Information Efficiency and Firm-Specific Return Variation

TL;DR: In this article, the authors show that low-R2 stocks have characteristics that facilitate private informed trade, i.e. lower information costs and fewer impediments to arbitrage, and that differences in R2 are driven as much by firm-specific volatility on days without private news as by private news on days with private news.

Abstract: Reasoning that private firm-specific information causes firm-specific return variation that drives down market-model R2s, Morck, Yeung, and Yu (2000) begin a large body of research which interprets R2 as an inverse measure of price informativeness. Low R2s or “synchronicity,” as it is called in this literature, signal that prices more efficiently incorporate private firm-specific information, and high R2s indicate less. For this to be true, we would expect that low-R2 stocks have characteristics that facilitate private informed trade, i.e. lower information costs and fewer impediments to arbitrage. However, in this paper we document the opposite: Low-R2 stocks are small, young, and followed by few analysts, and have high bid-ask spreads, high price impact, greater short-sale constraints and are infrequently traded. In fact, microstructure measures suggest that private-information events are less likely for low-R2 stocks than high, and that differences in R2 are driven as much by firm-specific volatility on days without private news as by firm-specific volatility on days with private news. These results call into question prior research using R2 to measure the information content of stock prices.

Summary

2. Data and Methodology

• First, the authors examine the association between market-model R 2 and impediments to informed trade for all NYSE, AMEX and NASDAQ listed stocks.
• Second, the authors estimate the probability of private information arrival based on a microstructure model by Easley, Kiefer, and O'Hara (1997) .
• The authors use the derived measures to directly estimate the impact of private information on returns.
• For practical and theoretical reasons described below, the authors limit this analysis to NYSE-listed stocks from 1993 through 2002.
• In this section the authors describe the data and methodology used to derive R 2 and the measures of private information and impediments to informed trade.

2.1. Return Based Measures and Impediments to Informed Trade

• Where R i,t is the total return on individual stock i, R Mkt,t is the value-weighted market return, and R Indi≠i,t is the value-weighted two-digit SIC industry return excluding firm i.
• In other analyses examining the impact of private information on returns in section 4, to allow the comparison of daily, weekly and monthly returns, the authors use 5-year non-overlapping periods.
• Details are described in the discussion of data below.

2.1.1. Size, Age, Turnover, Volume, and Illiquidity

• 1.2. Lesmond, Ogden, and Trzcinka (1999) Trading Costs Lesmond, Ogden and Trzcinka (1999) propose a model of trading costs which recognizes that the fundamental value of an asset is continuous while, due to trading frictions, the realization is 6 CRSP began covering NASDAQ stocks in 1973.
• Since the majority of low-R 2 stocks are listed on NASDAQ, the correlation between Age and R 2 is arguably biased upward.
• Measured returns of zero imply that the transaction costs are higher than any change in the fundamental value of the underlying asset.
• Observing the magnitude of returns needed to obtain a measurable non-zero return is indicative of the trading costs.
• The authors follow Lesmond, Ogden and Trzcinka (1999) in the estimation and calculation of trading costs as the difference between the upper and lower thresholds their model estimates.

2.1.4. Analyst Coverage

• Forecast in the I/B/E/S database is considered the earnings forecast date.
• The percent deviation of analyst count from the annual mean is used in regressions, in order to keep the interpretation of the coefficient estimates the same across years.
• Analyst count data are available from 1982.

3.1. Choice of Measures

• It is worth noting that direct trading costs affect the profitability of arbitrage through two channels.
• Second, wide spreads also raise the trading costs for the unformed.
• Easley, Kiefer, O'Hara and Paperman (1996) show that liquidity trading is decreasing in the size of transaction costs.
• In the subsections that follow, the authors motivate the choice of variables used to proxy for information costs, the cost of trade and liquidity.

3.1.1. Cost of Information

• Like analyst coverage, size and age have a dual role.
• In the Merton (1987) sense, few investors may follow small and young firms.
• If traders are unaware of a stock, then they cannot discover mispricing in the stock's returns -essentially cost of information is infinite.
• Ho and Michaely (1988) argue that if information acquisition is more costly for small firms then, in equilibrium, investors may optimally choose to learn less about small companies.
• Even if the costs of learning about small stocks are no greater, the potential gains from small stock investment may be too low to justify the investment of time and money.

3.1.2. Costs of Trade and Liquidity

• Short-sale constraints limit the ability to arbitrage.
• Diamond and Verrecchia (1987) argue that short-sale constraints reduce the speed of information incorporation in prices.
• As a proxy for shortsale constraints, the authors use change in the breadth of institutional ownership following Chen, Hong, and Stein (2002) who argue that reductions in the breadth of ownership signal that short-sale constraints are more binding and that prices are higher relative to their fundamentals.

3.2. Impediments to Informed Trade and Market-model R 2 : Evidence

• In the following sections, under the rational that high information costs, high trading costs and low liquidity create limits to arbitrage in which mispricing can persist, the authors examine the relation between model fit and impediments to trade.
• To investigate these differences, R 2 portfolio averages are presented, followed by simple correlations to understand if the patterns in the means mirror patterns at the observation level, and regressions to explore the incremental explanatory power of each of the variables and to see which impediments to trade are most closely associated with differences in R 2 .
• The bottom line across all analyses is the same: greater information costs, greater trading costs and lower liquidity are consistently associated with low market-model R 2 s and high idiosyncratic volatility.
• These findings are inconsistent with the notion that idiosyncratic volatility predominantly captures the incorporation of private information, and instead suggest the converse, that stocks with low market-model R 2 may be those with the greatest possibility of mispricing.

<INSERT TABLE 1 ABOUT HERE>

• A shows that relative to high-R 2 stocks, low-R 2 stocks tend to be young, small, illiquid, and have high trading costs.
• Low-R 2 stocks receive less attention from analysts.

3.2.2. R 2 and Impediments to Informed Trade: Correlations

• Table 1 , Panel C presents the average of yearly cross-sectional Pearson correlation coefficients in the bottom diagonal and Spearman rank correlation coefficients in the top diagonal.
• In brief, the correlations are consistent with the associations between portfolio averages and the measures of impediments to trade seen in Panel A. R 2 has high rank correlations with size (.59), analyst count(.49), trading cost (-.60), illiquidity (-.62) and the percentage of zero volume days (-.52).
• Except for analyst count, these correlations are noticeably weaker using the Pearson linear correlation, suggesting that there is a non-linear relation between these variables and model fit.
• Though lower, correlations for age (information cost) and change in breadth (relaxation of short sale constraints) are positive.
• The table also makes clear that these variables are strongly inter-related.

3.2.3. Regressions

• This transformation is identical to the log ratio of the explained variance to unexplained variance.
• 14 We pool these annual data and run the regressions over the entire sample.the authors.the authors.
• The White correction also controls for possible bias as a result of using the logistic transform of the regressand.
• The results are consistent with the correlations found in Table 1 .
• Lower information costs are associated with higher market-model R 2 s, as are lower trading costs and greater liquidity and less tightly binding short-sale constraints.

<INSERT TABLE 2 ABOUT HERE>

• Notable is the relatively strong association between R 2 and market capitalization and Amihud (2002) illiquidity.
• The findings in this section show that impediments to informed trade, higher information costs, higher trading costs, and lower liquidity are associated with a lower market-model R 2 .
• Industries with companies that have a worse information environment have lower average industry R 2 .

3.2.4. Changes in the Information Environment

• Using analyst forecasts from I/B/E/S the authors identify the first forecast ever made by any analyst or brokerage.
• Table 3 reports the R 2 in the year prior to the first analyst forecast, the R 2 in the year following, the difference between the two, the bootstrapped standard error (using 1000 iterations) and the percentage of differences that are positive.
• Table 3 shows many significant differences pre and post initiation of analyst coverage.
• The differences are positive for low-R 2 stocks and negative for high-R 2 stocks, suggesting that differences in R 2 s are a result of mean reversion rather than as a result of any improvement in the information environment that may have occurred when the first analyst began issuing forecasts.

4.1.1. The Frequency of Private Information Events

• A also presents the average arrival rate of expected informed trades, uninformed trades and PIN by R 2 portfolio.
• The panels show that both informed trade (µ) and uninformed trade are increasing in R 2 ; however, uninformed trades are increasing more rapidly.
• Panel B, confirms the associations suggested in the portfolio averages hold when examining correlations.
• In order to address the concern that measurement error has caused these associations, as robustness the authors follow Durnev, et al. (2003 Durnev, et al. ( , 2004) ) and group in each stock into industries based on the three-digit SIC industry grouping.
• While weaker, confirm the individual stock level findings.

4.1.2. Calculating the Private Information Measure

• Controlling for public news events, Roll (1988) finds low average market-model R 2 s using return data at the daily and monthly frequency.
• In this section the authors directly address the central question of this paper:.
• The authors begin this analysis by replicating Roll's (1988) results and controlling for known influences on the precision of model fit.

4.2. Idiosyncratic Volatility on News and Non-News Days

• To decompose idiosyncratic volatility into the portion associated with private news days and that associated with Non-Private News days.
• Because the probability of a private information event measure is computed on a daily basis, instead of using weekly returns as in Tables 1-4 , for these analyses the authors run the regression from Eq. (1) using daily returns.
• The authors obtain the residuals from the regression and calculate the portion of the Sum of Squared Errors (SSE) which occurs on days with a high probability of a private information event and those with a low probability of a private information event.
• In panel B the authors examine a much lower threshold, 50% and the results are very similar.

<INSERT TABLE 5 ABOUT HERE>

• The middle three columns (columns 4-6) display the average amount of SSE that occurs on No News days, Good News days, and Bad News days.
• Not surprisingly, the low-R 2 stocks have more idiosyncratic volatility over all.
• The interesting picture arises when examining the last three columns (columns 7-9), which shows the proportion of the total annual SSE that occurs on No News, Good News and Bad News days: about half the idiosyncratic volatility occurs on news days and the other on non-news days, and the differences between high-and low-R 2 portfolios are small.
• Another notable point is that because the roughly the same proportion of volatility is on News days vs. non-News days, whether a stock has a high R 2 or low, it suggests that each private-information-based trade has much greater impact on returns for low-R 2 stocks than on high.
• In the next section the authors examine how private information impacts returns.

<INSERT FIGURE 1 ABOUT HERE>

• 17 Again, in the monthly regressions the authors include Pastor and Stambaugh's (2003) liquidity measure as well.
• (6) Comparing bars 2 and 3, the authors see that controls for infrequent trading and bid-ask bounce improve model fit only marginally, by 0.06 for the lowest daily R 2 portfolio and under 0.01 for higher R 2 portfolios.
• Coefficients on the probabilities of good and bad news are what one would expect for a reasonable proxy for the evolution of information events: good news is associated with positive and significant returns and bad news, negative and significant.

4.3.3. Private Information or Noise?

• For the most part market the coefficients on the lagged trade imbalance measures are insignificant.
• Negative coefficients are significant at the 5% level, between 10% and 20% of the time.
• This suggests that for this fraction of stocks a portion of the change in price due to sell side trading is partially reversed within four days.
• Taken together these findings suggest that private information does play a role in explaining poor model fit and high idiosyncratic volatility, however, it is also clear that private information only explains a fraction of returns.
• Roll (1988) finds that public information explains little of stock returns.

5. Conclusion

• Using a microstructure model by Easley, Kiefer, and O'Hara (1997) , which allows us to estimate the arrival of information on a daily basis, the authors have examined the effect of private information on prices and they have found that private information explains as much as 14% of returns for low-R 2 stocks regressions using weekly data.
• Nonetheless, for the same stocks over 80% of returns remain unexplained either by common sources of return comovement, or private information.
• (3) Model (2) with one lag of own returns to control for bid-ask bounce, and 5 leads and lags, 2 leads and lags and one lead and lag at the daily, weekly and monthly frequencies respectively.
• Regressions are run in each of four 5-year non-overlapping windows from 1983 through 2002 and averaged over the entire period.
• Models (2) and (3) include the Pastor and Stambaugh (2003) illiquidity measure in regressions using monthly data.

Figures

Table 8. Impact of Buy/Sell Imbalance on Daily Returns (continued)

Table 2. Regressions of Market-model R2 on Impediments to Informed Trade This table presents the results of pooled time series/cross-sectional regressions of ln(R2/(1-R2)) on the impediments to trade measures defined in Table 1. To control for firm effects we use White (1980) heteroskedasticity corrected, (Rogers) clustered errors, clustering on firm. Coefficients on Age are multiplied by 1000. **, * indicate significance at the 1 and 5 percent level respectively.

Table 6. Average Portfolio R2s for Carhart Four-Factor Model Controlling for Bid-Ask Bounce and Infrequent Trading

Table 1. (continued)

Figure 1. Market-model R2s. These figures display the average adjusted R2s for each of 10 NYSE-adjusted-R2-sorted portfolios for each of 3 models at 3 frequencies. The models regress total stock returns on

Table 1. (continued)

Full text

September 2014
Information Efficiency
and Firm-Specific
Return Variation
Patrick J. Kelly
208

Information Efficiency and Firm-Specific Return Variation
*
Patrick J. Kelly
New Economic School
Version: September 2014
*
Special thanks to John Griffin, Spencer Martin, Jeff Coles, and Federico Nardari. I would also like to thank Chris
Anderson, Ana Balcarcel, George Cashman, Art Durnev, Paul Irvine, Jennifer Juergens, Lidia Kelly, Paul Koch, Olga
Kuzmina, Laura Lindsey, Dmitry Makarov, Felix Meschke, Laura Tuttle, Sriram Villupuram and seminar participants at
Arizona State University, the Bank of Canada, Drexel University, the University of Kansas, the Securities and Exchange
Commission, the University of South Florida, and Tulane University, for their insightful comments. I/B/E/S data are
generously provided by Carr Bettis and Camelback Research.
Patrick J. Kelly is an Associate Professor in the Department of Finance at the New Economic School, 100 Novaya Street, Skolkovo,
143025 Moscow, Russia. E-mail: pkelly@nes.ru tel: +7 (495) 956.95.08

Information Efficiency and Firm-Specific Return Variation
Abstract
Reasoning that private firm-specific information causes firm-specific return variation that drives
down market-model R
2
s, Morck, Yeung, and Yu (2000) begin a large body of research which
interprets R
2
as an inverse measure of price informativeness. Low R
2
s or “synchronicity,” as it is
called in this literature, signal that prices more efficiently incorporate private firm-specific
information, and high R
2
s indicate less. For this to be true, we would expect that low-R
2
stocks have
characteristics that facilitate private informed trade, i.e. lower information costs and fewer
impediments to arbitrage. However, in this paper we document the opposite: Low-R
2
stocks are
small, young, and followed by few analysts, and have high bid-ask spreads, high price impact, greater
short-sale constraints and are infrequently traded. In fact, microstructure measures suggest that
private-information events are less likely for low-R
2
stocks than high, and that differences in R
2
are
driven as much by firm-specific volatility on days without private news as by firm-specific volatility
on days with private news. These results call into question prior research using R
2
to measure the
information content of stock prices.

1. Introduction
The greatest portion of return variation is unexplained by current asset pricing models. On average,
standard models account for only 17% of daily return variation and 29% of monthly. Observing a
similar lack of model fit, after controlling for exposure to systematic risk, industry-specific factors,
and the occurrence of value-relevant public information, Roll (1988) concludes that the majority of
returns are explained either by private information or a “frenzy” unrelated to specific information.
Work by Morck, Yeung and Yu (2000, 2013), Durnev, Morck, Yeung and Zarowin (2003) and
Durnev, Morck, and Yeung (2004) provides evidence for the private information explanation. This
research shows that a low market-model R
2
(called “synchronicity” in this literature) is associated
with fewer legal and regulatory impediments to informed trade across countries, and within U.S.
markets more efficient corporate investment and returns which are more sensitive to future earnings
growth. This evidence is consistent with the notion that low R
2
s result from the incorporation of
private, firm-specific information which makes prices more informationally efficient and leads these
papers to posit that market-model R
2
is an inverse measure of “price informativeness” or
information efficiency.
1
This paper examines this contention that R
2
is an inverse measure of information efficiency. We
first look at the information environment surrounding stocks as categorized by this widely used
measure of information efficiency
2
and find that the information environment is particularly poor
for low-R
2
stocks. This alone would seem to contradict the proposition that R
2
varies inversely with
information efficiency. Second, we use microstructure measures to examine the impact private
information-based trade on idiosyncratic volatility and poor model fit (R
2
). In doing so, we provide
evidence that low R
2
s are associated with both private information and sources unrelated to specific
1
A number of studies provide corroborating evidence. When average R
2
is low, capital markets are more open (Li,
Morck, Yang, and Yeung, 2004), short sales are less constrained (Bris, Goetzmann, and Zhu, 2007), capital is better
allocated, and government ownership in the economy is less (Wurgler, 2000).
2
Cited by 348 published papers according to Thomson Reuters’ Web of Science on September 9, 2014.

2
information. Specifically, we estimate the probably of private information arrival on each day and
show that the average day with private information does in fact have higher idiosyncratic volatility
than the average day without, especially for low-R
2
(low synchronicity) stocks, consistent with the
arguments in Morck, Yeung and Yu (2000) and other papers. However, days with private
information are infrequent, occurring only 30% of the time for high-R
2
stocks, and only 15% of the
time for low R
2
. As a result, when aggregated over the course of a year, most idiosyncratic return
occurs on days without private information simply because there are more days without private
news. The fact that this is particularly true for low-R
2
stocks suggests that R
2
is a poor measure of
private information incorporation.
The idea that volatility might reflect information incorporation is not new. French and Roll
(1986), note that the key distinction between public and private information is that public
information affects prices the moment it becomes known, while private information is only revealed
through trading. French and Roll (1986) along with Barclay, Litzenberger, and Warner (1990), and
Jones, Kaul, and Lipson (1994) find differences in volatility during trading and non-trading hours.
Their evidence suggests that the greater portion of return volatility is due to the activity of private-
information driven traders.
On the other hand, Shiller (1981), LeRoy and Porter (1981), and West (1988) present evidence
that stock returns are significantly more volatile than the random arrival of new value relevant
information would permit in an efficient market. They show that rapid information incorporation
results in lower volatility, not higher, because changes in expected firm value that are incorporated in
a stock’s price sooner are more heavily discounted. West (1988) generalizes these models to show
that return variance is greater anytime the information set on which expectations are based is a
subset of all available information.