Optimal Portfolio Policies of Levered Investor in Presence of Default Risk

This paper presents a utility-based approach to value the borrower optimal behavior in presence of credit risk. The paper solves for the dynamic portfolio choices of a borrower. We thereby show that the presence of debt leads to a substantial modification in the borrower's behavior across states of the economy. It mainly says that debt makes the borrower more risk averse than an unlevered investor, by inducing a lower risk exposure across all states of the economy. Second, the model allow us to conclude that the borrower would unambiguously increase the risk exposure if his expectations concerning default at maturity are high Third, the model is able to capture the "flight to safety" phenomena for relatively unfavorable states of the economy. Fourth, the optimal risk exposure is increasing in the borrower's recovery rate level, while inducing a more conservative behavior in taking extra risk. In terms of the portfolio allocation in those state of the economy characterized from high default probability, the borrower whose preference structure is given by CRRA (CARA) utility function, will allocate more money in risky assets the higher (lower) is his own recovery rate. Lastly, the default probability, of a borrower is positively related with his own recovery rate Other results to follow.