On Optimal Risk/Return-Efficient Arbitrage Portfolio

Arbitrage portfolios arise extensively in the theory and practice of finance. However, compared to the standard portfolios, there are still somewhat little publications focusing on the analytics and empirical tests of the optimal arbitrage portfolios. Based on the comparison of the standard portfolio and the arbitrage portfolio, Fang (2006) introduces the strict definition of the arbitrage size, arbitrage portfolio and its return and then Fang (2007) and Fang (2008) respectively present mean-variance analyses for portfolios and arbitrage opportunities. However, it is very complicate to obtain the frontier arbitrage portfolio and there is no analytical formula for general frontier arbitrage portfolios since Fang´s definition of the arbitrage portfolio includes a non-smooth condition. In this paper, compared with the Sharp ratio, the optimal risk/return-efficient arbitrage portfolio is introduced, which will be shown to be related to Korkie and Turtle´s frontier arbitrage portfolio (Korkie and Turtle, 2002), and hence to be expressed by an analytical formula.