選擇權在裁製標的資產報酬／風險特徵之有效性

The Usefulness of Options in Tailoring the Return/Risk Characteristics of the Underlying Asset

選擇權投資組合的報酬分配是重要的，因為選擇權可以改變標的資產的報酬分配和其報酬／風險特徵，允許投資人依據偏好精確地裁製其報酬／風險。為了探究這些報酬／風險特徵，現有文獻一般使用模擬方法（例如，Bookstaber and Clarke, 1983）。本文提出一般化的架構來分析選擇權投資組合的報酬／風險特徵，使投資人可明確推導出持有選擇權投資組合至到期時報酬分配的機率密度函數（PDF）公式。這個架構的優點是，使用者可以很容易地分析報酬／風險特徵並進行嚴謹的驗證，克服文獻模擬的缺點。由於掩護性買權與保護性賣權策略，近來備受大型選擇權交易所和機構投資人的關注以及在文獻中缺乏對其風險／報酬分析的理論驗證，本文以此兩種策略為例來探討其重要的報酬／風險特徵。研究結果顯示，選擇權可以極顯著地改變標的資產的報酬分配及其報酬／風險特徵。

Understanding the return distributions of portfolio with options is important because options have altered the return distribution of the underlying asset and its return/risk characteristics, allowing investors to precisely tailor the return/risk to their preferences. To explore these return/risk characteristics, existing literature generally use the simulation methodology (e.g., Bookstaber and Clarke, 1983). This paper proposes a generalized framework to analyze the return/risk characteristics for a portfolio with options, enabling the investors to derive the explicit formula of the probability density function (PDF) of the return distribution for holding a portfolio with options till expiration. The merit with this framework is that the users can easily analyze the return/risk characteristics and conduct rigorous examinations, overcoming the shortcomings of simulation in the literature. Due to much attention of the covered call and protective put strategies paid recently by large option exchanges and institutional investors and the lack of theoretical examination of their risk/return analysis in the literature, this paper uses them as examples to explore their important return/risk characteristics. Our results indicate that options can very significantly alter the return distribution of the underlying asset and its return/risk characteristics.