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Showing papers on "Stock (geology) published in 2000"


Journal ArticleDOI
Yakov Amihud1
TL;DR: In this paper, the effects of stock illiquidity on stock return have been investigated and it was shown that expected market illiquidities positively affects ex ante stock excess return (usually called risk premium) over time.
Abstract: New tests are presented on the effects of stock illiquidity on stock return. Over time, expected market illiquidity positively affects ex ante stock excess return (usually called â¬Srisk premiumâ¬?). This complements the positive cross-sectional return-illiquidity relationship. The illiquidity measure here is the average daily ratio of absolute stock return to dollar volume, which is easily obtained from daily stock data for long time series in most stock markets. Illiquidity affects more strongly small firms stocks, suggesting an explanation for the changes â¬Ssmall firm effectâ¬? over time. The impact of market illiquidity on stock excess return suggests the existence of illiquidity premium and helps explain the equity premium puzzle.

5,333 citations


Journal ArticleDOI
TL;DR: This paper found that stock prices move together more in poor economies than in rich economies, and this "nding is not due to market size and is only partially explained by higher fundamentals".

2,122 citations


Journal ArticleDOI
TL;DR: In this article, the authors test the gradual information-diffusion model of Hong and Stein ~1999! and establish three key results: once one moves past the very smallest stocks, the profitability of momentum strategies declines sharply with firm size.
Abstract: Various theories have been proposed to explain momentum in stock returns. We test the gradual-information-diffusion model of Hong and Stein ~1999! and establish three key results. First, once one moves past the very smallest stocks, the profitability of momentum strategies declines sharply with firm size. Second, holding size fixed, momentum strategies work better among stocks with low analyst coverage. Finally, the effect of analyst coverage is greater for stocks that are past losers than for past winners. These findings are consistent with the hypothesis that firm-specific information, especially negative information, diffuses only gradually across the investing public.

1,983 citations


Journal ArticleDOI
Jeffrey Wurgler1
TL;DR: This paper found that the efficiency of capital allocation is negatively correlated with the extent of state ownership in the economy, positively correlated with firm-specific information in domestic stock returns, and positively associated with the legal protection of minority investors.

1,429 citations


Journal ArticleDOI
TL;DR: In this article, it is argued that no simple correlation can be established between corporate social performance and corporate financial performance, and it is suggested that corporate citizenship programs can be designed to help companies address reputational threats.
Abstract: It is argued that no simple correlation can be established between corporate social performance and corporate financial performance. The activities that generate CSP do not directly impact the company's financial performance, but instead affect the bottom line via its stock of reputational capital - the financial value of its intangible assets. It is suggested that corporate citizenship programs can be designed to help companies address reputational threats and opportunities to achieve reputational gains while mitigating reputational losses.

866 citations


Journal ArticleDOI
TL;DR: In this article, Chan, Hamao, and Lakonishok showed that the relationship between average return and book-to-market equity is as strong for 1929 to 1963 as for the subsequent period studied in previous papers.
Abstract: The value premium in U.S. stock returns is robust. The positive relation between average return and book-to-market equity is as strong for 1929 to 1963 as for the subsequent period studied in previous papers. A three-factor risk model explains the value premium better than the hypothesis that the book-to-market characteristic is compensated irrespective of risk loadings. FIRMS WITH HIGH RATIOS OF BOOK VALUE to the market value of common equity have higher average returns than firms with low book-to-market ratios ~Rosenberg, Reid, and Lanstein ~1985!!. Because the capital asset pricing model ~CAPM! of Sharpe ~1964! and Lintner ~1965! does not explain this pattern in average returns, it is typically called an anomaly. There are four common explanations for the book-to-market ~BE0ME! anomaly. One says that the positive relation between BE0ME and average return ~the so-called value premium! is a chance result unlikely to be observed out of sample ~Black ~1993!, MacKinlay ~1995!!. Out-of-sample evidence is, however, provided by Chan, Hamao, and Lakonishok ~1991!, Capaul, Rowley, and Sharpe ~1993!, and Fama and French ~1998!. They document strong relations between average return and BE0ME in markets outside the United States. Using a rather small sample of firms, Davis ~1994! finds that the relation between average return and BE0ME observed in recent U.S. returns extends back to 1941. We extend Davis’ data back to 1926, and we expand the coverage to all NYSE industrial firms. We find that the value premium in pre-1963 returns is close to that observed for the subsequent period in earlier work. These results argue against the sample-specific explanation for the value premium. The second story for the value premium is that it is not an anomaly at all. The higher average returns on high BE0ME stocks are compensation for risk in a multifactor version of Merton’s ~1973! intertemporal capital asset pricing model ~ICAPM! or Ross’s ~1976! arbitrage pricing theory ~APT!. Consistent with this view, Fama and French ~1993! document covariation in returns

818 citations


Journal ArticleDOI
TL;DR: In this article, the authors applied recently developed unit root and cointegration models to determine the appropriate Granger relations between stock prices and exchange rates using recent Asian flu data, and found that data from South Korea are in agreement with the traditional approach.

815 citations


Journal ArticleDOI
TL;DR: In this paper, the authors measure the growth in open market stock repurchases and the manner in which stock repurchase and dividends are used by U.S. corporations, and find that stock buybacks are very procyclical, while dividends increase steadily over time.

782 citations


Posted Content
TL;DR: In this paper, the authors investigate the relations between stock repurchases and distribution, investment, capital structure, corporate control, and compensation policies over the 1977-96 period and find that, throughout the sample period, firms repurchase stock to take advantage of potential undervaluation and, in many periods, to distribute excess capital.
Abstract: In this paper, I investigate the relations between stock repurchases and distribution, investment, capital structure, corporate control, and compensation policies over the 1977-96 period. I allow the significance of each motive to change over time to account for adjustments in the percentage of firms influenced by each motive. I find that, throughout the sample period, firms repurchase stock to take advantage of potential undervaluation and, in many periods, to distribute excess capital. However, firms also repurchase stock during certain periods to alter their leverage ratio, fend off takeovers, and counter the dilution effects of stock options.

763 citations


Journal ArticleDOI
TL;DR: In this article, the authors test whether the observed patterns in stock returns after quarterly earnings announcements are related to the proportion of firm shares held by institutional investors, a variable used by prior research to proxy for investor sophistication.
Abstract: This study tests whether the observed patterns in stock returns after quarterly earnings announcements are related to the proportion of firm shares held by institutional investors, a variable used by prior research to proxy for investor sophistication. Our findings show that the institutional holdings variable is negatively correlated with the observed post‐announcement abnormal returns. Our findings also show that traditional proxies for transaction costs (i.e., trading volume, stock price) as well as firm size have little incremental power to explain post‐announcement abnormal returns when institutional holdings is an explanatory variable. If institutional ownership is a valid proxy for investor sophistication, these findings suggest that the trading activity of unsophisticated investors underlies the predictability of stock returns after earnings announcements. However, tests evaluating the validity of institutional holdings as a proxy for investor sophistication yield only mixed results. This calls fo...

750 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigate the relation between stock repurchases and distribution, investment, capital structure, corporate control, and compensation policies over the 1977-96 period and find that, throughout the sample period, firms repurchase stock to take advantage of potential undervaluation and, in many periods, to distribute excess capital.
Abstract: In this article, I investigate the relation between stock repurchases and distribution, investment, capital structure, corporate control, and compensation policies over the 1977-96 period. I allow the significance of each motive to change over time to account for adjustments in the percentage of firms influenced by each motive. I find that, throughout the sample period, firms repurchase stock to take advantage of potential undervaluation and, in many periods, to distribute excess capital. However, firms also repurchase stock during certain periods to alter their leverage ratio, fend off takeovers, and counter the dilution effects of stock options. Copyright 2000 by University of Chicago Press.

Journal ArticleDOI
TL;DR: In this paper, the benefits and risks associated with opening of stock markets were examined and it was shown that stock returns increase immediately after market opening without a concomitant increase in volatility.
Abstract: This article is an exploratory examination of the benefits and risks associated with opening of stock markets. Specifically, we estimate changes in the level and volatility of stock returns, inflation, and exchange rates around market openings. We find that stock returns increase immediately after market opening without a concomitant increase in volatility. Stock markets become more efficient as determined by testing the random walk hypothesis. We find no evidence of an increase in inflation or an appreciation of exchange rates. If anything, inflation seems to decrease after market opening as do the volatility of inflation and volatility of exchange rates. Copyright 2000 by University of Chicago Press.

Journal ArticleDOI
TL;DR: In this article, the authors investigate the value of active mutual fund management by examining the stockholdings and trades of mutual funds and find that stocks widely held by funds do not outperform other stocks.
Abstract: We investigate the value of active mutual fund management by examining the stockhold? ings and trades of mutual funds. We find that stocks widely held by funds do not outper? form other stocks. However, stocks purchased by funds have significantly higher returns than stocks they sell?this is true for large stocks as well as small stocks, and for value stocks as well as growth stocks. We find that growth-oriented funds exhibit better stock selection skills than income-oriented funds. Finally, we find only weak evidence that funds with the best past performance have better stock-picking skills than funds with the worst past performance.

Journal ArticleDOI
TL;DR: The authors show that the sentiment of Wall Street strategists is unrelated to the sentiments of individual investors or that of newsletter writers, although sentiment of the last two groups is closely related, and find a negative relationship between sentiment of each of these three groups and future stock returns.
Abstract: Investors are not all alike, and neither are their sentiments. We show that the sentiment of Wall Street strategists is unrelated to the sentiment of individual investors or that of newsletter writers, although the sentiment of the last two groups is closely related. Sentiment can be useful for tactical asset allocation. We found a negative relationship between the sentiment of each of these three groups and future stock returns, and the relationship is statistically significant for Wall Street strategists and individual investors.

Journal ArticleDOI
TL;DR: This article found that trading volume is a significant determinant of the lead-lag patterns observed in stock returns, and the speed of adjustment of individual stocks confirms these findings, indicating that differential speed of adjusting to information was a significant source of the cross-autocorrelation patterns in short-horizon stock returns.
Abstract: This paper finds that trading volume is a significant determinant of the lead-lag patterns observed in stock returns. Daily and weekly returns on high volume portfolios lead returns on low volume portfolios, controlling for firm size. Nonsynchronous trading or low volume portfolio autocorrelations cannot explain these findings. These patterns arise because returns on low volume portfolios respond more slowly to information in market returns. The speed of adjustment of individual stocks confirms these findings. Overall, the results indicate that differential speed of adjustment to information is a significant source of the cross-autocorrelation patterns in short-horizon stock returns. BOTH ACADEMICS AND PRACTITIONERS HAVE LONG BEEN interested in the role played by trading volume in predicting future stock returns. 1 In this paper, we examine the interaction between trading volume and the predictability of short horizon stock returns, specifically that due to lead-lag cross-autocorrelations in stock returns. Our investigation indicates that trading volume is a significant determinant of the cross-autocorrelation patterns in stock returns. 2 We find that daily or weekly returns of stocks with high trading volume lead daily or weekly returns of stocks with low trading volume. Additional tests indicate that this effect is related to the tendency of high volume stocks to respond rapidly and low volume stocks to respond slowly to marketwide information.

Journal ArticleDOI
TL;DR: In this paper, the authors used a disaggregated approach to study the volatility of common stocks at the market, industry, and firm levels and found that over the period 1962-97 there has been a noticeable increase in firm-level volatility relative to market volatility.
Abstract: This paper uses a disaggregated approach to study the volatility of common stocks at the market, industry, and firm levels. Over the period 1962-97 there has been a noticeable increase in firm-level volatility relative to market volatility. Accordingly, correlations among individual stocks and the explanatory power of the market model for a typical stock have declined, while the number of stocks needed to achieve a given level of diversification has increased. All the volatility measures move together countercyclically and help to predict GDP growth. Market volatility tends to lead the other volatility series. Factors that may be responsible for these findings are suggested.

Journal ArticleDOI
TL;DR: In this article, the authors examined the long-term equilibrium relationship between the Singapore stock index and selected macroeconomic variables, as well as among stock indices of Singapore, Japan, and the United States.

Journal ArticleDOI
TL;DR: In the absence of new information, a shift in supply should not affect stock prices if demand curves for stocks are flat as discussed by the authors, and no price reversal occurred as trading volume returned to normal levels.
Abstract: Weights in the Toronto Stock Exchange 300 index are determined by the market values of the included stocks' public floats. In November 1996, the exchange implemented a previously announced revision of its definition of the public float. This revision, which increased the floats and the index weights of 31 stocks, conveyed no information and had no effect on the legal duties of shareholders. Affected stocks experienced statistically significant excess returns of 2.3 percent during the event week, and no price reversal occurred as trading volume returned to normal levels. These findings support downward sloping demand curves for stocks. An obvious event with which to examine the slope of demand curves for stocks is one that changes supply. In the absence of new information, a shift in supply should not affect stock prices if demand curves for stocks are flat. Scholes (1972), using a sample of secondary equity distributions, asks whether stocks are "unique works of art" or merely abstract claims to residual cash flows with many close substitutes, as is assumed in much of finance theory. Scholes finds that the negative price impact of secondary offerings depends on the seller's identity-implying the revelation of unfavorable informationand rules out a pure supply effect. Mikkelson and Partch (1985), also using a sample of registered and unregistered secondary offerings, find weak evidence of downward sloping demand curves, but are unable to cleanly distinguish this explanation from the alternative explanation based on unfavorable information. A different class of events-additions to widely followed stock market indexes-ostensibly provides a setting where information effects should not be present. Shleifer (1986) documents a permanent price increase for stocks

Journal ArticleDOI
TL;DR: In this paper, the authors studied the real cost of sub-optimality, defined as the difference between the market value of the instruments granted and the value managers place on those instruments, and derived a method to measure the deadweight cost associated with inefficient diversification.
Abstract: Finance theory has long recognized that the incentive-alignment benefits from equity-linked compensation plans are inevitably tempered by certain deadweight costs to the firm, but relatively little empirical work has been devoted to identifying and measuring those costs Boards and their compensation advisors attempt to measure the value of the compensation packages they award, rarely studying the real cost of such plans, measured as the difference between the market value of the instruments granted and the value managers place on those instruments This value difference arises because incentive plans compel managers to hold sub-optimal portfolios Sub-optimality occurs when managers prefer to hold a contingent claim on the firm's stock that differs from the one the compensation plan forces them to hold; financial engineering can, in principle, mitigate this cost Sub-optimality also results from the manager's loss of full portfolio diversification This latter source of sub-optimality is an unavoidable deadweight cost: to align incentives, the firm's managers must have concentrated exposures to that firm's specific risks, but this forced concentrated exposure prevents the manager from optimal portfolio diversification As a consequence, undiversified managers value stock or options at less than their market price, for equilibrium market returns, determined by well-diversified investment strategies, do not fully compensate managers for their exposure to the firm's total stock price volatility The firm, therefore, always faces a tradeoff between the benefit of aligning managerial incentives, and the cost of paying managers with instruments that the firm could otherwise issue at a higher price in the market This paper derives a method to measure the deadweight cost associated with inefficient diversification, and then estimates its magnitude for a broad spectrum of firms Empirically, this deadweight cost is quite large, particularly in rapidly growing, entrepreneurial-based firms For Internet firms, the estimated value of stock options to undiversified managers is only 53% of their cost to the firm, prompting questions of whether compensation plans in such firms are weighted too heavily towards incentive-alignment to be cost effective This result also has a further implication for those who interpret insider sales as signals of firm overvaluation: namely, managers can believe that their firm's stock is substantially undervalued by the market, and still prefer to sell stock, whenever they are not restricted from doing so

Journal ArticleDOI
TL;DR: In this article, the authors revisited the controversy surrounding stock option awards, and further the understanding of restricted stock grants, which have escaped similar research focus, and obtained convincing empirical support for most theoretical predictions about stock option award.
Abstract: The use of stock-based compensation for U.S. CEOs has increased significantly throughout the 1990s. Research interest, in particular on stock option compensation, has similarly increased, yet contradictory results create questions about the theoretical underpinnings. Therefore, we revisit the controversy surrounding stock option awards, and we further the understanding of restricted stock grants, which have escaped similar research focus. Using a recent data set, we obtain convincing empirical support for most theoretical predictions about stock option awards. We also find that restricted stock, due to its linear payoffs, is relatively inefficient in inducing risk-averse CEOs to accept risky, value-increasing investment projects. Copyright 2000 by University of Chicago Press.

Journal ArticleDOI
TL;DR: In this paper, the authors study new evidence from the 1990s for 1,060 Canadian repurchase programs and find that the Canadian stock market discounts the information in repurchase announcements, particularly for value stocks.
Abstract: During the 1980s, U.S. firms announcing stock repurchases earned favorable long-run returns. Recently, concerns have been raised over the robustness of these findings. This concern comes at a time of explosive growth in repurchase programs. Thus, we study new evidence from the 1990s for 1,060 Canadian repurchase programs. Moreover, because of Canadian law, we can carefully track repurchase activity monthly. Similarly to the situation in the United States, the Canadian stock market discounts the information in repurchase announcements, particularly for value stocks. Completion rates in Canada are sensitive to mispricing. Trades also appear linked to price movements; managers buy more shares when prices fall.

Journal ArticleDOI
TL;DR: This paper found that the impact of industrial sector effects is now roughly equal to that of country effects in the stock returns of the world's largest equity markets, suggesting that country-based approaches to global investment management may be losing their effectiveness.
Abstract: Historically, country effects have been dominant in explaining variations in global stock returns, even in the developed markets, and investors have segmented their allocations accordingly. We set out to investigate whether this situation still prevails. We found a significant shift in the relative importance of national and economic influences in the stock returns of the world's largest equity markets. In these markets, the impact of industrial sector effects is now roughly equal to that of country effects. In addition to supporting the notion of increasing global capital market integration, these findings suggest that country-based approaches to global investment management may be losing their effectiveness.

Book
01 Jul 2000

Book ChapterDOI
TL;DR: In this article, a review of the literature on the long-run performance of mergers and acquisitions is presented, concluding that long run performance is negative following mergers, though performance is non-negative (and perhaps even positive) following tender offers.
Abstract: While the bulk of the research on the financial performance of mergers and acquisitions has focused on stock returns around the merger announcement, a surprisingly, large set of papers has also examined long-run stock returns following acquisitions. We review this literature, concluding that long-run performance is negative following mergers, though performance is non-negative (and perhaps even positive) following tender offers. However, the effects of both methodology (see Lyon, Barber & Tsai, 1999) and chance (see Fama, 1998) may modify this conclusion. Two explanations of under performance (speed of price-adjustment and EPS myopia) are not supported by the data, while two other explanations (method of payment and performance extrapolation) receive greater support.

Journal ArticleDOI
TL;DR: In this paper, the authors argue that stock repurchases serve to add value in two main ways: (1) they provide managers with a tax-efficient means of returning excess capital to shareholders and (2) they allow managers to "signal" to investors their view that the firm is undervalued.
Abstract: Stock repurchases by U.S. companies experienced a remarkable surge in the 1980s and ‘90s. Indeed, in 1998, the total value of all stock repurchased by U.S. companies exceeded for the first time the total amount paid out as cash dividends. And the U.S. repurchase movement has gone global in the past few years, spreading not only to Canada and the U.K., but also to countries like Japan and Germany, where such transactions were prohibited until recently. Why are companies buying back their stock in such amounts? After dismissing the popular argument that stock repurchases boost earnings per share, the authors argue that repurchases serve to add value in two main ways: (1) they provide managers with a tax-efficient means of returning excess capital to shareholders and (2) they allow managers to “signal” to investors their view that the firm is undervalued. Returning excess capital is value-adding for two reasons: First, it helps prevent companies from pursuing growth and size at the expense of profitability and value. Second, by returning capital to investors, repurchases (like dividends) play the critically important economic function of allowing investors to channel their investment from mature or declining sectors of the economy to more promising ones. But if stock repurchases and dividends serve the same basic economic function, why are repurchases growing more rapidly? Part of the explanation is that, because repurchases are taxed as capital gains and dividends as ordinary income, repurchases are a more tax-efficient way of distributing excess capital. But perhaps even more important than their tax treatment is the flexibility that (at least) open market repurchases provide corporate managers-flexibility to make small adjustments in capital structure, to exploit (or correct) perceived undervaluation of the firm's shares, and possibly even to increase the liquidity of the stock, which could be particularly valuable in bear markets. For U.S. regulators, the growth in open market stock repurchases raises some interesting issues. Perhaps most important, companies are not required to (and rarely do) furnish their investors with details about a given program's structure, execution method, number of shares repurchased, or even its duration. Policy regulators (and corporate executives as well) should consider some of the benefits provided by other systems, notably Canada's, which provide greater transparency and more guidelines for the repurchase process.

Journal ArticleDOI
TL;DR: In this article, the existence of a significant, long-run relationship between stock prices and domestic and international economic activity in six European economies has been investigated using the Johansen Cointegration tests.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the relationship between the precision of public information about economic growth and stock market returns and showed that higher precision of signals tends to increase the risk premium, when signals are imprecise, and return volatility is U-shaped with respect to investors' risk aversion.
Abstract: Using a simple dynamic asset pricing model, this paper investigates the relationship between the precision of public information about economic growth and stock market returns. After fully characterizing expected returns and conditional volatility, I show that (i) higher precision of signals tends to increase the risk premium, (ii) when signals are imprecise the equity premium is bounded above independently of investors' risk aversion, (iii) return volatility is U-shaped with respect to investors' risk aversion, and (iv) the relationship between conditional expected returns and conditional variance is ambiguous. IN MODERN FINANCIAL MARKETS, investors are flooded with a variety of information: corporations' earnings reports, revisions of macroeconomic indexes, policymakers' statements, and political news. These pieces of information are processed by investors to update their projections of the economy's future growth rate, inflation rate, and interest rate. In turn, these changes in investors' expectations affect stock market prices. However, even though it is clear that asset prices react to new information, several questions arise regarding the relationship between the quality of information that investors receive and asset returns. For example, what kind of effect does a noisy signal on the "health" of the economy have on stock market prices? If information is noisy, is there a risk premium? Or is the risk premium completely independent of the quality of information investors receive? Also, how does the precision of the signals affect stock market volatility? If signals are more precise, does stock market volatility decrease or increase? Finally, can we infer how good investors' information is from the behavior of stock market returns? In this paper I study a dynamic asset pricing model where I try to answer the above questions. Specifically, I assume that stock dividends are generated by a diffusion process whose drift rate is unknown to investors and may

Journal ArticleDOI
TL;DR: This article presented an empirical model of housing supply derived from urban growth theory, which describes new housing construction as a function of changes in house prices and costs, rather than as the level of those variables.

Journal ArticleDOI
TL;DR: In this article, a sample of firms that adopt target ownership plans, under which managers are required to own a minimum amount of stock, was examined. And they found that prior to plan adoption, such firms exhibit low managerial equity ownership and low stock price performance.
Abstract: We examine a sample of firms that adopt "target ownership plans," under which managers are required to own a minimum amount of stock. We find that prior to plan adoption, such firms exhibit low managerial equity ownership and low stock price performance. Managerial equity ownership increases significantly in the two years following plan adoption. We also observe that excess accounting returns and stock returns are higher after the plan is adopted. Thus, for our sample of firms, the required increases in the level of managerial equity ownership result in improvements in firm performance.

Journal ArticleDOI
TL;DR: Angel et al. as mentioned in this paper found that the minimum bid-ask spread is wider after a stock split and brokers have more incentive to promote a stock, which is consistent with splits acting as an incentive to brokers to promote stocks.
Abstract: A traditional explanation for stock splits is that they increase the number of small shareholders who own the stock. A possible reason for the increase is that the minimum bid-ask spread is wider after a split and brokers have more incentive to promote a stock. I document a large number of small buy orders following Nasdaq and NYSE/AMEX splits during 1993 to 1994. I also find strong evidence that trading costs increase, and weak evidence that costs of market making decline following splits. This is consistent with splits acting as an incentive to brokers to promote stocks. STOCK SPLITS SEEM TO BE PURELY COSMETIC CHANGES with no real economic consequences. After a two-for-one split, each shareholder has twice as many shares, but each represents a claim on only half as much of the corporation's assets and earnings. However, one real consequence of a stock split is that the tick size increases as a proportion of the stock's price. Except for a small number of very low-priced issues, U.S. stocks listed on an exchange or on Nasdaq have a tick or minimum price variation of $0.125 during the sample period.' Thus, a decrease in the stock price and an increase in the relative tick size are indistinguishable consequences of a split. Some authors, notably Angel (1997), argue that splits are intended to move relative ticks to desired levels. Several empirical studies provide indirect evidence that is consistent with an increase in relative tick size as a motivation for splits. Desai and Jain (1997), Fama et al. (1969), Lakonishok and Lev (1987), and others document that splits occur after stocks have experienced significant price increases or, equivalently, after relative tick sizes have decreased significantly. Angel shows that there is far less dispersion internationally in relative tick sizes than in stock prices.