Dashan Huang

Singapore Management University – Lee Kong Chian School of Business

Fuwei Jiang

Singapore Management University – Lee Kong Chian School of Business

Jun Tu

Singapore Management University – Lee Kong Chian School of Business

Guofu Zhou

Washington University in St. Louis – Olin School of Business

Abstract

We document significant short-term time-series mean reversion in the up-market and momentum in the down-market. We find that the market risk premium for one to 12 months can be negatively predicted in the up-market and positively predicted in the down-market by a mean reversion indicator that is defined as the past year cumulative return of market portfolio minus its long term mean and standardized by its annualized volatility. This asymmetric predictability is significant in-sample and out-of-sample, and applies to cross-sectional portfolios sorted by size, book-to-market ratio, industry, momentum, and long- and short-term reversals. The finding of this paper is consistent with Veronesi (1999) that investors overreact to bad news in the up-market and underreact to good news in the down-market if they are uncertain about the market state.

Mean Reversion, Momentum and Return Predictability – Introduction

Time-series mean reversion and momentum in the stock market study whether future stock returns can be negatively or positively predicted by their past returns. For holding periods more than one year, Fama and French (1988) and Poterba and Summers (1988), among others, show that future stock returns can be negatively predicted by their past returns. For horizons less than one year, however, the evidence is subject to some controversy. For example, Jegadeesh (1991) finds that the next one month returns can be negatively predicted by their lagged multiyear returns. Lewellen (2002) shows the past one year returns negatively predict future monthly returns for up to 18 months. In contrast, Conrad and Kaul (1989) show that next month returns can be positively predicted by their past week or month returns since stocks display positive and significant autocorrelations. Moskowitz, Ooi, and Pedersen (2012) find that the past 12-month volatility-scaled returns positively predict the future one to 12 month volatility-scaled returns. These seemingly opposite findings raise the question of whether the stock market follows a time-series momentum or a mean reversion pattern for a short-term horizon.

This paper examines whether both mean reversion and momentum can coexist over time and explores conditions under which mean reversion is more pronounced than momentum, and verse visa. Investors have long held the view that the stock market fluctuates around its long-term mean. For example, John Bogle (2012), the legendary investor and founder of the Vanguard Group that manages billions of retirement funds for teachers and college professors, says that the number one rule of investing (out of his ten rules) is “Remember reversion to the mean.”

What is hot today may not be hot tomorrow. The stock market reverts to its long-term mean over the long run. To capture this idea, we simply define a mean reversion indicator (MRI) at any given time as the past year cumulative return minus its long term mean (the mean up to time t) and standardized by its annualized volatility.1 The intuition is that, when we look at the market this month, if the cumulative return since one year ago has already been 26%, the stock market will be more likely to go down than to go up next month since the long-term mean is less than 13%.

Investors also have long viewed that the stock market has up- and down-trends.3 The most popular concept of an up-market is defined as those periods during which the stock market index level is above its 200-day moving average. Otherwise, a down-market occurs. According to Siegel (1994), the use of the moving averages goes back at least to the 1930s. In practice, the 200-day moving average has been widely plotted for years in investment letters, trading softwares, and newspapers (such as Investor Business Daily).

Mean Reversion, Momentum and Return Predictability via SSRN