第五章 結論及建議
第二節 研究建議
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Against-Beta 於金融海嘯期間並無法有效改良原始的交易策略，推論的原因有 二：第一、投資人無法在金融海嘯期間明確辨別出流動性之高低，進而導致交 易策略失效，使得流動性指標的加入無法有效改良原始 Betting-Against-Beta；
第二、金融海嘯時因市場流動性不佳，使得流動性較低的股票無法順利交易，
再者，儘管投資人可能將持有資金投入高流動性的股票，即為 Amihud (2002)所 提出的流動性轉移(Flight to Liquidity)，但高流動性股票的需求上升，導致該股 票價格上揚進而降低其報酬率，進而使得以 P1(High)所建構的交易策略無法顯 著獲得正報酬。
本文最大的發現為流動性指標的加入長期而言，著實有助於改良傳統的 Betting-Against-Beta，同時因於建構投資組合時多了一層的篩選方法，故能以較 少的股票組成投資組合並執行交易策略，此概念也較符合交易策略的現實狀 況，換言之，投資人或經理人不需要以所有低 Beta 和高 Beta 的股票來建構投 資組合，只需以部分的股票即可執行交易策略。然而考量實務上的限制，像是 欲執行加入流動性指標的 Betting-Against-Beta 所形成的投資組合仍需耗費大量 的資金，故該策略較適合長期投資並不適合短線進出，再者，倘若市場為牛市 (Bull Market)，該策略之獲利性不見得必定優於其他單純交易策略(Pure Trading Strategy)，故可以考慮把加入流動性指標的 Betting-Against-Beta 與其他交易策 略形成混和的策略(Mixing Trading Strategies)。
第二節 研究建議
本研究所使用的 Beta 計算方法是根據 Frazzini and Pedersen (2014)，後續研 究者可利用其他 Beta 的計算方式去進行穩定性測試和進一步的探討，例如使用 最原始 Beta 的基本定義且將變異數和相關係數皆利用一年的時間計算，或是依 照 Scholes and Williams (1977)及 Dimson (1979)提出將非同步交易
(nonsynchronous trading)考慮 Beta 的計算方法，來比較研究結果是否有差異。
再者，本文使用的無風險利率是仿造 Frazzini and Pedersen (2014)利用一個月國
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庫債券利率(1-month T-Bill Rate)，後續發展可嘗試利用其他的指標作為無風險 利率，例如由 Auer and Schuhmacher (2015)提出可利用隔夜拆款利率(overnight repo rate)、隔夜指數交換(overnight index swap rate)、聯邦基金利率(the effective federal funds rate)及一個月倫敦銀行同業拆款利率(1-month LIBOR)。而關於流 動性指標的選取，本文依照 Zhou (2014)改良動能策略所使用的流動性指標，後 續研究者可使用 Amihud (2002)所提出的流動性不足指標(illiquidity indicator) 15 作為衡量流動性之代理變數，或是利用 Nishizaki et al. (2013)提出亦可利用價格 範圍對於週轉率的比率(daily price range to turnover ratio)16等其他變數進行探 討，並將流動性的組數提高以再次縮小建構交易策略所需的股票檔數，是以更 貼近投資行為。亦建議後續研究可將研究期間延長，例如選取 1966 年至 2015 年（共計 50 年）或是 1926 年至 2015 年（共計 90 年），並可進一步從月的績效 基準(monthly basis)下去探討 Betting-Against-Beta 是否存在一些規律，甚至可對 於研究期間的依照牛市或是熊市拆成子樣本做進一步的研究。最後，建議剔除 價格過低的股票以及考量交易成本已能更精確的計算出該交易策略的獲利性。
15 Amihud (2002)提出的流動性不足指標(Illiquidity Indicator)為𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖𝑚𝑚= 1/𝐷𝐷𝑖𝑖,𝑚𝑚∑𝐷𝐷𝑡𝑡=1𝑖𝑖,𝑚𝑚|𝑅𝑅𝑖𝑖𝑑𝑑|/
𝑉𝑉𝑀𝑀𝐿𝐿𝐷𝐷𝑖𝑖𝑑𝑑，其中𝐷𝐷𝑖𝑖,𝑚𝑚為第 i 檔股票於第 m 個月交易天數；𝑅𝑅𝑖𝑖𝑑𝑑為第 i 檔股票於第 m 個月之報酬率；
𝑉𝑉𝑀𝑀𝐿𝐿𝐷𝐷𝑖𝑖𝑑𝑑則為第 i 檔股票於第 m 個月之交易量。該指標愈大則代表流動性愈小，需要承受損失機 率與交易成本也就愈大。
16 價格範圍對於週轉率的比率(Daily Price Range to Turnover Ratio)定義為最高與最低交易價格 (Transaction Price)之差除以一天的週轉率。該比率愈小則代表流動性愈大。
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