Optimal Portfolio in Outperforming Its Liability Benchmark for a Defined Benefit Pension Plan

摘要 本文於確定給付退休金計劃下，探討基金經理人於最差基金財務短絀情境發生前極大化管理目標之最適投資組合，基金比值過程定義為基金現值與負債指標之比例，管理人將於指定最差基金比值發生前極大化達成既定經營目標之機率，隨時間改變之基金投資集合包括無風險之現金、債券與股票。本研究建構隨機控制模型描述此最適化問題，並以動態規劃方法求解，由結果歸納，經理人之最適策略包含極小化基金比值變異之避險因素，風險偏好及跨期投資集合相關之避險因素與模型狀態變數相關之避險因素。本研究利用馬可夫練逼近法逼近隨機控制的數值解，結果顯示基金經理人須握有很大部位的債券，且不同的投資期間對於最適投資決策有很大的影響。 關鍵字: 短絀、確定給付、負債指標、隨機控制、動態規劃。Abstract This paper analyzes the portfolio problem that is a pension fund manager has to maximize the possibility of reaching his managerial goal before the worst scenario shortfall occurs in a defined benefit pension scheme. The fund ratio process defined as the ratio between the fund level and its accrued liability benchmark is attained to maximize the probability that the predetermined target is achieved before it falls below an intolerable boundary. The time-varying opportunity set in our study includes risk-free cash, bonds and stock index. The problems are formulated as a stochastic control framework and are solved through dynamics programming. In this study, the optimal portfolio are characterized by three components, the liability hedging component, the intertemporal hedging component against changes in the opportunity set, and the temporal hedging component minimizing the variation in fund ratio growth. The Markov chain approximation methods are employed to approximate the stochastic control solutions numerically. The result shows that fund managers should hold large proportions of bonds and time horizon plays a crucial role in constructing the optimal portfolio. Keywords: shortfall; defined benefit; liability benchmark; stochastic control; dynamic programming