Lyapunov函數生成交易策略之實證分析

Abstract

1999 年Erhard Robert Fernholz 首先提出以函數生成交易策略的概念，藉由掌握函數的性質，我們便能夠控制在投資組合的行為。其優點在於對於市場模型的假設較少，而且不須估計參數，投資組合可直接由市場上觀察到的價格計算。 2016 年Ioannis Karatzas 與Johannes Ruf 考慮一類特別的函數─Lyapunov function─提出兩種函數生成交易策略(分別適用於投資大量股票與少量股票)並在數學上證明發生套利機會的充分條件以及所需時間。 然而，在上述的論文當中並沒有考慮到股利發放以及手續費對套利機會的影響，因此，本文研究方向為考慮股利發放與手續費對於函數生成交易策略的影響。

E.R Fernholz introduced the construction of a certain class of portfolios,which is known as "functionally-generated" portfolios,in 1999. Karatzas & Ruf(2016) consider a special class of generating functions, Lyapunov functions. In the paper, they not only review the results which are given by Fernholz, but also generalize the result from portfolio to trading strategies. However, these research does not consider the effect of dividend and transaction cost. Even the previous papers give the result that,under specific market property, the time period of investment is long enough, there exists arbitrage opportunity. As times of trading increases, the effect of transaction cost becomes much more important, it can turns the return from positive to negative. For instance, in Taiwan market, the transaction cost is about 0.06%of total investment. Therefore, transaction cost plays an important role in trading strategies.