In pension fund management, the most important decision to make is the choice of a portfolio of assets. It means how much assets to invest and how to maintain and change the division asset rate. This study is to show optimal investment portfolio for the long-term investors with each risk attitude. The assets should be composed of group of risk free bonds, defaultable bonds and stocks. The main theme in this literature is to study how investors can efficiently allocate wealth among several financial asset categories in order to achieve utility maximization in the presence of different risk-return combinations. For that purpose, I reflect on the risk aversion utility function of multi period investment managers. This paper investigates how investors who face both interest rate risk and credit risk in addition to equity risk can optimally allocate their financial wealth in a dynamic, no arbitrage, continuous-time setup. I model credit risk through a defaultable zero-coupon bond and solve the stochastic differential equation of the bond under the recovery to the market value scheme. From the study I derive the optimal portfolio for maximizing investors' utility function subject to their risk aversion. The risk in this study not only includes standard deviation as indicated in Makowitz's mean-variance study but also market risk, credit risk and equity risk. In this paper, I want to prove that bonds (including risk-free bonds) have as much risk as stocks do. Many investors look for returns (with risk adjusted) from corporate bond holdings that could be higher than those from equity or risk-free bonds. And most of pension investors also raise their allocations to corporate bonds. Following results are drawn from the study. First,, the more risk aversive managers are, the less are the weight of defautauble bonds they hold. It may mean the market risk and credit risk of bonds are stronger than those of stocks to investors utility. Second, the weight of defaultable bonds decreases more rapidly than that of stocks with increasing risk aversion by managers. It shows that managers' preference of credit risk is more important than risks of holding stocks. Third, with time horizon, the weight of risk free bonds can decrease. It implies that the weight of defautable bonds may increase in probably 5 to 7 years by then, the investors may believe that the corporate bonds can be held to their expiration. Above all, I want to show the bonds including risk-free bonds are not any safer than stocks when we consider interest risk, credit risk or other risks at the same time. The bonds are also exposed to various risks, so the fund managers must provide against these risks. And if investors' utility function can serve as a managing standard, we can consider asset allocation with reflection on macro economics and various risks.
