Can the Market Multiply and Divide? Non-Proportional Thinking in Financial Markets

68 Pages Posted: 26 Mar 2018 Last revised: 16 Apr 2019

See all articles by Kelly Shue

Kelly Shue

Yale School of Management; National Bureau of Economic Research (NBER)

Richard Townsend

University of California, San Diego (UCSD) - Rady School of Management

Multiple version iconThere are 2 versions of this paper

Date Written: April 6, 2019

Abstract

Nominal stock prices are arbitrary. Therefore, when evaluating how a piece of news should affect the price of a stock, rational investors should think in percentage rather than dollar terms. However, dollar price changes are ubiquitously reported and discussed. This may both cause and reflect a tendency of investors to think about the impact of news in dollar terms, leading to more extreme return responses to news for lower-priced stocks. We find a number of results consistent with such non-proportional thinking. First, lower-priced stocks have higher total volatility, idiosyncratic volatility, and market betas, after controlling flexibly for size. To identify a causal effect of price, we show that volatility increases sharply following pre-announced stock splits and drops following reverse stock splits. The returns of lower-priced stocks also respond more strongly to firm-specific news events, all else equal. The economic magnitudes are large: a doubling in a stock's nominal price is associated with a 20-30% decline in its volatility, beta, and return response to firm-specific news. These patterns are not exclusive to small, illiquid stocks; they hold even among the largest stocks. Non-proportional thinking can explain a variety of asset pricing anomalies such as long-run and short-run reversals, as well as the negative relation between past returns and volatility (i.e., the leverage effect). Our analysis also shows that the well-documented negative relation between risk (volatility or beta) and size is actually driven by nominal prices rather than fundamentals.

Keywords: Non-Proportional Thinking, Nominal Prices, Leverage Effect, Volatility, Underreaction, Overreaction

Suggested Citation

Shue, Kelly and Townsend, Richard, Can the Market Multiply and Divide? Non-Proportional Thinking in Financial Markets (April 6, 2019). 9th Miami Behavioral Finance Conference 2018. Available at SSRN: https://ssrn.com/abstract=3148311 or http://dx.doi.org/10.2139/ssrn.3148311

Kelly Shue (Contact Author)

Yale School of Management ( email )

135 Prospect Street
P.O. Box 208200
New Haven, CT 06520-8200
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Richard Townsend

University of California, San Diego (UCSD) - Rady School of Management ( email )

9500 Gilman Drive
Rady School of Management
La Jolla, CA 92093
United States

Register to save articles to
your library

Register

Paper statistics

Downloads
463
rank
57,804
Abstract Views
1,570
PlumX Metrics