Value Investing

A Model Of Anomaly Discovery

A Model of Anomaly Discovery by SSRN

Liu Qu


Lei Lu

Peking University – Guang Hua School of Management

Bo Sun

Board of Governors of the Federal Reserve System – Division of International Finance

Hongjun Yan

Yale University – International Center for Finance

May 8, 2015

FRB International Finance Discussion Paper No. 1128


We analyze a model of anomaly discovery. Consistent with existing evidence, we show that the discovery of an anomaly reduces its magnitude and increases its correlation with existing anomalies. One new prediction is that the discovery of an anomaly reduces the correlation between deciles 1 and 10 for that anomaly. Using data for 12 well-known anomalies, we find strong evidence consistent with this prediction. Moreover, the correlation between deciles 1 and 10 of an anomaly becomes correlated with the aggregate hedge-fund wealth volatility after the anomaly is discovered. Our model also sheds light on how to distinguish between risk- and mispricing-based anomalies.

A Model Of Anomaly Discovery – Introduction

A significant portion of the asset-pricing literature has been devoted to “anomalies,” empirical patterns that appear inconsistent with existing benchmark models. One popular approach to interpreting anomalies is risk-based. Take the value premium as an example. Its discovery is often attributed to Basu (1983). Since then, numerous models have been proposed to explain why value stocks are indeed riskier (than what CAPM implies) and so have higher expected returns.

We argue that this approach ignores the discovery aspect. In those risk-based models, investors know that value stocks are riskier and demand higher returns. As expected, higher average returns are realized for value stocks in the data. That is, in this view, there is no real discovery: Professor Basu was the last one in the world to find out about the value premium. Investors knew about this return pattern all along.

In contrast to the view above, it seems natural to expect discoveries to have significant effects on investors’ decisions and asset prices since, over the years, discoveries in academia have had increasingly important influences on the asset management industry. Many prominent asset management companies regularly organize academic seminars and conferences. Some explicitly claim that they identify investment ideas from academic research. In this paper, we explicitly model anomaly discovery and analyze its effects on asset prices, both theoretically and empirically.

We solve a simple model with two assets (asset 1 and asset 2) that have the same distribution for future cash flows. However, investors find asset 1 riskier because their endowment is correlated with asset 1’s cash flow, but not with asset 2’s. Consequently, in equilibrium, asset 1 has a lower price and a higher expected future return than asset 2. We call this return pattern an “anomaly,” which is risk-based since it is caused by investors’ risk consideration.

When this anomaly is discovered, some agents, who we call “arbitrageurs,” become aware of the return pattern and start exploiting it. To analyze the discovery effect, we construct an equilibrium without these arbitrageurs, which we call a “pre-discovery equilibrium,” and an equilibrium with these arbitrageurs, which we call a “post-discovery equilibrium.” The discovery effect is captured by the difference between the pre-and post-discovery equilibria.

Our model has the following implications. First, the discovery of an anomaly reduces its magnitude. This follows directly once we recognize that the discovery brings in arbitrageurs. Let us use the value premium as an example. It has been proposed that value stocks are riskier because they are more exposed to the business cycle. Arbitrageurs, however, may not find this risky, perhaps because they are wealthy and are themselves less exposed to the business cycle. Hence, they will exploit this anomaly and consequently reduce its magnitude.

Second, the discovery of an anomaly makes its return (i.e., the return from a long position in asset 1 and a short position in asset 2) more correlated with the returns from existing anomalies. This is due to a wealth effect when arbitrageurs exploit both existing anomalies and the newly discovered one. Suppose the return from existing anomalies is unexpectedly high one period, thus increasing arbitrageurs’ wealth. Everything else being equal, arbitrageurs will allocate more investment to all their opportunities, including the new anomaly. This higher investment pushes up the price of asset 1 and pushes down the price of asset 2, leading to a high return from the new anomaly this period. Similarly, a low return from existing anomalies leads to a low return from the newly discovered one. Hence, the wealth effect increases the correlation between the new anomaly return and the returns from existing anomalies.

anomaly discovery

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