Predicting stock returns in the capital asset pricing model using quantile regression and belief functions

Abstract

We consider an inference method for prediction based on belief functions in quantile regression with an asymmetric Laplace distribution. Specifically, we apply this method to the capital asset pricing model to estimate the beta coefficient and measure volatility under various market conditions at given levels of quantile. Likelihood-based belief functions are calculated from historical data of the securities in the S&P500 market. The results give us evidence on the systematic risk, in the form of a consonant belief function specified from the asymmetric Laplace distribution likelihood function given recorded data. Finally, we use the method to forecast the return of an individual stock.