最適跨期投資策略之套利與避險分析

最適跨期投資策略是近代財務文獻所探討的重要議題，Merton (1969, 1971) 首先建構回饋控制模型描述多期財務決策過程，利用動態規劃方法分析最適策略之套利與避險行為，但是考量投資限制及資產時間變動因素時，將大幅增加求解之複雜度。本研究回顧 Sorensen (1999) 之逼近模型，以平賭過程描述基金財富之未來價值，嘗試納入不同投資限制、風險偏好與市場風險之考量，以單期擬似動態規劃擬定最適策略，利用定值相對風險規避效用函數描述投資管理人之風險程度，於動態完備市場假設，以到期最適效用為目標檢視動態最適資產配置。歸納數值結果顯示，(1)風險規避程度增加時，投資於風險性資產之比例將下降，長年期債券之比例將增加；(2)無投資限制時，經理人可藉由幾項標的達成最適化資產配置，給定投資限制條件，資產配置無法完全反應套利與避險效果；(3)股票收益波動度增加，投資者將減少股票比例，增加投資債券市場以降低風險，並增加短年期債券之比例與降低長年期債券比例；(4)利率風險變大，投資於股票比例將些微增加，債券投資比例將稍許下降，而長短年期債券持有比例無明顯改變。
關鍵字：平賭過程、擬似動態規劃、定值相對風險規避、動態完備市場

Speculating and Hedging in Optimal Investment Strategy for Multi-Period Fund Management

　　　　　　　　　　　　　　(Shih-Chieh Chang)＊(Chang-Ye Tu)＊(Yi-Shu Deng)

This optimal investment strategy of long-term fund managers is one of the crucial issues discussed in modern financial literature. Merton (1969, 1971) initially explores the financial decision process by constructing the feedback control mechanism. Explicit solutions using dynamic programming are employed to analyze the arbitraging and hedging behaviors within the process. Unfortunately, this kind of approach becomes complicated when the investment constraints and dynamic pattern of the opportunity set are incorporated into the model. In this study, the quasi-dynamic approach proposed in Sorensen (1999) is carefully reviewed in analyzing optimal investment behaviors. A constant relative risk aversion (CRRA) utility function is adopted to depict the risk preference of investors within their investment time horizons. The optimal strategy is examined by maximizing the indirect utility function through the optimal growth portfolio. The results show: (1) the holding of risky assets decreases and long-term bonds increases as the manager risk aversion increases and (2) without investment restrictions, managers can achieve optimality.
Keywords: long-term fund management, optimal investment strategy, hedging