投資組合保險策略之報酬分配、特性及最適履約價

The Return Distribution, Properties, and Optimal Strike Price for the Portfolio Insurance Strategy

若標的股票的報酬分配為常態分配投資，投資組合保險策略所導出的報酬分配稱為左尖峰截尾的常態分配。現有的文獻對於此種分配之機率密度函數既無解析的公式，對其報酬分配的特性亦無嚴謹的證明，導致關於保護性賣權之預期報酬與風險的ㄧ些觀點論述不正確。除了彌補此缺憾外，本文之目的為探討保護性賣權之報酬／風險特性及執行績效下之最適履約價。詳言之，本文首先推導保護性賣權所產生的報酬機率密度函數、到期的報酬機率及探討其報酬分配特性。此外，與此種分配風險相關的參數，如偏態、峰態以及系統風險，本文亦嚴謹檢驗之。最後，本文探討執行保護性賣權最佳績效之最適履約價。

The portfolio insurance induced return distribution is called the left-peaked and truncated normal distribution if the underlying stock returns are normally distributed. Previous literature on this type of distribution neither provides an analytical formula for its probability density function (PDF), nor offers rigorous proofs for the properties of its return distribution, making some viewpoints concerning the expected return and risk of the protective puts incorrect. In addition to bridging this gap, the purpose of this paper is to investigate the characteristics of return/risk for protective put and the optimal strike price for the performance of protective put. Specifically, we first derive the PDF for the protective put and show the probability for some specific returns on the protective put and then investigate the properties of its return distribution. Furthermore, some risk relevant parameters such as skewness and kurtosis for this type of return distribution and the systematic risk for an insured portfolio are also examined. Finally, the optimal strike price that maximizes the performance of a protective put strategy is investigated.