Portfolio Choice With a Correlated Background Risk: Theory and Evidence

Abstract

We extend the static portfolio choice problem with a small background risk to the case of small partially correlated background risks. We show that respecting the theories under which risk substitution appears, except for the independence of background risk, it is perfectly rational for the individual to increase his optimal exposure to portfolio risk when risks are partially negatively correlated. Then, we test empirically the hypothesis of risk substitutability using INSEE data on French households. We find that households respond by increasing their stockholdings in response to the increase in future earnings uncertainty. This conclusion is in contradiction with results obtained in other countries. So, in light of these results, our model provides an explanation to account for the lack of empirical consensus on cross-country tests of risk substitution theory that encompasses and criticises all of them. ∗ This paper is strongly motivated by a common work with Andre Masson (Arrondel and Masson, 1996). The authors thank Rob Alessie, Jean-Marc Robin, Maximus Spadaro and two anymous referees for their comments on a previous version of the text. We acknowledge research support from CNRS and SEEUID. The second author acknowledges financial support from the Bank of Spain.