Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T23:35:27.676Z Has data issue: false hasContentIssue false
  • English
  • Français

RIGHT-TAIL INFORMATION IN FINANCIAL MARKETS

Published online by Cambridge University Press:  20 August 2013

Zhijie Xiao
Zhijie Xiao*
Affiliation:
Boston College
*
*Address correspondence to Zhijie Xiao, Department of Economics, Boston College, Chestnut Hill, MA 02467; e-mail: xiaoz@bc.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

It is well known that when investors evaluate risk or opportunity, they often depart from predictions of expected utility. In addition, for both academic and financial communities it is a familiar stylized fact that stock return distributions are not normal. Both empirical evidence and experimental evidence indicate that distributional information of asset returns has an important impact on investors. In this paper, we argue that the right-tail distributional information of returns can provide very valuable information to investors and portfolio managers, and right-tail information should be used together with other (say, left-tail) information in analyzing financial markets. Here, we introduce measures for the right-tail distribution. Quantile regression estimators for the right-tail measures are proposed, and their asymptotic properties are developed. Statistical inference on testing for changes of right-tail distribution is also discussed. A Monte Carlo experiment is conducted to evaluate the performance of the proposed estimator. The proposed estimation method may also be applied to estimation of other measures in finance.

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 1 , February 2014 , pp. 94 - 126
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Artzner, P., Delbaen, F., Eber, J.-M., & Heath, D. (1999) Coherent measures of risk. Mathematical Finance 9, 203–28.Google Scholar
Bai, J. (1996) Testing for parameter constancy in linear regressions: An empirical distribution function approach. Econometrica 64, 597–622.CrossRefGoogle Scholar
Bassett, G.W., Koenker, R., & Kordas, G. (2004) Pessimistic portfolio allocation and choquet expected utility. Journal of Financial Econometrics 2, 477–492.CrossRefGoogle Scholar
Barberis, N. & Huang, M. (2008) Stocks as lotteries: The implications of probability weighting for security prices. American Economic Review.CrossRefGoogle Scholar
Bühlmann, P. (1994) Blockwise bootstrapped empirical process for stationary sequences. Annals of Statistics 22, 995–1012.Google Scholar
Cai, Z. & Wang, X. (2008) “Nonparametric estimation of conditional VaR and expected shortfall.” Journal of Econometrics 147, 120–130.Google Scholar
Campbell, J., Lettau, M., Malkiel, B., & Xu, Y. (2001) Have individual stocks become more volatile? An empirical exploration of idiosyncratic risk. Journal of Finance 56, 1–43.Google Scholar
Chen, X., Koenker, R., & Xiao, Z. (2009) Copula-Based nonlinear quantile autoregression. Econometrics Journal 12(1).Google Scholar
Chernozhukov, V. (2005) Extremal quantile regression. Annals of Statistics 33(2) 806–839.Google Scholar
Chernozhukov, V. & Du, S. (2007) Extremal Quantiles and Value-at-Risk. New Palgrave.Google Scholar
Csörgő, M. & Horváth, L. (1997) Limit Theorems in Change-Point Analysis. Wiley.Google Scholar
Diebold, F.X., Gunther, T.A., & Tay, A.S. (1998) Evaluating density forecasts with applications to financial risk management. International Economic Review 39, 863–883.Google Scholar
Engle, R. (1982) Autoregressive conditional heteroscedasticity with estimates of variance of United Kingdom inflation. Econometrica 50, 987–1008.Google Scholar
Hall, P. & Heyde, C.C. (1980) Martingale Limit Theory and Its Applications. Academic Press.Google Scholar
Inoue, A. (2001) Testing for distributional change in time series. Econometric Theory 17, 156–187.Google Scholar
Kahneman, D. & Tversky, A. (1979) Prospect theory: An analysis of decision under risk. Econometrica 47, 263–291.Google Scholar
Knight, K. (2001) Limiting distributions of linear programming estimators. Extremes 4, 87–103.Google Scholar
Koenker, R. (2005) Regression Quantiles. Cambridge University Press.CrossRefGoogle Scholar
Koenker, R. & Basset, G. (1978) Regression quantiles. Econometrica 46, 33–50.Google Scholar
Koenker, R. & Zhao, Q. (1996) Conditional quantile estimation and inference for ARCH models. Econometric Theory 12, 793–813.CrossRefGoogle Scholar
Koenker, R. & Xiao, Zhijie (2006) Quantile Autoregression. Journal of the American Statistical Association 101, 980–990.Google Scholar
Koul, H.L. (1991) A weak convergence result useful in robust autoregression. Journal of Statistical Planning and Inference 29, 1291–1308.Google Scholar
Koul, H.L. (1996) Asymptotics of some estimators and sequential residual empiricals in nonlinear time series. Annals of Statistics 245, 380–404.Google Scholar
Koul, H.L. & Mukherjee, K. (1994) Regression quantiles and related processes under long range dependent errors. Journal of Multivariate Analysis 51, 318–337.Google Scholar
Künsch, H.R. (1989) The jackknife and the bootstrap for general stationary observations. Annals of Statistics 17, 1217–1241.Google Scholar
Markowitz, H. (1952) Portfolio selection. Journal of Finance 7(1), 77–91.Google Scholar
Peligrad, M., Utev, S., & Wu, W.B. (2007) A maximal L-p inequality for stationary sequences and its applications. Proceedings of the American Mathematical Society 135, 541–550.CrossRefGoogle Scholar
Portnoy, S. (1984) Tightness of the sequence of empirical c.d.f. processes defined from regression fractiles. In Franke, J., Hardle, W., & Martin, D. (eds.), Robust and Nonlinear Time Series Analysis. Lecture Notes in Statistics, Vol. 26, pp. 231–246. Springer.Google Scholar
Portnoy, S. & Koenker, R. (1989) Adaptive L-estimation for linear models. Annals of Statistics 17, 362–381.CrossRefGoogle Scholar
RiskMetrics Group (1996)Google Scholar
Ruppert, D. & Carroll, R.J. (1980) Trimmed least squares estimation in the linear model. Journal of the American Statistical Association 75, 828–838.Google Scholar
Scaillet, O. (2004) Nonparametric estimation and sensitivity analysis of expected shortfall. Mathematical Finance 14, 115–129.Google Scholar
Statman, M. (2004) The diversification puzzle. Financial Analysts Journal 60(4), 44–53.Google Scholar
Su, L. & Xiao, Z. (2008) Testing structural change via regression quantiles. Statistics and probability letters. 78, 2768–2775.Google Scholar
Tversky, A. & Kahneman, D. (1992) Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5, 297–323.Google Scholar
Wan, C. & Xiao, Z. (2010) Idiosyncratic Volatility and the Cross-section of Stock Returns. Working paper.Google Scholar
Xiao, Z. & Koenker, R. (2009) Conditional quantile estimation and inference for GARCH models. Journal of the American Statistical Association 104(488), 1696–1712.Google Scholar
Xiao, Z., Linton, O., Carroll, R., & Mammen, E.. (2003) More efficient kernel estimation in nonparametric regression with autocorrelated errors. Journal of the American Statistical Association 98(464), 980–992.Google Scholar