台灣可轉換公司債動態套利的策略與影響因素之實證分析

An Empirical Study on the Strategies and Influential Factors for Dynamic Arbitrage of Convertible Bonds in Taiwan

張銓浩(Chuan-Hao Chang)

指導教授 ： 倪衍森

淡江大學/管理學院/管理科學研究所企業經營碩士在職專班/碩士(2011年)

https://doi.org/10.6846/TKU.2011.00004

摘要

可轉債靜態套利已行之多年，但因其操作手法簡單以及可轉債市場漸趨效率性，致使靜態套利機會日漸稀少，故衍生出可轉債動態套利模式，而金融操作實務上普遍使用以Black and Scholes模型所求出之Delta係數作為可轉債動態套利中避險比例之計算依據。有鑒於可轉債漸趨效率性，與標的普通股連動性增加，故本文嘗試發展另一套創新之套利模式-以兩者間之相關係數做為可轉債動態套利中普通股放空比例之依歸，探討其獲利之可能性，並且與金融實務上普遍使用的Delta值作為放空比例之動態套利組合來比較報酬率孰佳。篩選10檔可轉債為樣本並求出10檔可轉債與其連結之標的普通股間的相關係數與Delta值，此外為表彰本研究之客觀性與實用性，遂選擇近幾年來股市多空頭交錯震盪劇烈的2008年作為動態套利部位操作期間，以3個月為一期，分別各進行4期動態套利操作，每天均模擬套利組合出場損益，10檔可轉債共計模擬5,000筆，並精密地將實務操作時的所有交易成本與利息收入全數納入，試圖驗證考量相關係數之動態套利是否無論股市走多或走空均有機會獲利。最後再以回歸模型來對影響動態套利盈虧因素做進一步的分析。
經實證結果，提出以下五點結論：
1.在研究期間無論考量相關係數或Delta係數來承作可轉債動態套利合計整年度總損益仍皆為正報酬，顯示可轉債動態套利大有可為。
2.10檔可轉債當中有8檔在實證中顯示以相關係數作為放空比例之動態套利組合報酬大幅高出以Delta係數做為放空比例達2倍以上不等，由此可以推論，無論股市走多或走空，以相關係數做為放空比例來操作可轉債動態套利組合均優於以Delta值做為放空比例來操作可轉債動態套利組合。
3.波動率與可轉債動態套利操作績效呈正相關，最佳之波動度大約在60%以上，有9成以上的機率可獲取正報酬，無論考量相關係數或考量Delta值來承作可轉債動態套利亦然，故此建議可於波動度低時進場建立可轉債套利部位，於波動度高時平倉獲利了結。
4.溢價率對於動態套利盈虧的影響呈正相關，溢價率越高時，可轉債動態套利的獲利空間有擴大的可能性；因此建議於可轉債處於價內、價平獲小幅價外時進場建立可轉債套利部位，於溢價率升高時出場獲利了結，可獲致較佳之套利效果。
5.交易成本對可轉債動態套利盈虧成負相關，操作時須將實務上之交易成本納入，以獲致最真實之損益數字。

關鍵字

可轉債 ； 動態套利 ； 相關係數 ； 波動率 ； 溢價率 ； 交易成本

並列摘要

Convertible bond static arbitrage has been prevailing for years. However, such arbitrage opportunities have been decreasing because it's easily replicable due to its lack of technical barrier. Moreover, the market has become more efficient. Therefore, a derivative is developed – the dynamic convertible arbitrage model ("DCAM"). In practice, the financial industry has widely adopted the Delta factor by Black and Scholes model as the hedging ratio for DCAM.
Given the gradually more efficient convertible market and the increasing correlation of convertibles with underlying stocks, we will discuss in the thesis about developing an innovative arbitrage model. Firstly, we evaluate the possibility to profit by using the correlation between convertibles and their underlying stocks as the hedging ratio for DCAM. Moreover, we compare such rate of return with that of the widely adopted method mentioned above, namely the method adopting the Delta ratio.
To elaborate on the methodology, ten convertible bonds that meet the research criteria were chosen as sample. Firstly, we calculate the correlation between the convertibles and their underlying stocks and the Delta ratios of the ten sample convertibles. For objectivity and practicality, the trading tenor is defined as the year of 2008, in which the stock market was extremely volatile. Each period has three months, and therefore there are four periods in total for DCAM trading. For each trading day, we simulate the profit/loss as if the position is squared on the day. In total, there are 5,000 simulations for the ten sample convertibles. Subsequently, we calculate the net return by including all trading costs and interest income incurred in the real market. The goal is to examine whether we can profit regardless of the market condition if we adopt the innovative method mentioned above, namely using the correlation. Finally, we use regression to analyze the variables that impact the profit/loss of dynamic convertible arbitrage trading. Based on the practical research, we have four conclusions:
1. All ten sample convertibles have positive total annual returns during the volatile 2008, regardless which ratio (correlation or Delta) is adopted for DCAM. Therefore, we conclude that dynamic convertible arbitrage still has value.
2. Eight out of ten sample convertibles have more than twice return by using the correlations rather than the Deltas as hedging ratio for DCAM. To conclude, the correlation DCAM model outperforms the Delta DCAM in either bull or bear market.
3. The convertible volatility is positively correlated to the return of DCAM. The optimal volatility is about 60% or above, with which there is 90% to profit. The conclusion applies for both the correlation DCAM and the Delta DCAM. Based on this conclusion, we can suggest that investors can establish convertible arbitrage position during low-volatility period and realize the profit when the volatility picks up.
4. The convertible premium is positively correlated to the return of DCAM. The higher the premium, the more likely that DCAM profit will increase. Therefore, we suggest that investors enhance the arbitrage strategy by establishing convertible arbitrage position when the convertible is in-the-money, at par, or slightly out-of-the money, and realize the profit when the premium picks up.
5. Trading costs is negatively correlated to the return of DCAM. Therefore, the transaction costs shall include, to get the most realistic results.

並列關鍵字

Convertible Bond ； Dynamic Arbitrage ； Correlation Coefficient ； Volatility ； Premium Rate ； Trading Costs

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