Speculating on Higher Order Beliefs

Higher order beliefs – beliefs about others’ beliefs – may be important for trading behavior and asset prices, but have received little systematic empirical examination due to challenges in measurement. We study more than twenty years of evidence from the Robert Shiller Investor Confidence surveys, which directly elicit details on individual and institutional investors’ higher order beliefs about the U.S. stock market. We find that investors’ higher order beliefs provide substantial motivations for non-fundamental speculation, e.g., to buy into a stock market perceived to be overvalued. Guided by the evidence, we construct a theoretical model that reveals that higher order beliefs may substantially amplify stock market fluctuations. When investors exhibit the same fundamental belief biases that they attribute to other investors, phenomena such as overreaction, momentum, and reversal can persist in equilibrium even though everybody knows about them. *This is a substantially revised version of “Asset Pricing with Higher Order Beliefs. ” We thank Federica Ambrosio, Natee Amornsiripanitch, Marios Angeletos, Nick Barberis, Paul Fontanier, Stefano Giglio, Will Goetzmann, Leandro Gomes, Paul Goldsmith-Pinkham, Gary Gorton, Peter Hansen, Zhen Huo, Jon Ingersoll, Toomas Laarits, Yukun Liu, Ben Matthies, Toby Moskowitz, Milad Nozari, Cameron Peng, Julia Selgrad, Kelly Shue, Alp Simsek, Sam Slocum, Aleh Tsyvinski, Joao Paulo Valente, and seminar participants at Yale SOM, Purdue Daniels, Chicago Booth, Caltech, UNC Kenan-Flagler, Harvard Business School, Emory Goizueta, the New York Fed, NYU Stern, Columbia Business School, the Treasury OFR, BC Carroll, and Stanford GSB for helpful comments and conversations. We are grateful to Bob Shiller for sharing data, and the Yale ICF for data support. †School of Management, Yale University. Email: paul.schmidt-engelbertz@yale.edu. ‡Daniels School of Business, Purdue University. Email: kvasude@purdue.edu. Higher order beliefs – beliefs about others’ beliefs – are important in many equilibrium models in economics and finance. As emphasized by a strand of primarily theoretical literature starting with Keynes (1936), higher order beliefs may be particularly important for understanding investor behavior and financial market fluctuations. This is because investors have strong profit incentives to trade based on predictions of others’ beliefs rather than their own valuations, potentially leading asset prices to deviate substantially from fundamental values.1 Despite their ubiquity and potential importance, higher order beliefs have received little systematic empirical examination, primarily due to challenges in measurement. In this paper, we examine survey data on investors’ higher order beliefs, and consider the corresponding asset pricing implications. Our data come from the Robert Shiller Investor Confidence survey, which directly elicits investors’ perceptions of other investors’ beliefs. The survey also reports investors’ return expectations, which embed additional information about higher order beliefs. This is because an investor’s return expectations reflect her forecasts of other investors’ future stock market demand, which, in turn, depend on her forecasts of their beliefs. Guided by the evidence, we construct a theoretical model that illustrates the potential importance of higher order beliefs in driving stock market fluctuations. Below, we summarize our empirical and theoretical findings. Empirical Results. While previous work has documented episodes of non-fundamental speculation – e.g., buying into risky assets perceived to be overvalued – our headline finding is that for the U.S. stock market, non-fundamental speculation is the rule, not the exception.2 Higher order beliefs play an important role in driving non-fundamental speculation. To illustrate this point, we examine the Shiller survey, which, for more than 20 years, has asked individual and institutional investors a number of questions regarding their stock market expectations. Particularly relevant for our exploration, the survey asks investors if they perceive other investors to be overly optimistic (or pessimistic) about the U.S. stock market’s prospects, as well as if they perceive the stock market to be overor under-valued. The majority of survey respondents report that others have mistaken beliefs, and the direction of investors’ reported higher order beliefs coincide with their perception of the underor over-valuation of the stock market. We find that when investors report that others are overly optimistic, they also report expectations of higher than average returns for the short term (1-to-3 months ahead), before expecting reversion in subsequent periods. A natural, higher order belief-based interpretation is that investors forecast other investors will become even more optimistic in the near term, fueling short horizon returns, before optimism and prices revert. These expectations 1For example, De Long et al. (1990) note that George Soros “has been generally successful. by betting not on fundamentals but, he claims, on future crowd behavior. ” Brunnermeier and Nagel (2004) argue the evidence from the dot-com bubble is “consistent with the view that hedge fund managers were able to predict some of the investor sentiment that was arguably behind the wild fluctuations in valuations of technology stocks. ” 2This is speculation in the sense of Keynes (1936) and Harrison and Kreps (1978). We use the prefix ‘nonfundamental’ to distinguish from another common use of the term, where investors buy or sell an asset based on their relative optimism and pessimism about the asset’s fundamental value, e.g., Simsek (2021).