Cross Risk Apportionment And Non-Financial Correlated Background Uncertainty

Abstract

This paper considers a portfolio problem with one safe asset and one risky asset in the presence of background risk. We assume that the background risk is a non-financial variable and it is correlated to financial risk. The aim of this paper is to investigate the effect of correlation on portfolio choices. While we find that an increase in correlation lowers (raises) the expected utility for mixed correlation averse (seeking) individuals, contrary to intuition, it does not  necessarily reduce (increase) the investment in the risky asset. We determine the conditions needed to reduce (increase) the investment and find that these conditions can be related to cross risk apportionment, which is the type of preferences for the combination of good and bad. We also introduce ambiguity into the correlation and investigate its effects on the portfolio choices.

Keywords: Ambiguity, Background Uncertainty, Bivariate Utility Function, Cross Risk Apportionment, Linear Payoff, Portfolio Choice