2019 AQR Insight Award First Prize
When pricing financial assets, rational agents should think in terms of proportional price changes, i.e., returns. However, stock price movements are often reported and discussed in dollar rather than percentage units, which may cause investors to think that news should correspond to a dollar change in price rather than a percentage change in price. Non-proportional thinking in financial markets can lead to return underreaction for high-priced stocks and overreaction for low-priced stocks. Consistent with a simple model of non-proportional thinking, we find that total volatility, idiosyncratic volatility, and market beta are significantly higher for stocks with low share prices, controlling for size. To identify a causal effect of price, we show that volatility increases sharply following stock splits and drops following reverse stock splits. The economic magnitudes are large: non-proportional thinking can explain the “leverage effect” puzzle, in which volatility is negatively related to past returns, as well as the volatility-size and beta-size relations in the data. We also show that low-priced stocks drive the long-run reversal phenomenon in asset pricing, and the magnitude of reversals can be sorted by price, holding past returns and size constant. Finally, we show that non-proportional thinking biases reactions to news that is itself reported in nominal-per-share units rather than the appropriate scaled units. Investors react to nominal earnings per share surprises, after controlling for the earnings surprise scaled by share price. The reaction to the nominal earnings surprise reverses in the long run, consistent with correction of mispricing.
This document is not intended to, and does not relate specifically to any investment strategy or product that AQR offers. It is being provided merely to provide a framework to assist in the implementation of an investor’s own analysis and an investor’s own view on the topic discussed herein.
This document has been provided to you solely for information purposes and does not constitute an offer or solicitation of an offer or any advice or recommendation to purchase any securities or other financial instruments and may not be construed as such. The factual information set forth herein has been obtained or derived from sources believed by the author and AQR Capital Management, LLC (“AQR”) to be reliable but it is not necessarily all-inclusive and is not guaranteed as to its accuracy and is not to be regarded as a representation or warranty, express or implied, as to the information’s accuracy or completeness, nor should the attached information serve as the basis of any investment decision. This document is not to be reproduced or redistributed to any other person. The information set forth herein has been provided to you as secondary information and should not be the primary source for any investment or allocation decision. Past performance is not a guarantee of future performance. Diversification does not eliminate the risk of experiencing investment losses.
This material is not research and should not be treated as research. This paper does not represent valuation judgments with respect to any financial instrument, issuer, security or sector that may be described or referenced herein and does not represent a formal or official view of AQR. The views expressed reflect the current views as of the date hereof and neither the author nor AQR undertakes to advise you of any changes in the views expressed herein.
The information contained herein is only as current as of the date indicated, and may be superseded by subsequent market events or for other reasons. Charts and graphs provided herein are for illustrative purposes only. The information in this presentation has been developed internally and/or obtained from sources believed to be reliable; however, neither AQR nor the author guarantees the accuracy, adequacy or completeness of such information. Nothing contained herein constitutes investment, legal, tax or other advice nor is it to be relied on in making an investment or other decision. There can be no assurance that an investment strategy will be successful. Historic market trends are not reliable indicators of actual future market behavior or future performance of any particular investment which may differ materially, and should not be relied upon as such. Diversification does not eliminate the risk of experiencing investment losses.
The information in this paper may contain projections or other forward-looking statements regarding future events, targets, forecasts or expectations regarding the strategies described herein, and is only current as of the date indicated. There is no assurance that such events or targets will be achieved, and may be significantly different from that shown here. The information in this document, including statements concerning financial market trends, is based on current market conditions, which will fluctuate and may be superseded by subsequent market events or for other reasons.