Beta herding means convergence of market betas of individual stocks that arises from investors’ biased perceptions. Adverse beta herding denotes the dispersion of such betas that arises from a reversal of the bias. A new paper suggests that overconfidence in predictions of overall market direction and positive sentiment are key drivers of beta convergence, while uncertainty and negative sentiment are conducive to beta dispersion. Knowing which trends prevail helps macro trading. First, beta herding implies that directional market moves create price distortions (as the bad rise and fall with the good). Second, adverse beta herding causes low-beta stock returns to outperform high-beta stock returns on a risk-adjusted basis. This reinforces and qualifies what is commonly known as the “low beta bias” of equity returns.

Hwang, Soosung, Alexandre Rubesam, and Salmon, Mark (2018), “Overconfidence, Sentiment and Beta Herding: A Behavioral Explanation of the Low-Beta Anomaly”. Online Paper, August 1, 2018.

The post ties in with SRSV’s summary lecture on price distortions.

The below are quotes from the paper. Emphasis and cursive text have been added. Also we replaced the term “compression” with the term “convergence”, as the latter seemed to be more commonly used for the equalization of market betas.

What is beta herding?

Beta herding represents the cross-sectional convergence of betas…due to investors’ biased perceptions. Adverse beta herding represents the cross-sectional dispersion of betas away from the market [average] beta due to investors’ biased perceptions…Beliefs about the market are biased due to changes in confidence or sentiment… Individual betas [in beta herding] are biased towards the market beta regardless of their equilibrium risk-return relationship.”

“In practice, when beta herding arises, investors may buy assets whose returns increase less than the market because these assets would appear relatively cheap. Likewise, they may sell assets whose returns increase more than the market because these assets would seem to be relatively expensive and the opportunity for taking apparent profits might be hard to resist.”

“The concept of beta herding differs from other herding measures proposed in the [academic] literature in several respects. It measures bias in the risk-return relationship when investors herd or disperse because of their behavioral biases (over- or under-confidence and optimism or pessimism). Thus, we focus directly on deviations from the equilibrium risk-return relationship rather than on the clustering behavior of market experts such as analysts or institutional investors.”

How does beta herding arise?

“Individual asset prices move together regardless of their fundamentals…[due] to two well-known behavioral biases in finance: investor overconfidence and sentiment.

  • We demonstrate that the cross-sectional difference in the expected returns and betas of individual assets is suppressed when investors are overconfident about signals of the market outlook, and thus their…prediction of the market return is overly affected by these signals… Investors receive a noisy signal to predict the market return…Informed overconfident investors… believe that the signal is more precise than it actually is.
  • A comparable convergence of betas arises in the presence of investor sentiment. When optimistic views about the market outlook prevails, individual betas are biased towards the market beta.

The opposite case is also possible: when investors are under-confident about the market outlook or their sentiment is pessimistic, the difference between individual betas increases. The convergence or dispersion of betas reflects, in aggregate, micro models of informational herding or adverse herding, respectively, and gives rise to cross-sectional distortion in asset returns.”

“Although the driving forces behind investor overconfidence and sentiment are different, they have a common effect on betas through a biased probability distribution of expected returns. When this form of biased expectation exists among investors, they will follow the performance of the market portfolio when buying or selling assets, and thereby betas are biased towards the market beta…

  • If investors are overconfident and overestimate the precision of their signals for the overall market, individual betas are biased towards the [average] market beta. On the other hand, individual betas are biased away from the market beta when investors are under-confident about their signals for market…
  • When a strong positive (negative) sentiment prevails such that a similar level of sentiment occurs for individual assets regardless of their equilibrium risk-return relationship, individual betas are biased towards (away from) the market beta.”

Why is beta herding relevant for macro trading?

“The consequence of adverse beta herding is that the risk-return relationship in the CAPM does not work in asset pricing… When high betas are downward-biased and low betas are upward-biased, asset returns are more likely to track market movements, rather than those suggested by the equilibrium risk-return relation.”

When investors are overconfident the expected returns of high and low beta assets are downward and upward biased toward the market return, respectively. On the other hand, when investors are under-confident expected returns are biased away from the expected market return.”

[Adverse beta herding also may explain] the low-beta anomaly, whereby low beta stocks outperform high beta stocks on a risk-adjusted basis.

What is the empirical evidence for beta herding?

“Beta herding can be easily measured by the cross-sectional variance of standardized-betas, which are equivalent to the t-statistics of beta estimates. The standardized-beta provides information on the precision of the beta estimate in addition to its magnitude, and more importantly, makes it possible to compare the dynamics of beta herding over different periods.”

“We have applied our measure to the US stock market…over the sample period from January 1967 to June 2016…Our measure of beta herding is robust to macro factors [and] business cycles.”

“We… document the low-beta anomaly for value-weighted decile portfolios formed on standardized-betas: a high-minus-low standardized-beta portfolio earns -0.37% per month (-4.3% per year) during the sample period…. the effects of adverse beta herding on the low-beta anomaly increase with market uncertainty and volatility… The dramatic variation of the dispersion of standardized-betas over time suggests that the low-beta anomaly…is unlikely to produce stable returns over time.”

“We find that the low-beta anomaly is observed only after periods of adverse beta herding, when the dispersion of standardized-betas increases: for value-weighted decile portfolios formed on standardized-betas, the risk-adjusted return of the high-minus-low portfolio over the 12 months following adverse beta herding is -11.4% per year, whereas the returns are not different from zero following periods of no beta herding or high beta herding. The effects of adverse beta herding on standardized-beta sorted portfolios are quite persistent and remain significant over two years. These results also hold for portfolios formed on OLS betas or for different holding periods.”


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