Portfolio selection and portfolio frontier with background risk

• We derive two-fund separation property under background risk.
• We investigate portfolio frontier shapes with background risk.
• We analyze portfolio variances with background risk or not.
• We derive Zero-Beta CAPM theory under background risk.

This study analyzes individual portfolio selection in the presence of background risk. Under the expected utility framework, this study determines necessary and sufficient conditions of utility functions for two-fund monetary separation with independently additive and multiplicative background risks, respectively. Under a mean–variance framework, this study analyzes the portfolio frontier characteristic given dependently additive background risk. The main findings include the two-fund separation property, portfolio frontier shapes, and a portfolio variance comparison between situations with and without background risk and Zero-Beta CAPM. In particular, the portfolio frontier constructed from n risky assets plus one riskless asset is analogous with only n risky assets.