The expectation of future outcomes is a key input for our decision-making. In recent years, thanks to the work by leading scholars such as Andrei Shleifer, Stefan Nagel, David Thesmar and Ulrike Malmendier, we've learned a great deal about how our diagnostic heuristic, extrapolation, fading memory, and life experiences shape our subjective expectations.

In asset pricing, the traditional paradigm has been the risk-return tradeoff. Any premium earned not by taking on additional systematic risk is called mispricing, as if risk-aversion is the only justified behavioral trait that warrants a premium. While we agree that risk-aversion is a fundamental trait of human beings because it is essential for our ancestors to survive, one could argue that our expectation formation processes are as fundamental as risk-aversion, and they are also hard-wired by evolution, not for being accurate, but for helping us navigate the world and survive. Therefore, I believe that going against our innate nature of forming expectations in certain biased ways should also be justified for earning a "behavioral premium."

In my recent paper, titled "Which Expectation? Toward a Unified Framework of Expectation-based Asset Pricing," I build an asset pricing framework that encompasses two expectation formation processes: sticky expectation in cash flow level, and extrapolation on cash flow growth. I show that this framework can unify several well-known anomalies such as value, investment, profitability, momentum, and reversal. More importantly, the model generates unique predictions about the shape and the dynamics of the term structure of investors' expectation error.

Consistent with the model's predictions, I show that a new measure of growth expectation error robustly predicts stocks' future returns negatively.

This measure of expectation error also partly explains the value, profitability, and low-investment premium.

The interaction between sticky expectation and growth extrapolation naturally generates short-term momentum and long-term reversal which I also verify in the data.

The unique and new prediction from the model is that these firm characteristics should also predict an upward sloping forecast error term structure. For example, a value firm may have a very accurate current-period earnings forecast, but since investors may have underestimated the growth rate, the gap between actual and forecasted earnings for the next fiscal period should be positive, and this gap should be increasingly positive for longer horizons. I show this is indeed the case. Book-to-market, asset growth, and profitability predict analysts' expectation error term structure.

The model also makes predictions about the dynamics of the error term structure. When the current period cash flow realizes, investors see the earnings surprise and adjust their expectations on cash flow level and cash flow growth in a sticky way. The previous two-period ahead expectation now becomes one-period ahead, so it is no longer subject to the bias in growth expectation so this forecast becomes relatively accurate. However, the forecasts at all other horizons are still subject to that growth expectation error which is corrected only slowly over time.

So the model says that during an earnings announcement, the firm characteristics should predict a parallel shift in the expectation term structure even though these characteristics predict an upward sloping error term structure.

This prediction also is strongly supported by the data. This finding provides an explanation for the alpha persistence of certain trading strategies.

The contribution of this paper is not to invent any new biases or to say that all anomalies are about expectation errors. But I do bring two prominent expectation biases into the same model and show that it gives consistent predictions for many of the facts we see, and that it also yields new predictions that other models may find difficult to generate. Therefore, I argue that it is important to deepen our understanding of the exact expectation formation processes. We know, and I show a little bit in the paper, that we still do not have an expectation formation model that fits all the aspects of the data. So there is still a lot of work to be done in this field.

About the author

Yingguang Zhang joined Peking University, Guanghua School of Management as an Assistant Professor in Finance in 2019. He received his Ph.D. in Finance from the University of Southern California, Marshall School of Business, and his Bachelor's degrees in Economics and Statistics from the University of California at Berkeley.

Yingguang specializes in empirical asset pricing and behavioral finance. His recent research focuses on the joint dynamics of market participants' expectation and asset prices. His work has been presented at international conferences such as CQA 2019, AFA 2019, SFS Cavalcade 2018. His paper "The Earnings Announcement Return Cycle" won the best paper award at CQA 2019.