In this dissertation, I explore the impact of idiosyncratic risk on asset returns. The first essay examines how idiosyncratic risk affects the cross-section of stock returns. I use an exponential GARCH model to forecast expected idiosyncratic volatility and employ a combination of the size effect, value premium, return momentum and short-term reversal to measure relative mispricing. I find that stock returns monotonically increase in idiosyncratic risk for relatively undervalued stocks and monotonically decrease in idiosyncratic risk for relatively overvalued stocks. This phenomenon is robust to various subsamples and industries, and cannot be explained by risk factors or firm characteristics. Further, transaction costs, short-sale constraints and information uncertainty cannot account for the role of idiosyncratic risk. Overall, these findings are consistent with the limits of arbitrage arguments and demonstrate the importance of idiosyncratic risk as an arbitrage cost. The second essay studies the cross-sectional determinants of delta-hedged stock option returns with an emphasis on the pricing of volatility risk. We find that the average delta-hedged option returns are significantly negative for most stocks, and they decrease monotonically with both total and idiosyncratic volatility of the underlying stock. Our results are robust and cannot be explained by the Fama-French factors, market volatility risk, jump risk, or the effect of past stock return and volatility-related option mispricing. Our results strongly support a negative market price of volatility risk specification that is proportional to the volatility level. Reflecting this volatility risk premium, writing covered calls on high volatility stocks on average earns about 2% more per month than selling covered calls on low volatility stocks. This spread is higher when it is more difficult to arbitrage between stock and option. / text

本文提出一個動態隱含波動度函數模型，以改善一般隱含波動度函數難以隨時間的經過而調整波動度曲線且無法描述資料的時間序列特性等缺點。本文模型為兩階段隱含波動度函數模型，分別配適隱含波動度函數的時間穩定(time-invariant)部分與時間不穩定(time-variant)部分。 本文模型在波動度的時間不穩定部分配適非對稱GARCH(1,1)過程，以描述隱含波動度的時間序列特性。本文使用的非對稱GARCH(1,1)過程將標的資產的正報酬與負報酬對價平隱含波動度的影響分別估計，並將蘊含於歷史價平隱含波動度中的訊息及標的資產報酬率與波動度之間的關連性藉由價平隱含波動度過程納入隱含波動度函數中，使隱含波動度函數能納入波動度的時間序列特性及資產報酬與波動度的相關性，藉此納入最近期的市場資訊，以增加隱含波動度模型的解釋及預測能力。時間穩定部分則根據Pena et al.(1999)的研究結果，取不對稱二次函數形式以配適實證上發現的笑狀波幅現象。時間穩定部分並導入相對價內外程度做為變數，以之描述價內外程度、距到期時間、及價平隱含波動度三者的交互關係；並以相對隱含波動度作為被解釋變數，使隱含波動度函數模型除理論上包含了比先前文獻提出的模型更多的訊息及彈性外，還能描繪「隱含波動度函數隨波動度的高低水準而變動」、「越接近到期日，隱含波動度對價內外程度的曲線越彎曲」、「隱含波動度函數為非對稱的曲線」、「波動度和資產價格有很高的相關性」等實證上常發現的現象。 本文以統計測度及交易策略之獲利能力檢定模型的解釋能力及預測能力是否具有統計與經濟上的顯著性。本文歸納之前文獻提出的不同隱含波動度函數模型，並以之與本文提出的模型做比較。本文以台指選擇權五分鐘交易頻率的成交價作為實證標的，以2003年1月1日~2006年12月31日作為樣本期間，並將模型解釋力及AIC作為模型樣本內配適能力之比較標準，我們發現本文提出的模型具有最佳的資料解釋能力。本文以2006年7月1日~2006年12月31日作為隱含波動度模型預測期間，以統計誤差及delta投資策略檢定模型的預測能力是否具有統計及經濟上的顯著性。實證結果指出，本文提出的模型對於預測下一期的隱含波動度及下一期的選擇權價格，皆有相當良好的表現。關於統計顯著性方面，我們發現本文提出的動態隱含波動度函數模型對於未來的隱含波動度及選擇權價格的預測偏誤約為其他隱含波動度函數模型的五分之一，而預測方向正確頻率亦高於預測錯誤的頻率且超過50%。關於經濟顯著性方面，本文使用delta投資組合進行經濟顯著性檢定，結果發現在不考慮交易成本下，本文提出的模型具有顯著的獲利能力。顯示去除標的資產價格變動對選擇權造成的影響後，選擇權波動度的預測準確性確實能經由delta投資組合捕捉；在考慮交易成本後，各模型皆無法獲得超額報酬。最後，本文提出的動態隱含波動度函數模型在考量非同步交易問題、30分鐘及60分鐘等不同的資料頻率、不同的投資組合交易策略後，整體的結論依然不變。 / This paper proposes a new implied volatility function to facilitate implied volatility forecasting and option pricing. This function specifically takes the time variation in the option implied volatility into account. Our model considers the time-variant part and fits it with an asymmetric GARCH(1,1) model, so that our model contains the information in the returns of spot asset and contains the relationship of the returns and the volatility of spot asset. This function also takes the time invariant in the option implied volatility into account. Our model fits the time invariant part with an asymmetric quadratic functional form to model the smile on the volatility. Our model describes the phenomena often found in the literature, such as the implied volatility level increases as time to maturity decreases, the curvature of the dependence of implied volatility on moneyness increases as options near maturity, the implied volatility curve changes as the volatility level changes, and the implied volatility function is an asymmetric curve. For the empirical results, we used a sample of 5 minutes transaction prices for Taiwan stock index options. For the in-sample period January 1, 2003–June 30, 2006, our model has the highest adjusted- and lowest AIC. For the out-of-sample period July 1, 2006–December 31, 2006, the statistical significance shows that our model substantially improves the forecasting ability and reduces the out-of-sample valuation errors in comparison with previous implied volatility functions. We conjecture that such good performance may be due to the ability of the GARCH model to simultaneously capture the correlation of volatility with spot returns and the path dependence in volatility. To test the economic significance of our model, we examine the profitability of the delta-hedged trading strategy based on various volatility models. We find that although these strategies are able to generate profits without transaction costs, their profits disappear quickly when the transaction costs are taken into consideration. Our conclusions were unchanged when we considered the non-synchronization problem or when we test various data frequency and different strategies.

第一篇論述討論處置效果於選擇權市場的實證。處置效果係指投資人在處分資產時，傾向盡快賣出有未實現利得的投資部位，並且繼續持有有未實現損失的投資部位的行為偏誤現象。文獻上有關處置效果的實證多半集中在股票市場而少有於選擇權市場的實證。選擇權市場一般認為是具有私有資訊及較具備金融知識與經驗的投資人會選擇交易的市場。本文實證處置效果在指數選擇權市場上的影響。我們認為對於選擇權投資人來說，價內外程度是最重要且顯而易見的資訊，是很直觀可以衡量可能利得及損失的參考點。相較於傳統衡量根據過去交易價格所形成的未實現損益指標，價內外程度更能吸引投資人的注意力。以本文所提出的基於價內外程度衡量之賣出傾向指標(Moneyness-based Propensity to Sell, MPS)以及根據Grinblatt and Han (2005)所形成的調整後未實現資本利得指標(adjusted Capital Gains Overhang, ACGO)，每周將買權(賣權)排序成五等分後，我們發現持有最高等分的MPS或ACGO的買權(賣權)並賣出最低等分的買權(賣權)所形成的投資組合能夠產生超額報酬，顯示處置效果在指數選擇權市場亦存在。利用雙重排序(double sorting)的方法，我們發現MPS相較於ACGO，是較能夠在選擇權市場捕捉處置效果的指標。第二篇論述討論相似度衡量策略在期貨市場獲利的可能性。文獻上對於技術交易是否能產生顯著的報酬結果並不一致，然而實務上分析過去的價格走勢並使用技術指標所產生的訊號，是廣泛被接受的。現有測試技術交易指標獲利能力的文獻，通常假設投資人在實證測試的樣本期間一致性的參考某個交易指標產生的交易訊號並依此交易。然而實務上投資人可能同時參考不同的交易指標，每次交易可能根據不同交易指標所產生的訊號，且投資人會從歷史交易價格走勢中尋找類似於現有走勢的狀況，以這些歷史走勢接續的報酬率做為現有走勢未來報酬率的預期值。本文中我們提出一個較符合實際狀況的決策過程來描述技術交易投資人的行為，並重新檢視技術交易的獲利能力。我們提出的決策過程包含三個步驟。首先投資人建立一個特徵向量，包含投資人所認為足以預測未來報酬率並足以描述現況的指標。第二個步驟，投資人從過去某段期間中尋找相似於現有特徵向量的歷史狀況，並以這些歷史狀況接續的報酬率來作為預測的根據。最後，投資人依照過去的歷史狀況與現在有多相似，作為接續報酬率的加權權重，並以相似度權重加權平均報酬來做為未來報酬率的預測值，我們將依照相似度加權報酬所產生交易訊號所形成的策略稱為相似度衡量交易策略(Similarity-based trading rules)。我們檢視相似度衡量交易策略在九個不同的期貨市場中的獲利能力，在考量data-snooping及交易成本後，每日相似度衡量交易策略仍在其中六個市場中獲得顯著的報酬率。 / The disposition effect, which refers to the tendency of investors to selling their winning investments too soon and to hold losing investments too long, has been well-documented in the extant literature. However, while empirical researches focus on examining the behavioral bias in the stock market, little attention is paid to the option market, where most informed investors and sophisticated traders gather. This essay tests for the disposition effect on the index options market. We argue that moneyness, the most salient and readily available information for option investors, is a natural reference point for potential gains and losses, which likely attracts market participants’ attention more than traditional measures that are based on past trading prices. Based on the Moneyness-based Propensity to Sell (MPS) measure that we introduce and an adjusted capital gains overhang (ACGO) measure of Grinblatt and Han (2005), we find that a strategy formed by buying calls/puts in the highest MPS or ACGO quintile and selling those in the lowest quintile would generate significant abnormal returns, suggesting the presence of the disposition effect. Using double sorting method, we find that the MPS is better as a measure in capturing the disposition effect on the options market than the ACGO. While the literature documents mixed results for the profitability of technical trading rules, the use of technical buy/sell signals based on analyzing past prices is widely accepted by practitioners. The existing literature on testing the predictive ability of technical trading mostly assumes that a technical investor consistently makes investment decisions based on the buy/sell signals according to one particular trading rule during the entire sample period. However this may be far from reality. Technical investors may simultaneously make predictions based on different technical indicators and follow different technical signals. Furthermore, they analyze historical price patterns that are similar to the current market condition and make assessment of future returns based on the subsequent returns of these similar patterns. The process is known as charting. We attempt to propose a more realistic decision-making process that incorporates the similarity-based predictors to account for technical investors’ decisions in the real world and reexamine the profitability of technical trading rules. The proposed process includes three steps. First, the investor attempts to predict future returns based on a vector of current characteristics that is sufficient for his assessment of the future returns and to depict the present scenario of the stock market. Second, the investor searches for the similar patterns in a specific time window prior to the current date and make an assessment of the future returns based on how similar these past patterns and the current pattern are and how rewarding the subsequent returns of the similar patterns are. Third, the investor is assumed to form a similarity-based indicator which is an assessment of the future returns depended on the similarity-weighted average of all previously observed values of the subsequent returns. The technical investor is then assumed to buy/sell according to the signals generated by the similarity-based trading rules (SBTR). We examine the profitability of the SBTR in nine futures markets and find significantly positive and robust returns after considering the data-snooping adjustments and transaction costs in six of the nine markets.