Discussions on the role of higher-order beliefs (investor beliefs about the beliefs of other investors) in financial markets can be traced back to Keynes’ (1936) comparison of the stock market to a beauty contest. Investors “are concerned,” he famously said, “not with what an investment is really worth to a man who buys it for keeps, but with what the market will value it at [. . .] three months or a year hence.” Interest in higher-order beliefs models continues today. An anecdotal example of the role of higher-order beliefs is the downgrade of Citigroup by analyst Meredith Whitney in the financial crisis, which caused a large stock-price drop. In her downgrade, Whitney seemed to only reiterate information in reports by other analysts. Because her downgrade was not based on new information, the reaction likely originated from investors that thought Whitney would catalyze investor beliefs.

Despite an extensive theoretical literature, higher-order belief models have received little attention in the empirical accounting and finance literature. In a recent paper, consistent with the predictions of higher-order beliefs models, we find that stocks that have optimistic (pessimistic) consensus analyst recommendations and are currently held by many short-term institutions exhibit large stock-return reversals. Their large past outperformance (underperformance) is followed by large negative (positive) future abnormal returns. The predictable return reversals originate from overreaction to past recommendation releases and the correction of these overreactions around future releases

In standard asset-pricing models with a representative investor, higher-order beliefs do not matter, and stock prices reflect the discounted expected value of future dividends. This is different from models that feature multiple investors with heterogeneous information. In these models, the average expectation of all investors determines stock prices, and investors’ beliefs about other investors’ beliefs can cause a deviation between the prices and the fundamental values of stocks. In higher-order beliefs models, public information plays an important role in the evolution of stock prices. Investors know that public information affects the average belief about the next period’s stock price, as all investors observe the public information and combine it with their private information. Because short-term investors are interested only in the next period’s stock price, they rationally overweight the public signal compared with private signals. This may lead to a short-term overreaction of the stock price to public information, which is subsequently reversed when investors synchronize their trading in the opposite direction to correct the mispricing. We refer to this mechanism as the “higher-order beliefs hypothesis.”

We test this hypothesis by examining whether short-term investors overweight widely disseminated public information about stocks, leading to stock return predictability. For the public information, we use analyst stock-recommendation releases, which are visible and widely followed public events that affect stock prices. At the same time, there are several indications that analyst recommendations contain limited fundamental information. Our proxy for the presence of short-term investors is fund turnover, which is the average portfolio turnover of a firm’s institutional investors. Our tests use U.S. stocks, but we confirm our main results for international stocks. We demonstrate that short-term institutional ownership and extreme analyst recommendations (“strong buys” and “sells”) are mean-reverting over periods of one to two years but not in related ways, which implies that both variables are strongly predictable.

We then document predictable return reversals for stocks with extreme analyst recommendations and ownership by many short-term institutions: Across the same one- to two-year period both the presence of short-term institutions and recommendations mean-revert. Using portfolio sorts, we show that, for high fund-turnover stocks (top quintile), the value-weighted long-short portfolio that sells (buys) stocks with the most optimistic (pessimistic) recommendations has an annualized five-factor alpha of 8.3 percent (t-stat of 3.41). These future alphas reflect return reversals, as the stocks with the most optimistic (pessimistic) current recommendations had positive (negative) alphas in the past. To show that our results are driven by analyst recommendations, we calculate event-time cumulative abnormal returns (CARs) around recommendation releases. The stocks that have the most optimistic (pessimistic) analysts and are held by many short-term institutions had much higher (lower) CARs around previous recommendation releases. Large parts of these CARs are reversed around future recommendation releases, when recommendations revert to the mean.

The return reversals support an interpretation that analyst recommendations act as coordinating signals for higher-order beliefs traders, leading first to return overreactions and then to return reversals. However, the return patterns may also be consistent with an alternative “information-source hypothesis,” which holds that short-term institutions are more likely to outsource their investment decisions to analysts; that is, to use analyst recommendations more strongly as inputs in their fundamentals-based valuations, relative to long-term institutions. To rule out this alternative we test a series of predictions from models of higher-order beliefs.

• First, we examine the cumulative abnormal returns of analyst recommendations at times when firms release earnings news. Consistent with the predictions of higher-order belief models, the reversal pattern in cumulative abnormal returns of high fund-turnover stocks is more pronounced when recommendations are released around earnings news. In contrast, under the alternative hypothesis, updated earnings news would increase the availability of fundamental information, making short-term institutions less reliant on – and less likely to overweight – analyst recommendations.
• Second, in models of higher-order beliefs, traders price stocks by combining private and public signals. The models therefore imply that coordination around public signals is stronger if the private signal is noisier. Consistent with this prediction, the reversal pattern in cumulative abnormal returns at high fund-turnover stocks is more pronounced at firms with high fundamental uncertainty; that is, among stocks with noisier private signals (high earnings volatility, R&D, and intangibles).
• Third, theoretical models predict that, in the presence of higher-order beliefs traders, stock prices exhibit drift after public information is released; that is, prices move only slowly towards fundamental values. This effect should be particularly strong for stocks whose ownership includes many short-term institutions. Empirically, stocks with more short-term institutions show stronger initial price reactions and stronger price drifts following recommendation changes. We validate these results by documenting particularly strong price reactions and drift at high fund-turnover stocks during the 1998-2000 tech bubble. This evidence supports the predictions of higher-order beliefs models but not the information-source hypothesis. Under the alternative hypothesis, stronger price drift is expected at stocks with more long-term institutions, if such investors, relying less on analysts as an input, act with some delay due to information processing or capital constraints.
• Fourth, models of higher-order beliefs predict that short-term institutions trade more often in response to recommendation changes as they overweight public information. Indeed, on the days when recommendation changes are released, short-term institutions trade more often into stocks with positive recommendation changes and trade out of stocks with negative recommendation changes. In the post-recommendation period, short-term institutions continue to trade in the direction of the recommendation changes. When we consider institutional flow over the next year, however, short-term institutions trade out of stocks (into stocks) with positive (negative) recommendation releases in the past. Trading by short-term institutions directly in response to recommendation changes is also consistent with the information-source hypothesis. However, the alternative hypothesis does not explain short-term institutions’ trading patterns in the post-recommendation period. If recommendations are an information source for short-term traders, the only prediction that follows is that their trading would be concentrated around the recommendation changes.

This post comes to us from professors Martijn Cremers at the University of Notre Dame, Ankur Pareek at the University of Nevada, Las Vegas, and Zacharias Sautner at the Frankfurt School of Finance & Management. It is based on their recent paper, “Short-Term Institutions, Analyst Recommendations, and Mispricing: The Role of Higher-Order Beliefs,” published in the Journal of Accounting Research and available here.