On-Line Portfolio Selection with Moving Average Reversion

On-line portfolio selection has attracted increasing interests in machine learning and AI communities recently. Empirical evidences show that stock's high and low prices are temporary and stock price relatives are likely to follow the mean reversion phenomenon. While the existing mean reversion strategies are shown to achieve good empirical performance on many real datasets, they often make the single-period mean reversion assumption, which is not always satisfied in some real datasets, leading to poor performance when the assumption does not hold. To overcome the limitation, this article proposes a multiple-period mean reversion, or so-called Moving Average Reversion (MAR), and a new on-line portfolio selection strategy named "On-Line Moving Average Reversion" (OLMAR), which exploits MAR by applying powerful online learning techniques. From our empirical results, we found that OLMAR can overcome the drawback of existing mean reversion algorithms and achieve significantly better results, especially on the datasets where the existing mean reversion algorithms failed. In addition to superior trading performance, OLMAR also runs extremely fast, further supporting its practical applicability to a wide range of applications.Comment: ICML201

Are Price-Earnings Ratios Mean Reverting? An Empirical Study

Mean reversion in stock prices is a highly studied area in the financial literature with controversial findings. While some economists have found evidence of mean reverting processes in stock prices, many argue in favor of the Efficient Market Hypothesis which states stock prices are random walk processes. This paper seeks to add to the literature on mean reversion but testing for evidence in price-earnings ratios rather than stock prices. The study employs a robust regression model controlling for company-specific and general market factors that influence price-earnings ratio deviations. After correcting for heteroskedasticity, serial correlation, and unit root processes, the results indicate mean reverting behavior does exist in US equities from 2008- 2017 and mean reversion in price-earnings ratios may occur more quickly than mean reversion of stock prices. The outcome of this paper also implies some level of endogeneity in the Three-Factor-Model proposed by Fama and French (1992)

Mean Reversion in International Stock Markets: An Empirical Analysis of the 20th Century

This paper analyzes mean reversion in international stock markets during the period 1900-2008, using annual data. Our panel of stock indexes in seventeen developed countries, covering a time span of more than a century, allows us to analyze in detail the dynamics of the mean-reversion process. In the period 1900-2008 it takes stock prices about 13.8 years, on average, to absorb half of a shock. However, using a rolling-window approach we establish large fluctuations in the speed of mean reversion over time. The highest mean reversion speed is found for the period including the Great Depression and the start of World War II. Furthermore, the early years of the Cold War and the period covering the Oil Crisis of 1973, the Energy Crisis of 1979 and Black Monday in 1987 are also characterized by relatively fast mean reversion. Overall, we document half-lives ranging from a minimum of 2.1 years to a maximum of 23.8 years. In a substantial number of time periods no significant mean reversion is found at all, which underlines the fact that the choice of data sample contributes substantially to the evidence in favor of mean reversion. Our results suggest that the speed at which stocks revert to their fundamental value is higher in periods of high economic uncertainty, caused by major economic and political events.mean reversion, market efficiency

Downside risk of derivative portfolios with mean-reverting underlyings

We carry out a Monte-Carlo simulation of a standard portfolio management strategy involving derivatives, to estimate the sensitivity of its downside risk to a change of mean-reversion of the underlyings. We find that the higher the intensity of mean-reversion, the lower the probability of reaching a pre-determined loss level. This phenomenon appears of large statistical significance for large enough loss levels. We also find that the higher the mean-reversion intensity of the underlyings, the longer the expected time to reach those loss levels. The simulations suggest that selecting underlyings with high mean-reversion effect is a natural way to reduce the downside risk of those widely traded assets.Monte Carlo simulation; mean-reverting underlyings

Mean Reversion Expectations and the 1987 Stock Market Crash: An Empirical Investigation

After the stock market crash of 1987, Fischer Black proposed a model in which he explained the crash by inconsistencies in the formation of expectations of mean reversion in stock returns. Following this explanation, a model that allows for mean reversion in stock returns is estimated on daily stock index data around the crash of 1987. The results strongly support Black’s hypothesis. Simulations show that on Friday Oct 16, 1987, a crash of 20 percent or more had a probability of more than seven percent.stock-market crash, mean reversion, stock return predictability, change-points

Mean Reversion in Equilibrium Asset Prices

Recent empirical studies have found that stock returns contain substantial negative serial correlation at long horizons. We examine this finding with a series of Monte Carlo simulations in order to demonstrate that it is consistent with an equilibrium model of asset pricing. When investors display only a moderate degree of risk aversion, commonly used measures of mean reversion in stock prices calculated from actual returns data nearly always lie within a 60 percent confidence interval of the median of the Monte Carlo distributions. From this evidence, we conclude that the degree of serial correlation in the data could plausibly have been generated by our model.