. Junker and A. May (2005), ‘Measurement of aggregate risk with copulas’, Econom. J. 8, pp. 428–454. Zbl1125.91351
- [15] A. Juri and M. Wüthrich (2002), ‘Copula convergence theorems for tail events’, Insurance Math. Econom. 30, pp. 405–420. [Crossref] Zbl1039.62043
- [16] H.R. Künsch (1989), ‘The jackknife and the bootstrap for general stationary observations’, Ann. Statist. 17, pp. 1217–1241. [Crossref] Zbl0684.62035
- [17] A.J. McNeil, R. Frey, and P. Embrechts (2005), Quantitative Risk Management, Princeton University Press. Zbl1089.91037
- [18] R.B. Nelsen (2006), An Introduction to Copulas, Springer, second edition. Zbl1152.62030
- [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] D.N. Politis (2003), ‘The impact of bootstrap methods on time series analysis’, Statist. Sci. 18, pp. 219–230. [Crossref] Zbl1332.62340
- [21] J.P. Romano and M. Wolf (2005), ‘Stepwise multiple testing as formalized data snooping’, Econometrica 73, pp. 1237–1282. Zbl1153.62310
- [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] 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] A. Sklar (1959), ‘Fonctions de répartition à n dimensions et leurs marges’, Publ. Inst. Statist. Univ. Paris 8, 229–231.
- [25] A.W. van der Vaart (1998), Asymptotic Statistics, Cambridge University Press. Zbl0910.62001
- [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 ?

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