回歸平均的探索

Abstract

回歸平均在金融市場以很多不同的形式存在，且這些形式都符合於有效率的市場。然而，投資者與學者意味的回歸平均定義始終缺乏。本文提出關於時間序列回歸平均的定義且領悟平均隨時間變化的潛在意義。使用波動率指數、美國十年公債的利率與布蘭特原油和西德州中級原油的價差之周資料，估計回歸平均的水平與速度。結果顯示回歸平均的現象並非永續而是間斷性地存在，且不同的時間週期導致不一致的結果。

Mean reversion exists in many different forms within financial markets, and none of these forms is necessarily inconsistent with efficient markets. However, there is a lack of precision in what many investment practitioners and scholars mean by the term “mean reversion”. In this paper, we propose a formal definition of what most investment practitioners and scholars seem to mean by “mean reversion”. In this paper, we recognize the potential significance of time variation in price reversion, and propose a time-dependent definition of mean reversion, which is based on the Ornstein-Uhlenbeck (O-U) process and the Geometric Brownian Motion (GBM). Using weekly data of VIX (Volatility Index) traded in CBOE from 1990 to 2007, interest rate of the United States Treasury Benchmark Bond 10-year from 1984 to 2007 and the spread between Brent crude oil and West Texas Intermediate crude oil traded in NYMEX from 1997 to 2007 to estimate the level and speed of mean reversion, and we show that the mean reversion phenomenon is not persistent but recurring, and there are inconsistent results by using different time scales.