  Selecting stock portfolios and assessing their relative volatility risk
compared to the market as a whole, market indices, or other portfolios is of
great importance to professional fund managers and individual investors alike.
Our research uses the cross-sectional intrinsic entropy (CSIE) model to
estimate the cross-sectional volatility of the stock groups that can be
considered together as portfolio constituents. In our study, we benchmark
portfolio volatility risks against the volatility of the entire market provided
by the CSIE and the volatility of market indices computed using longitudinal
data. This article introduces CSIE-based betas to characterise the relative
volatility risk of the portfolio against market indices and the market as a
whole. We empirically prove that, through CSIE-based betas, multiple sets of
symbols that outperform the market indices in terms of rate of return while
maintaining the same level of risk or even lower than the one exhibited by the
market index can be discovered, for any given time interval. These sets of
symbols can be used as constituent stock portfolios and, in connection with the
perspective provided by the CSIE volatility estimates, to hierarchically assess
their relative volatility risk within the broader context of the overall
volatility of the stock market.
