Tick size, NYSE rule 118, and ex-dividend day stock price behavior

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Abstract

Bali and Hite (1998) and Dubofsky (1992) propose models in which market microstructure effects play a role in the ex-dividend day price drop anomaly. Bali and Hite suggest that the anomaly is caused solely by price discreteness, while Dubofsky suggests that NYSE Rule 118 is also involved. We test these models by examining cum- to ex-day price drops during the one-eighth, one-sixteenth, and decimal tick size regimes. While the evidence is qualitatively consistent with Dubofsky's predictions, neither model is satisfactory in a quantitative sense. One of our main empirical findings is that no significant decline was evident in the magnitude of the ex-day anomaly after the tick size reduction.

Introduction

According to Miller and Modigliani (1961), in a frictionless perfect capital market with no uncertainty, the share price following a dividend should fall by exactly the amount of the dividend paid on each share. However, empirical works on this issue have consistently found that, on average, stock prices drop by less than the dividend amount on the ex-dividend date. This unusual ex-dividend day price behavior has many economists searching for an acceptable explanation.

In a widely cited study, Elton and Gruber (1970) note that because investors care only about after-tax returns, a higher tax on dividend income than on capital gains will result in an ex-dividend price drop that is smaller than the dividend. They find that the price drop to dividend ratio is only 0.778 for a large sample of dividend distributions in 1966 and 1967. They also find that the price drop to dividend ratio is directly related to the level of the dividend yield. Elton and Gruber believe that this relation stems from the formation of tax clienteles for stocks of different dividend yields. They interpret the empirical findings as evidence consistent with the hypothesis that investors have a tax-induced preference for capital gains over dividends.

Both Kalay (1982) and Miller and Scholes (1982) suggest that the Elton and Gruber tax clientele hypothesis appears to be inconsistent with a no-arbitrage equilibrium. Another prominent study, by Frank and Jagannathan (1998), casts serious doubt on the validity of the tax-effect explanation. Frank and Jagannathan find that in Hong Kong the average stock price drop on ex-dividend days is also smaller than the dividend amount, even though neither dividends nor capital gains are taxed.

Some recent work on the ex-day price drop phenomenon focuses on market microstructure effects as potential explanations for the observed anomaly. Two important papers are found in this literature: Dubofsky (1992) and Bali and Hite (1998). Dubofsky argues that ex-dividend day excess returns arise from the mechanics of NYSE Rule 118, AMEX Rule 132, and the fact that prices are constrained to discrete tick multiples (i.e., price discreteness). Bali and Hite suggest that the ex-day price drop anomaly is caused solely by price discreteness.

NYSE Rule 118 and AMEX Rule 132 dictate that, on ex-cash dividend days, open limit orders to buy stocks are reduced by the cash dividend amount. With discrete prices, if the resulting price is not a tick multiple, it is further lowered to the next tick. Prices in limit sell orders are not changed. For example, if the tick size is $0.125 ($1/8) and a dividend is $0.15, then the price of limit buy orders will be adjusted down by $0.25 and limit sell orders will not be adjusted. Dubofsky argues that if on the ex-day the bid-ask spread is still constrained by the adjusted open limit orders, then the bid-ask spread is wider than normal and not symmetric around the expected ex-dividend day adjusted price. This asymmetry will lead to smaller measured price drops than dividends.

Bali and Hite (1998) present an ex-day price drop model in which prices are restricted to multiples of a tick. Their model indicates that investors will never be willing to pay more for a dividend than its value, and they show that the equilibrium ex-day price drop will be the amount of the dividend rounded to the next smaller tick. For example, if the tick size is $1/8 and the dividends are $0.20 and $0.25, then the ex-day price drops will both be $0.125.

In this paper we conduct direct empirical tests of the impact of price discreteness and NYSE Rule 118 on ex-dividend day price behavior. We try to determine whether the data are consistent with Dubofsky's model or that proposed by Bali and Hite. Recently, the NYSE converted from $1/8 ticks to $1/16 ticks and finally to decimals. We use data in all three tick size regimes to test the two models. We report five main findings. (1) For the most common dividend amounts, the ex-day price drop is just as likely to be the tick above the dividend as to be the tick below the dividend. (2) Regression analysis shows that the average price drop does not equal the tick below the dividend. (3) For all three tick size regimes, the average cum-day bid to ex-day bid price drop is larger than the dividend on average, which is larger than the cum-day ask to ex-day ask price drop. (4) The opening bid-ask spread is larger on the ex-day than on the cum-day. (5) No significant reduction is found in the difference between the dividend amount and average ex-day price drop as the tick size is reduced. All of these findings are inconsistent with Bali and Hite (1998). While these results are qualitatively consistent with Dubofsky (1992), they contradict Dubofsky at a quantitative level if we take Dubofsky's fully constrained model literally.1 Therefore, something important is still missing from these models.

Beyond our general findings, two features of our study are worth mentioning. First, we use a relatively large sample to perform an extensive examination and comparison of the different price drop relations using cum-day close to ex-day open prices as well as cum-day close to ex-day close prices. Past research on ex-dividend day price behavior mostly examines cum-day close to ex-day close price drops.2 A major difficulty in the empirical research is that the close-to-close price drops are very noisy. Eades et al. (1994) document large variations over time in average ex-dividend day abnormal returns. Boyd and Jagannathan (1994) find that the ex-day price drop is very noisy, and hence inference based on one or a few years’ data will be imprecise. We address this problem by using a relatively large sample to examine the cum-day close to ex-day open price drop in addition to the close-to-close price drop. This allows us to make more precise inferences because the overnight price drop is much less noisy than the close-to-close price drop. For example, in our sample, the overnight price drop has a standard deviation of $0.399, whereas the cum-day close to ex-day close price drop has a standard deviation of $0.728. This means that, in terms of inference about the average ex-day price drop, one observation in our sample is equivalent to nearly two (i.e., 0.728/0.399=1.82) observations in a sample that contains only close prices. Our sample, therefore, of more than 52,000 observations is equivalent to more than 94,000 observations of close-to-close price drops.

Second, we use a relatively large sample to examine ex-day drops in quoted prices and changes in the bid-ask spread. Past research mainly uses transaction prices. Using the bid-ask spread and quote data, we can test the model predictions about changes in market quotes. For example, our finding that the price drop from cum-day close ask to ex-day open ask is substantially smaller than that from cum-day close bid to ex-day open bid is consistent with Dubofsky's (1992) predictions.

Recently, Graham et al. (2003) also examine the effect of tick size reduction on the ex-dividend day price drop anomaly. Like us, they find that after the decimalization the ex-dividend day price drop anomaly did not go away. But they attribute the persistence of the anomaly to a tax change around the time of the decimalization and conclude that their results support the tax-effect explanation of the ex-day price drop anomaly.

The remainder of the paper is organized as follows. In Section 2 we present the testable implications of the Dubofsky and Bali and Hite models. In Section 3 we discuss the data and econometric modeling used in the analysis. In Section 4 we present our major empirical findings. Section 5 concludes the paper. We give a detailed discussion of some econometric issues in the Appendix.

Section snippets

Model predictions and testable implications

Bali and Hite (1998) and Dubofsky (1992) make different predictions about the size of ex-day price drops. Both models assume that no informational event occurs from the cum- to the ex-day. Bali and Hite's model predicts that the ex-day price drop will always equal the tick below the dividend. That is, when the tick size is $0.125, dividends less than or equal to $0.125 should have price drops of zero; dividends greater than $0.125 but less than or equal to $0.25 should have price drops of

Data description and econometric modeling

Our data come from the Center for Research in Security Prices (CRSP) database and the NYSE Trade and Quote (TAQ) database along with the list of decimal conversion dates available from the NYSE. We collect information about all the ordinary, cash, and taxable dividend distributions made to NYSE stocks from January 1993 to December 2001 from the CRSP database. We exclude cases in which a firm made multiple distributions on the same date. We collect information about dividend amount, prices,

Empirical results

We now discuss our empirical findings.

Concluding remarks

Dubofsky (1992) and Bali and Hite (1998) offer novel market microstructure explanations to the ex-dividend day price drop anomaly. Bali and Hite's model predicts that the ex-day price drop should equal the tick below the dividend. Dubofsky's model suggests that both the mechanics of NYSE Rule 118 and price discreteness are involved in the price drop anomaly. Using a relatively large sample of data with different tick sizes, we examine the predictions of both models. Our evidence is inconsistent

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We thank an anonymous referee, Hank Bessembinder, Bruce Costa, Tony Crawford, Ravi Jagannathan, Mike Lemmon, Uri Loewenstein, Tim Manuel, Jakki Mohr, Barbara Reider, and seminar participants at the Federal Reserve Bank of Atlanta for helpful comments. We are responsible for any errors or omissions.

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