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Payout policy, taxes, and the relation between returns and the bid–ask spread
Journal of Banking & Finance 30 (2006) 37–58 www.elsevier.com/locate/jbf
Payout policy, taxes, and the relation between returns and the bid–ask spread Aron A. Gottesman a, Gady Jacoby
b,*
a
b
Department of Finance and Economics, Lubin School of Business, Pace University, New York, NY 10038, USA Department of Accounting and Finance, 474 Drake Centre, I.H. Asper School of Business, Faculty of Management, University of Manitoba, Winnipeg MB, Canada R3T-5V4 Received 18 February 2004; accepted 13 December 2004 Available online 25 March 2005
Abstract Recent evidence demonstrates that corporate payout policy has shifted from the nearly exclusive use of dividend payout to the inclusion of stock repurchase, primarily through open markets. This trend has been attributed to the tax advantages associated with repurchase relative to dividends. In this paper, we introduce personal taxation and stock repurchase to reexamine the relation between returns and the bid–ask spread. Our model provides insight into the nature of this relation. Tests performed using NYSE, AMEX, and NASDAQ data provide empirical support of our theoretical conclusions. We conclude that the firmÕs choice of payout policy influences the relation between returns and spreads. Ó 2005 Elsevier B.V. All rights reserved. JEL classification: G12 Keywords: Asset pricing; Bid–ask spread; Liquidity; Payout policy; Tax
*
Corresponding author. Tel.: +1 204 474 9331; fax: +1 204 474 7545. E-mail address: [email protected] (G. Jacoby).
0378-4266/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2004.12.003
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1. Introduction There is extensive evidence that, since the early 1980s, corporate payout policy has shifted from the nearly exclusive use of dividend payout to the inclusion of openmarket stock repurchase (Allen and Michaely, 2001; Bagwell and Shoven, 1989; Fama and French, 2001; Jagannathan et al., 2000). This trend has been attributed to the personal tax advantages associated with repurchase relative to dividends (Allen and Michaely, 2001).1 Support for this explanation comes from Green and Hollifield (2003), who argue that using stock repurchase instead of dividend payout leads to savings of 40–50% of the present value of the personal tax liability. Allen and Michaely (2001) report that repurchasing firms almost exclusively use open market repurchases to distribute cash. These firms must act under SEC Rule 10b–18 that specifies the guidelines that govern open-market repurchases. This rule requires that firms engaging in an open market repurchase use only one broker or dealer on any single day. Thus, the use of stock repurchase has important implications for the study of liquidity, as investors in firms performing open market-repurchase bear a cost for the immediacy service provided by the broker or dealer. Investors in firms issuing dividends do not face such costs. Hence, while stock repurchase is the dominant strategy from a personal tax perspective, there is a tradeoff between the personal tax advantages of stock repurchase and liquidity costs. In this paper, we derive a theoretical model based on Amihud and Mendelson (1986) that relates returns to the bid–ask spread but allows for stock repurchase and personal taxation. Our extended model demonstrates that stock repurchase can be superior to dividends as a payout methodology when personal taxation is included. This result differs from the one identified in Amihud and MendelsonÕs taxfree environment, in which dividends are always dominant. We identify a critical bid–ask spread level that determines the firmÕs optimal payout policy, and demonstrate that the personal tax advantage of stock repurchase dominates immediacy services costs of open-market repurchase for firms with spreads lower than the critical spread. On the other hand, firms with spreads exceeding the critical spread will choose to pay dividends, because repurchase immediacy costs exceed the related tax advantage. In Amihud and MendelsonÕs (1986) tax-free model, dividends always dominate repurchase due to immediacy costs associated with open-market repurchase. This yields a concave gross relation between returns and the relative spread. In contrast, in our model repurchase can dominate dividends due to personal taxation. When
1
Other factors may have contributed to the increased popularity of stock repurchase as well. Allen and Michaely (2001) note that dividends exhibit a general upward trend with decreases occurring only rarely, while stock repurchases are highly responsive to the firmÕs earnings and general economic conditions. Thus, stock repurchase provides the firm with a higher degree of flexibility. Brockman and Chung (2001) argue that the relaxed regulatory requirements associated with stock repurchases make them more attractive than dividend payouts. Grullon and Ikenberry (2000) provide empirical evidence indicating that stock repurchase programs are liquidity enhancing for the firmÕs stock.
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spreads are lower than the critical spread, and firms choose to repurchase, the relation between gross returns and relative spread can be concave, convex, or both. When spreads are greater than the critical spreads, and firms choose to pay dividends, the relation between gross returns and relative spread is concave, as Amihud and Mendelson find for their tax-free economy. Our model further shows that Amihud and MendelsonÕs clientele effect holds for all assets, regardless of whether they pay through dividends or through repurchase. We empirically test the major hypothesis of our analysis through studying the relation between returns and relative bid–ask spreads, using CRSP, TAQ, and COMPUSTAT data for stocks listed on NYSE, AMEX, and NASDAQ. Consistent with the theory, we provide evidence of the existence of a concave relation between returns and relative spreads for portfolios of stocks associated with firms that exclusively use dividends as their payout vehicle. This relation disappears for firms paying exclusively through stock repurchase. These findings represent evidence that the firmÕs choice of payout vehicle influences the relation between returns and spreads. The remainder of this paper is organized as follows. Section 2 presents the derivation of the theoretical model. Section 3 presents the empirical evidence. Section 4 concludes the paper.
2. Model In this section we examine the impact of personal taxation on the relation between returns and the bid–ask spread. We outline the main assumptions and discuss the effect of taxes on the firmÕs choice of cash distribution. We then investigate the relation between returns and the bid–ask spread under personal taxation. 2.1. Personal taxes and cash distribution Amihud and MendelsonÕs (1986) model describes a concave relation between gross returns and relative spread. They assume no taxes and describe a world with M investors indexed by i, i = 1, 2, . . . , M. A portfolio is held by a type i investor with initial wealth Wi. Investor iÕs time horizon, Ti, is random and exponentially distributed, with E½T i ¼ l1 i . At time Ti, the investor liquidates the portfolio to a market maker for the quoted bid price. There are N + 1 assets indexed by j, j = 0, 1, . . . , N, where asset j pays dj, a perpetual positive cash flow, per unit of time. Asset j has a trading cost reflected by a relative spread of Sj. Asset 0 has zero relative spread with unlimited supply. Amihud and Mendelson number investor types through increasing expected hold1 1 ing horizons l1 1 6 l2 6 6 lM and securities through increasing relative spread ratios 0 = S0 6 S1 6 6 SN. Market makers stand by in the market to provide immediacy services. For each security j they quote an ask price, Vj, and a bid price, Vj(1 Sj). Amihud and Mendelson further assume a stationary infinite horizon economy, where assets pay a constant dividend stream. Assets bear no taxes and transaction or other costs, and asset prices are constant over time.
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Bagwell and Shoven (1989), Fama and French (2001), Jagannathan et al. (2000), and Allen and Michaely (2001) report a steady increase in repurchases activity starting in the early 1980s. These studies suggest that while repurchase is increasingly popular, it is not a complete substitute for dividends. Green and Hollifield (2003) provide evidence regarding the excess tax costs associated with dividend distributions relative to repurchase activity. They argue that, net of personal taxes, stock repurchase is superior to dividends. Support for this conclusion is provided in Allen and Michaely (2001). Dividends are taxed as ordinary income, with a higher effective tax rate compared to the capital gains tax rate that applies to stock repurchase. Thus, there is a substantial tax disadvantage for dividends compared to repurchases. This tax differential requires separate tax rates in modeling. For dividend-paying firms, we assume that asset j pays a perpetual constant pre-tax dividend, dj, taxed at a rate sp. Note that dj is the cash flow available for distribution to shareholders each period. Thus the after-tax perpetual dividend is equal to dj(1 sp) per unit of time. We assume that open market repurchase is the preferred payout vehicle for firms using stock repurchase. According to Allen and Michaely (2001) and Grullon and Ikenberry (2000), a large proportion of firms engaged in stock repurchase employ open market repurchase. For example, Allen and Michaely report that open market repurchases represented more than 95% of the dollar value of total shares repurchased in 1998. We therefore assume that firms act under the guidelines that govern open market repurchases, set by the SEC in 1982, with the adoption of Rule 10b–18.2 This rule requires firms engaged in open market repurchase to follow several guidelines. Specifically, and relevant to this paper, the rule requires that the firm use only one broker or dealer on any single day of repurchase to buy back its stock. Based on the above, we assume that, for firms choosing repurchase as payout policy, the dollar amount repurchased for asset j (by firm j) is dj. The variable dj represents the cash flow available for distribution to shareholders each period, and is a perpetual positive and constant cash flow per unit of time. Consistent with Rule 10b–18, we assume that shareholders sell the repurchased shares to the issuer in the open market through a market maker for the quoted bid price. Hence, the periodic after-spread, but pre-tax, cash flow from stock repurchase to the shareholder is dj(1 Sj). In this stationary infinite horizon economy, where assets pay a constant repurchase stream, asset prices remain constant over time. Thus the after-spread repurchase income, net of the relevant cost basis, is taxed as capital gains. Letting Cj denote the percentage of the initial cost of asset j (Vj) that is attributed to the dollar amount repurchased, the cost basis relevant to repurchase is CjVj. When the capital gains tax rate, sc, is applied to stock repurchase, the periodic after-spread and after-tax cash flow from stock repurchase to the shareholder is dj(1 Sj) [dj(1 Sj) CjVj]sc. In this modeling environment, repurchase dominates dividends as a value maximizing method of payment to shareholders, when for firm j:
2 47 Fed Reg. 53333 (November 26, 1982). For a detailed discussion of this rule, see Allen and Michaely (2001).
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d j ð1 S j Þ ½d j ð1 S j Þ C j V j sc > d j ð1 sp Þ: The spread under which firm j breaks even between the two payment methodologies s sc ð1mj Þ C V is given by S p ð1s , where mj ¼ dj j j . For firms with Sj < S* the personal tax cÞ advantage of stock repurchase dominates the immediacy services costs of open-market repurchase, and these firms will choose to repurchase. On the other hand, firms with Sj > S* will choose to pay dividends, due to the dominance of repurchase liquidity costs relative to the related tax advantage. Finally, firms will be indifferent when Sj = S*. Note that sc < 1, sp > sc due to the tax disadvantage associated with dividends, and mj < 1 due to the fact that a capital gain associated with repurchase is guaranteed in this economy. It follows that 0 < S* < 1. We number security types through increasing relative spread ratios 0 = S0 6 S1 6 6 Sk 6 S* 6 Sk+1 6 6 SN. Thus, for firms 0 through k repurchase dominates dividends, while for firms k + 1 through N, dividends are dominant. Amihud and Mendelson assume a stationary infinite horizon economy, where assets generate a constant stream of cash flow available for distribution to shareholders. This implies that at the time of purchase, an investor pays the ask price, Vj, for security j, and at the time of liquidation s/he receives the bid price, Vj(1 Sj). Thus, the investor suffers a capital loss of VjSj at liquidation. In our economy, with taxation, we assume that the investor receives a tax return for this capital loss.3 Thus, the investor suffers an after-tax capital loss of VjSj(1 sc), and the after-tax revenue at liquidation is given by: Vj(1 Sj(1 sc)). In light of this discussion of tax-related issues, we next study the relation between returns and the bid–ask spread with taxation. 2.2. The relation between returns and the bid–ask spread with taxes 2.2.1. Dividends For dividend-paying firms (k + 1 through N), our analysis of after-tax returns is similar to that of Amihud and Mendelson (1986), with a small modification for tax issues related to a capital loss that occurs at the time of liquidation. Amihud and MendelsonÕs propositions still hold in the current case for dividend-paying firms. For these (k + 1 through N), the expected present value of the portfolio held by a type-i investor is (Z " # ) ( " #) N N Ti X X qy qT i ET i e xij d j ð1 sp Þ dy þ ET i e xij V j ð1 S j ð1 sc ÞÞ ; 0
j¼0
j¼0
where xij is the number of units of asset j held by investor i, and q is the risk free return on the zero-spread asset. The above expression is the sum of the expected present value of continuous net cash flow from dividends during investor iÕs holding 3 Capital losses can be used by taxable individual investors to reduce taxes on realized gains, or to offset limited amounts of nongain income (Poterba and Weisbenner, 2001).
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period and the expected present value of the investorÕs net liquidation revenue. All cash flows are after tax. Similar to Amihud and Mendelson (1986), the net return on asset j for a dividendpaying firm in such an economy is given by4 rDij ¼
d j ð1 sp Þ li S j ð1 sc Þ; Vj
ð1Þ
where rDij = expected net (spread- and tax-adjusted) return of dividend-paying asset j to investor i. d j ð1sp Þ = pre-spread and after-tax return on security j. Vj liSj(1 sc) = expected after-tax spread cost on asset j for investor i (li is the liquidation probability for investor i). We denote the modified gross (pre-spread and pre-tax) return for a dividend-payd ing firm as rDj V jj , and rearrange the above equation as follows: rDij þ li S j ð1 sc Þ rDj ¼ : ð2Þ ð1 sp Þ Thus, for dividend-paying firms the gross return on asset j is linear in the expected relative spread.5 Following Amihud and Mendelson, we assume no short sales; hence the investor with the superior bid determines the asset equilibrium price. Investors have heterogeneous expected holding periods. The investor that outbids all others agrees to accept the minimum expected net return. Investor i will purchase the asset j that provides the highest net return, as follows:
rDi ¼ max frDij g:
ð3Þ
j¼1;2;...;n
rD þl S ð1s Þ
c i j . Therefore, the equilibrium The gross return for investor i on asset j is i ð1s pÞ gross return on asset j is the minimal required expected gross return across investors: D ri þ li S j ð1 sc Þ rDj ¼ min : ð4Þ i¼0;1;2;...;M ð1 sp Þ
Thus, a modified version of Proposition 2 in Amihud and Mendelson (1986) still holds, and in equilibrium the observed market (gross) return is an increasing and concave piecewise-linear function of the relative spread. As in Amihud and Mendel
son (1986), we can prove this proposition through letting fi ðSÞ ¼
rD i þli S j ð1sc Þ . ð1sp Þ
Through the above minimization, the gross return on an asset with a relative spread S is 4 Note that in this paper the terms gross and net are used in reference to both bid–ask spread costs and taxes. 5 Below, we demonstrate that under repurchase, the linearity in Eq. (2) does not hold, giving rise to a convex return–bid–ask spread relation at the individual asset level.
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f ðSÞ ¼ min fi ðSÞ:
43
ð5Þ
i¼1;2;...;M
Proposition 2 of Amihud and Mendelson follows from the fact that monotonicity is preserved in f(S) (the minimum function), and a minimum of a finite collection of linear functions is concave piecewise-linear. This proof of a concave piecewise-linear relation between the expected gross returns and the relative spread is in the context of the definition of the gross return as a linear function of the expected relative spread for a dividend-paying firm. 2.2.2. Stock repurchase For the repurchasing firms (0 through k), the expected present value of the portfolio held by a type-i investor is (Z " # ) N Ti X qy ET i e xij ðd j ð1 S j Þ ½d j ð1 S j Þ C j V j sc Þ dy 0
j¼0
(
"
þ ET i eqT i
N X
#) xij V j ð1 S j ð1 sc ÞÞ
;
ð6Þ
j¼0
where xij and q are as defined for the dividend case. Implicit in the above expression is the assumption that the firm splits its stocks so that the repurchase does not change the number of units of asset j held by every investor i. That is, we assume that xij remains constant. The above expression is the sum of the expected present value of continuous net cash flow from stock repurchases during investor iÕs holding period and the expected present value of the investorÕs liquidation revenue, net of the aftertax bid–ask spread cost. As derived in Appendix A, this expression can be written as: ðli þ qÞ
1
N X
xij ½d j ð1 S j Þ ½d j ð1 S j Þ C j V j sc þ li V j ð1 S j ð1 sc ÞÞ:
j¼0
ð7Þ Thus, given asset bid–ask prices, a type-i investor maximizes the expected present value of the portfolio through solving the following optimization problem: max xij
N X
xij ½d j ð1 S j Þ ½d j ð1 S j Þ C j V j sc þ li V j ð1 S j ð1 sc ÞÞ;
j¼0
subject to N X
xij V j 6 W i
and
xij P 0
for all j ¼ 0; 1; . . . ; N ;
ð8Þ
j¼0
where Wi denotes investor iÕs wealth. The modified net (after-spread and after-tax) expected return for repurchasing firms, rRij , is: rRij ¼
d j ð1 S j Þð1 sc Þ þ C j sc li S j ð1 sc Þ: Vj
ð9Þ
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For repurchasing firms we denote the modified gross (pre-spread and pre-tax) return d as rRj V jj . Thus, the modified expected gross rate of return is: rRj ¼
rRij C j sc þ li S j ð1 sc Þ : ð1 S j Þð1 sc Þ
ð10Þ
Eq. (10) demonstrates that under repurchase, the gross return is a strictly increasing and convex function in the relative spread cost Sj. Contrast Eq. (10) with Eq. (2), where gross return is a strictly increasing and linear function in the relative spread when dividends dominate repurchase. If, for a given price vector V, investor i chooses the asset with
rRi ¼
max frRij g;
ð11Þ
j¼0;1;2;...;N
then the equilibrium gross return on asset j is the minimal required gross return across all investors: rRi C j sc þ li S j ð1 sc Þ R rj ¼ min : ð12Þ i¼0;1;2;...;M ð1 S j Þð1 sc Þ Stated differently, the equilibrium price of asset j is determined by the highest bidder, as follows: d j ð1 S j Þð1 sc Þ V j ¼ max : ð13Þ i¼0;1;2;...;M rRi C j sc þ li S j ð1 sc Þ If the asset is held by investor i in equilibrium, we can rewrite Eq. (13) as: V j ¼
d j ð1 S j Þð1 sc Þ þ C j V j sc rRi
li V j S j ð1 sc Þ
rRi
:
ð14Þ
The first term on the right-hand side of Eq. (14) is the present value of net perpetual cash flow from open market stock repurchase. The second term is the expected present value of after-tax cash outflows from the cost of transacting the asset. In the following proposition we demonstrate that Amihud and MendelsonÕs clientele effect still holds for repurchasing firms. Proposition 1. In equilibrium, higher-spread assets are held by longer-term investors (clientele effect). Proof. Consider assets j and h with S* > Sh P Sj. Suppose that in equilibrium asset j is held by a type-i investor and asset h is held by investor i + 1, where li P li+1 This, with maximization (11), implies that rRij P rRih and rRiþ1;j P rRiþ1;h . Substituting from Eq. (9) we get: d j ð1 S j Þð1 sc Þ þ C j sc li S j ð1 sc Þ V j P
d h ð1 S h Þð1 sc Þ þ C h sc li S h ð1 sc Þ V h
ð15Þ
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and d h ð1 S h Þð1 sc Þ þ C h sc liþ1 S h ð1 sc Þ V h P
d j ð1 S j Þð1 sc Þ þ C j sc liþ1 S j ð1 sc Þ: V j
ð16Þ
This implies that (li li+1)(Sh Sj) P 0. Thus, Sh P Sj when li > li+1. The proof for non-consecutive portfolios follows immediately. h As in Amihud and Mendelson, the current model predicts that for repurchasing firms long-term investors will tend to hold illiquid assets, while short-term investors will hold the more liquid assets. Next, in Proposition 2, we modify Amihud and MendelsonÕs proposition regarding the concavity of the relation between gross return and spread. Proposition 2. In equilibrium, the relation between gross return and spread is increasing and piecewise-convex. Proof. Let
gi ðSÞ ¼
rRi C j sc þ li S j ð1 sc Þ : ð1 S j Þð1 sc Þ
ð17Þ
Through minimization (12), the market gross and pre-tax return on an asset with relative spread S is gðSÞ ¼ min gi ðSÞ i¼1;2;...;M
ð18Þ
and Proposition 2 follows from the fact that monotonicity is preserved in g(S) (the minimum function), and a minimum of a finite collection of convex functions is piecewise-convex. h 2.3. The return–bid–ask spread relation The analysis in the previous two subsections demonstrates that the required expected gross return is increasing in spreads for all spread levels, regardless of payout policy. This relation is found to be increasing and piecewise-convex for firms paying through repurchase (0 through k), with Sj < S*. For dividend-paying firms (k + 1 through N), with Sj > S*, the relation is increasing and concave piecewise-linear as in Amihud and Mendelson (1986). For repurchasing firms, with Sj 2 [0, S*), minimization (12) does not produce a clear result with respect to the curvature of the minimum function relating the expected gross return and the relative spread. In general, the relation between the expected gross return and the relative spread is positive, but it could be concave, convex, or both, as demonstrated in Fig. 1.
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Panel A Gross
S*
Relative Spread
Panel B Gross Return
S*
Relative Spread
Fig. 1. The relation between gross return and relative spread with taxation. In Panel A, there are relatively more short-term investors concentrated around lower spreads in the [0, S*] spread interval, hence the relation between gross return and relative spread is approximately concave for lower levels of the relative spread. As the relative spread approaches S*, the approximated relation becomes convex. In Panel B, there are relatively more investors concentrated around spreads approaching S* in the [0, S*] spread interval, hence the relation between gross return and relative spread will be convex for lower spread levels. As the relative spread approaches S*, the approximated relation becomes concave.
The exact shape of the function depends on the concentration of investors across the spectrum of spreads, which, according to the clientele effect, corresponds to the concentration of investors across investment horizons. If, for example, there are relatively more short-term investors concentrated around lower spreads in the [0, S*] spread interval, then the relation between gross return and relative spread relation will be approximately concave for lower levels of the relative spread. As the relative spread approaches S*, the approximated relation becomes convex (see Panel A of Fig. 1). If, on the other hand, there are relatively more investors concentrated around spreads approaching S* in the [0, S*] spread interval, then the relation between gross
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return and relative spread will be convex for lower spread levels. As the relative spread approaches S*, the approximated relation becomes concave (see Panel B of Fig. 1). Intuitively, for repurchasing firms, two opposing effects influence the curvature of the relation between gross return and relative spread. In Proposition 1 we prove that Amihud and MendelsonÕs (1986) clientele effect holds for repurchasing firms. Therefore, in equilibrium, short-term investors hold lower-spread assets than long-term investors, and short-term assets are traded more frequently than long-term assets. The concave relation is driven by Amihud and MendelsonÕs (1986) observation that the value of an asset is the present value of perpetual dividends minus the present value of perpetual spread costs that are incurred every time that the asset is liquidated, as presented in Eq. (14). Since short-term assets are traded more frequently than long-term assets, the expected present value of cash flows associated with perpetual liquidation of short-term assets is more sensitive to change in the spread than long-term assets. This implies that for short-term assets, a given increase in the spread will result in a larger increase in the required gross return relative to longterm assets, hence the concave relation. But there is an opposing effect as well. As the spread ratio increases, the present value of the after-tax and after-spread perpetual cash flow from open market stock repurchase diminishes, as does the net return. Theoretically, as the relative spread approaches 100 percent the investor will demand infinite compensation in terms of expected gross return before purchasing such an asset, as presented in Eq. (10). This explains the convex relation for repurchasing firms. For dividend paying firms, with Sj 2 [S*, 1), the analysis produces a concave relation between the expected gross return and the relative spread for all firms, similar to Amihud and Mendelson (1986). For these firms, the clientele effect is the only factor that determines the curvature, hence the concave relation. Since S* is the break-even spread level that results in the same net return under both payout methodologies, it can be shown that the gross return for every investor i under dividends, fi(S), is identical to the same investorÕs gross return under repurchase, gj(S). Thus, at a spread level of S* we have gS = f(S) and, therefore, the minimum function is continuous. Overall, with taxation, the expected relation between gross return and relative spread is increasing for all spread levels. In terms of curvature, one cannot determine whether the relation is concave, convex, or both for spreads lower than S*, but for spreads greater than S* the relation is concave.
3. Empirical evidence Amihud and Mendelson (1986) provide empirical evidence in support of the existence of a concave relation between the expected gross return and the relative spread. The data used for their empirical test is sampled from the New York Stock Exchange (NYSE) for the years 1960–1979. Allen and Michaely (2001) demonstrate that during this time period dividend payout was the preferred distribution vehicle for most firms. Thus, Amihud and MendelsonÕs model, which was derived under the dividend
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payment assumption, is suitable to the payout methodology environment during that time period, and one should expect the data to support the existence of a concave relation. However, given Allen and MichaelyÕs evidence that, as of the early 1980s, stock repurchase is the dominant distribution vehicle, analysis based on more recent data is warranted. In this section we test the major hypothesis of our analysis through studying the relation between returns and relative bid–ask spreads. Consistent with the theory, we provide evidence of the existence of a concave relation between returns and relative spreads for portfolios of stocks associated with firms that exclusively use dividends as their payout vehicle. This relation disappears for firms paying exclusively through stock repurchase. 3.1. Data and methodology The data set consists of all nonfinancial firms trading on NYSE, AMEX, or NASDAQ between January 1993 and December 1999 from the Center for Research and Security Prices (CRSP) database, for which intraday spread data is available on the Trade and Quote (TAQ) database, and for which accounting data is available on the COMPUSTAT database. Allen and Michaely (2001) demonstrate that during this time period open-market repurchase is the dominant payout vehicle for most firms initiating new cash distributions to their shareholders. Thus, our sample period is appropriate for testing the implications of our model, which allows for firms to implement payout through either dividends and repurchase. Monthly returns, extracted from CRSP, are calculated as the percentage change in the value of one dollar of investment during month t. Monthly returns are adjusted for distributions so that comparisons can be made on an equivalent basis before and after distributions. Monthly spreads are the time-weighted average relative bid–ask spreads, for bid and ask quotes reported on the TAQ consolidated trade files between 9:30 AM and 4:30 PM of a given trading day. Time-weighted averaging of relative bid–ask spreads is performed across all trading days for the month under consideration. We exclude all observations where the bid price, ask price, bid size in number of round lots, or ask size in number of round lots are valued at zero. We also exclude all observations where the ask price is 1.5 times larger than the bid price. The relative spread for stock j in month t is calculated as: S jt ¼
askjt bidjt askjt bidjt : ¼ pricejt ðaskjt þ bidjt Þ=2
ð19Þ
Of the observations that remain following the above filtering, we retain the last quote for each second, and estimate the time-weighted average bid–ask spreads.6 We extract a number of additional variables for each observation. Beta is calculated as the sum of the slopes in the regression of excess returns on the current and previous monthÕs excess market returns. Beta estimation is performed using data
6
This methodology is from Joel HasbrouckÕs Empirical Market Microstructure website.
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from the 36 months before the month under consideration. Hence, we exclude any stock without a 36-month history of complete return data. We include a single lag in the estimation, following Fama and French (1992). Specifically, we estimate the beta coefficient using the following regression model: Rjt ¼ aj þ bjt1 Rmt þ bjt2 Rmt1 þ ejt :
ð20Þ
The variable Rjt is the month-t excess returns over the 90-day T-bill rate of stock j. Rmt and Rmt1 are month t and t 1 excess market returns, calculated as the excess return of the value weighted portfolio in the given month. We define the beta for stock j which can vary across time (t), as bjt = bjt1 + bjt2. Fama and French (1992) find that the market value of the firmÕs equity and the ratio of the book value of common equity to its market capitalization both capture cross-sectional variation in returns. To account for these factors, we extract ME and BE/ME for each stock. ME is the market value of the firmÕs equity on the final day of the month, extracted from CRSP. Following Fama and French (1992), BE/ME is calculated as the ratio of book value of common equity plus balance-sheet deferred taxes for the year of the observation to ME, extracted from COMPUSTAT. We eliminate any observation for which any variable is missing. Following the above, we identify a sample of 196,924 monthly firm observations. To account for other time-varying risk factors not captured in beta, we also extract MOMENTUM, SMB, and HML.7 MOMENTUM is the average return on two high prior return portfolios minus the average return on two low prior portfolios. SMB is the difference in returns across small and big stock portfolios controlling for the same weighted average book-to-market equity in the two portfolios. HML is the difference in returns between high and low book-to-market equity portfolios. Following Eleswarapu and Reinganum (1993) who find that the empirical return–spread relation is different for January compared to other months, we also identify the month of the observation, MONTH, to control for this effect.8 We next form three separate samples on the basis of payout policy, similar to Grullon and Michaely (2002). For each observation, we identify dividend (DIV) and repurchase (REPO) policy for the firm for the year, as reported on COMPUSTAT. Following Grullon and Michaely (2002), DIV is the total dollar amount of dividends declared on the common stock, while REPO is the expenditure on the purchase of common and preferred stocks minus any reduction in the value of the net number of preferred shares outstanding. The first sample consists of all 196,924 observations, regardless of payout policy. The second sample consists of the 44,656 observations of firms with positive dividends and zero repurchase for the year
7 This data was obtained from Kenneth FrenchÕs website. We thank an anonymous referee for suggesting we include these factors in our tests. 8 The results are generally similar to the use of an indicator variable that is equal to unity if the month of the observation is January.
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A.A. Gottesman, G. Jacoby / Journal of Banking & Finance 30 (2006) 37–58
during which the observation occurs. The third sample consists of the 34,029 observations of firms with zero dividends and positive repurchase. Panel A of Table 1 pre-
Table 1 Descriptive statistics ALL DIV, ALL REPO (n = 196,924)
DIV > 0, REPO = 0 (n = 44,656)
DIV = 0, REPO > 0 (n = 34,029)
Mean
Std.
Mean
Std.
Mean
Std.
0.1622 0.0430 1.3616 2.0852 0.8732 3.3743 3.0776 3.5811 3.4330
0.0077 0.0252 0.9642 19.7685 0.5746 1.1579 0.1302 0.3220 6.6165
0.1044 0.0276 0.9117 1.9468 0.6898 3.0646 2.8632 3.2732 3.4359
0.0103 0.0389 1.4417 18.6585 0.5883 1.4490 0.2224 0.9634 6.6772
0.1741 0.0399 1.2588 1.8061 0.8623 3.7987 3.3131 3.9925 3.4343
Panel A: Monthly firm observations R 0.0104 S 0.0388 b 1.3166 ln(ME) 19.0076 ln(BE/ME) 0.6685 MOMENTUM 1.2612 SMB 0.1860 HML 0.5864 MONTH 6.6643
Panel B: Portfolios R S b ln(ME) ln(BE/ME) MOMENTUM SMB HML MONTH
ALL DIV, ALL REPO (n = 2100)
DIV > 0, REPO = 0 (n = 2100)
DIV = 0, REPO > 0 (n = 2100)
0.0111 0.0395 1.3518 19.6139 0.4551 1.2148 0.1310 0.3694 6.5000
0.0077 0.0250 0.9570 20.3734 0.4050 1.2148 0.1310 0.3694 6.5000
0.0120 0.0441 1.5544 18.9699 0.4322 1.2148 0.1310 0.3694 6.5000
0.0585 0.0368 1.2582 1.8843 0.4275 3.1908 2.9198 3.4293 3.4529
0.0479 0.0222 0.8269 1.5494 0.2921 3.1908 2.9198 3.4293 3.4529
0.0730 0.0376 1.3417 1.7284 0.5073 3.1908 2.9198 3.4293 3.4529
Mean, standard deviation, and number of observations are reported separately for three samples formed on the basis of payout policy. ALL DIV, ALL REPO includes all observations, regardless of payout policy. DIV > 0, REPO = 0 includes observations associated with positive dividends and zero repurchase during the year of the observation. DIV = 0, REPO > 0 includes observations associated with zero dividend and positive repurchase during the year of the observation. Panel A reports descriptive statistics for all monthly firm observations between January 1993 through December 1999. Panel B reports descriptive statistics for portfolios consisting of 25 equally weighted portfolios for each month, formed through ranking the monthly firm observations on the basis of spread and beta. Variable definitions are as follows: R is the monthly return, adjusted for distributions, in excess of the 90-day T-bill rate. S is the timeweighted average relative bid–ask spreads, for bid and ask quotes for the firmÕs stock between 9:30 AM and 4:30 PM, averaged across all trading days for the month under consideration. b is the sum of the coefficient estimates in a regression of firm excess return against current period and single lag market excess return. ln(ME) is the natural logarithm of the market value of the firmÕs equity. ln(BE/ME) is the natural logarithm of the book value of common equity plus balance-sheet deferred taxes for the year of the observation. MOMENTUM is the average return on two high prior return portfolios minus the average return on two low prior portfolios. SMB is the difference in returns across small and big stock portfolios controlling for the same weighted average book-to-market equity in the two portfolios. HML is the difference in returns between high and low book-to-market equity portfolios. MONTH is the month of the observation.
A.A. Gottesman, G. Jacoby / Journal of Banking & Finance 30 (2006) 37–58
51
sents descriptive statistics for the three samples. It is notable that spread and beta are lowest for the sample of positive dividend and zero repurchase observations.9 For each of these samples, the relation between returns and liquidity costs is explored through forming 25 equally weighted portfolios for each month in the sample. Portfolio formation takes place as follows. Stocks are first placed into one of five relative spread portfolio groups based on their relative spread ranking. We next rank each stock in each of the five relative spread portfolio groups on the basis of beta, and each of the five relative spread portfolio groups is further subdivided into five portfolios based on the beta ranking. For the sample of monthly portfolios formed using all cross-sectional pooled observations, the average portfolio consists of approximately 93.8 observations, with portfolio size ranging between 37 and 123 observations. For the sample associated with positive dividends and zero repurchase, the average portfolio consists of approximately 21.3 observations, ranging between 16 and 24 observations. For the sample associated with zero dividend and positive repurchase, the average portfolio consists of approximately 16.2 observations, ranging between 2 and 31 observations. We next pool the 25 portfolios we form each month across all 84 months in the sample period for a sample size of 2100 separate portfolios for each payout policy.10 Panel B of Table 1 presents descriptive statistics for the portfolios associated with each of the payout policy samples. Similar to the sample presented in Panel A, both spread and beta are lowest for the sample of positive dividend and zero repurchase observations, and highest for the sample of zero dividend and positive repurchase. Because an identical number of portfolios are created each month for all three samples, it is unsurprising that the values of momentum, SMB, HML, and MONTH are identical for all portfolio samples. Table 2 presents the average excess return, relative spread, and beta values for each of the five relative spread and five beta groupings. Panel A of Table 2 indicates that excess return is negatively related to spread, a result that is monotonic for all payout policy samples. However, Panel B indicates that excess return is positively related to beta, though this result is not monotonic for all samples. Hence, the negative return–spread relation may be attributable to other factors that vary across groupings. As we will present shortly, our multivariate tests provide evidence of a positive relation. Table 3 presents correlations between the variables. Recognizing the large negative correlation between ln(ME) and ln(Spread), we orthogonalize ln(ME) on
9 While our model predicts that dividend-paying stocks will tend to have higher spreads than repurchasing firmsÕ spreads, this result only applies when all other factors are controlled. The lower spreads reported in Table 1 are unsurprising, as they can be attributed to the fact that the beta for the positive dividend zero repurchase sample (0.96) is much lower than that of the zero dividend positive repurchase sample (1.44). 10 We pool the portfolios across all months, instead of averaging portfolios across months (e.g., Eleswarapu, 1997), as averaging across months does not permit testing of the time-varying risk factors we include in our tests (momentum, SML, HMB).
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Table 2 Average excess return, relative spread, and beta values for relative spread and beta groupings ALL DIV, ALL REPO
DIV > 0, REPO = 0
DIV = 0, REPO > 0
R
R
S
R
S
S
b
b
b
Panel A: Spread groupings Lowest 0.0167 0.0072 0.0138 0.0144 0.0112 0.0250 0.0084 0.0438 Highest 0.0053 0.1070
1.1108 1.3130 1.4402 1.4972 1.3977
0.0142 0.0084 0.0083 0.0047 0.0027
0.0062 0.0105 0.0162 0.0264 0.0657
0.8468 0.9496 0.9405 0.9939 1.0544
0.0240 0.0141 0.0103 0.0060 0.0058
0.0100 0.0199 0.0319 0.0505 0.1084
1.6275 1.5926 1.6373 1.5069 1.4076
Panel B: Beta groupings Lowest 0.0072 0.0409 0.0047 0.0388 0.0068 0.0388 0.0110 0.0389 Highest 0.0256 0.0400
0.1885 0.6763 1.2000 1.8181 3.2530
0.0058 0.0050 0.0057 0.0070 0.0149
0.0256 0.0244 0.0251 0.0245 0.0254
0.0985 0.4855 0.8753 1.3112 2.2116
0.0102 0.0082 0.0068 0.0128 0.0222
0.0453 0.0436 0.0434 0.0437 0.0446
0.0465 0.8363 1.4093 2.0632 3.5096
The average value of excess return, spread, and beta are presented for each of the five relative spread (Panel A) and five beta (Panel B) groupings, reported separately for three samples formed on the basis of payout policy. ALL DIV, ALL REPO includes all observations, regardless of payout policy. DIV > 0, REPO = 0 includes observations associated with positive dividends and zero repurchase during the year of the observation. DIV = 0, REPO > 0 includes observations associated with zero dividend and positive repurchase during the year of the observation. Portfolios are formed each month through ranking the monthly firm observations on the basis of spread and beta. Variable definitions are as follows: R is the monthly return, adjusted for distributions, in excess of the 90-day T-bill rate. S is the time-weighted average relative bid–ask spreads, for bid and ask quotes for the firmÕs stock between 9:30 AM and 4:30 PM, averaged across all trading days for the month under consideration. b is the sum of the coefficient estimates in a regression of firm excess return against current period and single lag market excess return.
ln(Spread), and use the orthogonalized variable in our regression tests.11 To test for the predicted relation, we estimate the following three regression models across our 2100 portfolios: Rpt ¼ a0 þ a1 lnðS pt Þ þ d0 X þ ept ;
ð21Þ
Rpt ¼ a0 þ a1 S 2pt þ d0 X þ ept ;
ð22Þ
Rpt ¼ a0 þ a1 lnðS pt Þ þ a2 S 2pt þ d0 X þ ept ;
ð23Þ
where Rpt is the excess return on portfolio p for month t; Spt is the average relative spread of portfolio p for month t; a and d are regression coefficients, and X is the vector of control variables, as follows: X ¼ ½bpt ; lnðMEÞOrthogonalized; lnðBE=MEÞ; MOMENTUM; SMB; HML; MONTH:
ð24Þ
11 The results are generally similar when the raw version of ln(ME) is used as a regressor instead of the orthogonalized version.
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Table 3 Correlations [1] R ln(S) S2 b ln(ME) ln(BE/ME) MOMENTUM SMB HML MONTH
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
0.0340 0.0204 0.5880 0.0402 0.0720 0.0093 0.0415 0.8597 0.4324 0.0796 0.1201 0.3327 0.1882 0.1130 0.3448 0.0368 0.0500 0.0260 0.0157 0.0097 0.0007 0.1825 0.0150 0.0052 0.0092 0.0090 0.0098 0.0034 0.1161 0.0389 0.0144 0.0174 0.0011 0.0073 0.5798 0.4018 0.0156 0.0056 0.0043 0.0080 0.0102 0.0117 0.2912 0.0836 0.2417
Correlations are presented for the sample of all observations, regardless of payout policy (ALL DIV, ALL REPO). Variable definitions are as follows: R is the monthly return, adjusted for distributions, in excess of the 90-day T-bill rate. S is the time-weighted average relative bid–ask spreads, for bid and ask quotes for the firmÕs stock between 9:30 AM and 4:30 PM, averaged across all trading days for the month under consideration. b is the sum of the coefficient estimates in a regression of firm excess return against current period and single lag market excess return. ln(ME) is the natural logarithm of the market value of the firmÕs equity. ln(BE/ME) is the natural logarithm of the book value of common equity plus balance-sheet deferred taxes for the year of the observation. MOMENTUM is the average return on two high prior return portfolios minus the average return on two low prior portfolios. SMB is the difference in returns across small and big stock portfolios controlling for the same weighted average book-to-market equity in the two portfolios. HML is the difference in returns between high and low book-to-market equity portfolios. MONTH is the month of the observation.
We perform our estimations using HansenÕs (1982) Generalized Method of Moments (GMM) to account for potential serial correlation and heteroscedasticity.12 The regression results are presented in Table 4. We perform the estimation separately for the three samples that we formed based on payout policy. Panels A, B, and C present the results, respectively, for the sample of all observations, regardless of payout policy; for the sample associated with positive dividends and zero repurchase; and for the sample associated with zero dividends and positive repurchase.
3.2. Regression results For the sample of portfolios based on all observations regardless of payout policy (Table 4, Panel A), the results of the first model verify Amihud and MendelsonÕs finding of concavity. The coefficient associated with the ln(Spt) variable is positive and significant at the 5% level. The results of the second model demonstrate that the coefficient associated with the S 2pt variable is positive. While insignificant at the 10% level, this coefficient is significant at the 12% level (5% level when OLS estimation is used). Thus, based on these regression models, the estimated return–spread
12
The results are generally similar when OLS estimation is used instead of GMM.
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A.A. Gottesman, G. Jacoby / Journal of Banking & Finance 30 (2006) 37–58
Table 4 Multivariate analysis Variable
(1)
(2)
(3)
Panel A: ALL DIV, ALL REPO Intercept ln(S) S2 b ln(ME) Orthogonalized ln(BE/ME) MOMENTUM SMB HML MONTH
0.0014 0.0005 0.0309*** 0.0037*** 0.0071*** 0.0051*** 0.002***
0.8264 0.0017 0.0016 0.0259*** 0.0037*** 0.0071*** 0.005*** 0.0019***
0.0673*** 0.0141*** 1.5278 0.0018 0.004* 0.0299*** 0.0037*** 0.007*** 0.0052*** 0.002***
Adjusted R2 N
0.2967 2100
0.2945 2100
0.2975 2100
0.0367*** 0.0069**
0.0107**
Panel B: DIV > 0, REPO = 0 Intercept ln(S) S2 b ln(ME) Orthogonalized ln(BE/ME) MOMENTUM SMB HML MONTH
0.0009 0.0015 0.0311*** 0.0033*** 0.0043*** 0.0026** 0.0007**
0.6543 0.0012 0.0006 0.0277*** 0.0033*** 0.0043*** 0.0025** 0.0007**
0.0396** 0.0084** 2.5979 0.001 0.004** 0.0296*** 0.0033*** 0.0042*** 0.0027** 0.0007**
Adjusted R2 N
0.1667 2100
0.1656 2100
0.1674 2100
0.0153*** 0.0032**
0.0025
Panel C: DIV = 0, REPO > 0 Intercept ln(S) S2 b ln(ME) Orthogonalized ln(BE/ME) MOMENTUM SMB HML MONTH
0.0011 0.0014 0.021*** 0.0038*** 0.0089*** 0.005*** 0.0017***
0.5958 0.0011 0.0003 0.0203*** 0.0039*** 0.0089*** 0.005*** 0.0016***
0.0279 0.0036 0.1277 0.0011 0.001 0.0212** 0.0038*** 0.0089*** 0.005*** 0.0017***
Adjusted R2 N
0.2475 2100
0.2474 2100
0.2472 2100
0.0308*** 0.0043
0.0142***
The generalized method of moments is used to estimate the following three models: Rpt ¼ a0 þ a1 lnðS pt Þ þ d0 X þ ept ; Rpt ¼ a0 þ a1 S 2pt þ d0 X þ ept ; Rpt ¼ a0 þ a1 lnðS pt Þ þ a2 S 2pt þ d0 X þ ept ;
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55
Table 4 (continued ) where a and d are coefficients and X = [bpt, ln(ME) Orthogonalized, ln(BE/ME), MOMENTUM, SMB, HML, MONTH]. Estimation is performed separately for three portfolio samples formed on the basis of payout policy. ALL DIV, ALL REPO (Panel A) includes all observations, regardless of payout policy. DIV > 0, REPO = 0 (Panel B) includes observations associated with positive dividends and zero repurchase during the year of the observation. DIV = 0, REPO > 0 (Panel C) includes observations associated with zero dividend and positive repurchase during the year of the observation. Variable definitions are as follows: R is the monthly return, adjusted for distributions, in excess of the 90-day T-bill rate. S is the timeweighted average relative bid–ask spreads, for bid and ask quotes for the firmÕs stock between 9:30 AM and 4:30 PM, averaged across all trading days for the month under consideration. b is the sum of the coefficient estimates in a regression of firm excess return against current period and single lag market excess return. ln(ME) is the natural logarithm of the market value of the firmÕs equity. ln(BE/ME) is the natural logarithm of the book value of common equity plus balance-sheet deferred taxes for the year of the observation. MOMENTUM is the average return on two high prior return portfolios minus the average return on two low prior portfolios. SMB is the difference in returns across small and big stock portfolios controlling for the same weighted average book-to-market equity in the two portfolios. HML is the difference in returns between high and low book-to-market equity portfolios. MONTH is the month of the observation. *** ** * , , denote significance at the 1%, 5% and 10% levels, respectively.
relation may be concave and/or convex for the entire sample. In general, this is in agreement with our model. In the third model, we jointly test for concavity and convexity. The coefficient associated with ln(Spt) is positive, at the 1% level, while the coefficient associated with S 2pt is negative and insignificant. The reversal of the coefficient sign for the convexity variable may be an artifact of the high multicolinearity between ln(Spt) and S 2pt The beta coefficients are insignificant in all models, as in Fama and French (1992). The adjusted R2 associated with all three models are similar, and range in value between 0.2945 and 0.2975. Overall, these results provide evidence that for the sample of all firms the relation between excess return and relative spread is concave, while evidence of convexity is weak. For the sample of portfolios associated with positive dividends and zero repurchase (Table 4, Panel B), we once again verify Amihud and MendelsonÕs findings of concavity. The coefficient associated with the ln(Spt) variable in the first model is positive and significant at the 5% level. The results of the second model do not identify a convex relation, as the coefficient associated with the S 2pt variable is insignificant. In the third model, the coefficient associated with ln(Spt) is significantly positive at the 5% level, while the coefficient associated with S 2pt is insignificantly negative. Once again, the beta coefficients are insignificant in all models, as in Panel A. The adjusted R2 associated with all three models are again highly similar, and range in value between 0.1656 and 0.1674. Overall, there is evidence that the relation between excess return and relative spread is concave for the positive dividends and zero repurchase portfolios, with no support for convexity. These results support the concave return–spread relation predicted by our theoretical model for dividend-paying assets. It is also in agreement with Amihud and Mendelson (1986) result. This is not surprising given the fact that Amihud and MendelsonÕs sample can be considered as a sample of dividend-paying stocks (and no repurchase), since during their sample period vast majority of firms used dividends as their preferred payout vehicle.
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Recall that our theoretical model predicts that the return–spread relation can be concave, convex or both for repurchasing firms. Although this prediction is untestable, we feel that an empirical study of the nature of this relation is still important. Specifically, if we find that the estimated relation is different than that estimated for dividend-paying firms, then one can conclude that the payout policy is a factor in determining the nature of the underlying return–spread relation. For the sample of portfolios associated with zero dividends and positive repurchase (Table 4, Panel C), we find no significant evidence of concavity. The coefficients associated with ln(Spt) are insignificant in both regression models in which it appears. The coefficients associated with S 2pt are positive and insignificant at the 10% level. But it is noteworthy that while insignificant at the 10% level, the coefficient associated with S 2pt is significant at the 14% level (12% level when OLS estimation is used) for model 2. As we found in Panels A and B, the beta coefficients are insignificant in all models, and the adjusted R2 associated with all three models are similar, ranging in value between 0.2472 and 0.2475. Overall, our results clearly indicate that, as our theoretical model predicts, the firmÕs choice of payout policy influences the relation between returns and spread. This relation is increasing and concave for dividend-paying firms. At the same time, there is very weak evidence supporting a convex relation between returns and spread for firms choosing to repurchase.
4. Summary and conclusion We examine the impact of personal taxation on the relation between gross return and relative bid–ask spread. Following evidence presented by Allen and Michaely (2001) regarding corporate payout policy, we revisit Amihud and MendelsonÕs (1986) model, and present personal taxation that sometimes makes stock repurchase a superior payout vehicle compared to dividends. In Amihud and MendelsonÕs taxfree environment, firms will pay shareholders only through dividends. The extended model predicts that the relation between gross return and relative spread can be concave, convex, or both for highly liquid assets with low relative spreads that tend to pay to shareholders through repurchase. This relation turns concave for thinly traded dividend-paying assets with higher relative spread ratios. Our model further shows that Amihud and MendelsonÕs clientele effect holds for all assets, regardless of whether they payout dividends or through repurchase. We demonstrate that in addition to the concavity caused by the clientele effect, the influence of spreads on repurchase proceeds will generate a convex relation, resulting in a curvature that is characterized by both concavity and convexity. We use NYSE, AMEX, and NASDAQ return data from CRSP, together with time-weighted bid–ask spread TAQ data and accounting data from COMPUSTAT to test the major hypothesis of our analysis through studying the relation between returns and the relative bid–ask spread. We provide evidence supporting the main prediction of our model, that the firmÕs choice of payout vehicle has influences the relation between returns and spreads. An interesting direction for future research
A.A. Gottesman, G. Jacoby / Journal of Banking & Finance 30 (2006) 37–58
57
is whether payout policy is a function of the stockÕs bid–ask spread, after controlling for firm characteristics. Acknowledgement The authors thank Yakov Amihud, Kevin Davis, Charles Mossman and Cameron Morrill for their input. The authors thank the Social Sciences and Humanities Research Council of Canada for financial support. All errors are the exclusive fault of the authors. Appendix A The expected present value of the portfolio held by a type-i investor is given by
(Z
"
Ti
e
ET i
qy
0
N X
# xij ðd j ð1 S j Þ ½d j ð1 S j Þ C j V j sc Þ dy
j¼0
(
"
þ ET i e
qT i
)
N X
#) xij V j ð1 S j ð1 sc ÞÞ
;
j¼0
where xij is the number of units of asset j held by investor i, and q is the riskless return on the zero-spread asset. We rewrite this term as: " # Z N Ti X xij ðd j ð1 S j Þ ½d j ð1 S j Þ C j V j sc Þ ET i eqy dy j¼0
þ
0
"
N X
# xij V j ð1 S j ð1 sc ÞÞ ET i feqT i g:
j¼0
Since we assume that the investorÕs investment horizon, Ti, is exponentially distributed with E½T i ¼ l1 we write: i " #Z Z t N 1 X xij ðd j ð1 S j Þ ½d j ð1 S j Þ C j V j sc Þ li eli t eqy dy dt j¼0
þ V j ð1 S j ð1 sc ÞÞ
0
Z
0
1
li eli t eqt dt: 0
Integrating the above expression yields: " #Z N 1 li X xij ðd j ð1 S j Þ ½d j ð1 S j Þ C j V j sc Þ eli t ð1 eqt Þ dt q j¼0 0 " # N X li þ xij V j ð1 S j ð1 sc ÞÞ : li þ q j¼0
58
A.A. Gottesman, G. Jacoby / Journal of Banking & Finance 30 (2006) 37–58
Solving the integral and rearranging, we find: ðli þ qÞ1
N X
xij ½d j ð1 S j Þ ½d j ð1 S j Þ C j V j sc þ li V j ð1 S j ð1 sc ÞÞ:
j¼0
References Allen, F., Michaely, R., 2001. Payout policy. In: Constantinides, G., Harris, M., Stulz, R. (Eds.), Handbook of Economics. North-Holland. Amihud, Y., Mendelson, H., 1986. Asset pricing and the bid–ask spread. Journal of Financial Economics 15, 223–249. Bagwell, L.S., Shoven, J.B., 1989. Cash distributions to shareholders. Journal of Economic Perspectives 3, 129–140. Brockman, P., Chung, D., 2001. Managerial timing and corporate liquidity: Evidence from actual share repurchases. Journal of Financial Economics 61, 417–448. Eleswarapu, V.R., 1997. Cost of transacting and expected returns in the NASDAQ market. Journal of Finance 52, 2113–2127. Eleswarapu, V.R., Reinganum, M.R., 1993. The seasonal behavior of the liquidity premium in asset pricing. Journal of Financial Economics 34, 373–386. Fama, E.F., French, K.R., 1992. The cross-section of expected stock returns. Journal of Finance 47, 427– 465. Fama, E.F., French, K.R., 2001. Disappearing dividends: Changing firm characteristics or lower propensity to pay? Journal of Financial Economics 60, 3–43. Green, R.C., Hollifield, B., 2003. The personal-tax advantages of equity. Journal of Financial Economics 67, 175–216. Grullon, G., Ikenberry, D., 2000. What do we know about stock repurchase?. Journal of Applied Corporate Finance 13, 31–51. Grullon, G., Michaely, R., 2002. Dividends, share repurchases, and the substitution hypothesis. Journal of Finance 57, 1649–1684. Hansen, L., 1982. Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054. Jagannathan, M., Stephens, C., Weisbach, M., 2000. Financial flexibility and the choice between dividends and stock repurchases. Journal of Financial Economics 57, 355–384. Poterba, J., Weisbenner, S., 2001. Capital gains tax rules, tax-loss trading, and turn-of-the year returns. Journal of Finance 56, 353–368.
Payout policy, taxes, and the relation between returns and the bid–ask spread Aron A. Gottesman a, Gady Jacoby
b,*
a
b
Department of Finance and Economics, Lubin School of Business, Pace University, New York, NY 10038, USA Department of Accounting and Finance, 474 Drake Centre, I.H. Asper School of Business, Faculty of Management, University of Manitoba, Winnipeg MB, Canada R3T-5V4 Received 18 February 2004; accepted 13 December 2004 Available online 25 March 2005
Abstract Recent evidence demonstrates that corporate payout policy has shifted from the nearly exclusive use of dividend payout to the inclusion of stock repurchase, primarily through open markets. This trend has been attributed to the tax advantages associated with repurchase relative to dividends. In this paper, we introduce personal taxation and stock repurchase to reexamine the relation between returns and the bid–ask spread. Our model provides insight into the nature of this relation. Tests performed using NYSE, AMEX, and NASDAQ data provide empirical support of our theoretical conclusions. We conclude that the firmÕs choice of payout policy influences the relation between returns and spreads. Ó 2005 Elsevier B.V. All rights reserved. JEL classification: G12 Keywords: Asset pricing; Bid–ask spread; Liquidity; Payout policy; Tax
*
Corresponding author. Tel.: +1 204 474 9331; fax: +1 204 474 7545. E-mail address: [email protected] (G. Jacoby).
0378-4266/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2004.12.003
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1. Introduction There is extensive evidence that, since the early 1980s, corporate payout policy has shifted from the nearly exclusive use of dividend payout to the inclusion of openmarket stock repurchase (Allen and Michaely, 2001; Bagwell and Shoven, 1989; Fama and French, 2001; Jagannathan et al., 2000). This trend has been attributed to the personal tax advantages associated with repurchase relative to dividends (Allen and Michaely, 2001).1 Support for this explanation comes from Green and Hollifield (2003), who argue that using stock repurchase instead of dividend payout leads to savings of 40–50% of the present value of the personal tax liability. Allen and Michaely (2001) report that repurchasing firms almost exclusively use open market repurchases to distribute cash. These firms must act under SEC Rule 10b–18 that specifies the guidelines that govern open-market repurchases. This rule requires that firms engaging in an open market repurchase use only one broker or dealer on any single day. Thus, the use of stock repurchase has important implications for the study of liquidity, as investors in firms performing open market-repurchase bear a cost for the immediacy service provided by the broker or dealer. Investors in firms issuing dividends do not face such costs. Hence, while stock repurchase is the dominant strategy from a personal tax perspective, there is a tradeoff between the personal tax advantages of stock repurchase and liquidity costs. In this paper, we derive a theoretical model based on Amihud and Mendelson (1986) that relates returns to the bid–ask spread but allows for stock repurchase and personal taxation. Our extended model demonstrates that stock repurchase can be superior to dividends as a payout methodology when personal taxation is included. This result differs from the one identified in Amihud and MendelsonÕs taxfree environment, in which dividends are always dominant. We identify a critical bid–ask spread level that determines the firmÕs optimal payout policy, and demonstrate that the personal tax advantage of stock repurchase dominates immediacy services costs of open-market repurchase for firms with spreads lower than the critical spread. On the other hand, firms with spreads exceeding the critical spread will choose to pay dividends, because repurchase immediacy costs exceed the related tax advantage. In Amihud and MendelsonÕs (1986) tax-free model, dividends always dominate repurchase due to immediacy costs associated with open-market repurchase. This yields a concave gross relation between returns and the relative spread. In contrast, in our model repurchase can dominate dividends due to personal taxation. When
1
Other factors may have contributed to the increased popularity of stock repurchase as well. Allen and Michaely (2001) note that dividends exhibit a general upward trend with decreases occurring only rarely, while stock repurchases are highly responsive to the firmÕs earnings and general economic conditions. Thus, stock repurchase provides the firm with a higher degree of flexibility. Brockman and Chung (2001) argue that the relaxed regulatory requirements associated with stock repurchases make them more attractive than dividend payouts. Grullon and Ikenberry (2000) provide empirical evidence indicating that stock repurchase programs are liquidity enhancing for the firmÕs stock.
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spreads are lower than the critical spread, and firms choose to repurchase, the relation between gross returns and relative spread can be concave, convex, or both. When spreads are greater than the critical spreads, and firms choose to pay dividends, the relation between gross returns and relative spread is concave, as Amihud and Mendelson find for their tax-free economy. Our model further shows that Amihud and MendelsonÕs clientele effect holds for all assets, regardless of whether they pay through dividends or through repurchase. We empirically test the major hypothesis of our analysis through studying the relation between returns and relative bid–ask spreads, using CRSP, TAQ, and COMPUSTAT data for stocks listed on NYSE, AMEX, and NASDAQ. Consistent with the theory, we provide evidence of the existence of a concave relation between returns and relative spreads for portfolios of stocks associated with firms that exclusively use dividends as their payout vehicle. This relation disappears for firms paying exclusively through stock repurchase. These findings represent evidence that the firmÕs choice of payout vehicle influences the relation between returns and spreads. The remainder of this paper is organized as follows. Section 2 presents the derivation of the theoretical model. Section 3 presents the empirical evidence. Section 4 concludes the paper.
2. Model In this section we examine the impact of personal taxation on the relation between returns and the bid–ask spread. We outline the main assumptions and discuss the effect of taxes on the firmÕs choice of cash distribution. We then investigate the relation between returns and the bid–ask spread under personal taxation. 2.1. Personal taxes and cash distribution Amihud and MendelsonÕs (1986) model describes a concave relation between gross returns and relative spread. They assume no taxes and describe a world with M investors indexed by i, i = 1, 2, . . . , M. A portfolio is held by a type i investor with initial wealth Wi. Investor iÕs time horizon, Ti, is random and exponentially distributed, with E½T i ¼ l1 i . At time Ti, the investor liquidates the portfolio to a market maker for the quoted bid price. There are N + 1 assets indexed by j, j = 0, 1, . . . , N, where asset j pays dj, a perpetual positive cash flow, per unit of time. Asset j has a trading cost reflected by a relative spread of Sj. Asset 0 has zero relative spread with unlimited supply. Amihud and Mendelson number investor types through increasing expected hold1 1 ing horizons l1 1 6 l2 6 6 lM and securities through increasing relative spread ratios 0 = S0 6 S1 6 6 SN. Market makers stand by in the market to provide immediacy services. For each security j they quote an ask price, Vj, and a bid price, Vj(1 Sj). Amihud and Mendelson further assume a stationary infinite horizon economy, where assets pay a constant dividend stream. Assets bear no taxes and transaction or other costs, and asset prices are constant over time.
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Bagwell and Shoven (1989), Fama and French (2001), Jagannathan et al. (2000), and Allen and Michaely (2001) report a steady increase in repurchases activity starting in the early 1980s. These studies suggest that while repurchase is increasingly popular, it is not a complete substitute for dividends. Green and Hollifield (2003) provide evidence regarding the excess tax costs associated with dividend distributions relative to repurchase activity. They argue that, net of personal taxes, stock repurchase is superior to dividends. Support for this conclusion is provided in Allen and Michaely (2001). Dividends are taxed as ordinary income, with a higher effective tax rate compared to the capital gains tax rate that applies to stock repurchase. Thus, there is a substantial tax disadvantage for dividends compared to repurchases. This tax differential requires separate tax rates in modeling. For dividend-paying firms, we assume that asset j pays a perpetual constant pre-tax dividend, dj, taxed at a rate sp. Note that dj is the cash flow available for distribution to shareholders each period. Thus the after-tax perpetual dividend is equal to dj(1 sp) per unit of time. We assume that open market repurchase is the preferred payout vehicle for firms using stock repurchase. According to Allen and Michaely (2001) and Grullon and Ikenberry (2000), a large proportion of firms engaged in stock repurchase employ open market repurchase. For example, Allen and Michaely report that open market repurchases represented more than 95% of the dollar value of total shares repurchased in 1998. We therefore assume that firms act under the guidelines that govern open market repurchases, set by the SEC in 1982, with the adoption of Rule 10b–18.2 This rule requires firms engaged in open market repurchase to follow several guidelines. Specifically, and relevant to this paper, the rule requires that the firm use only one broker or dealer on any single day of repurchase to buy back its stock. Based on the above, we assume that, for firms choosing repurchase as payout policy, the dollar amount repurchased for asset j (by firm j) is dj. The variable dj represents the cash flow available for distribution to shareholders each period, and is a perpetual positive and constant cash flow per unit of time. Consistent with Rule 10b–18, we assume that shareholders sell the repurchased shares to the issuer in the open market through a market maker for the quoted bid price. Hence, the periodic after-spread, but pre-tax, cash flow from stock repurchase to the shareholder is dj(1 Sj). In this stationary infinite horizon economy, where assets pay a constant repurchase stream, asset prices remain constant over time. Thus the after-spread repurchase income, net of the relevant cost basis, is taxed as capital gains. Letting Cj denote the percentage of the initial cost of asset j (Vj) that is attributed to the dollar amount repurchased, the cost basis relevant to repurchase is CjVj. When the capital gains tax rate, sc, is applied to stock repurchase, the periodic after-spread and after-tax cash flow from stock repurchase to the shareholder is dj(1 Sj) [dj(1 Sj) CjVj]sc. In this modeling environment, repurchase dominates dividends as a value maximizing method of payment to shareholders, when for firm j:
2 47 Fed Reg. 53333 (November 26, 1982). For a detailed discussion of this rule, see Allen and Michaely (2001).
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d j ð1 S j Þ ½d j ð1 S j Þ C j V j sc > d j ð1 sp Þ: The spread under which firm j breaks even between the two payment methodologies s sc ð1mj Þ C V is given by S p ð1s , where mj ¼ dj j j . For firms with Sj < S* the personal tax cÞ advantage of stock repurchase dominates the immediacy services costs of open-market repurchase, and these firms will choose to repurchase. On the other hand, firms with Sj > S* will choose to pay dividends, due to the dominance of repurchase liquidity costs relative to the related tax advantage. Finally, firms will be indifferent when Sj = S*. Note that sc < 1, sp > sc due to the tax disadvantage associated with dividends, and mj < 1 due to the fact that a capital gain associated with repurchase is guaranteed in this economy. It follows that 0 < S* < 1. We number security types through increasing relative spread ratios 0 = S0 6 S1 6 6 Sk 6 S* 6 Sk+1 6 6 SN. Thus, for firms 0 through k repurchase dominates dividends, while for firms k + 1 through N, dividends are dominant. Amihud and Mendelson assume a stationary infinite horizon economy, where assets generate a constant stream of cash flow available for distribution to shareholders. This implies that at the time of purchase, an investor pays the ask price, Vj, for security j, and at the time of liquidation s/he receives the bid price, Vj(1 Sj). Thus, the investor suffers a capital loss of VjSj at liquidation. In our economy, with taxation, we assume that the investor receives a tax return for this capital loss.3 Thus, the investor suffers an after-tax capital loss of VjSj(1 sc), and the after-tax revenue at liquidation is given by: Vj(1 Sj(1 sc)). In light of this discussion of tax-related issues, we next study the relation between returns and the bid–ask spread with taxation. 2.2. The relation between returns and the bid–ask spread with taxes 2.2.1. Dividends For dividend-paying firms (k + 1 through N), our analysis of after-tax returns is similar to that of Amihud and Mendelson (1986), with a small modification for tax issues related to a capital loss that occurs at the time of liquidation. Amihud and MendelsonÕs propositions still hold in the current case for dividend-paying firms. For these (k + 1 through N), the expected present value of the portfolio held by a type-i investor is (Z " # ) ( " #) N N Ti X X qy qT i ET i e xij d j ð1 sp Þ dy þ ET i e xij V j ð1 S j ð1 sc ÞÞ ; 0
j¼0
j¼0
where xij is the number of units of asset j held by investor i, and q is the risk free return on the zero-spread asset. The above expression is the sum of the expected present value of continuous net cash flow from dividends during investor iÕs holding 3 Capital losses can be used by taxable individual investors to reduce taxes on realized gains, or to offset limited amounts of nongain income (Poterba and Weisbenner, 2001).
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period and the expected present value of the investorÕs net liquidation revenue. All cash flows are after tax. Similar to Amihud and Mendelson (1986), the net return on asset j for a dividendpaying firm in such an economy is given by4 rDij ¼
d j ð1 sp Þ li S j ð1 sc Þ; Vj
ð1Þ
where rDij = expected net (spread- and tax-adjusted) return of dividend-paying asset j to investor i. d j ð1sp Þ = pre-spread and after-tax return on security j. Vj liSj(1 sc) = expected after-tax spread cost on asset j for investor i (li is the liquidation probability for investor i). We denote the modified gross (pre-spread and pre-tax) return for a dividend-payd ing firm as rDj V jj , and rearrange the above equation as follows: rDij þ li S j ð1 sc Þ rDj ¼ : ð2Þ ð1 sp Þ Thus, for dividend-paying firms the gross return on asset j is linear in the expected relative spread.5 Following Amihud and Mendelson, we assume no short sales; hence the investor with the superior bid determines the asset equilibrium price. Investors have heterogeneous expected holding periods. The investor that outbids all others agrees to accept the minimum expected net return. Investor i will purchase the asset j that provides the highest net return, as follows:
rDi ¼ max frDij g:
ð3Þ
j¼1;2;...;n
rD þl S ð1s Þ
c i j . Therefore, the equilibrium The gross return for investor i on asset j is i ð1s pÞ gross return on asset j is the minimal required expected gross return across investors: D ri þ li S j ð1 sc Þ rDj ¼ min : ð4Þ i¼0;1;2;...;M ð1 sp Þ
Thus, a modified version of Proposition 2 in Amihud and Mendelson (1986) still holds, and in equilibrium the observed market (gross) return is an increasing and concave piecewise-linear function of the relative spread. As in Amihud and Mendel
son (1986), we can prove this proposition through letting fi ðSÞ ¼
rD i þli S j ð1sc Þ . ð1sp Þ
Through the above minimization, the gross return on an asset with a relative spread S is 4 Note that in this paper the terms gross and net are used in reference to both bid–ask spread costs and taxes. 5 Below, we demonstrate that under repurchase, the linearity in Eq. (2) does not hold, giving rise to a convex return–bid–ask spread relation at the individual asset level.
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f ðSÞ ¼ min fi ðSÞ:
43
ð5Þ
i¼1;2;...;M
Proposition 2 of Amihud and Mendelson follows from the fact that monotonicity is preserved in f(S) (the minimum function), and a minimum of a finite collection of linear functions is concave piecewise-linear. This proof of a concave piecewise-linear relation between the expected gross returns and the relative spread is in the context of the definition of the gross return as a linear function of the expected relative spread for a dividend-paying firm. 2.2.2. Stock repurchase For the repurchasing firms (0 through k), the expected present value of the portfolio held by a type-i investor is (Z " # ) N Ti X qy ET i e xij ðd j ð1 S j Þ ½d j ð1 S j Þ C j V j sc Þ dy 0
j¼0
(
"
þ ET i eqT i
N X
#) xij V j ð1 S j ð1 sc ÞÞ
;
ð6Þ
j¼0
where xij and q are as defined for the dividend case. Implicit in the above expression is the assumption that the firm splits its stocks so that the repurchase does not change the number of units of asset j held by every investor i. That is, we assume that xij remains constant. The above expression is the sum of the expected present value of continuous net cash flow from stock repurchases during investor iÕs holding period and the expected present value of the investorÕs liquidation revenue, net of the aftertax bid–ask spread cost. As derived in Appendix A, this expression can be written as: ðli þ qÞ
1
N X
xij ½d j ð1 S j Þ ½d j ð1 S j Þ C j V j sc þ li V j ð1 S j ð1 sc ÞÞ:
j¼0
ð7Þ Thus, given asset bid–ask prices, a type-i investor maximizes the expected present value of the portfolio through solving the following optimization problem: max xij
N X
xij ½d j ð1 S j Þ ½d j ð1 S j Þ C j V j sc þ li V j ð1 S j ð1 sc ÞÞ;
j¼0
subject to N X
xij V j 6 W i
and
xij P 0
for all j ¼ 0; 1; . . . ; N ;
ð8Þ
j¼0
where Wi denotes investor iÕs wealth. The modified net (after-spread and after-tax) expected return for repurchasing firms, rRij , is: rRij ¼
d j ð1 S j Þð1 sc Þ þ C j sc li S j ð1 sc Þ: Vj
ð9Þ
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For repurchasing firms we denote the modified gross (pre-spread and pre-tax) return d as rRj V jj . Thus, the modified expected gross rate of return is: rRj ¼
rRij C j sc þ li S j ð1 sc Þ : ð1 S j Þð1 sc Þ
ð10Þ
Eq. (10) demonstrates that under repurchase, the gross return is a strictly increasing and convex function in the relative spread cost Sj. Contrast Eq. (10) with Eq. (2), where gross return is a strictly increasing and linear function in the relative spread when dividends dominate repurchase. If, for a given price vector V, investor i chooses the asset with
rRi ¼
max frRij g;
ð11Þ
j¼0;1;2;...;N
then the equilibrium gross return on asset j is the minimal required gross return across all investors: rRi C j sc þ li S j ð1 sc Þ R rj ¼ min : ð12Þ i¼0;1;2;...;M ð1 S j Þð1 sc Þ Stated differently, the equilibrium price of asset j is determined by the highest bidder, as follows: d j ð1 S j Þð1 sc Þ V j ¼ max : ð13Þ i¼0;1;2;...;M rRi C j sc þ li S j ð1 sc Þ If the asset is held by investor i in equilibrium, we can rewrite Eq. (13) as: V j ¼
d j ð1 S j Þð1 sc Þ þ C j V j sc rRi
li V j S j ð1 sc Þ
rRi
:
ð14Þ
The first term on the right-hand side of Eq. (14) is the present value of net perpetual cash flow from open market stock repurchase. The second term is the expected present value of after-tax cash outflows from the cost of transacting the asset. In the following proposition we demonstrate that Amihud and MendelsonÕs clientele effect still holds for repurchasing firms. Proposition 1. In equilibrium, higher-spread assets are held by longer-term investors (clientele effect). Proof. Consider assets j and h with S* > Sh P Sj. Suppose that in equilibrium asset j is held by a type-i investor and asset h is held by investor i + 1, where li P li+1 This, with maximization (11), implies that rRij P rRih and rRiþ1;j P rRiþ1;h . Substituting from Eq. (9) we get: d j ð1 S j Þð1 sc Þ þ C j sc li S j ð1 sc Þ V j P
d h ð1 S h Þð1 sc Þ þ C h sc li S h ð1 sc Þ V h
ð15Þ
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and d h ð1 S h Þð1 sc Þ þ C h sc liþ1 S h ð1 sc Þ V h P
d j ð1 S j Þð1 sc Þ þ C j sc liþ1 S j ð1 sc Þ: V j
ð16Þ
This implies that (li li+1)(Sh Sj) P 0. Thus, Sh P Sj when li > li+1. The proof for non-consecutive portfolios follows immediately. h As in Amihud and Mendelson, the current model predicts that for repurchasing firms long-term investors will tend to hold illiquid assets, while short-term investors will hold the more liquid assets. Next, in Proposition 2, we modify Amihud and MendelsonÕs proposition regarding the concavity of the relation between gross return and spread. Proposition 2. In equilibrium, the relation between gross return and spread is increasing and piecewise-convex. Proof. Let
gi ðSÞ ¼
rRi C j sc þ li S j ð1 sc Þ : ð1 S j Þð1 sc Þ
ð17Þ
Through minimization (12), the market gross and pre-tax return on an asset with relative spread S is gðSÞ ¼ min gi ðSÞ i¼1;2;...;M
ð18Þ
and Proposition 2 follows from the fact that monotonicity is preserved in g(S) (the minimum function), and a minimum of a finite collection of convex functions is piecewise-convex. h 2.3. The return–bid–ask spread relation The analysis in the previous two subsections demonstrates that the required expected gross return is increasing in spreads for all spread levels, regardless of payout policy. This relation is found to be increasing and piecewise-convex for firms paying through repurchase (0 through k), with Sj < S*. For dividend-paying firms (k + 1 through N), with Sj > S*, the relation is increasing and concave piecewise-linear as in Amihud and Mendelson (1986). For repurchasing firms, with Sj 2 [0, S*), minimization (12) does not produce a clear result with respect to the curvature of the minimum function relating the expected gross return and the relative spread. In general, the relation between the expected gross return and the relative spread is positive, but it could be concave, convex, or both, as demonstrated in Fig. 1.
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Panel A Gross
S*
Relative Spread
Panel B Gross Return
S*
Relative Spread
Fig. 1. The relation between gross return and relative spread with taxation. In Panel A, there are relatively more short-term investors concentrated around lower spreads in the [0, S*] spread interval, hence the relation between gross return and relative spread is approximately concave for lower levels of the relative spread. As the relative spread approaches S*, the approximated relation becomes convex. In Panel B, there are relatively more investors concentrated around spreads approaching S* in the [0, S*] spread interval, hence the relation between gross return and relative spread will be convex for lower spread levels. As the relative spread approaches S*, the approximated relation becomes concave.
The exact shape of the function depends on the concentration of investors across the spectrum of spreads, which, according to the clientele effect, corresponds to the concentration of investors across investment horizons. If, for example, there are relatively more short-term investors concentrated around lower spreads in the [0, S*] spread interval, then the relation between gross return and relative spread relation will be approximately concave for lower levels of the relative spread. As the relative spread approaches S*, the approximated relation becomes convex (see Panel A of Fig. 1). If, on the other hand, there are relatively more investors concentrated around spreads approaching S* in the [0, S*] spread interval, then the relation between gross
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return and relative spread will be convex for lower spread levels. As the relative spread approaches S*, the approximated relation becomes concave (see Panel B of Fig. 1). Intuitively, for repurchasing firms, two opposing effects influence the curvature of the relation between gross return and relative spread. In Proposition 1 we prove that Amihud and MendelsonÕs (1986) clientele effect holds for repurchasing firms. Therefore, in equilibrium, short-term investors hold lower-spread assets than long-term investors, and short-term assets are traded more frequently than long-term assets. The concave relation is driven by Amihud and MendelsonÕs (1986) observation that the value of an asset is the present value of perpetual dividends minus the present value of perpetual spread costs that are incurred every time that the asset is liquidated, as presented in Eq. (14). Since short-term assets are traded more frequently than long-term assets, the expected present value of cash flows associated with perpetual liquidation of short-term assets is more sensitive to change in the spread than long-term assets. This implies that for short-term assets, a given increase in the spread will result in a larger increase in the required gross return relative to longterm assets, hence the concave relation. But there is an opposing effect as well. As the spread ratio increases, the present value of the after-tax and after-spread perpetual cash flow from open market stock repurchase diminishes, as does the net return. Theoretically, as the relative spread approaches 100 percent the investor will demand infinite compensation in terms of expected gross return before purchasing such an asset, as presented in Eq. (10). This explains the convex relation for repurchasing firms. For dividend paying firms, with Sj 2 [S*, 1), the analysis produces a concave relation between the expected gross return and the relative spread for all firms, similar to Amihud and Mendelson (1986). For these firms, the clientele effect is the only factor that determines the curvature, hence the concave relation. Since S* is the break-even spread level that results in the same net return under both payout methodologies, it can be shown that the gross return for every investor i under dividends, fi(S), is identical to the same investorÕs gross return under repurchase, gj(S). Thus, at a spread level of S* we have gS = f(S) and, therefore, the minimum function is continuous. Overall, with taxation, the expected relation between gross return and relative spread is increasing for all spread levels. In terms of curvature, one cannot determine whether the relation is concave, convex, or both for spreads lower than S*, but for spreads greater than S* the relation is concave.
3. Empirical evidence Amihud and Mendelson (1986) provide empirical evidence in support of the existence of a concave relation between the expected gross return and the relative spread. The data used for their empirical test is sampled from the New York Stock Exchange (NYSE) for the years 1960–1979. Allen and Michaely (2001) demonstrate that during this time period dividend payout was the preferred distribution vehicle for most firms. Thus, Amihud and MendelsonÕs model, which was derived under the dividend
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payment assumption, is suitable to the payout methodology environment during that time period, and one should expect the data to support the existence of a concave relation. However, given Allen and MichaelyÕs evidence that, as of the early 1980s, stock repurchase is the dominant distribution vehicle, analysis based on more recent data is warranted. In this section we test the major hypothesis of our analysis through studying the relation between returns and relative bid–ask spreads. Consistent with the theory, we provide evidence of the existence of a concave relation between returns and relative spreads for portfolios of stocks associated with firms that exclusively use dividends as their payout vehicle. This relation disappears for firms paying exclusively through stock repurchase. 3.1. Data and methodology The data set consists of all nonfinancial firms trading on NYSE, AMEX, or NASDAQ between January 1993 and December 1999 from the Center for Research and Security Prices (CRSP) database, for which intraday spread data is available on the Trade and Quote (TAQ) database, and for which accounting data is available on the COMPUSTAT database. Allen and Michaely (2001) demonstrate that during this time period open-market repurchase is the dominant payout vehicle for most firms initiating new cash distributions to their shareholders. Thus, our sample period is appropriate for testing the implications of our model, which allows for firms to implement payout through either dividends and repurchase. Monthly returns, extracted from CRSP, are calculated as the percentage change in the value of one dollar of investment during month t. Monthly returns are adjusted for distributions so that comparisons can be made on an equivalent basis before and after distributions. Monthly spreads are the time-weighted average relative bid–ask spreads, for bid and ask quotes reported on the TAQ consolidated trade files between 9:30 AM and 4:30 PM of a given trading day. Time-weighted averaging of relative bid–ask spreads is performed across all trading days for the month under consideration. We exclude all observations where the bid price, ask price, bid size in number of round lots, or ask size in number of round lots are valued at zero. We also exclude all observations where the ask price is 1.5 times larger than the bid price. The relative spread for stock j in month t is calculated as: S jt ¼
askjt bidjt askjt bidjt : ¼ pricejt ðaskjt þ bidjt Þ=2
ð19Þ
Of the observations that remain following the above filtering, we retain the last quote for each second, and estimate the time-weighted average bid–ask spreads.6 We extract a number of additional variables for each observation. Beta is calculated as the sum of the slopes in the regression of excess returns on the current and previous monthÕs excess market returns. Beta estimation is performed using data
6
This methodology is from Joel HasbrouckÕs Empirical Market Microstructure website.
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from the 36 months before the month under consideration. Hence, we exclude any stock without a 36-month history of complete return data. We include a single lag in the estimation, following Fama and French (1992). Specifically, we estimate the beta coefficient using the following regression model: Rjt ¼ aj þ bjt1 Rmt þ bjt2 Rmt1 þ ejt :
ð20Þ
The variable Rjt is the month-t excess returns over the 90-day T-bill rate of stock j. Rmt and Rmt1 are month t and t 1 excess market returns, calculated as the excess return of the value weighted portfolio in the given month. We define the beta for stock j which can vary across time (t), as bjt = bjt1 + bjt2. Fama and French (1992) find that the market value of the firmÕs equity and the ratio of the book value of common equity to its market capitalization both capture cross-sectional variation in returns. To account for these factors, we extract ME and BE/ME for each stock. ME is the market value of the firmÕs equity on the final day of the month, extracted from CRSP. Following Fama and French (1992), BE/ME is calculated as the ratio of book value of common equity plus balance-sheet deferred taxes for the year of the observation to ME, extracted from COMPUSTAT. We eliminate any observation for which any variable is missing. Following the above, we identify a sample of 196,924 monthly firm observations. To account for other time-varying risk factors not captured in beta, we also extract MOMENTUM, SMB, and HML.7 MOMENTUM is the average return on two high prior return portfolios minus the average return on two low prior portfolios. SMB is the difference in returns across small and big stock portfolios controlling for the same weighted average book-to-market equity in the two portfolios. HML is the difference in returns between high and low book-to-market equity portfolios. Following Eleswarapu and Reinganum (1993) who find that the empirical return–spread relation is different for January compared to other months, we also identify the month of the observation, MONTH, to control for this effect.8 We next form three separate samples on the basis of payout policy, similar to Grullon and Michaely (2002). For each observation, we identify dividend (DIV) and repurchase (REPO) policy for the firm for the year, as reported on COMPUSTAT. Following Grullon and Michaely (2002), DIV is the total dollar amount of dividends declared on the common stock, while REPO is the expenditure on the purchase of common and preferred stocks minus any reduction in the value of the net number of preferred shares outstanding. The first sample consists of all 196,924 observations, regardless of payout policy. The second sample consists of the 44,656 observations of firms with positive dividends and zero repurchase for the year
7 This data was obtained from Kenneth FrenchÕs website. We thank an anonymous referee for suggesting we include these factors in our tests. 8 The results are generally similar to the use of an indicator variable that is equal to unity if the month of the observation is January.
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A.A. Gottesman, G. Jacoby / Journal of Banking & Finance 30 (2006) 37–58
during which the observation occurs. The third sample consists of the 34,029 observations of firms with zero dividends and positive repurchase. Panel A of Table 1 pre-
Table 1 Descriptive statistics ALL DIV, ALL REPO (n = 196,924)
DIV > 0, REPO = 0 (n = 44,656)
DIV = 0, REPO > 0 (n = 34,029)
Mean
Std.
Mean
Std.
Mean
Std.
0.1622 0.0430 1.3616 2.0852 0.8732 3.3743 3.0776 3.5811 3.4330
0.0077 0.0252 0.9642 19.7685 0.5746 1.1579 0.1302 0.3220 6.6165
0.1044 0.0276 0.9117 1.9468 0.6898 3.0646 2.8632 3.2732 3.4359
0.0103 0.0389 1.4417 18.6585 0.5883 1.4490 0.2224 0.9634 6.6772
0.1741 0.0399 1.2588 1.8061 0.8623 3.7987 3.3131 3.9925 3.4343
Panel A: Monthly firm observations R 0.0104 S 0.0388 b 1.3166 ln(ME) 19.0076 ln(BE/ME) 0.6685 MOMENTUM 1.2612 SMB 0.1860 HML 0.5864 MONTH 6.6643
Panel B: Portfolios R S b ln(ME) ln(BE/ME) MOMENTUM SMB HML MONTH
ALL DIV, ALL REPO (n = 2100)
DIV > 0, REPO = 0 (n = 2100)
DIV = 0, REPO > 0 (n = 2100)
0.0111 0.0395 1.3518 19.6139 0.4551 1.2148 0.1310 0.3694 6.5000
0.0077 0.0250 0.9570 20.3734 0.4050 1.2148 0.1310 0.3694 6.5000
0.0120 0.0441 1.5544 18.9699 0.4322 1.2148 0.1310 0.3694 6.5000
0.0585 0.0368 1.2582 1.8843 0.4275 3.1908 2.9198 3.4293 3.4529
0.0479 0.0222 0.8269 1.5494 0.2921 3.1908 2.9198 3.4293 3.4529
0.0730 0.0376 1.3417 1.7284 0.5073 3.1908 2.9198 3.4293 3.4529
Mean, standard deviation, and number of observations are reported separately for three samples formed on the basis of payout policy. ALL DIV, ALL REPO includes all observations, regardless of payout policy. DIV > 0, REPO = 0 includes observations associated with positive dividends and zero repurchase during the year of the observation. DIV = 0, REPO > 0 includes observations associated with zero dividend and positive repurchase during the year of the observation. Panel A reports descriptive statistics for all monthly firm observations between January 1993 through December 1999. Panel B reports descriptive statistics for portfolios consisting of 25 equally weighted portfolios for each month, formed through ranking the monthly firm observations on the basis of spread and beta. Variable definitions are as follows: R is the monthly return, adjusted for distributions, in excess of the 90-day T-bill rate. S is the timeweighted average relative bid–ask spreads, for bid and ask quotes for the firmÕs stock between 9:30 AM and 4:30 PM, averaged across all trading days for the month under consideration. b is the sum of the coefficient estimates in a regression of firm excess return against current period and single lag market excess return. ln(ME) is the natural logarithm of the market value of the firmÕs equity. ln(BE/ME) is the natural logarithm of the book value of common equity plus balance-sheet deferred taxes for the year of the observation. MOMENTUM is the average return on two high prior return portfolios minus the average return on two low prior portfolios. SMB is the difference in returns across small and big stock portfolios controlling for the same weighted average book-to-market equity in the two portfolios. HML is the difference in returns between high and low book-to-market equity portfolios. MONTH is the month of the observation.
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51
sents descriptive statistics for the three samples. It is notable that spread and beta are lowest for the sample of positive dividend and zero repurchase observations.9 For each of these samples, the relation between returns and liquidity costs is explored through forming 25 equally weighted portfolios for each month in the sample. Portfolio formation takes place as follows. Stocks are first placed into one of five relative spread portfolio groups based on their relative spread ranking. We next rank each stock in each of the five relative spread portfolio groups on the basis of beta, and each of the five relative spread portfolio groups is further subdivided into five portfolios based on the beta ranking. For the sample of monthly portfolios formed using all cross-sectional pooled observations, the average portfolio consists of approximately 93.8 observations, with portfolio size ranging between 37 and 123 observations. For the sample associated with positive dividends and zero repurchase, the average portfolio consists of approximately 21.3 observations, ranging between 16 and 24 observations. For the sample associated with zero dividend and positive repurchase, the average portfolio consists of approximately 16.2 observations, ranging between 2 and 31 observations. We next pool the 25 portfolios we form each month across all 84 months in the sample period for a sample size of 2100 separate portfolios for each payout policy.10 Panel B of Table 1 presents descriptive statistics for the portfolios associated with each of the payout policy samples. Similar to the sample presented in Panel A, both spread and beta are lowest for the sample of positive dividend and zero repurchase observations, and highest for the sample of zero dividend and positive repurchase. Because an identical number of portfolios are created each month for all three samples, it is unsurprising that the values of momentum, SMB, HML, and MONTH are identical for all portfolio samples. Table 2 presents the average excess return, relative spread, and beta values for each of the five relative spread and five beta groupings. Panel A of Table 2 indicates that excess return is negatively related to spread, a result that is monotonic for all payout policy samples. However, Panel B indicates that excess return is positively related to beta, though this result is not monotonic for all samples. Hence, the negative return–spread relation may be attributable to other factors that vary across groupings. As we will present shortly, our multivariate tests provide evidence of a positive relation. Table 3 presents correlations between the variables. Recognizing the large negative correlation between ln(ME) and ln(Spread), we orthogonalize ln(ME) on
9 While our model predicts that dividend-paying stocks will tend to have higher spreads than repurchasing firmsÕ spreads, this result only applies when all other factors are controlled. The lower spreads reported in Table 1 are unsurprising, as they can be attributed to the fact that the beta for the positive dividend zero repurchase sample (0.96) is much lower than that of the zero dividend positive repurchase sample (1.44). 10 We pool the portfolios across all months, instead of averaging portfolios across months (e.g., Eleswarapu, 1997), as averaging across months does not permit testing of the time-varying risk factors we include in our tests (momentum, SML, HMB).
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Table 2 Average excess return, relative spread, and beta values for relative spread and beta groupings ALL DIV, ALL REPO
DIV > 0, REPO = 0
DIV = 0, REPO > 0
R
R
S
R
S
S
b
b
b
Panel A: Spread groupings Lowest 0.0167 0.0072 0.0138 0.0144 0.0112 0.0250 0.0084 0.0438 Highest 0.0053 0.1070
1.1108 1.3130 1.4402 1.4972 1.3977
0.0142 0.0084 0.0083 0.0047 0.0027
0.0062 0.0105 0.0162 0.0264 0.0657
0.8468 0.9496 0.9405 0.9939 1.0544
0.0240 0.0141 0.0103 0.0060 0.0058
0.0100 0.0199 0.0319 0.0505 0.1084
1.6275 1.5926 1.6373 1.5069 1.4076
Panel B: Beta groupings Lowest 0.0072 0.0409 0.0047 0.0388 0.0068 0.0388 0.0110 0.0389 Highest 0.0256 0.0400
0.1885 0.6763 1.2000 1.8181 3.2530
0.0058 0.0050 0.0057 0.0070 0.0149
0.0256 0.0244 0.0251 0.0245 0.0254
0.0985 0.4855 0.8753 1.3112 2.2116
0.0102 0.0082 0.0068 0.0128 0.0222
0.0453 0.0436 0.0434 0.0437 0.0446
0.0465 0.8363 1.4093 2.0632 3.5096
The average value of excess return, spread, and beta are presented for each of the five relative spread (Panel A) and five beta (Panel B) groupings, reported separately for three samples formed on the basis of payout policy. ALL DIV, ALL REPO includes all observations, regardless of payout policy. DIV > 0, REPO = 0 includes observations associated with positive dividends and zero repurchase during the year of the observation. DIV = 0, REPO > 0 includes observations associated with zero dividend and positive repurchase during the year of the observation. Portfolios are formed each month through ranking the monthly firm observations on the basis of spread and beta. Variable definitions are as follows: R is the monthly return, adjusted for distributions, in excess of the 90-day T-bill rate. S is the time-weighted average relative bid–ask spreads, for bid and ask quotes for the firmÕs stock between 9:30 AM and 4:30 PM, averaged across all trading days for the month under consideration. b is the sum of the coefficient estimates in a regression of firm excess return against current period and single lag market excess return.
ln(Spread), and use the orthogonalized variable in our regression tests.11 To test for the predicted relation, we estimate the following three regression models across our 2100 portfolios: Rpt ¼ a0 þ a1 lnðS pt Þ þ d0 X þ ept ;
ð21Þ
Rpt ¼ a0 þ a1 S 2pt þ d0 X þ ept ;
ð22Þ
Rpt ¼ a0 þ a1 lnðS pt Þ þ a2 S 2pt þ d0 X þ ept ;
ð23Þ
where Rpt is the excess return on portfolio p for month t; Spt is the average relative spread of portfolio p for month t; a and d are regression coefficients, and X is the vector of control variables, as follows: X ¼ ½bpt ; lnðMEÞOrthogonalized; lnðBE=MEÞ; MOMENTUM; SMB; HML; MONTH:
ð24Þ
11 The results are generally similar when the raw version of ln(ME) is used as a regressor instead of the orthogonalized version.
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Table 3 Correlations [1] R ln(S) S2 b ln(ME) ln(BE/ME) MOMENTUM SMB HML MONTH
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
0.0340 0.0204 0.5880 0.0402 0.0720 0.0093 0.0415 0.8597 0.4324 0.0796 0.1201 0.3327 0.1882 0.1130 0.3448 0.0368 0.0500 0.0260 0.0157 0.0097 0.0007 0.1825 0.0150 0.0052 0.0092 0.0090 0.0098 0.0034 0.1161 0.0389 0.0144 0.0174 0.0011 0.0073 0.5798 0.4018 0.0156 0.0056 0.0043 0.0080 0.0102 0.0117 0.2912 0.0836 0.2417
Correlations are presented for the sample of all observations, regardless of payout policy (ALL DIV, ALL REPO). Variable definitions are as follows: R is the monthly return, adjusted for distributions, in excess of the 90-day T-bill rate. S is the time-weighted average relative bid–ask spreads, for bid and ask quotes for the firmÕs stock between 9:30 AM and 4:30 PM, averaged across all trading days for the month under consideration. b is the sum of the coefficient estimates in a regression of firm excess return against current period and single lag market excess return. ln(ME) is the natural logarithm of the market value of the firmÕs equity. ln(BE/ME) is the natural logarithm of the book value of common equity plus balance-sheet deferred taxes for the year of the observation. MOMENTUM is the average return on two high prior return portfolios minus the average return on two low prior portfolios. SMB is the difference in returns across small and big stock portfolios controlling for the same weighted average book-to-market equity in the two portfolios. HML is the difference in returns between high and low book-to-market equity portfolios. MONTH is the month of the observation.
We perform our estimations using HansenÕs (1982) Generalized Method of Moments (GMM) to account for potential serial correlation and heteroscedasticity.12 The regression results are presented in Table 4. We perform the estimation separately for the three samples that we formed based on payout policy. Panels A, B, and C present the results, respectively, for the sample of all observations, regardless of payout policy; for the sample associated with positive dividends and zero repurchase; and for the sample associated with zero dividends and positive repurchase.
3.2. Regression results For the sample of portfolios based on all observations regardless of payout policy (Table 4, Panel A), the results of the first model verify Amihud and MendelsonÕs finding of concavity. The coefficient associated with the ln(Spt) variable is positive and significant at the 5% level. The results of the second model demonstrate that the coefficient associated with the S 2pt variable is positive. While insignificant at the 10% level, this coefficient is significant at the 12% level (5% level when OLS estimation is used). Thus, based on these regression models, the estimated return–spread
12
The results are generally similar when OLS estimation is used instead of GMM.
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A.A. Gottesman, G. Jacoby / Journal of Banking & Finance 30 (2006) 37–58
Table 4 Multivariate analysis Variable
(1)
(2)
(3)
Panel A: ALL DIV, ALL REPO Intercept ln(S) S2 b ln(ME) Orthogonalized ln(BE/ME) MOMENTUM SMB HML MONTH
0.0014 0.0005 0.0309*** 0.0037*** 0.0071*** 0.0051*** 0.002***
0.8264 0.0017 0.0016 0.0259*** 0.0037*** 0.0071*** 0.005*** 0.0019***
0.0673*** 0.0141*** 1.5278 0.0018 0.004* 0.0299*** 0.0037*** 0.007*** 0.0052*** 0.002***
Adjusted R2 N
0.2967 2100
0.2945 2100
0.2975 2100
0.0367*** 0.0069**
0.0107**
Panel B: DIV > 0, REPO = 0 Intercept ln(S) S2 b ln(ME) Orthogonalized ln(BE/ME) MOMENTUM SMB HML MONTH
0.0009 0.0015 0.0311*** 0.0033*** 0.0043*** 0.0026** 0.0007**
0.6543 0.0012 0.0006 0.0277*** 0.0033*** 0.0043*** 0.0025** 0.0007**
0.0396** 0.0084** 2.5979 0.001 0.004** 0.0296*** 0.0033*** 0.0042*** 0.0027** 0.0007**
Adjusted R2 N
0.1667 2100
0.1656 2100
0.1674 2100
0.0153*** 0.0032**
0.0025
Panel C: DIV = 0, REPO > 0 Intercept ln(S) S2 b ln(ME) Orthogonalized ln(BE/ME) MOMENTUM SMB HML MONTH
0.0011 0.0014 0.021*** 0.0038*** 0.0089*** 0.005*** 0.0017***
0.5958 0.0011 0.0003 0.0203*** 0.0039*** 0.0089*** 0.005*** 0.0016***
0.0279 0.0036 0.1277 0.0011 0.001 0.0212** 0.0038*** 0.0089*** 0.005*** 0.0017***
Adjusted R2 N
0.2475 2100
0.2474 2100
0.2472 2100
0.0308*** 0.0043
0.0142***
The generalized method of moments is used to estimate the following three models: Rpt ¼ a0 þ a1 lnðS pt Þ þ d0 X þ ept ; Rpt ¼ a0 þ a1 S 2pt þ d0 X þ ept ; Rpt ¼ a0 þ a1 lnðS pt Þ þ a2 S 2pt þ d0 X þ ept ;
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55
Table 4 (continued ) where a and d are coefficients and X = [bpt, ln(ME) Orthogonalized, ln(BE/ME), MOMENTUM, SMB, HML, MONTH]. Estimation is performed separately for three portfolio samples formed on the basis of payout policy. ALL DIV, ALL REPO (Panel A) includes all observations, regardless of payout policy. DIV > 0, REPO = 0 (Panel B) includes observations associated with positive dividends and zero repurchase during the year of the observation. DIV = 0, REPO > 0 (Panel C) includes observations associated with zero dividend and positive repurchase during the year of the observation. Variable definitions are as follows: R is the monthly return, adjusted for distributions, in excess of the 90-day T-bill rate. S is the timeweighted average relative bid–ask spreads, for bid and ask quotes for the firmÕs stock between 9:30 AM and 4:30 PM, averaged across all trading days for the month under consideration. b is the sum of the coefficient estimates in a regression of firm excess return against current period and single lag market excess return. ln(ME) is the natural logarithm of the market value of the firmÕs equity. ln(BE/ME) is the natural logarithm of the book value of common equity plus balance-sheet deferred taxes for the year of the observation. MOMENTUM is the average return on two high prior return portfolios minus the average return on two low prior portfolios. SMB is the difference in returns across small and big stock portfolios controlling for the same weighted average book-to-market equity in the two portfolios. HML is the difference in returns between high and low book-to-market equity portfolios. MONTH is the month of the observation. *** ** * , , denote significance at the 1%, 5% and 10% levels, respectively.
relation may be concave and/or convex for the entire sample. In general, this is in agreement with our model. In the third model, we jointly test for concavity and convexity. The coefficient associated with ln(Spt) is positive, at the 1% level, while the coefficient associated with S 2pt is negative and insignificant. The reversal of the coefficient sign for the convexity variable may be an artifact of the high multicolinearity between ln(Spt) and S 2pt The beta coefficients are insignificant in all models, as in Fama and French (1992). The adjusted R2 associated with all three models are similar, and range in value between 0.2945 and 0.2975. Overall, these results provide evidence that for the sample of all firms the relation between excess return and relative spread is concave, while evidence of convexity is weak. For the sample of portfolios associated with positive dividends and zero repurchase (Table 4, Panel B), we once again verify Amihud and MendelsonÕs findings of concavity. The coefficient associated with the ln(Spt) variable in the first model is positive and significant at the 5% level. The results of the second model do not identify a convex relation, as the coefficient associated with the S 2pt variable is insignificant. In the third model, the coefficient associated with ln(Spt) is significantly positive at the 5% level, while the coefficient associated with S 2pt is insignificantly negative. Once again, the beta coefficients are insignificant in all models, as in Panel A. The adjusted R2 associated with all three models are again highly similar, and range in value between 0.1656 and 0.1674. Overall, there is evidence that the relation between excess return and relative spread is concave for the positive dividends and zero repurchase portfolios, with no support for convexity. These results support the concave return–spread relation predicted by our theoretical model for dividend-paying assets. It is also in agreement with Amihud and Mendelson (1986) result. This is not surprising given the fact that Amihud and MendelsonÕs sample can be considered as a sample of dividend-paying stocks (and no repurchase), since during their sample period vast majority of firms used dividends as their preferred payout vehicle.
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Recall that our theoretical model predicts that the return–spread relation can be concave, convex or both for repurchasing firms. Although this prediction is untestable, we feel that an empirical study of the nature of this relation is still important. Specifically, if we find that the estimated relation is different than that estimated for dividend-paying firms, then one can conclude that the payout policy is a factor in determining the nature of the underlying return–spread relation. For the sample of portfolios associated with zero dividends and positive repurchase (Table 4, Panel C), we find no significant evidence of concavity. The coefficients associated with ln(Spt) are insignificant in both regression models in which it appears. The coefficients associated with S 2pt are positive and insignificant at the 10% level. But it is noteworthy that while insignificant at the 10% level, the coefficient associated with S 2pt is significant at the 14% level (12% level when OLS estimation is used) for model 2. As we found in Panels A and B, the beta coefficients are insignificant in all models, and the adjusted R2 associated with all three models are similar, ranging in value between 0.2472 and 0.2475. Overall, our results clearly indicate that, as our theoretical model predicts, the firmÕs choice of payout policy influences the relation between returns and spread. This relation is increasing and concave for dividend-paying firms. At the same time, there is very weak evidence supporting a convex relation between returns and spread for firms choosing to repurchase.
4. Summary and conclusion We examine the impact of personal taxation on the relation between gross return and relative bid–ask spread. Following evidence presented by Allen and Michaely (2001) regarding corporate payout policy, we revisit Amihud and MendelsonÕs (1986) model, and present personal taxation that sometimes makes stock repurchase a superior payout vehicle compared to dividends. In Amihud and MendelsonÕs taxfree environment, firms will pay shareholders only through dividends. The extended model predicts that the relation between gross return and relative spread can be concave, convex, or both for highly liquid assets with low relative spreads that tend to pay to shareholders through repurchase. This relation turns concave for thinly traded dividend-paying assets with higher relative spread ratios. Our model further shows that Amihud and MendelsonÕs clientele effect holds for all assets, regardless of whether they payout dividends or through repurchase. We demonstrate that in addition to the concavity caused by the clientele effect, the influence of spreads on repurchase proceeds will generate a convex relation, resulting in a curvature that is characterized by both concavity and convexity. We use NYSE, AMEX, and NASDAQ return data from CRSP, together with time-weighted bid–ask spread TAQ data and accounting data from COMPUSTAT to test the major hypothesis of our analysis through studying the relation between returns and the relative bid–ask spread. We provide evidence supporting the main prediction of our model, that the firmÕs choice of payout vehicle has influences the relation between returns and spreads. An interesting direction for future research
A.A. Gottesman, G. Jacoby / Journal of Banking & Finance 30 (2006) 37–58
57
is whether payout policy is a function of the stockÕs bid–ask spread, after controlling for firm characteristics. Acknowledgement The authors thank Yakov Amihud, Kevin Davis, Charles Mossman and Cameron Morrill for their input. The authors thank the Social Sciences and Humanities Research Council of Canada for financial support. All errors are the exclusive fault of the authors. Appendix A The expected present value of the portfolio held by a type-i investor is given by
(Z
"
Ti
e
ET i
qy
0
N X
# xij ðd j ð1 S j Þ ½d j ð1 S j Þ C j V j sc Þ dy
j¼0
(
"
þ ET i e
qT i
)
N X
#) xij V j ð1 S j ð1 sc ÞÞ
;
j¼0
where xij is the number of units of asset j held by investor i, and q is the riskless return on the zero-spread asset. We rewrite this term as: " # Z N Ti X xij ðd j ð1 S j Þ ½d j ð1 S j Þ C j V j sc Þ ET i eqy dy j¼0
þ
0
"
N X
# xij V j ð1 S j ð1 sc ÞÞ ET i feqT i g:
j¼0
Since we assume that the investorÕs investment horizon, Ti, is exponentially distributed with E½T i ¼ l1 we write: i " #Z Z t N 1 X xij ðd j ð1 S j Þ ½d j ð1 S j Þ C j V j sc Þ li eli t eqy dy dt j¼0
þ V j ð1 S j ð1 sc ÞÞ
0
Z
0
1
li eli t eqt dt: 0
Integrating the above expression yields: " #Z N 1 li X xij ðd j ð1 S j Þ ½d j ð1 S j Þ C j V j sc Þ eli t ð1 eqt Þ dt q j¼0 0 " # N X li þ xij V j ð1 S j ð1 sc ÞÞ : li þ q j¼0
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A.A. Gottesman, G. Jacoby / Journal of Banking & Finance 30 (2006) 37–58
Solving the integral and rearranging, we find: ðli þ qÞ1
N X
xij ½d j ð1 S j Þ ½d j ð1 S j Þ C j V j sc þ li V j ð1 S j ð1 sc ÞÞ:
j¼0
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