Portfolio Optimization with a Defaultable Security

by Tomasz R. Bielecki of the Illinois Institute of Technology, and
Inwon Jang of Merrimack College

February 27, 2007

Abstract: In this paper we derive a closed-form solution for a representative investor who optimally allocates her wealth among the following securities: a credit-risky asset, a default-free bank account, and a stock. Although the inclusion of a credit-related financial product in the portfolio selection is more realistic, no closed-form solutions to date are given in the literature when a recovery value is considered in the event of a default. While most authors have assumed some recovery scheme in their initial model set up, they do not address the portfolio problem with a recovery when a default actually occurs. Given the tractability of the recovery of market value, we solved the optimal portfolio problem for the representative investor whose utility function is a Constant Relative Risk Aversion utility function.

We find that the investor will allocate larger fraction of wealth to the defaultable security as long as the default-event risk is priced. These results are very intuitive and reasonable since it indicates that if the default risk premium is not priced properly the investor purchases less defaultable securities.

Keywords: Portfolio optimization, defaultable security, credit risk, recovery of market value.

Published in: Asia-Pacific Financial Markets, Vol. 13, No. 2, (June 2006), pp. 113-127.

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