論選擇權預期報酬與風險特徵

On the Option Expected Return and Risk Characteristics

選擇權可以改變標的資產的報酬分配與其報酬／風險特徵，投資人得以精確地裁剪投資組合的風險，配合個人的偏好。與過去大量的文獻關注於選擇權的定價問題相對照，本文聚焦於選擇權被持有至到期的報酬與風險之理論與實證上的探討，以彌補過去文獻的缺憾。本文首先推導選擇權被持有至到期的報酬機率分配函數（PDFs），因此投資人得以預估選擇權的報酬率落在某區間的機率。其次，本文探討選擇權的報酬與風險之特性。最後，本文檢驗台指選擇權之報酬率與波動性之實際型態與理論型態吻合的程度。有趣的是，實際型態（雖然實證資料無法涵蓋所有的價位（moneyness））大致符合理論型態。雖然，Coval and Shumway （2001）的理論結果也與本文實證結果一致，但他們的理論結果只侷限於價內的部份，而且實證所採用的價位資料更為狹窄。

Options can alter the return distribution of the underlying asset and its risk-return characteristics, allowing investors to precisely tailor their risks to their preferences. In contrast with a lot of literature on option pricing, this paper focuses on the theoretical and empirical nature of option returns and risks for holding options up to expiration. We firstly derive the probability density functions (PDFs) for calls and puts, enabling investors to calculate the probabilities that option returns will fall in some ranges. We then investigate the properties of their expected returns and variances. Finally, we use TAIEX Options to examine the patterns of option returns and volatilities as functions of option strike price. Interestingly, we find that the actual patterns of option returns and volatilities, though under a narrower range of strike prices, are consistent with our theoretical predictions. Although the actual patterns of option returns are also consistent with Coval and Shumway (2001), their propositions only deal with the range of security prices for which the options are in the money, and moreover their empirical data for the moneyness of options are even in a narrower range.