Stock Selection And The Optimal Arbitrage Portfolio Choice When Compared With The Standard Portfolio Analysis

Arbitrage is defined as risk-free arbitrage in general textbooks. It shows a portfolio with the opposite positions of securities, which will surely bring non-negative return at sometime in the future. Generalized definition of arbitrage is in terms of arbitrage opportunities, that there exists an arbitrage portfolio, the expected return of which should yield not less than other arbitrage portfolios with the same risk. In China, with the short selling permitted, the arbitrage is considered more. However, even the definition of the arbitrage portfolio is not clear.Arbitrage portfolios are also known as self-financing portfolios or zero weighted portfolios. Fang Shuhong(2006) pointed out that the definition of arbitrage portfolio without size constraints is not accurate. When arbitrage portfolio is irrelevant to its size, the efficient frontier will be the expansion or contraction of the size of one optimal arbitrage portfolio with some certain return. In order to form a normative definition of arbitrage portfolio and get the correct efficient frontier, a constraint of size should be added.Based on the findings of Fang Shuhong(2006&2007), the author explores the difference between the arbitrage portfolio and the standard investment portfolio and how arbitrage portfolio impact the investment strategy. In addition, the numerical analysis based on the data of practical stock return is completed to research the properties of arbitrage portfolio.