市场风险与违约风险同时存在下的最优资产配置

摘要

The emergence of default risks, such as subprime mortgage crisis, Dubai credit crisis, and European sovereign debt crisis, has become an additional risk to market risks. It is important to understand how risk investors optimally allocate their wealth in the face of both market (e. g. interest rae risk) and default risks.rnDefault risk is the possibility that counterparty in a financial contract fails to fulfil a contractual commitment. Many financial instruments, including defautable bonds, vulnerable claims, and credit derivatives, are default-risk sensitive. This study investigates how investors allocate their wealth in four investment tools, including defaultable bond, stock, treasury, money market account in order to maximize the expect utility of their terminal wealth with a stochastic term structure for interest rates. Using Ito's Lemma formula, we assess the dynamics of defaultable bond, stock, treasury, and the money market account. Using the Martingale approach, we can derive optimal solutions to assess market and default risks by assuming that the utility is constant absolute risk aversion utility (CARA). If the utility function is CARA, the optimal strategy for stocks will have the "myopic" effect. The optimal strategy for treasuries is an increasing function of the interest rate risk premium. In another word, an investor will purchase more treasuries when the interest rate risk premium is increased.rnWhen the jump-risk premium is greater than one, investors will optimally invest in the defaultable bond because optimal strategy for the defaultable bond is an increasing function of the jump-risk premium. Holding other factors constant, investors purchase more defaultable bonds when the price of the jump-risk is increased. The optimal strategy for defaultable bond is a decreasing function of the loss rate. The greater the loss rate the lower the investor can recover. The optimal strategy of defaultable bonds depends on the investment horizon. The investor allocates more when she has longer investment horizon.%本文研究了当投资者同时面临市场风险(利率风险)和违约风险时,如何对可违约债券、国债、股票以及银行存款进行最优配置的问题.利用简约化模型来刻画可违约债券的违约风险,并给出其价格的动态方程.通过鞅方法给出了此优化问题的解析解,结果表明:股票的最优投资策略与Merton模型的结果相同；国债的最优投资策略是利率风险溢价的增函数；可违约债券的最优投资策略与跳跃(违约)风险溢价密切相关,只有当可违约债券的跳跃风险溢价大于1,即市场对跳跃风险进行风险补偿时,投资者才会持有可违约债券；否则,投资者对可违约债券的最优投资为零.