基差波動與套利策略之研究─以ETF 為例

The Study of the Volatility in the Basis and the Arbitrage Strategy─For the Case of ETF

薛文雄(Wen-Shyong Shiue)

指導教授 ： 張國華

中原大學/工學院/工業工程研究所/碩士(2005年)

https://doi.org/10.6840/cycu200500229

摘要

摘要
近年來，衍生性金融商品相繼地推出，提供投資人新的投資工具以及利用
較少資金賺取更多報酬的機會。在本研究中，我們利用衍生性金融商品的搭
配，以尋求投資機會，找出獨立於股票市場且報酬率要穩定及優於定存利率之
投資策略。我們從研究市場指數和期貨指數之間的差值找出投資機會，來進行
投資套利，這差值即是所謂的基差。
我們假設期貨與現貨均服從SDE (Stochastic Different Equation)，利用基差
的動態模式，且考慮到期日效應，觀察有無套利投資機會，當基差大於分配中
決定的臨界值時，我們在市場與期貨之間進行交易，進而配合投資策略，以求
穩定獲利。我們利用本地的ETF 與期貨來做實證的操作，觀察獲利情形。
關鍵字（詞）：基差、隨機過程、到期日效應、ETF

關鍵字

基差 ； 隨機過程 ； 到期日效應 ； ETF

並列摘要

In recent years, the emergence of new financial derivatives provides investors
new investment products and supply speculators and arbitragers the opportunity to
earn more profit with less fund.
In this thesis, we consider the index futures and study the stochastic behavior
of the corresponding basis. We assume that the futures price and spot price follow
stochastic differential equation (SDE). Next, the important parameters of the process
were defined with taking the maturity effect into account. Furthermore, basing on
the underlying stochastic process, the arbitrage opportunity was defined as well. The
timing to trade was determined by calculating the distribution of the maximum and
minimum of the basis. In the market portfolio, the Taiwan Top 50 Tracker Fund
(the first ETF in Taiwan) is used as the part of the stock on hand to discuss that
whether TTT can be the replacement of the Taiwan 50 Index (TSE50) and TTT
is utilized to make arbitrage with the Taiwan 50 Index Futures (T5F) when TTT
is discount (premium) and T5F is positive spread (negative spread). In addition, a
linear program was set up to find a portfolio of which the resulting profit with futures
is close to the one obtained from the market starting form the transaction date.
The compare of the performance of investment strategy between two portfolios
will be made. The returns of TTT and the portfolio are higher than the interest rate
of saving deposit and are independent of the market. The investment compound of
TTT & T5F is better than the investment compound of portfolio & TX.
keywords: Basis; stochastic process; Maturity effect; ETF.

並列關鍵字

stochastic process ； Maturity effect ； Basis ； ETF.

參考文獻

[6] Chi, C. J. (2004) ” A Study ofETFs inArbitrage of Taiwan Stock Index Futures,”

MSCI Taiwan Index Futures,” Master thesis, National Cheng Kung University.

[2] Bhanot, K. (1998) ”Stochastic Volatility Functions Implicit in Eurodollar Futures

No. 8, 895-909.

Master thesis, Tamkang University.