Investor Attention and the Cross-section of Analyst Coverage

Charles Martineau and Marius Zoican

Bank of Lithuania
October 16, 2020

Motivation

Analyst coverage across stocks (2017Q4)

What drives the demand for information?

  • Investors need information to choose portfolios.
  • Limited attention can lead to suboptimal investment decisions:
  1. Portfolio under-diversification
  2. Home bias

What drives the supply for information?

  • A key source of information comes from equity analysts, who disseminate financial information through reports.

​How does investor attention impact analyst coverage choices?

Analyst objective

Maximize trading volume & revenue for brokerage house.

(Groysberg, Healy, and Maber, 2011)

Research question

This paper

  • Empirical: How much does investor attention matter for analyst coverage choices?
  • Theory: Build a noisy REE model to understand how attention constraints drive analyst coverage.

Contributions

Results

  • Investor attention explains 21.52% of cross-sectional variation in analyst coverage -- second only to firm size.
  • Model predicts coverage clustering, consistent with the data.
  • Coverage clustering first     , then      in attention capacity.
  • Relaxing cognitive constraints may not lead to more balanced coverage.
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Literature

A growing literature shows that investor attention plays an important role in asset pricing at determining, e.g.,:

  • price efficiency (Hirshleifer and Teoh, 2009)
  • risk premium (Andrei and Hasler, 2015)
  • return predictability (Da, Engelberg, and Gao, 2011)
  • comovement (Peng and Xiong, 2006)

​However, we know little on how investor attention influence information supply in financial markets.

Empirical results

A measure of attention

 

  • Bloomberg provides a daily score, ranging from 0 to 4, to reflect the (abnormal) investor attention.
  • We follow Ben-Rephael, Da, and Israelsen (2017).
  • The score measures the number of times terminal users actively search and read articles about a particular stock.
  • We collect the score between 2012-2017 and take yearly averages.

Investor attention and analyst coverage

\text{N. Analyst}_{i,t} = \alpha +\beta_1 \text{Ln(MCAP)}_{i,t} + \beta_2\textcolor{red}{\text{Attention}} _{i,t} + Controls + \text{Industry}_{i,t} + \text{Year}_t + \epsilon_{i,t}
\text{Investor attention is 2nd largest contributor to } R^2

*using Shapley-Owen decomposition

Analysts are more sensitive to attention for well-covered stocks

Model

Model ingredients

Assets

Two risky-assets in zero net supply, paying off at t=2

1. A high-precision asset H:

2. A low-precision asset L:

v_H\sim\mathcal{N}\left(0,\tau_{v,H}^{-1}\right)
v_L\sim\mathcal{N}\left(0,\tau_{v,L}^{-1}\right)
  1. Continuum of investors I with unit endowment and CARA preferences: 
  2. Noise traders (i.i.d. across stocks) with variance 
  3. Two analysts (k) who provide a public signal for one asset:

 

\tau_x^{-1}
U_\textbf{I}=-\mathbb{E}\left[\exp\left(-\gamma \tilde{W}_2\right)\right]
y_k=v+\epsilon_k \text{ with } \epsilon_k\sim\mathcal{N}\left(0,\tau^{-1}\right)

Agents

Investor attention and learning

Each investor j can acquire unbiased signals about stock i:

s_{i,j}=\tilde{v}_i+\epsilon_{i,j}, \text{ where } \epsilon_{i,j}\sim\mathcal{N}\left(0,\tau^{-1}_{\epsilon i,j}\right)

Investors choose the signal precision, but have finite learning (attention) capacity  K:

\sum_{i\in\left\{H,L\right\}} \phi_{i} \tau_{\epsilon i,j} \leq K.

Learning cost is lower if more analysts cover stock i

(through a "familiarity" argument):

\phi(n_i)=\frac{1}{n_i}

(note decreasing returns to scale)

Analyst coverage as data compression

Analyst coverage as data compression

Analyst objective

i_j^\star=\arg\max_{i} f\times\mathbb{E}\left[\frac{1}{n^\star_i}\text{Volume}_i\right].
  • Sell-side analysts work for brokerage houses.
  • Brokerage houses charge a fee f per unit of traded volume.
  • Therefore, analysts choose to cover stocks to maximize expected volume for their brokerage house:

Model timing

Solving for equilibrium: Market clearing

\tilde{p} = p_v \tilde{v} + p_y \tilde{y} + p_x \tilde{x}-f.

(i) Conjecture linear price:

(ii) Optimal demand from investor j, conditional on signal:

\mathcal{D}_j\left(p \mid s_j\right) = \frac{\mathbb{E}\left[\tilde{v}\mid s_p, y, s_j\right]-p-f}{\gamma \text{var}\left[v\mid s_p, y, s_j\right]}.
\int_j \mathcal{D}_j\left(p \mid s_j\right) + \tilde{x} =0.

(iii) Market clearing condition:

(iv) Clearing price:

\tilde{p}=\underbrace{\frac{\tau_\epsilon + \rho^2 \tau_x}{\tau_v+\tau_y+\tau_\epsilon+\rho^2 \tau_x}}_{p_v} \tilde{v} + \underbrace{\frac{\tau_y}{\tau_v+\tau_y+\tau_\epsilon+\rho^2 \tau_x}}_{p_v} \tilde{y}+ \underbrace{\frac{\rho\tau_x+\gamma}{\tau_v+\tau_y+\tau_\epsilon+\rho^2 \tau_x}}_{p_x} \tilde{x}-f,

Solving for equilibrium: Private signals

\max_{\tau_{\epsilon,i}} \prod_i \left(\underbrace{\left(\tau_{\epsilon,i}+\tau_{vi}+\tau_{yi}+\rho_i^2 \tau_x\right)}_{\equiv \hat{\tau}_i} \frac{\tau_{vi}+\tau_{yi}+p_{x,i}^2 \tau_x^{-1}}{\tau_{vi}+\tau_{yi}}\right).

Following Verrecchia (1982), problem boils down to:

Posterior precision

A measure of price impact

Investors have zero mass so take price as given.

Problem becomes:

\mathcal{L}=\sum_i \ln\left(\tau_{\epsilon i}+\tau_{vi}+\tau_{yi}+\rho^2 \tau_x\right) + \psi \left[K-\sum_i\frac{1}{n_i}\tau_{\epsilon i}\right] +\sum_i \lambda_i\tau_{\epsilon i},

Text

Attention constraint

Investors only learn about H if capacity is large enough

Optimal signal acquisition and coverage

\text{Volume}_i\left(n_i\right)=\mathbb{E} \int_j \left| \mathcal{D}_j\left(p \mid s_j\right)\right|
=\sqrt{\frac{2}{\pi}} \sqrt{\frac{\tau^\star_{\epsilon i} \left(n_i\right)}{\gamma^2}+\tau_{xi}^{-1}}.

Solving for equilibrium: analysts' problem

The expected volume in a given stock i is:

Mechanism

  • Coverage         Private learning        Confidence in signal  Volume 
  • Public forecasts are common knowledge       influence prices, but not volumes.
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Analyst choice

U_j\left(H\right)=f\times\left[\alpha\frac{1}{2}\text{Volume}_H\left(2\right)+\left(1-\alpha\right)\text{Volume}_H\left(1\right)\right].

If analyst j covers stock H, her utility is:

If analyst j covers stock H, her utility is:

U_j\left(L\right)=f\times\left[\alpha\text{Volume}_L\left(1\right)+\left(1-\alpha\right)\frac{1}{2}\text{Volume}_L\left(2\right)\right].

If analyst j covers stock L, her utility is:

The equilibrium probability to cover stock H is:

\alpha^\star=\max\left\{0,\frac{2\text{Volume}_H\left(1\right)-\text{Volume}_L\left(2\right)}{2\left[\text{Volume}_H\left(1\right)+\text{Volume}_L\left(1\right)\right]-\left[\text{Volume}_H\left(2\right)+\text{Volume}_L\left(2\right)\right]}\right\}

Equilibrium analyst coverage distribution

Coverage odds-ratio can exceed risk odds-ratio

Example: If stock L has a payoff variance 3x that of stock $H$, it can have up to 10x more analyst coverage in expectation

Analyst coverage and noise trading

Coverage clustering

empirical evidence

Median coverage in the cross-section of stocks

A closer look at coverage clustering

Conclusions

  • Investor attention explains 21.52% of cross-sectional variation in analyst coverage -- second only to firm size.
  • For very limited investors attention, analysts are better off sharing a crowded space rather than trying to differentiate and cover neglected stocks.

  • The implications of our model match empirical patterns: the significant analyst coverage clustering in U.S. equities.

  • A skewed information supply can disproportionately benefit large firms to the expense of small, "neglected" firms.

Conclusions

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