STOCK MARKET TRADING, PRICE FORMATION, AND OPTIMAL MANAGEMENT COMPENSATION: THEORY AND EVIDENCE* by
Gerald T. Garvey† Michael S. McCorry‡ Peter L. Swan§ Department of Finance Faculty of Economics University of Sydney NSW 2006 AUSTRALIA July 1996
Abstract
How do corporate decision-makers make use of the information conveyed by their stock prices? This paper presents a simple model in which traders’ private information is partially impounded into a firm’s stock price, which is in turn used in an optimal incentive contract for its CEO. In a sample of large US corporations, we find evidence to support the model’s prediction of a positive relationship between a CEO’s observed pay-for-performance and the information content and volume of market order flow, controlling for firm size and riskiness. We conclude that stock prices which convey more information are used more intensively in incentive contracts. Key words: Executive compensation; Incentives; Market microstructure; Information content. JEL classification: J33; G32
*
We wish to thank the Australian Research Council (Grant A79602884) for financial support. We also wish to thank John E. Garen for generously supplying the data used in Garen (1994) and the Institute for the Study of Security Markets (ISSM) for supplying transactions data. Thanks also to Charles Cao, Jerry Feltham, Esther GalOr, Gordon Hanka, Burton Hollifield, Mark Huson, Ken Lehn, Wayne Mikkelson, Harold Mulherin, Dennis Sheehan, Martin Wu, and seminar participants at Penn State and the Universities of Pittsburgh, Alberta, and Oregon for helpful suggestions.
†
Associate Professor of Finance, Department of Finance, University of Sydney NSW 2006 Australia. Email:
[email protected].
‡
Lecturer in Finance and Senior Research Fellow, Securities Industry Research Centre of Asia-Pacific (SIRCA), Department of Finance, University of Sydney. Email:
[email protected]. §
National Australia Bank Foundation Professor of Finance and Director of Research, SIRCA, Department of Finance, University of Sydney. Email:
[email protected]. [Corresponding author].
1. Introduction Noisy rational expectations models have clarified and extended Hayek’s (1945) insight that prices provide information as well as terms of trade and incentives to market participants.1 The idea that asset prices transmit decision-relevant information to productive agents in the economy, however, remains largely undocumented.2 In this paper, we examine whether a corporation’s stock price conveys valuable information to boards and outside shareholders about the performance of top managers. The weak average linkage between CEO compensation and stock prices documented by Jensen and Murphy (1990a, b) is consistent with the view that stock prices are a poor source of information for incentive contracts, either because noise traders drive prices from fundamentals (eg., DeLong, Shleifer, Summers and Waldmann, 1990) or because the signals observed by rational, informed traders convey little about the CEO’s value-added (Paul, 1992). Jensen and Murphy (1990a, b) take the position that stock prices do convey potentially valuable information about the performance and abilities of top managers, but are not used by boards for fear of adverse publicity or political costs. The weak average relationship documented by Jensen and Murphy (1990a, b) leaves open the possibility that some firms take advantage of highly informative prices while others choose not to bear the costs of linking their CEO’s pay to their less informative stock prices. We focus exclusively on cross-sectional differences in the information content of stock prices, and ask whether firms tie their CEO’s wealth more closely to the price when the price is more informative. This proposition is obviously true if we compare publicly-traded firms with privately-held firms. The pay of the average CEO in the publicly-traded Jensen-Murphy (1990a, b) sample is positively related to the stock price, and such a price is simply unavailable to privately held firms.3 We focus on variation in the compensation practices between large, publicly traded firms. We adapt Glosten and Milgrom’s (1985) model, in which traders’ private information is partially impounded into prices, to produce a testable version of the hypothesis that firms
1
See Grossman (1989) for a summary of the theory and Lang, Litzenberger, and Madrigal (1992) for some
supportive evidence. 2
Leland (1992) points out that insider trading will generally not increase welfare unless timely information
conveyed by stock prices significantly improves real decision-making. Evidence against this idea is provided by Jennings and Mazzeo (1991), who find that corporate managers do not alter their acquisition strategies in the light of stock market reactions. 3
While firms that have been taken private often feature sizable management ownership, they cannot link bonuses
to stock price performance, nor can they use stock option schemes. Also, many management buyouts return to public ownership so that shares are again traded before management cashes-out; see Kaplan (1991).
1
whose stock prices communicate more information should make greater use of the price in determining their CEO’s compensation. In particular, we show that the stock price is a more valuable signal of CEO performance when the price is more responsive to market order flow. The intuition is that price is more responsive to a given direction and magnitude of order flow when market-makers believe traders have more precise private information. We also present the additional hypothesis, derived from Holmstrom and Tirole’s (1993) model of optimal insider ownership and stock market trading, that stock prices are more informative when the shares are more heavily traded. Essentially, stock prices are expected to be more useful for incentive purposes (a) when a given amount of trade conveys more information, and (b) when there is a greater amount of such trade (holding constant the information content of a given unit of trade). Alternative hypotheses are either that firms with more informative stock prices simply do not use this information, or that stock prices are informative about future cashflows but not about the CEO’s value-added (e.g., Paul, 1992). To test these hypotheses, we focus on variation in the compensation practices between the large, publicly traded firms in the Jensen and Murphy (1990b) sample. As Garen (1994) stresses, the linkage between CEO wealth and the firm’s stock price performance varies widely between such firms. Despite this, Garen (1994) and Yermack (1995) find that measures suggested by standard principal-agent theory, including the variance in stock prices as well as the variance in accounting earnings, explain little of the cross-sectional variation in CEO incentive compensation.4 We use the wide variation in the underlying stock price formation process, which determines the price informativeness of stock prices, to explain their use in executive incentive plans.5 We find that CEO incentives from stock options, dismissal, and bonus payments are strongly positively related to the average change in stock price produced by a trade of one million dollars and, less reliably, to the rate at which the stock is
4
In the Garen (1994) principal-agent model there is an insurance motive such that a greater variance of stock
returns is expected to result in a lower pay-performance sensitivity. Only very weak statistical support was found for this proposition. Yermack (1995) tests a model in which options will be used to link CEO pay to share market performance when the information content in accounting earnings is low relative to the information content in share prices. A high variance in either variable is assumed to represent ‘noise’ and hence the absence of information content. He finds that the ratio of the variance in accounting returns to the variance in stock market returns is not statistically significant using the standard criteria. 5
To illustrate, the ratio of the dollar value of trade to market capitalization for our sample of 261 large firms in
1988 is 0.76 on average; about 3/4 of the firm’s market value changes hands over the year. Two of the most heavily traded stocks, Raychem and Zenith Corporations, have a market capitalization of approximately $500 million but annual turnover is well over twice the market capitalization (2.15 for Zenith and 2.85 for Raychem). Torchman and Manville Corporations have market capitalizations of approximately $1 billion but less than onefourth of their share value changed hands over the year 1988 (0.20 for Torchman and 0.045 for Manville).
2
traded (defined as total annual dollar volume divided by market capitalization). The data thus do not support either the hypothesis that informative stock prices are disregarded, or that stock prices are informative about future cash-flows but not about the CEO’s contribution. While an ideal test would somehow isolate stock price information which is relevant to the CEO’s contribution, the strong statistical relationship between the overall information content of share prices and the CEO’s incentive pay supports the hypothesis that market trading conveys valuable information about the CEO’s performance. One plausible alternative explanation for our findings is that that the CEO’s private knowledge of good prospects encourages her to take larger positions in her firm’s securities. We find, however, that direct CEO shareholdings are unrelated to both the information content of share prices and to the volume of share trading. While the positive relationship between incentives and the responsiveness of prices to order flow is partially due to the fact that both factors decrease in firm size, the relationship continues to hold when size is held constant. Finally, we find that corporations with traded options substitute out of bonus and dismissal incentives and into CEO stock option plans. Thus, the data provide support for the joint hypotheses that (a) CEO incentive compensation is affected by the informativeness of the stock price and (b) that organized exchanges produce both privately and socially valuable information in addition to liquidity. The paper is organized as follows. Section 2 presents our model and hypotheses. Section 3 presents the data and empirical tests, and Section 4 concludes. 2. Theory 2.1. The Model In our model of the stock market, there is only one round of trade and prices change only in response to order flow. We neglect public sources of information such as earnings reports which can be and are used directly in determining CEO compensation without going through the stock price.6 In fact, stock prices are likely to complement public announcements by summarizing their implications for the firm’s discounted cash-flows. Any such “interpretation” of public information takes place through market trade and is captured by our model. The CEO’s effort affects firm value in the following way. Shareholders have rights to the firm’s terminal cash-flows, which can take on one of two values: zero and V > 0. The good outcome occurs with probability q(a) and the bad occurs with probability (1-q(a)) where a is the manager’s action which affects the probability of the good outcome according to
6
See, for example, Bizjak, Brickley, and Coles (1993) on the use of accounting and stock market measures of
management performance.
3
∂q/∂a ≡ qa > 0, qaa < 0. The manager has a cost of effort function denoted C(a) with ∂q/∂a ≡ Ca > 0, Caa > 0 and has next-best employment opportunity yielding an expected utility level normalized at zero. Shareholders are risk-neutral and the manager is risk-averse with respect to income. For concreteness, we assume that her preferences are logarithmic. In our model incentive contracts cannot be written directly on terminal cash-flows but must instead be linked to observed stock prices. This assumption simply reflects the fact that the firm’s actual distribution to shareholders are not fully revealed during the career of any given executive in a solvent, ongoing corporation. Management incentive contracts are written on the firm’s stock price which is determined as follows. Trade is assumed to take place after the manager has made her effort choice, since otherwise the price could only reflect conjectures about the manager’s action and would be useless for incentive purposes. For simplicity, we assume only one round of trade and following Glosten and Milgrom (1985), only one unit may be traded. Market microstructure models such as Glosten and Milgrom (1985) are most often used to study the intraday behavior of prices and transactions. The time horizon appropriate for management compensation is in years, rather than days or hours, and we take the individual CEO’s contract as the unit of analysis. Our purpose here is to characterize a representative set of trades and associated prices for a given firm, and to link these variables to the CEO’s incentive contract. We assume that market-making is perfectly competitive and there are no administrative or inventory costs of executing a trade. Hence, the price at which trades are executed reflect the expected value of the stock contingent on observed order flow. The manager’s pay can be conditioned on the realization of (Pbuy, Psell) where Pbuy is the price at which the market-maker will execute a buy order from the public and Psell is the price he quotes to fill a sell order.7 P0 is the price before order flow is revealed and reflects unconditional expectations about the manager’s effort decision and the firm’s resulting cash-flows. We denote by mbuy the manager’s compensation when a trader buys a share and the price rises to Pbuy and by msell her pay when the price falls to Psell. This is without loss of generality as there are only two possible stock prices in our model. Traders are equally likely to be one of two familiar types. The first type, termed liquidity traders, are equally likely to buy or sell for reasons unrelated to the firm’s cash-flows. Their demands are assumed to be inelastic in the range of equilibrium prices. The second type, termed informed traders, base their demands on additional information about the firm’s cash-flows. Specifically, when the firm’s true cash-flows are V, informed traders correctly observe this fact with probability 1-ε. They receive the incorrect signal that the firm’s cash-
7
We avoid referring to Pbuy and Psell as bids and asks because such quotes reflect inventory and execution costs,
vary in the number of shares that can be traded at the quoted prices, and take place at short time-intervals. We return to these issues in the empirical section.
4
flows are zero with probability ε. Similarly, when the firm’s cash-flows are zero, informed traders observe zero with probability 1-ε and observe a false positive signal of V with probability ε. To ensure that the signal is informative, we assume ε < ½. Trade takes place through risk-neutral, perfectly competitive market-makers who know ε, q(a), C(a), and the manager’s incentive contract. The resulting stock market produces prices which are characterized by Lemma 1 (all proofs are provided in the Appendix). LEMMA 1: There will be a buy order in the market with probability φ = ½ [1/2 + q(ae) + ε 2q(ae)ε] and a sell order with probability 1-φ where ae is the manager’s expected effort choice. The resulting prices are given by: 3 − 2ε Pbuy = Vq (a e ) − mbuy ; 2φ ∆ ≡ Pbuy − Psell
1 + 2ε Psell = Vq (a e ) − msell ; 2(1 − φ )
(
(1)
)
(1 − q (a e )(1 − 2ε ) e = Vq (a ) − mbuy − msell . φ (1 − φ )
The prices in Lemma 1 reflect the expected terminal payments to shareholders contingent on observed order flow. Since the manager’s payments are triggered by the observed stock price, they must be incorporated into prices. The variable ∆ is defined as the information incorporated into stock prices and reflects two forces. First, it decreases as the informed trader’s knowledge becomes less precise (so that ε increases). Second, it decreases as the difference (mbuy - msell) increases since the manager receives a larger portion of any innovation in the stock price. This quantity is not, however, exogenous. Rather, we assume optimal incentive contracts in which mbuy and msell are chosen by shareholders to maximize their expected wealth. In so doing, the shareholders must satisfy two constraints which are standard in the agency literature. First, the manager must agree to join the firm, which requires:
(
)
Μ ≡ φ ln mbuy + (1 − φ ) ln( msell ) − C( a) ≥ 0.
(2)
Second, the manager chooses the action which maximizes her expected utility, which implies the first-order condition:8 q (1 − 2ε ) ∂Μ ∂φ = ln m buy − ln(m sell ) − Ca = a ln m buy − ln(m sell ) − Ca = 0 . ∂a ∂a 2
( ( )
8
)
( ( )
The first-order approach is valid here since the second-order condition is:
5
)
∂ 2 Μ q aa = (1 − 2ε ) − Caa < 0 . ∂a 2 2
(3)
The considerations underlying (3) differ slightly from those in the standard incentive literature, because contracts are written on the observed stock price (Pbuy or Psell) rather than on terminal cash-flows (V or zero). If contracts were written on terminal cash-flows, the first term of (3) would be qa, the extent to which increased effort increases the probability of the firm’s cash-flows being V rather than zero. In an ongoing corporation with publicly traded claims, incentives are based on stock prices and other forecasts of future earnings. The first term in (3), qa(1-2ε)/2, captures the manager’s effect on the firm’s stock price. With probability one-half, trade is driven by liquidity considerations which are unrelated to the manager’s action. If the trade is not liquidity-driven, it is still based on a noisy observation of the true outcome, V or zero. By increasing effort, the manager increases the probability that the true outcome is V by the factor qa, and this is observed by the informed trader with probability (1-2ε). As ε decreases, stock price movements become increasingly reflective of the true outcome and hence of the manager’s efforts. The buy-price, sell-price discrepancy also increases, because the market-makers are at a greater informational disadvantage. The resulting equilibrium linkage between management incentives and the cost of trading are stated in the following proposition: PROPOSITION 1: So long as the manager is provided with any effort incentive and the revision in prices due to order flow ∆ is positive, her optimal incentive payment α ≡ mbuy msell strictly increases in ∆.
The intuition is that a reduction in ε, and hence an increase in the precision of the informed trader’s knowledge, increases the responsiveness of the price to order flow, ∆. When ε is low, an increase in the manager’s effort is more likely to result in the informed trader accurately observing the high signal of V and submitting a buy order. Strictly speaking, ε is the only exogenous variable that drives the relationship in Proposition 1. All our conclusions follow, however, if information is endogenous in the sense that informed traders can expend resources to reduce the error ε.9 When traders have more precise information, the stock price becomes more informative and is used more intensively in determining the manager’s compensation.
9
Expression (A6) characterizing the optimal α is equally valid if the errors are endogenous; prices are more
informative about the CEO’s action and about terminal cash-flows when ε is small for any reason. The remaining question, which we do not directly address here, is what attributes of firms’ production and marketing environment affect the costs of gathering relevant, private information. Our interest here is in whether stock prices actually convey such information to corporate decision-makers.
6
Information content is not the only consideration in an optimum managerial incentive contract. Liquidity considerations are summarized in the following proposition: 2.2. Discussion While Proposition 1 is intuitive, it relies on two key assumptions that are not universally adopted in the compensation literature. First and most obviously, we simply assume that management compensation contracts are chosen to maximize stockholder wealth subject to the informational constraints imposed by the stock market. Second and less obviously, our results rely on the assumption that informed traders observe a signal of future cash-flows which in turn carries information about both the CEO’s action and the firm’s exogenous luck. Specifically, a lower value of ε implies more precise information about both terminal cashflows and about the manager’s action. Paul (1992) stresses that informed traders are directly interested in foreknowledge of V, and only incidentally concerned with the manager’s action choice. If informed traders can choose which signal to observe, they will choose the one which is most informative about V. This signal is not necessarily the one which is most useful to the board in evaluating the CEO. If it is not, order flow could be highly informative about terminal cash-flows (which would imply a large ∆), but not be highly informative about the CEO’s action. Stock prices will be informative about the CEO’s action to the extent that profit-maximizing speculators are guided by an (extended) invisible hand to produce information about the CEO’s action despite their relatively narrow interest in trading profits. Our Proposition 1 focusses on the information content of to order flow but since trades are restricted to a single unit we ignore differences in the volume of order flow. This issue features prominently in Holmstrom and Tirole (1993) who allow for multiple trade sizes in a model which, like ours, has informed traders who observe a signal which is informative about CEO actions (see their Proposition 3). Their results imply that stock prices will be used more intensively in CEO compensation when there is more average liquidity trade in the shares. The idea is that informed traders have a greater incentive to gather information about such stocks. Their analysis is couched in terms of the distribution of order flow by liquidity traders, which is not directly observable. We analyze a simplified version of their model (which is based on Kyle, 1985) in the appendix and show that expected informed order flow is directly related to the observed total volume of trade in a firm’s shares. Once we add the insight from Holmstrom and Tirole (1993) to the implications of our Proposition 1 then the empirical predictions from this section are, essentially, that the stock price will be more useful as a signal of CEO performance when a given amount of order flow is more informative, and when there is more overall order flow. We now construct a test of these predictions.
7
3. Empirical Results 3.1. The Data 3.1.1. Sources and Descriptive Statistics The sources of our data are summarized in Table 1. The initial sample of 430 firms with pay−performance sensitivities estimated for 1988 from Jensen and Murphy (1990b) was reduced to 261 by a number of considerations. Some of the original firms disappeared due to merger or acquisition. Another eight firms for which share price data was available from the NYSE were excluded due to the absence of Compustat data or large discrepancies between the accounting value of assets and market capitalization.10 We excluded firms traded on NASDAQ because their infrequent quote revisions precluded reliable estimates of trade informativeness. Additional firms were excluded on the grounds that our informativeness measure (see below) is not defined for negative values. Our data on CEO incentives, firm size, and other non-stock-market attributes are similar to those described by Garen (1994). They are drawn from Jensen and Murphy (1990b) and from Compustat. All the share price revision and trade data is extracted from the Institute for the Study of Security Markets (ISSM) transactions file databases. A literal interpretation of our model would suggest the use of the bid-ask spread to measure the information content of order flow. However, our model of optimal CEO compensation envisions a board of directors who incorporate observed prices in the CEO’s contract based on their information content. Bid and ask quotes inevitably contain noninformational elements, such as inventory and order processing costs. We could follow approaches such as Glosten and Harris (1988) to filter out these influences. Such an approach would still overlook the problem that the quotes used to compute the bid-ask spread have limited “depth”, that is, they are only valid for relatively small trades. Moreover, such depth varies across firms in ways which may bear no relation to informativeness.11 The information content of order flow is most reliably captured by the effect of a given trade on the midpoint between the buy and sell prices, since the midpoint represents the market’s expected value of the firm based on all previous trades.12 In terms of the model,
10
The exclusion of these firms made negligible difference to the estimates.
11
See Brennan and Subrahmanyam (1995) for a lucid presentation of alternative ways to measure the effect of
trade on observed prices at the firm-level. 12
This measure is related to the notion of “market impact” which attempts to capture the cost borne by a large
trader. The primary difference between midpoint revision and market impact is that market impact focuses on the extent to which a large trade cuts into the schedule, while we focus on the revision to the midpoint of the quotes that are produced by a large trade. Market impact is a measure of the cost of transacting, while we are interested in the information conveyed by the trade.
8
quoted prices after a representative standardized buy order would be centered on our buy price Pbuy, and quotes after a sell order would be centered on our sell price Psell. Hence ∆ = Pbuy Psell in our model is exactly equal to the expected revision in the previous midpoint for a unit of order flow. This approach extends the existing empirical literature on CEO incentives, in which the “noise” content (obverse of informativeness) of stock prices and/or accounting earnings is proxied by their observed variance (see Yermack, 1995, for a recent and careful example of this approach). Smith and Watts (1992) and Holmstrom and Tirole (1993) both argue that the observed variance of the security price has an ambiguous relationship to the value of stock prices in motivating the CEO. While we use measures of variance in the empirical work to capture elements of “noise”, our approach focuses on the “signal” content of the price as revealed by the market’s response to order flow. In computing our measure of midpoint revision from ISSM data, vectors containing only clean trades (trades without special condition codes such as late or out-of-sequence) and market-best quotes are created. For every trade, the change in the midpoint of the spread is computed as the absolute difference between the midpoint of the market-best quote immediately following a trade and the midpoint of the outstanding market-best quote at the time of the trade. The dollar value of every trade is computed as the trade price times the number of shares, which is regressed (using Ordinary Least Squares) against the absolute change in quote midpoint. This regression coefficient is then converted into a measure of midpoint revision for a trade size of $1 million.13 Our measures are averaged over the entire calendar year 1988 for each firm in order to capture fundamental, durable aspects of each firm’s trading environment which are relevant for long-term compensation contracts.14 While our midpoint revision coefficient should be representative of long-term security price informativeness, it clearly suppresses a great deal of detail about the actual process of trade in each firm’s shares. For example, we focus on changes in observed inside quotes, whereas quoted prices on the NYSE need not reflect the terms on which traders actually transact because of the prospect of price improvement whereby trades are executed between the market-best ask and bid prices. This will typically occur when a market order (i) hits a hidden limit order, or (ii) the specialist "stops" the order
13
Our reported results utilize the dollar midpoint revision method. In the robustness section, however, we also
consider percentage midpoint revisions. 14
We also computed the measures for each firm over the entire calendar year 1990 and are comforted by the fact
that the correlation between market impact measures in 1988 and 1990 exceeds 0.85, and the corresponding correlation for the percentage bid-ask spreads is nearly 0.5.
9
and someone in the crowd subsequently hits the order.15 The point here is that our measure is not concerned with transactions costs, the measurement of which could be affected by trades within the quotes. Rather, we are concerned with trades which convey information, and hence, alter the midpoint of the spread. So long as the midpoint of the observed spread is an unbiased measure of the midpoint of the effective spread, as it should be, our measure of informativeness is not affected. In any case, the specialist is only likely to provide price improvement to floor traders and others whom he believes are not informed. Observed mid-point revisions will be smaller if there are large numbers of buy and sell limit orders that are close to the inside quotes, that is, if the market has “depth”. If the parties who submitted such limit orders are rational, of course, their willingness to submit such orders implies that the trader who will take the other side is unlikely to have a great deal of private information. A small midpoint revision still reflects limited information content in order flow. Similarly, rational parties will submit limit orders which are much further from the current quotes in stocks where traders are likely to have private information. For our purposes, what is critical is the extent to which the market as a whole responds to a given amount of order flow. Two supplementary measures of trade in each firm’s securities that are suggested by theory are also computed. First, the dollar volume of trade divided by the average market value of equity is used to test the hypothesis derived from Holmstrom and Tirole (1993) that thicker trading produces more informative prices and more share-based incentives (see Appendix). Second, and more speculatively, we include a dummy variable which takes on the value one for the 204 firms in our sample which have publicly traded stock options. While such short-lived options have little in common with the non-publicly traded and far longerlived CEO options, their existence is likely to be an indication of greater information content in the midpoint revisions to the share price and to a greater trading propensity. If trading reveals valuable information, such firms should use stock options more intensively to motivate the CEO. The means, medians, minima, maxima, and standard deviations of the data used are summarized in Table 2. After excluding firms with negative midpoint revision measures, the sample size is 261 firms. The pay-performance sensitivities show the increase in the CEO’s wealth from a $1,000 increase in the stock price of the corporation. The overall figure for the original Jensen and Murphy (1990b) sample is higher than reported here because our sample selection process excluded a number of smaller firms with higher pay-performance sensitivity.
15
Several recent studies such as Petersen and Fialkowski (1994) have developed measures of “effective spread”
to more accurately measure the spreads faced by traders. Additionally, McInish and Wood (1995) discuss the specialist practice of hiding limit orders, which results in quoted spreads being wider than the “true” spread nearly 50% of the time on the NYSE.
10
In all cases, both CEO stock ownership and size measures (assets or market value) are skewed to the right. Our percentage bid-ask spreads are somewhat lower than those in McInish and Wood (1992), again because our firms are (on average) large. 3.1.2. Some Details on Measures of Stock Price Information Content Tables 3 and 4 present some additional information on our measures of the effect of trade on prices. Table 3 reports the regression of our midpoint revision measure on size and volatility. These results are reassuring in that one expects larger firms and firms with more average trade volume to be less affected by large dollar trades, and stocks with higher volatility should have more information asymmetry. Equally important, size, volatility and trade volume explain less than 10% of the variation in midpoint revision, so that multicollinearity is not a severe problem. In Table 4 the log of the percentage bid-ask spread is regressed on two size measures (the log of market capitalization and the log of the book value of assets), as well as volatility, volume, and our midpoint revision measure. As expected, the bid-ask spread is significantly negatively related to both measures of size and to trade volume, and positively related to security price volatility. These results are consistent with existing evidence on the determinants of the bid-ask spread (eg., Glosten and Harris, 1988). The negative coefficient on the midpoint revision measure was not expected, but may reflect the specialist’s affirmative duty to make a market (see Dutta and Madhavan, 1994, for a model of this idea, and Brennan and Subrahmanyam, 1996, for a similar finding in a larger sample). A notable feature of the results in Table 4 is that the bid-ask spread measures are highly correlated with variables which also affect the use of the stock price in CEO incentive pay. Tables 3 and 4 show how our price informativeness measure is related to size and volatility over the entire sample. Table 5 provides additional insight into the distribution of market impact and trade volume by focusing on some extreme cases. We characterize those firms which fell into the top and bottom 50 of our sample in both price revision and trade volume to market capitalization. Those firms in the top 50 should have the most informative stock prices, and those in the bottom should have the least informative prices. As in the regressions in Table 3, neither measure of information content is simply a function of size or industry. Firms with the most informative stock prices also seem to be more labor-intensive than those with the least informative prices, judging from the ratio of sales to employees. Finally, Table 5 indicates that CEO incentive pay is used more intensively in the high informativeness group. We now examine this finding more systematically. 3.2. Market Trading and CEO Incentives Tests of our hypotheses about the determinants of CEO compensation are reported in Table 6. The main results are presented in the first regression column with stock options plus
11
dismissal incentives plus the present value of bonus incentives as the dependent variable. The only excluded source of incentive pay are shares held by the CEO. Column two uses shareownership sensitivities and column three uses total sensitivities. All regressions use the book value of assets as the size measure. We do this because Garen (1994) finds that total assets perform better as an explanator of CEO incentives than does the market value of equity. As we confirm in the next section, our key results involving the midpoint revision measure are not affected by the choice of size measure. Four additional variables are included as controls. The first of these is the log of volatility. The inclusion of the scale measure (the log of the book value of assets), in conjunction with volatility follows from two key considerations. First, since our volatility measure is on a percentage basis, the inclusion of size captures the fact that CEOs bear more risk and are more likely to encounter wealth constraints in bearing a given percentage value change of a larger firm. Second, as argued by Rosen (1982), the marginal product of management effort will also be a function of size. The third control variable is the proportion of outside directors. This proportion could be significant either because board composition directly affects the contract negotiated between the CEO and the board or because the CEO influences the composition of the board. The fourth control variable is the experience of the CEO as measured by the years the CEO has spent as a director, which helps capture the career issues stressed by Gibbons and Murphy (1992). Our main finding is the significant positive effect of both midpoint revision and the bidask spread on CEO incentive pay. This result is consistent with our Proposition 1. When there is a higher information content in stock price, the stock price is more valuable as a managerial incentive device and hence managerial incentive payments will be more responsive to stock price. The control for firm size (the log of the book value of assets), is also negative and significant as expected. Volatility has a borderline significant negative coefficient, which is to be expected since the CEO would demand a higher premium for having his wealth tied to a riskier stock (see Garen, 1994, for alternative explanations and results). Neither the proportion of outside directors nor the years of the CEO as a director have any statistically significant effect on CEO incentives due to bonuses, stock options, or dismissals.16 The coefficients on midpoint revision and bid-ask spread are relatively large as well as statistically different from zero. Size (measured here as the log of total assets) has the largest overall effect on CEO incentives, which is not surprising since it undoubtedly captures a host of effects including the relative importance of effort, the importance of CEO wealth
16
This may seem inconsistent with our model if outside members are necessary to implement pay-for
performance. See Agrawal and Knoeber (1995), however, for evidence that outside board members are not necessarily more effective monitors of management.
12
constraints, monitoring costs, and so forth. An increase of one standard deviation in asset size reduces non-share incentives by 0.24 standard deviations. The corresponding standardized coefficients for our trading measures are not much smaller: 0.21 for the bid-ask spread and 0.14 for midpoint revision. Moreover, the market response coefficients are larger than the standardized coefficient on volatility, which equals -0.11. The second column of Table 6 reports regression results with the CEO’s shareownership incentives as the dependent variable. While our theory of optimal α makes no distinction between the source of the linkage between CEO compensation and stock price performance, real-world CEOs stockholdings need not reflect an effort incentive contract administered by the board. Shares carry votes as well as cash-flow rights, and some CEOs undoubtedly wish to maintain their ability to influence the board or deter a potential hostile bidder. Some CEOs have also inherited stockholdings from the founders. Even if the board provides inducements for the CEO to purchase shares, she can typically add to or even sell some of his shareholdings (see Giammarino, Heinkel, and Hollifield, 1994). Consistent with the notion that CEO stockholdings are not necessarily driven by the principal-agent considerations we have stressed here, few of our results from column one continue to hold. Neither midpoint revision nor the spread have a significant relationship to CEO stockholdings (see Glosten and Harris, 1988, for a similar finding using insider ownership and the bid-ask spread). The volatility variable is now positive but not significant. The scale variable, the log of the book value of assets, is still highly significant. In contrast to our results with non-share incentives, the proportion of outside directors and the years of experience of the CEO as a director, are highly significant (1% level; see also Murphy, 1986, for similar results). A higher proportion of outside directors and a less experienced CEO is associated with a lower level of stock ownership incentives. While the last two results are both strong statistically, it is plausible that the causation is reversed. For example, a CEO with large stock holdings may be in a powerful position to resist the appointment of outsiders to the board. A CEO who has acquired a great deal of seniority as a director may effectively be entrenched and large CEO stockholdings may have contributed to that entrenchment. Family stockholdings may also be associated with longevity of the CEO as a director and the appointment of a smaller proportion of outsiders to the board. The final column of regression results in Table 6 is for the sum of pay- and stockincentives. The coefficients are essentially the linear sum of those from the two constituent regressions. None of the results in Table 6 change qualitatively if we use Tobin’s Q (market over book value of assets) as an additional explanatory variable. Table 7 presents additional evidence that market trading reveals important information about the CEO’s performance. The first column adds our measure of trade volume (dollar volume in 1988 divided by average market value of equity) plus the dummy variable for traded options to the regression in column one of Table 6. The positive and borderline
13
significant association between trade volume and CEO incentives tends to support Holmstrom and Tirole’s (1993) argument that a more liquid stock market produces more useful information about CEO performance. The presence of traded options does not seem to affect either total non-share incentives (column one of Table 7) or the absolute importance of stock option incentives (column two). It is worth noting that our measures of the information content of order flow have substantial power in explaining the use of options. Yermack (1995) finds, as we do, that more standard measures such as volatility and Tobin’s Q have no such power. Column three provides further information on the effect of public markets on CEO incentives by documenting that the incentive packages of firms with traded options include more option incentives relative to bonus and dismissal incentives. This finding is consistent with the notion that, like stock markets, organized options markets increase the value of such contracts in assessing the CEO’s performance. 3.3. Alternative Variable and Regression Specifications Table 8 documents that our key results are robust to some plausible alternative empirical measures and regression specifications. The first column uses market capitalization rather than assets as the measure of size. The bid-ask spread and trade volume coefficients both fall to insignificance in this case. This is not surprising since volume is divided by market capitalization and because the bid-ask spread is even more strongly related to market capitalization than to the book value of assets (see Table 4). The coefficient on midpoint revision, our most direct measure of the information content of market order flow, increases slightly in size and statistical significance. Our midpoint revision measures are in dollar terms, that is, they capture how much the absolute price is moved by a trade of one million dollars. It could be argued that percentage revisions are more relevant. Column 2 shows that our results continue to hold if we adopt this measure, and indeed the standardized coefficient on midpoint revision increases to 0.22. Column 3 shows that our results are not simply a hidden industry effect. It includes dummy variables for agriculture, mining, and construction; manufacturing; transportation and communications; utilities; wholesale and retail trade; finance, insurance and real estate; and services. The last two industries apparently make somewhat greater use of CEO incentive plans tied to the stock price, but the effects are not significant at even the 20% level. Thus, in summary, Table 8 indicates that our finding that CEO incentive plans are used more intensively when market order flow has more information content is not due to measurement problems or to excluded variables. 4. Conclusions Our key finding is that when the prices produced by organized securities markets contain more information, they are used more intensively in evaluating and motivating 14
corporate CEOs. Position-taking by market traders seems to reveal important information about the performance of key corporate decision makers, even though traders have no intent to exercise direct control over the firm, as would be the case in a takeover bid. Rather, our results appear to be another manifestation of the invisible hand; traders who are presumably interested in pecuniary gain and risk-management provide corporate boards with valuable information about the performance of top managers. Moreover, as Holmstrom and Tirole (1993, p. 707) stress, they are credible because they are objective, third-party assessments. There is some limited evidence that formal options markets also produce relevant information. More detailed research about the process of information-gathering and trading on securities markets would clearly be of value. Direct information about traders’ activities, such as the number of analysts who follow a particular stock, could improve our understanding of how stock prices are formed and used by corporations. The empirical literature on security market microstructure has tended to focus on the measurement of transaction costs or the resolution of apparent anomalies in asset pricing. This paper demonstrates that microstructure-based research can enhance our understanding of corporate behavior as well as behavior of financial markets.
15
Appendix A PROOF OF LEMMA 1: We begin by computing φ, the probability of a buy order. With probability 1/2 the trader is motivated by liquidity considerations, which is assumed to lead to a buy with probability 1/2. With probability 1/2, the trader is informed. With probability q, the true outcome is V which is observed by the informed trader with probability 1-ε. With probability (1-q) the true outcome is zero but the informed trader observes V with probability ε. The summed probability of these events yields φ =(1/2)[1/2 + q(1-ε) + (1-q)ε] = (1/2)[1/2 + q + ε - 2qε] and (1-φ) = (1/2)[3/2 - q - ε + 2qε]. The expected value of a share conditional on a buy order can be written: Pbuy = qV (Pr Liquidity buy ) + V (Pr Informed , correctly observeV buy ) + 0(Pr Informed , incorrectly observeV buy ) − mbuy =
(A1)
1 qV qV (3 − 2ε ) + Vq (1 − ε ) + 0(1 − q )ε − mbuy = − mbuy . φ 2 2φ Similarly, when there is a sell order we have Psell =
1 qV qV (1 + 2ε ) + Vqε + 0(1 − q)(1 − ε ) − m sell = − m sell , 1−φ 2 2(1 − φ )
(A2)
and (3 − 2ε )(1 − φ ) − φ (1 + 2ε ) (1 − q)(1 − 2ε ) ∆ ≡ Pbuy − Psell = qV −α . − α = qV φ (1 − φ ) 2φ (1 − φ )
(A3)
PROOF OF PROPOSITION 1: Since the bid and ask prices are unbiased estimates of terminal cash-flows we can write the shareholders’ objective denoted Λ as simply that of maximizing qV - φmbuy - (1-φ)msell = φA + (1-φ)B subject to the constraints (2) and (3) in the
16
text with associated Lagrange multipliers ω and µ, respectively. The first-order conditions for optimal management pay are therefore:
∂Λ φω ∂φ 1 = −φ + +µ = 0; ∂mbuy ∂a mbuy mbuy ∂Λ ∂φ 1 (1 − φ )ω = − (1 − φ ) + −µ = 0. ∂msell ∂a msell msell
(A4)
Rearranging (A4) yields:
∂φ / ∂a q (1 − 2ε ) =ω+µ a ; φ 2φ ∂φ / ∂a q (1 − 2ε ) =ω−µ =ω−µ a . 1− φ 2(1 − φ )
mbuy = ω + µ msell
(A5)
We can therefore express the incentive component as:
α ≡ mbuy − msell =
µq a 1 − 2ε 1 − 2ε µqa 1 − 2ε + = . 2 φ 1− φ 2 φ (1 − φ )
(A6)
Using the expression (A3) for ∆ , substituting into the right-hand side of (A6), and solving for α provided 2Vq(1-q) > µqa , yields:
α=∆
µq a . 2Vq (1 − q ) − µq a
(A7)
Hence the optimal α is positive provided 2Vq(1-q) > µqa and ∆ is also positive, with α strictly increases in ∆. QED Volume and Liquidity Trade in the Kyle (1985)/Holmstrom and Tirole (1993) Model Market-makers are perfectly competitive and risk-neutral and there is only one informed trader who is also risk-neutral. There is only one round of trade and net liquidity order flow equals the random variable u ∼ N(0, σ2u). The firm’s share price P is determined by the market in anticipation of a terminal payout which we denote by V = a + v where v∼ N(0, σ2v ). The informed trader perfectly observes the firm’s terminal cash-flows before submitting his order x. All parties use linear strategies. First, denote the order placement strategy of the informed trader by x(V) = b + βV and denote market order flow by y ≡ x + u = b + βV + u The (linear) zero-profit pricing rule of the market-maker is denoted P(y) = Vm + λy. The first term, Vm, is the unconditional expectation of terminal cash-flows. Since the expected value of v is normalized to zero, Vm equals the market’s expectation of the manager’s effort, am.
17
Given the informed trader’s strategy, the market-maker sets prices that allow him to break even given the information conveyed by order flow, which implies: P( y) = V m + λy = a m + λ (u + b + β ( a − a m )) .
(A9)
The informed trader chooses his strategy to maximize expected wealth with the only cost of taking a large position being the associated midpoint revision. In this case the informed trader chooses x to maximize I = x(a - am + v - λx). The first-order condition:
∂I = a − a m + v − 2 λx = 0 , ∂x
(A10)
implies that x = (a - am+v)/2λ and β = 1/2λ. Net order flow to the market is now simply ψ ≡ β(a+v) + u where ψ is a normally distributed random variable with mean zero and variance β2σv2 + σ2u = (σu/σv)2σv2 + σu2 = 2σu2. The expected volume of trade is the expected absolute value of ψ. Expected buy volume from informed and liquidity traders (which equals expected sell volume) is equal to the value of a call option with an exercise price of zero written on an asset whose returns are distributed normally with mean price zero and variance 2σu2. The value of such an option strictly increases in the variance of the underlying asset’s returns (see Brennan, 1979). QED.
18
References Agrawal, Anup and Charles R. Knoeber, 1994, Firm performance and control mechanisms to control agency problems between managers and shareholders, Working paper 29-94, (The Wharton School, University of Pennsylvania). Bizjak, John, James Brickley, and Jeffrey Coles, 1993, Stock-based compensation and investment behavior, Journal of Accounting and Economics 6, 349-372. Brennan, Michael J., 1979, The pricing of contingent claims in discrete time models, Journal of Finance 34, 53-68. Brennan, Michael J. and Avinidhar Subrahmanyam, 1996, Market microstructure and asset pricing: On the compensation for illiquidity in stock returns, Journal of Financial Economics 41, 441-464. Brennan, Michael J. and Avinidhar Subrahmanyam, 1995, Investment analysis and price formation in securities markets, Journal of Financial Economics 38, 361-381. DeLong, J. Bradford, Andrei Shleifer, Lawrence H. Summers, and Robert J. Waldmann, 1990, Noise trader risk in financial markets, Journal of Political Economy 98, 703-738. Dutta, Prajit K. and Ananth Madhavan, 1995, Price continuity rules and insider trading, Journal of Financial and Quantitative Analysis 30, 199-221. Garen, John E., 1994, Executive compensation and principal-agent theory, Journal of Political Economy, 102, 1175-1199. Giammarino, Ronald M., Robert Heinkel, and Burton Hollifield, 1994, Corporate financing decisions and anonymous trading, Journal of Financial and Quantitative Analysis 29, 351378. Gibbons, Robert and Kevin J. Murphy, 1992, Optimal incentive contracts in the presence of career concerns: Theory and evidence, Journal of Political Economy 100, 468-505. Glosten, Lawrence and Lawrence Harris, 1988, Estimating the components of the bid-ask spread, Journal of Financial Economics 21, 123-142. Glosten, Lawrence and Paul R. Milgrom, 1985, Bid, ask, and transaction prices in a specialist market with heterogeneously informed traders, Journal of Financial Economics 14, 71100. Grossman, Sanford J., 1989, The informational role of prices (MIT Press, Cambridge MA). Hayek, Frederich, 1945, The use of knowledge in society, American Economic Review. Holmstrom, Bengt R. and Jean Tirole, 1993, Market liquidity and performance monitoring, Journal of Political Economy 101, 678-709. Institute for the Study of Security Markets (ISSM), 1993, Documentation for the NYSE, AMEX, and NASD Transactions File Databases (University of Memphis). Jennings, Robert H. and Michael A. Mazzeo, 1991, Stock price movements around acquisition announcements and management’s response, Journal of Business 64, 139-157.
19
Jensen, Michael C. and Kevin J. Murphy, 1990a, Performance pay and top-management incentives, Journal of Political Economy 98, 225-264. Jensen, Michael C. and Kevin J. Murphy, 1990b, CEO incentives - it’s not how much you pay, but how, Harvard Business Review 69, 138-153. Kaplan, Steven N., 1991, The staying power of leveraged buyouts, Journal of Financial Economics 29, 287-313. Kyle, Albert S., 1985, Continuous auctions and insider trading, Econometrica 54, 1315-1336. Lang, Larry H. P., Robert H. Litzenberger, and Vicente Madrigal, 1995, Testing financial market equilibrium under asymmetric information, Journal of Political Economy 100, 317-339. Lee, C. M. C., 1993, Market integration and price execution for NYSE-listed securities, Journal of Finance 48, 1009-1038. Leland, Hayne S., 1992, Insider trading: Should it be prohibited? Journal of Political Economy 100, 859-890. Lippert, Robert L. and William T. Moore, 1994, Compensation contracts of chief executive officers: Determinants of pay-performance sensitivity, Journal of Financial Research 17, 321-332. McInish, Thomas H., and Robert A. Wood, 1992, An analysis of intraday patterns in bid/ask spreads for NYSE stocks, Journal of Finance 47, 753-764. McInish, Thomas H., and Robert A. Wood, 1995, Hidden limit orders on the NYSE, Journal of Portfolio Management 21. Murphy, Kevin, 1992, Incentives, learning and compensation: A theoretical and empirical investigation of managerial labor contracts, Rand Journal of Economics 17, 59-76. Paul, Jonathan M, 1992, On the efficiency of stock-based compensation, Review of Financial Studies 5, 471-502. Petersen, M.A., and D. Fialkowski, 1992, Posted versus effective spreads: Good prices or bad quotes? Journal of Financial Economics 35, 269-292. Rosen, Sherwin, 1982, Authority, control and the distribution of earnings, Bell Journal of Economics 13, 311-323. Smith, Clifford W. Jr. and Ross Watts, 1992, The investment opportunity set and corporate financing, dividend, and compensation policies, Journal of Financial Economics 32, 263292. White, Hal A, 1980, A heteroskedasticity-consistent covariance matrix and a direct test for heteroskedasticity, Econometrica 48, 817-838. Yermack, David, 1995, Do corporations award CEO stock options effectively? Journal of Financial Economics 39, 237-269.
20
Table 1 Data sources and derivations for the 1988 cross-section of 261 NYSE-listed firms. Variable
Source
Pay (Including Option)-Related Performance Sensitivity per $1,000
Jensen and Murphy (1990b)
Stock Ownership Sensitivity per $1,000
Jensen and Murphy (1990b)
Salary and Bonus, 1988 in $
Corporate proxy statement (Garen, 1994)
Years of Current CEO as Director
Corporate proxy statement (Garen, 1994)
Outside Directors as a Proportion of the Total Number of Directors
Corporate proxy statement (Garen, 1994)
Total Book Value of Assets, 1988
Compustat (Garen, 1994)
Industry Dummy Variables for Firms, 1988
Compustat (Garen, 1994)
Market Capitalization, Average 1988
Average number of shares outstanding (beginning and end of year number of shares) times average price using Institute for the Study of Security Markets (ISSM) data.
Volatility (×1,000)
The midpoint of the bid-ask spread (MP): MP = (Ask + Bid)/2 was computed using ISSM data. The change in the midpoint (CMP), CMP = (MPt − MPt-1)/MPt-1, was then obtained. Finally, the variance of CMP, (S2p)
2 n n n = ∑ CMPt2 − ∑ CMP t t = 1 t =1
(n − 1) , where n is
the total number of CMP’s during the year. Midpoint Revision per Trade of $1 million, 1988
The absolute change in the midpoint of the bid-ask spread in response to an order of $1 million. The absolute change in the midpoint is regressed using OLS against the dollar value of each trade made during 1988 for each stock and the regression coefficient is then adjusted to represent an order of $1 million. ISSM data is used. The percentage midpoint revision is computed by dividing the absolute change in the midpoint by the initial midpoint prior to the trade.
Time Weighted % Bid-Ask Spread, 1988
Using the method of McInish and Wood (1992): %BAS = [(askbid)/(ask+bid)/2} and TWBAS =
n ∑ % BAS t (T t + 1 − T t ) t =1
n n ∑ T t , where ∑ T t is the total t =1 t =1
time (in seconds) over the year for which there were quotes outstanding, and (Tt+1 - Tt) gives the time (in seconds) that a quote was outstanding, and n is the number of quotes over the year. ISSM data is used. Trade Volume
Total dollar value of turnover in 1988 divided by average market capitalization, using ISSM data.
Options Traded Dummy Variable
ISSM NYSE database for 1988.
21
Table 2 Descriptive statistics for our sample of 261 stocks based on the Jensen and Murphy (1990b) and Garen (1994) data sets, augmented by data from the trade-by-trade NYSE data base from the Institute for the Study of Security Markets (ISSM) for 1988. Variable
Pay (Including Option)-Related Performance Sensitivity per $1,000 change in shareholder wealth Stock Ownership Sensitivity per $1,000 Change in shareholder wealth Salary and Bonus, 1988 in $
Mean
Minimum
Maximum
(Median)
Standard Deviation
2.761
4.891
-8.99
55.6
25.81
0.000
95.46
$566,000
$175,000
6,730,000
9.35
1.00
78.00
0.115
0.231
0.952
$5,158
$38.9
$53,434
$5,912
$1,149.1
$1,825.2
(1.43) 8.076 (0.007) $854,950 (790,000)
Years of Current CEO as Director
13.41 (1.00)
Outside Directors as a Proportion of the Total Number of Directors Total Book Value of Assets, 1988, in $ million Market Capitalization, Average 1988, in $ million Volatility (×1,000)
0.757 (0.231) $2,697 ($1,091) $4,027m ($2,326) 0.0405
($635) 0.128
0.00215
1.924
0.0389
0.000006
0.547
0.677
0.266
7.37
0.458
0.0450
2.856
(0.0217) Midpoint Revision per $1 million of trades Time Weighted % Bid-Ask Spread, 1988 Trade Volume
0.0199 (0.0143) 1.058 (0.966) 0.758 (0.642)
22
Table 3 The estimated coefficients of the cross-sectional Ordinary Least Squares regression of the log of the absolute change in the mid-point of the bid-ask spread in response to a trade of a given size ($1million) on the NYSE during 1988 estimated using 261 stocks on two measures of firm size (firstly, the log of average market capitalization and, secondly, the log of the total book value of assets), and the average share price volatility for each stock and the average trading volume measured by the ratio of total trading volume to market capitalization for each stock for 1988: LN MRi = b0 + either b1 LN MCi or b2 LN BVAi + b3 LN VOLATi + b4 TRVOLi + ei , where LN MR is the log of the midpoint revision to the bid-ask spread in response to a trade of a given size, LN MC is the log of average stock market capitalization, LN BVA is the log of the book value of assets and TRVOL is trade volume give by the ratio of the dollar value of turnover to market capitalization. The absolute values of the t-statistics (in parentheses) are computed using White’s (1980) heteroskedastic consistent covariance matrix. Dependent Variable
Log of Midpoint Revision Utilizing Market Utilizing Book Value Capitalization of Assets
Coefficients of the Independent Variables: b0 Constant
-1.90** (2.00)
-1.27** (1.76)
− 0.156 (1.23)
b1 Log Market Capitalization
b2 Log Book Value of Assets
-0.288* (3.28)
b3 Log Volatility
0.303** (2.22)
0.292** (2.52)
b4 Trade Volume
-0.798** (2.57)
-0.635** (2.18)
261 0.0631 42.9
261 0.0994 51.4
No. of Observations R2 Adj. F (from zero)
Note: * Indicates statistically significant at the 1% level, ** at the 5% level, *** at the 10% level, two-tailed tratio test.
23
Table 4 The estimated coefficients of the cross-sectional Ordinary Least Squares regression of the log of the bid-ask spread on the NYSE during 1988 estimated using 261 stocks on two measures of firm size (firstly, the log of average market capitalization and, secondly, the log of the total book value of assets), and also the average share price volatility for each stock and the average trading volume measured by the ratio of total trading volume to market capitalization for each stock for 1988 LN BASi = b0 + either b1 LN MCi or b2 LN BVAi + b3 LN VOLATi + b4 TRVOLi +b5 LN MR+ ei ,
where LN BAS is the log of the average time-weighted bid-ask spread, LN MC is the log of average stock market capitalization, LN BVA is the log of the book value of assets, TRVOL is trade volume give by the ratio of the dollar value of turnover to market capitalization and LN MR is the log of the midpoint revision to the bid-ask spread in response to a trade of given size. The absolute values of the t-statistics (in parentheses) are computed using White’s (1980) heteroskedastic consistent covariance matrix. Dependent Variable
Log of the Bid-Ask Spread Utilizing Market Utilizing Book Value Capitalization of Assets
Coefficients of the Independent Variables: b0 Constant
2.50* (21.8)
1.66* (15.8)
− 0.182* (10.6)
b1 Log Market Capitalization
−0.0454* (3.84)
b2 Log Book Value of Assets
b3 Log Volatility
0.312* (15.0)
0.399* (18.8)
b4 Trade Volume
-0.0227* (2.99)
0.00227 (0.0663)
b5 Log of the Midpoint Revision
-0.0227* (4.31)
-0.0239* (3.18)
261 0.800 212
261 0.706 129
No. of Observations R2 Adj. F (from zero)
Note: * Indicates statistically significant at the 1% level, ** at the 5% level, *** at the 10% level, two-tailed tratio test.
24
Table 5 Data for Companies Ranked in the Top and Bottom Fifty by Both Midpoint Revision and Trading Volume. Only six out of the 261 companies in the 1988 cross-section were ranked in the top fifty by both the magnitude of the mid-point revision, MR, in response to a trade and by trading volume, TRVOL, the ratio of 19 TRVOL, the ratio of the 1988 turnover to average 1988 market capitalization. Of these six, the summary statistics of two representitive companies is shown in the table along with the mean values for all six companies. Only four companies were ranked by both criteria in the bottom fifty. Once again, two representative are shown in the table along with the mean values for all four companies.
Company Name Industry Midpoint Revision for $ Mil. Trade $Volume as % Market Capitalisation $ Volume of Trading (ISSM)($ Mil.) Market Capitalisation (Average) ($ Mil.) Book Value Assets ($ Mil.) Market Capitalisation to Book Value of Assets Employment (1,000s) Sales ($ Mil.) Sales per Employee Present Value of Salary and Bonus Incentivesa Dismissal Incentivesa Stock Option Incentivesa Pay Related Wealtha (Sum of above) CEO Stock Ownershipa Total Incentivesa (Inclusive of ownership) CEO Salary and Bonus in $mill. No. of Shares Traded per Year ($ Mil.) Average No. of Trades per Year Average $ Value per Trade Time Weighted % Spread Volatility*1,000 based on Spread Midpoint. Options Traded
Companies Ranked in Top 50 Bally Mfg. Corp. Zenith Electronics Amusement Serv. Electronic Equip. 0.04791 0.03732 2.5221 2.3035 1,347 1,168 534 507 1,605 267 0.3327 1.9012 29.63 35.00 1,676 2,363 57 68 6.79 7.44 0.71 0.05 4.11 2.27 11.6 9.76 7.5 1.98 19.11 11.73 1.82 0.44 69 54 52,082 37,774 25,856 30,932 1.17752 1.25303 0.02806 0.04722 Yes Yes
Meanb 0.03561 1.6774 1,583 1,059 951 1.4513 24.00 2,397 111 6.24 0.25 2.16 8.65 1.99 10.64 0.92 55 31,900 53,956 1.09158 0.03662
Companies Ranked in Bottom 50 National City Co. Witco Corp. Meanc Commerc. Bank. Chemicals 0.00120 0.00009 0.00665 0.0450 0.3099 0.5242 87 243 24,932 1,936 783 6,205 397 375 4363 4.8774 2.0896 4.8694 14.92 7.76 60.43 3,530 1,428 10,143 237 184 171 -2.6 1.97 1.18 0.21 0.04 0.13 0.78 2.5 0.96 -1.61 4.52 2.26 0.2 20.09 4.15 -1.41 24.61 6.42 0.64 0.55 0.69 3 7 88 1,394 4,062 44,976 62,537 59,723 60,497 0.69222 0.95593 0.88146 0.00802 0.01029 0.01477 No No
Table 6 The coefficients of the cross-sectional Ordinary Least Squares regressions of the log of non shareownership, share-ownership and total-performance sensitivity for 1988, respectively, estimated using 261 stocks on the log of the revision to the midpoint of the bid-ask spread in response to a trade of given size, the log of the bid-ask spread itself, the log of volatility, the log of the book value of assets, the proportion of outside directors and the number of years spent by the CEO as a director: Firstly, LN NSOSi , secondly LN SOSi and, thirdly, LN TPSi = b0 + b1 LN MRi + b2 LN BASi + b3 LN VOLATi + b4 LN BVAi +b5PRODi + b6 CEOYEARSi+ ei , where the dependent variables are, firstly, LN NSOS, is the log of the non-share ownership sensitivities made up of the option, dismissal and the present value of salary and bonus sensitivities, secondly, LN SOS is the log of share-ownership sensitivities, and, finally, LN BVA is the log of total sensitivities made up of the sum of share and non-share sensitivities. The independent variables consist of LN MR, the log of the midpoint revision to the bid-ask spread in response to a trade of a given size, LN BAS, the log of the bidask spread, LN VOLAT, the log of volatility, LN BVA, the log of the book value of assets, PROD, the proportion of outside directors making up the board, and CEOYEARS, the number of years spent by the CEO as a director. The absolute values of the t-statistics (in parentheses) are computed using White’s (1980) heteroskedastic consistent covariance matrix. Variable
Non-Share Ownership Sensitivity
Share Ownership Sensitivity
Total Sensitivity
6.95** (2.15)
66.4* (2.93)
73.4* (3.20)
b1 Log Midpoint Revision
0.374* (3.38)
0.435 (0.945)
0.809*** (1.68)
b2 Log Bid-Ask Spread
2.45** (2.19)
-3.35 (0.500)
-0.921 (0.132)
b3 Log Volatility
-0.591*** (1.63)
4.17 (1.51)
3.58 (1.25)
b4 Log Book Value of Assets
− 0.847* (3.63)
− 2.72* (2.61)
− 3.57* (3.32)
2.24 (0.995)
− 39.1* (2.32)
− 36.9** (2.18)
− 0.0189 (0.78)
0.605* (2.85)
0.585* (2.82)
261 0.122 19.0
261 0.125 7.17
261 0.136 7.81
Coefficients of the Independent Variables: b0 Constant
b5 Proportion Outside Directors
b6 Years of CEO as Director
Number of Observations R2 Adj. F (from zero)
Note: * Indicates statistically significant at the 1% level; ** at the 5% level and *** at the 10% level, two-tailed t-ratio test.
27
Table 7 In the first column the Ordinary Least Squares regression coefficients are shown using NSOS, non-share ownership sensitivities, made up of the sum of the option, dismissal and present value of salary and bonus sensitivities, as the dependent variable, as in Table 6. The second column shows the option sensitivities alone, while the third column utilizes as the dependent variable the ratio of the option sensitivities to non-share ownership sensitivities. The independent variables in Table 7 are the same as in Table 6 except for the addition of two additional independent variables, TRVOL, the ratio of the dollar value of share market turnover to market capitalization and OT, a dummy variable which is unity if options are traded and is zero otherwise. The absolute values of the t-statistics (in parentheses) are computed using White’s (1980) heteroskedastic consistent covariance matrix. Non-Share Ownership Sensitivities
Option Sensitivities
Option Sensitivities/(NonShare Ownership Sensitivities)
Constant
6.40** (2.33)
1.91 (1.36)
0.988 (1.53)
Trade Volume
1.14*** (1.79)
0.0690 (0.217)
-0.133 (1.13)
Options Traded
-0.168 (0.183)
0.392 (1.06)
0.410* (3.13)
Log Midpoint Revision
0.429* (3.52)
0.172** (2.46)
0.0292 (0.806)
Log Bid-Ask Spread
2.38*** (1.85)
1.38** (2.07)
-0.169 (0.593)
Log Volatility
-0.623 (1.51)
-0.115 (0.633)
0.201 (1.21)
Log Book Value of Assets
-0.868* (3.22)
-0.286* (2.72)
0.0118 (0.294)
2.30 (1.05)
2.04** (2.18)
0.191 (0.581)
-0.0143 (0.610) 261 0.118 15.2
-0.00471 (0.0369) 261 0.128 15.7
-0.00553 (1.09) 259 0.0337 9.37
Variable
Proportion Outside Directors
Years of CEO as Director No. of Obs. R2 Adj. F (from zero)
28
Note: * Indicates statistically significant at the 1% level; ** at the 5% level and *** at the 10% level, two-tailed tratio test.
29
Table 8 The dependent variable in each of the three Ordinary Least Squares cross-sectional regressions is NSOI, non-share ownership sensitivities, as in Table 7. However, the variable LN MC, the log of market capitalization, replaces LN BVA, the log of the book value of assets, in the first column. In the second column the variable LN MR, the log of the midpoint revision, is replaced by the midpoint revision expressed in terms of the percentage change instead of the absolute difference, and, finally, in the third column a variety of industry dummy variables are also included. The absolute values of the t-statistics (in parentheses) are computed using White’s (1980) heteroskedastic-consistent covariance matrix. Variable
Market Capitalization as Size Measure 11.9* (2.61)
Percentage Midpoint Revision 8.18* (2.61)
Industry Dummies Included+ 4.41 (1.25)
Trade Volume
0.360 (0.659)
1.09*** (1.76)
1.16*** (1.79)
Log Midpoint Revision
0.483* (4.37)
Constant
0.500* (3.17)
Log (Percentage Midpoint Revision)
0.452* (3.64)
Log Bid-Ask Spread
0.888 (0.876)
1.88*** (1.80)
2.24** (1.99)
Log Volatility
-0.495 (1.32)
-0.604 (1.52)
-0.555 (1.41)
-0.888* (3.75)
-0.639* (3.17)
Log Book Value of Assets
Log Market Capitalization
-1.36* (2.99)
Proportion Outside Directors
2.38 (1.04)
2.33 (1.04)
1.46 (0.495)
-0.00806 (0.368)
-0.0138 (0.587)
-0.0125 (0.542)
261 0.105 16.3
261 0.125 17.4
259 0.128 10.5
Years of CEO as Director
No. of Obs. R2 Adj. F (from zero)
30
+
Industries in the sample are: agriculture, mining and construction; manufacturing; transportation and communications; utilities; wholesale and retail trade; finance, insurance and real estate; and services. Note: * Indicates statistically significant at the 1% level; ** at the 5% level and *** at the 10% level, two-tailed t-ratio test.
31
