Capital Asset Pricing Model with Interval Data

We used interval-valued data to predict stock returns rather than just point valued data. Specifically, we used these interval values in the classical capital asset pricing model to estimate the beta coefficient that represents the risk in the portfolios management analysis. We also use the method to obtain a point valued of asset returns from the interval-valued data to measure the sensitivity of the asset return and the market return. Finally, AIC criterion indicated that this approach can provide us better results than use the close price for prediction.

[1]  C. Manski.  Partial Identification of Probability Distributions , 2003 .

[2]  Songsak Sriboonchitta,et al.  Quantile Regression Under Asymmetric Laplace Distribution in Capital Asset Pricing Model , 2015, Econometrics of Risk.

[3]  Anthony W. Hughes,et al.  A Quantile Regression Analysis of the Cross Section of Stock Market Returns , 2002 .

[4]  Andrea Wiencierz,et al.  Likelihood-based Imprecise Regression , 2012, Int. J. Approx. Reason..

[5]  Francisco de A. T. de Carvalho,et al.  Centre and Range method for fitting a linear regression model to symbolic interval data , 2008, Comput. Stat. Data Anal..

[6]  Phil Diamond,et al.  Least squares fitting of compact set-valued data , 1990 .

[7]  Cathy W. S. Chen,et al.  Smooth Transition Quantile Capital Asset Pricing Models with Heteroscedasticity , 2011, Computational Economics.

[8]  W. Sharpe.  CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* , 1964 .

[9]  J. Lintner.  THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS , 1965 .

[10]  Francisco de A. T. de Carvalho,et al.  A New Method to Fit a Linear Regression Model for Interval-Valued Data , 2004, KI.

[11]  Wolfgang Näther,et al.  Linear Regression with Random Fuzzy Variables: Extended Classical Estimates, Best Linear Estimates, Least Squares Estimates , 1998, Inf. Sci..

[12]  M. Gil,et al.  Least squares fitting of an affine function and strength of association for interval-valued data , 2002 .

[13]  Dominikus Noll,et al.  Generic Gâteaux-differentiability of convex functions on small sets , 1990 .

[14]  C. Manski,et al.  Inference on Regressions with Interval Data on a Regressor or Outcome , 2002 .

[15]  Lynne Billard,et al.  Dependencies and Variation Components of Symbolic Interval-Valued Data , 2007 .