Econometrics of Risk pp 219-231 | Cite as
Quantile Regression Under Asymmetric Laplace Distribution in Capital Asset Pricing Model
Abstract
We used a quantile regression under asymmetric Laplace distribution for predicting stock returns. Specifically, we apply this method to the classical capital asset pricing model (CAPM) to estimate the beta coefficient which measure risk in the portfolios management analysis at given levels of quantile. Quantile regression estimation is equivalent to the parametric case where the error term is asymmetrically Laplace distributed. Finally, we use the method to measures the volatility of a portfolio relative to the market.
Keywords
Asymmetric Laplace distribution Capital asset pricing Financial econometric Quantile regressionNotes
Acknowledgments
The authors thank Prof. Dr. Hung T. Nguyen for his helpful comments and suggestions. We would like to thank referee’s comments and suggestions on the manuscript.
References
- 1.Barnes, L.M., Hughes, W.A.: A Quantile Regression Analysis of the Cross Section of Stock Market Returns. Federal Reserve Bank of Boston, Working Paper (2002)Google Scholar
- 2.Chen, W.S.C., Lin, S., Yu, L.H.P.: Smooth transition quantile capital asset pricing models with heteroscedasticity. Comput. Econ. 40, 19–48 (2012)CrossRefMATHGoogle Scholar
- 3.Koenker, R.: Quantile Regression, vol. 38. Cambridge University Press (2005)Google Scholar
- 4.Koenker, R., Gilbert, B.J.: Regression quantiles. Econom.: J. Econom. Soc. 33–50 (1978)Google Scholar
- 5.Kotz, S., van Drop, R.J.: Link between two-sided power and asymmetric Laplace distributions: with applications to mean and variance approximations. Stat. Probab. Lett. 71, 383–394 (2005)CrossRefMATHGoogle Scholar
- 6.Linden, M.: A model for stock return distribution. Int. J. Financ. Econ. 6, 159–169 (2001)CrossRefGoogle Scholar
- 7.Lintner, J.: The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Rev. Econ. Stat. 47(1), 12–37 (1965)CrossRefGoogle Scholar
- 8.Mukherji, S.: The capital asset pricing model’s risk-free rate. Int. J. Bus. Financ. Res. 5, 793–808 (2011)Google Scholar
- 9.Noh, H., Ghouch, A., Keilegom, I.: Quality of Fit Measures in the Framework of Quantile. Université catholique de Louvain, Discussion Paper (2011)Google Scholar
- 10.Sánchez, B.L., Lachos, H.V., Labra, V.F.: Likelihood based inference for quantile regression using the asymmetric Laplace distribution. J. Stat. Comput. Simul. 81, 1565–1578 (2013)Google Scholar
- 11.Sharpe, William F.: Capital asset prices: a theory of market equilibrium under conditions of risk. J. Financ. 19(3), 425–442 (1964)MathSciNetGoogle Scholar