Quantile Prediction in the Capital Asset Pricing Model Using Histogram-Valued Data

The purpose of this paper is to introduce an approach to prediction quantile on Capital Asset Pricing Model (CAPM) using histogram-valued data. This study applies this purpose to predict the 5-min returns of two prominent stocks, namely Apple (AAPL) and Microsoft (MSFT), within the S&P500 market covering from January 1, 2019, to June 30, 2023. Moreover, we obtain data for the S&P500 index and US government bonds, representing the market return and risk-free rates, respectively. In this study we found that all quantiles of AAPL stock returns exhibit beta values greater than one, indicating that investing in AAPL will have a higher return than market return, while all quantiles of MSFT stock returns exhibit beta values less than one, indicating that investing in MSFT will have a less return than market return. Additionally, the results of the R-squared value of AAPL confirm the dynamic relationship between the asset and the market return at various levels of quantiles. On the other hand, the R-squared value for MSFT exhibits peaks in both the lower and upper quantile ranges of the U-shape curve which provides insights into the dynamics of MSFT stock returns in relation to the market returns at various quantile levels.