共整合向量模型之平均數-變異數動態投資組合方法探討

Abstract

本文的資產價格數列模型，採用PCB 共整合模型，將它整理成VAR(1)的型式，式子中的參數，必須符合本文的公式，然後我們藉由這個模型，使用Markowitz(1952)提出的平均數－變異數最佳化方法(Mean－Variance optimization approach)－固定風險、求報酬最大化的目標下，延伸作多期資產配置，再分別對一階段方法、二階段方法作討論。在有交易成本及截距項的情況下，比較這二種方法，同樣風險下的淨期望報酬。另外也比較，在特殊例子下，一階段方法與二階段方法，何種方法在同樣的風險下，能為我們帶來較大的淨期望報酬。

This paper uses the PCB Cointegration Model to organize the sequence information of the price of financial commodity into the VAR(1) type. The parameters in the formula VAR(1) must meet the formulas in this paper. We extend Markowitz’s mean-variance optimization approach published in 1952, which is to maximize the return under the fixed risk, to multi-stage asset allocation, and use this new model to discuss the one-stage method and the two-stage method. The paper then compares the net returns of the two methods when undertaking the same risk, under the condition of transaction cost and intercept. We will also examine the one-stage method and the two-stage method in the special cases to determine which one can bring the better net expected return under the same risk.