R2: Does it Matter for Firm Valuation?

A considerable amount of research has been devoted to why R² differs across firms or markets, but little attention has been paid to the consequences of this difference. We fill this gap by investigating how differing R² affects investors’ assessment of firm value. Using a sample of 90,111 firm‐year observations from 1970 to 2004, we find that higher R² leads to higher firm valuation and that, on average, high‐R² firms experience significant underperformance in the long run. These results suggest that high‐R² firms tend to be overpriced.     

Relation between bid–ask spread,impact and volatility in order-driven markets

We show that the cost of market orders and the profit of infinitesimal market-making or -taking strategies can be expressed in terms of directly observable quantities, namely the spread and the lag-dependent impact function. Imposing that any market taking or liquidity providing strategies is at best marginally profitable, we obtain a linear relation between the bid–ask spread and the instantaneous impact of market orders, in good agreement with our empirical observations on electronic markets. We then use this relation to justify a strong, and hitherto unnoticed, empirical correlation between the spread and the volatility per trade, with R ²s exceeding 0.9. This correlation suggests both that the main determinant of the bid–ask spread is adverse selection, and that most of the volatility comes from trade impact. We argue that the role of the time-horizon appearing in the definition of costs is crucial and that long-range correlations in the order flow, overlooked in previous studies, must be carefully factored in. We find that the spread is significantly larger on the NYSE, a liquid market with specialists, where monopoly rents appear to be present.     

R-Squared and Dividend Payout: Evidence from the Korean Market

The authors investigate R ² and its relationship with dividend payouts in the Korean stock market. R ² is derived from the market model regression. Their results are consistent with the previous literature on corporate governance and dividend payouts: they find that R ² is higher for business group (chaebol) firms and that there is a negative relationship between R ² and dividend payout. However, the relationship is not stronger for the business group firms than for the non-business group firms. The findings elucidate the relationship between R ² and dividend payout policy in the United States.     

VOLUME AND R2: A FIRST LOOK

Roll (1988) reports that when days on which public announcements occur are excluded from a regression of stock returns on market returns, the R²s are largely unaffected. To explain his findings, Roll suggests that much of the firm-specific movements in common stocks may be a result of private information or occasional trading frenzy. As a test of Roll's conjecture, volume is used in this study as a proxy to capture the impact of firm-specific information and irrational trading. If Roll's conjecture is correct, the R² should rise when high-volume days are excluded from a regression of stock returns on market returns. The results presented here are consistent with that prediction, but they are not strong.     

Opaque financial reports and R2: Revisited

In this study, we revisit the link between R² (synchronicity) and earnings management (opacity) because of the importance of the ongoing debate on the relation between idiosyncratic risk and earnings management in the finance and accounting literatures. Hutton et al. (J. Financial Economics, 2009) provide evidence of a positive link between opacity and R². They interpret their finding to imply that firms with high R² (high synchronicity) have less firm-specific information impounded in their stock price. Our results for this relationship fail to unequivocally support the results reported in Hutton et al. (2009). We show that their results are not only time variant but also not robust to the alternative empirical technique recommended for panel data by Petersen (2009) and alternative estimation of discretionary accruals adjusted for firm performance prescribed by Kothari et al. (2005). We also find no support for a convex relation between idiosyncratic risk and opacity. The findings documented in this study substantially revise some of Hutton et al.'s findings in this important and growing area of research.     

Universal price impact functions of individual trades in an order-driven market

The trade size ω has a direct impact on the price formation of the stock traded. Econophysical analyses of transaction data for the US and Australian stock markets have uncovered market-specific scaling laws, where a master curve of price impact can be obtained in each market when stock capitalization C is included as an argument in the scaling relation. However, the rationale of introducing stock capitalization in the scaling is unclear and the anomalous negative correlation between price change r and trade size ω for small trades is unexplained. Here we show that these issues can be addressed by taking into account the aggressiveness of orders that result in trades together with a proper normalization technique. Using order book data from the Chinese market, we show that trades from filled and partially filled limit orders have very different price impacts. The price impact of trades from partially filled orders is constant when the volume is not too large, while that of filled orders shows power-law behavior r?～?ω^α with α?≈?2/3. When returns and volumes are normalized by stock-dependent averages, capitalization-independent scaling laws emerge for both types of trades. However, no scaling relation in terms of stock capitalization can be constructed. In addition, the relation α?=?α_ω/α _r is verified for some individual stocks and for the whole data set containing all stocks using partially filled trades, where α_ω and α _r are the tail exponents of trade sizes and returns. These observations also enable us to explain the anomalous negative correlation between r and ω for small-size trades.     

Passive Institutional Ownership,R2 Trends,and Price Informativeness

A distinctive trend in the capital markets over the past two decades is the rise in equity ownership of passive financial institutions. We propose that this rise has a negative effect on price informativeness. By not trading around firm‐specific news, passive investors reduce the firm‐specific component of total volatility and increase stock correlations. Consistent with this hypothesis, we find that the growth in passive institutional ownership is robustly associated with the growth in market model R²s of individual stocks since the early 1990s. Additionally, we find a negative relation between passive ownership and earnings predictability, an informativeness proxy.     

Trading Volume and Transaction Costs in Specialist Markets

Prior work with competitive rational expectations equilibrium models indicates that there should be a positive relation between trading volume and differences in beliefs or information among traders. We show that this result is sensitive to whether and how transaction costs are modeled. In a specialist market with endogenous transaction costs we show that trading volume can be negatively related to the degree of informational asymmetry in the market. Our analysis highlights the dependence of volume on market structure, and our results suggest that the “volume effects” of corporate or macroeconomic events reflect a decrease, rather than an increase, in heterogeneity of beliefs or asymmetry of information.     

Performance of Foreign and Global Mutual Funds: The Role of Security Selection,Region‐Shifting,and Style‐Shifting Abilities

We examine the performance of U.S.‐based foreign and global funds after controlling for their regional and style exposure. We show that, on average, the total performance (TP) and security selection abilities of both foreign and global funds are significantly negative and exhibit short‐term predictability. Additionally, R² reflects funds’ security selection abilities, consistent with previous findings for domestic mutual funds. Investors can earn higher abnormal returns and TP in the short run by purchasing past winners with low R² than by purchasing past losers with high R². However, there is no evidence of predictability in the funds' region‐shifting and style‐shifting abilities.     

Does Greater Firm‐Specific Return Variation Mean More or Less Informed Stock Pricing?

Roll [1988] observes low R² statistics for common asset pricing models due to vigorous firm‐specific return variation not associated with public information. He concludes that this implies “either private information or else occasional frenzy unrelated to concrete information”[p. 56]. We show that firms and industries with lower market model R² statistics exhibit higher association between current returns and future earnings, indicating more information about future earnings in current stock returns. This supports Roll's first interpretation: higher firm‐specific return variation as a fraction of total variation signals more information‐laden stock prices and, therefore, more efficient stock markets.     

The Feldstein-Horioka Puzzle and Spurious Ratio Correlation

This study shows that the Feldstein-Horioka puzzle resembles a spurious ratio correlation due to a common deflator (Pearson 1896/7). Empirically, the Feldstein-Horioka specification and its counterpart with an arbitrary deflator – final domestic demand – give similar results. Monte Carlo results also indicates that the slope β and R² of the ratio regression are upward biased. Theoretically, assuming each of the original undeflated variables are linear homogeneous functions of the deflator and random disturbances, formulas for β and R² are derived. As saving and investment rates are numerically small relative to the disturbances, both β and R² are predominantly determined by the disturbances and they tend towards unity when the disturbances are close in magnitude. The Feldstein-Horioka results are therefore noisy, though not entirely spurious, and do not necessarily reflect a strong correlation between investment and savings.     

Pricing Model Performance and the Two‐Pass Cross‐Sectional Regression Methodology

Over the years, many asset pricing studies have employed the sample cross‐sectional regression (CSR) R² as a measure of model performance. We derive the asymptotic distribution of this statistic and develop associated model comparison tests, taking into account the impact of model misspecification on the variability of the CSR estimates. We encounter several examples of large R² differences that are not statistically significant. A version of the intertemporal capital asset pricing model (CAPM) exhibits the best overall performance, followed by the Fama–French three‐factor model. Interestingly, the performance of prominent consumption CAPMs is sensitive to variations in experimental design.     

Opaque financial reports, R, and crash risk

We investigate the relation between the transparency of financial statements and the distribution of stock returns. Using earnings management as a measure of opacity, we find that opacity is associated with higher R²s, indicating less revelation of firm-specific information. Moreover, opaque firms are more prone to stock price crashes, consistent with the prediction of the Jin and Myers [2006. R² around the world: new theory and new tests. Journal of Financial Economics 79, 257–292] model. However, these relations seem to have dissipated since the passage of the Sarbanes-Oxley Act, suggesting that earnings management has decreased or that firms can hide less information in the new regulatory environment.     

Trading volume and firm-specific announcements: Implications for the market model

The market model is commonly used in finance to study events and to evaluate security performance. With daily data, it is not uncommon to find low R-squares, in the range 0–10%. Prior studies have attempted to improve the fit of the model by excluding observations associated with high trading volume. In this study, we compare the results of the high-volume-exclusion approach with the more direct firm-specific announcement exclusion approach. The announcement approach excludes observations associated with Wall Street Journal Index news items regarding the firm. By excluding the [−1,0] fays relative to such news in a sample of 68 firms, we find that R-squares increase significantly by about 5%. By excluding the days relative to earnings announcements only, R-squares increase by about 4%. These results are then compared to the high-volume-exclusion approach. It is found that this approach is more efficient as an 8% increase in R-squares is produced.The results of this study provide valuable evidence to empiricists by comparing the two approaches to improving the fit of the market model. The high-volume -exclusion approach provides higher R-squares. However, the relative efficiency of the two approaches should be balanced against the arguments for the methodologically correct approach. The advantage of using the firm-specific announcement exclusion approach is that there is more confidence of excluding only firm-specific movements from the estimation of the market model. It also allows a researcher to quickly and unambiguously identify the announcements and delete the corresponding observations. Furthermore, we find that about 50% of the improved fit, relative to the volume approach, can be accomplished by excluding earnings announcements. The methodological disadvantage of using the high-volume-exclusion approach is that it is affected not only by firm-specific announcements but also by other factors, such as the heterogeneity of investor expectations. These factors may influence the choice of using firm-specific announcements rather than the high-volume approach despite the lower increment in R-squares.     

Measuring price discovery: The variance ratio, the R, and the weighted price contribution

We analyze the statistical properties of three price discovery measures: The variance ratio, the weighted price contribution (WPC), and the R² of unbiasedness regressions. We find that, if the price process is a driftless martingale, only the WPC is an unbiased estimator for the return variance explained during a time interval. For autocorrelated processes with a drift, only the R² of the unbiasedness regression is consistent, but it is biased for small samples.     

R around the world: New theory and new tests

Morck, Yeung and Yu show that R² is higher in countries with less developed financial systems and poorer corporate governance. We show how control rights and information affect the division of risk bearing between managers and investors. Lack of transparency increases R² by shifting firm-specific risk to managers. Opaque stocks with high R²s are also more likely to crash, that is, to deliver large negative returns. Using stock returns from 40 stock markets from 1990 to 2001, we find strong positive relations between R² and several measures of opaqueness. These measures also explain the frequency of crashes.     

EMPIRICAL EVIDENCE ON THE IMPACT OF THE BID-ASK SPREAD ON THE CHARACTERISTICS OF CRSP DAILY RETURNS

It is widely recognized that Center for Research in Security Prices (CRSP) returns may differ from “true” returns because of the bid-ask effect. Using a large sample of New York Stock Exchange and American Stock Exchange securities, I confirm a discernible bid-ask effect, the magnitude and importance of which decrease with the security's price level (increase with the spread). I find volatility estimates using CRSP returns to be greater than those based on quote returns. However, market model properties, such as β and R², are generally unaffected. Bid-ask effects are clearly apparent in event studies, but because of certain offsetting effects commonly used test statistics remain unaffected. Low-priced stocks (below $2.00) do not conform to these patterns. Finally, the evidence raises the possibility that the existing literature on filter rule tests may underestimate the bid-ask spread component of transaction costs.     

Identifying unexpected accruals: a comparison of current approaches

While prior research, as noted in our paper, often uses various accrual prediction models to detect earnings management, not much is known about the accuracy, both relative and absolute, associated with these models. Our paper investigates the accuracy of six different accrual prediction models, and offers the following findings. Only the Kang – Sivaramakrishnan (1995) model performs moderately well. The remaining five models provide little ability to predict total accruals: they are less accurate than a naïve model which predicts that total accruals equal −5% of the total assets (TA) for all firms and years. Conventional R² values from a regression of actual accruals on predicted accruals are less than zero for a substantial majority of firms for these five models. These low R² values in the prediction period contrast sharply with the much higher R² values that are obtained within the estimation period. Similar performance is observed when predicting current accruals alone. However, the relative rankings of the different models are altered somewhat: the Jones (1991) model is then the only model that exhibits some predictive ability.     

Fund Manager Use of Public Information: New Evidence on Managerial Skills

We show theoretically that the responsiveness of a fund manager's portfolio allocations to changes in public information decreases in the manager's skill. We go on to estimate this sensitivity (RPI) as the R² of the regression of changes in a manager's portfolio holdings on changes in public information using a panel of U.S. equity funds. Consistent with RPI containing information related to managerial skills, we find a strong inverse relationship between RPI and various existing measures of performance, and between RPI and fund flows. We also document that both fund‐ and manager‐specific attributes affect RPI.