保護性上下限與保護性賣權之風險∕報酬特徵比較及其最適履約價

A Comparison of the Risk/Return Characteristics between Protective Collars and Protective Puts and the Optimal Strike Prices

保護性上下限與保護性賣權對資產價格下跌都具有保護功能，各具優劣。事實上，保護性上下限為保護性賣權的變形。因保護性賣權的保險成本太高，保護性上下限策略是在保護性賣權策略下另外賣出買權來降低保險成本，甚至零成本，也可能產生淨權利金收入。然而，此猶如刀之兩面，有利亦有弊：若遇到資產價格未預期地大漲，利用保護性上下限反而喪失了資產增值的空間，因此，資產上漲潛力的損失與保險成本的降低存在有一均衡點。過去有關保護性上下限與保護性賣權的一些文獻僅止於實證面，探討不同市場（如：金融風暴期間、景氣上升期間）下兩種保護性策略績效的差異。本文則從理論上進一步有系統地探討在各種經濟變數（如：股價成長率、波動率等）變動下，兩資產保護策略的績效、風險與報酬特徵之差異及均衡兩策略績效之最適買權履約價。研究結果顯示，本文模式可完美地解釋兩資產保護策略風險與報酬的差異及投資人在實際應用上如何選取最適的履約價。

Protective collars and protective puts all provide the function of asset downside protection, each having its own advantage and disadvantage. Actually, a protective collar is a variant of a protective put. Since buying protective puts can be expensive, writing additional out-of-the-money (OTM) calls can substantially reduce the cost of puts. In fact, it is possible to construct a protective collar that is either “costless” (called a “zero-cost collar”) or even generate a net credit for investors. Yet, this is like the other edge of a knife—a merit often accompanies a shortage. The main drawback of the protective collar is that the investor gives away the upside potential if it happens to have unexpected asset price rallies. Therefore, there must exist a tradeoff between the reduction of protection cost and the loss of upside potential for protective collars. Past literature on the protective collars and protective puts only emphasizes empirically on the difference in performance under different markets (e.g., financial crises periods, booming markets, etc.). The purposes of this paper are first to theoretically investigate and to compare the performance, risk/return characteristics, and the optimal strike prices that balance the benefits and shortage for the two strategies under various economic scenarios (e.g., the growth rate of asset price, volatility of asset price, etc.), and then to obtain the optimal strike price for the call option in the protective collar. The results indicate that the models presented in this paper can perfectly explain the differences in risk and returns for the two asset protection strategies, and suggest the optimal strike prices in practical uses.