# How to Explain Momentum with Rational Investors — It’s complicated.

//, Momentum Investing Research, \$mtum/How to Explain Momentum with Rational Investors — It’s complicated.

## How to Explain Momentum with Rational Investors — It’s complicated.

By | 2017-08-18T17:03:23+00:00 February 14th, 2017|Research Insights, Momentum Investing Research, \$mtum|1 Comment

A recent theory paper from researchers at NYU and Rutgers attempts to explain the empirical evidence on stock serial correlation (e.g., short-term reversal, long-term stock reversal, and classic stock momentum). The interesting wrinkle with this paper is the authors don’t need to assume irrational trading behavior to generate momentum effects.

The core assumptions are as follows:

• The authors assume a group of traders who don’t always trade based purely on fundamentals. For example, a trader may trade for liquidity reasons because they need money for a down payment on a house.
• The authors also need the assumption that a liquidity trader’s demands can’t be perfectly equated to supply/demand in real-time and thus might move prices away from fundamental value in unpredictable ways.

The “noise” created by liquidity traders moving prices away from their efficient level can create a level of uncertainty. The authors then show that this uncertainty can give rise to serial correlation effects such as momentum and reversals.(1)

To highlight the relationship, the authors rely on some simple concepts and mathematics that are completely transparent and intuitive (har har).(2)

For example, proposition 1 is as follows:

The authors are kind enough to map out their multi-page proof in the appendix — below is a simple highlight:

As the analysis highlights, proving that momentum effects can be derived in a world without irrational traders and improper expectation formation is straight forward…Yikes!

## The Dynamics of Belief Formation and Price Momentum

• Alex Dontoh
• Johua Ronen
• Bharat Sarath

In classical perfect and complete markets, prices form a Martingale and stock returns (or equivalently, successive price changes) are serially uncorrelated. However, there is considerable evidence in the finance literature showing that stock returns are serially correlated both in the short and the long-term. This empirical phenomenon has been viewed as a violation of semistrong efficiency and has resulted in considerable discussion in the literature. In this paper we demonstrate that within a multi-period noisy rational expectations equilibrium framework, a first order autoregressive (AR-1) liquidity trading process, by itself, suffices to give rise to systematic correlations in price changes, either positive or negative, depending on the specific parameters of the process, even if the (unknown) underlying liquidation value is fixed. That is, unsystematic random fluctuations in observed prices arising from factors such as liquidity trading affect Bayesian belief formation, and thereby trading strategies, in such a way that equilibrium price changes can manifest both momentum and reversals.

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References   [ + ]

 1 ↑ The mechanism seems similar to the limit of arbitrage argument put forth by De Long, Shleifer, Summers, and Waldmann. Also the mechanism outlined in John Hussman’s article 2 ↑ Note, what follows is mostly tongue in cheek. The paper is actually quite interesting and I respect the thought leadership from the authors. Nonetheless, this paper highlights the massive effort academic researchers invest in order to try and explain various empirical phenomenon in the stock market.

### About the Author: Wesley R. Gray, Ph.D.

After serving as a Captain in the United States Marine Corps, Dr. Gray earned a PhD, and worked as a finance professor at Drexel University. Dr. Gray’s interest in bridging the research gap between academia and industry led him to found Alpha Architect, an asset management that delivers affordable active exposures for tax-sensitive investors. Dr. Gray has published four books and a number of academic articles. Wes is a regular contributor to multiple industry outlets, to include the following: Wall Street Journal, Forbes, ETF.com, and the CFA Institute. Dr. Gray earned an MBA and a PhD in finance from the University of Chicago and graduated magna cum laude with a BS from The Wharton School of the University of Pennsylvania.

### One Comment

1. Stef February 15, 2017 at 5:56 am

In physics this reminds me of collapse theories (e.g. GRW in quantum mechanics), that try to solve the paradoxes associated with the measurement problem by introducing unnecessary mathematical complications to explain the wavefunction collapse, because they don’t what to abandon their initial dogmas. The same seems to be the case here with the dogma that market participants are rational.