The option to repurchase stock.
* Open market share repurchase programs are a common corporate event. During the 1980s and early 1990s, thousands of US firms announced such programs. The market reaction to the announcement of an open market share repurchase program is on average about 3.5%.(1) Several hypotheses have been offered to explain this positive response. Some have argued that such programs are a tax-efficient alternative to paying cash dividends. It has also been suggested that these programs optimally adjust capital structure. Perhaps the most widely discussed explanation is the signaling hypothesis, which suggests that the positive market reaction to repurchase announcements is a reflection of management's favorable information about the firm's future prospects.(2)
In some respects, this explanation for the positive market reaction to open market programs is appealing. However, other aspects of the signaling hypothesis as it relates to open market programs are more troubling. A primary concern of this hypothesis is that costs be imposed on firms which deliberately choose to signal falsely. As such, the market may view those announcements which are observed as credible. In a share repurchase, the substantive cost essentially lies in the acquisition of shares. If open market repurchase programs were firm commitments, the cost of false signaling is not difficult to see. Companies choosing to "falsely" signal end up repurchasing shares at prices above their "true" long-run value to the detriment of non-selling shareholders.
Yet, open market repurchase programs are not firm commitments. When corporate boards authorize managers to acquire shares on the open market, these programs, by design, not only give managers discretion as to when to acquire shares, but also whether to buy back the number of shares authorized. This lack of commitment is occasionally mentioned by managers at the time of the repurchase announcement. For example, in August 1995, H.O. Woltz, chairman of Insteel Industries said, "Whether any shares will in fact be repurchased remains to be seen. We believe that given the authority to buy shares places the company in a position where it can respond quickly should the opportunity arise." Similarly, at the announcement of a buyback by Newbridge Network, Jim Avis, vice president, said that the August 1995 program was "an indication that we want to be in a position to legally repurchase shares when the time is right." Thus, not all programs are fully completed and some are not initiated, a rather surprising result if the news of an open market program is to be viewed as a credible information signal.(3) At the time of the announcement, it is not clear what the firm's true intention might be. Of course, as time passes after a program has been established, firms might undertake actions that restore credibility, For example, managers might volunteer details of their transactions as they occur. One would also expect managers to readily disclose when all of the shares authorized for repurchase have been acquired. Yet surprisingly, managers rarely volunteer such information. If managers are choosing to repurchase shares as a means of deliberately signaling that share prices are undervalued, open market programs would not appear to be the optimal vehicle to convey such a message, particularly when more effective mechanisms such as fixed price or Dutch-auction tender offers exist (see Vermaelen, 1984; and Comment and Jarrell, 1991). Yet, nevertheless, according to Securities Data Corporation, 90% of all repurchase programs announced between 1985 and 1996 were to be conducted through open market transactions.
Alternatively, it is also possible that although managers may not choose to deliberately signal via open market programs, such program announcements convey unintended valuation signals. For example, it is possible that the primary motive for undertaking a program might be to alter capital structure or to distribute excess cash. Managers interested in maximizing shareholder wealth conceivably would be less inclined to make such decisions if they viewed their stock as overvalued, Hence, the announcement of a repurchase may indirectly reveal management's positive outlook. Although this is surely a possibility, the dramatic increase in the adoption of open market programs recently experienced would seem to suggest that other issues may be involved. For example, in i 994, the adoption rate among corporate America was so high that one of every four firms in the S&P 500 initiated a program. Even if these programs were not intended as deliberate information signals, the notion that so many managers of the US's most closely monitored firms would find their stock undervalued at the same point in time seems unlikely.
Of course, signaling may not be the only factor affecting the market response to open market buyback announcements. For example, open market stock buybacks have been argued to be a tax-efficient way firms can distribute wealth in comparison to cash dividends. While nevertheless plausible, various facts are difficult to reconcile with the tax hypothesis. First, buyback activity did not decrease as expected following the 1986 tax reform act when the differential between dividends and long-term gains was abolished (see Bagwell and Shoven, 1989). Second, recent evidence suggests that there is little substitution effect between dividends and share buybacks as companies that repurchase shares generally do not pay out less dividends than otherwise (see Dunsby, 1995). Finally, the tax hypothesis is seemingly inconsistent with the observation mentioned earlier that some firms, after announcing a buyback program, subsequently purchase few or no shares.
Clearly, such traditional explanations of the market response to open market repurchase programs like the signaling and tax hypotheses have merit and may indeed be a factor in some cases. Yet the goal of this paper is to introduce an alternative explanation that may also be affecting the market reaction--an explanation which explicitly recognizes the flexibility managers have in deciding whether or not to repurchase stock. In essence, these programs expand the company's investment opportunity set by authorizing management to use the firm's resources along with their "insider" valuation of the firm to the benefit of long-term shareholders, Managers concerned with long-term shareholder wealth will tend to buy back stock when they perceive the stock as undervalued and forego repurchasing shares otherwise. Hence, stock prices should increase around the repurchase announcement to reflect the fact that the company has created an option to exchange the market value of the stock for its "true" value. Thus, even if al the lime of the repurchase announcement managers have no superior information, and the market price of the stock is "fair," these programs will typically contain valuable options, and the market reaction to program announcements should be positive.
The fact that share prices increase by creating what appears to be a "free" option does not lead to the presumption that companies are treated to a "free lunch." The intuition supporting this is simply that buyback programs allow the firm to capture rents to the benefit of long-term investors when prices deviate from true value, not unlike how insiders personally benefit when trading on their own account under similar circumstances. To the extent that no price deviations exist, these programs are valueless as would be insider trading. However, to the extent that deviations arise on occasion, buyback programs allow a portion of the superior information advantage of managers to accrue to the firm. The model we present, in essence, represents the expected value of these potential rents. Given this framework, the irony would be if share prices did not rise at the announcement of an open market repurchase programs, as a "free-lunch" would then exist for long-term shareholders who buy and hold the stock subsequent to the announcement.
Using Margrabe's (1978) model for exchange options, specific predictions about the value of the repurchase option are readily attainable. Namely, the value of the option is predicted to be positively related to the volatility of the stock, the fraction of shares the company may repurchase, and the potential for mispricing in the future. Evidence consistent with these predictions is found in a sample of 892 open market repurchases announced in the US between 1980 and 1990. Specifically, for stocks with high volatility and where the opportunities for departures from true value might be viewed as unusually high, the average announcement return to the repurchase announcement is 7.13%. On the opposite side of the spectrum, for stocks with low volatility and where mispricing opportunities would seem to be low, the average announcement return is only 2.28%. In general, however, it should be pointed out that the relevance of the option effect depends crucially on assumptions about market efficiency. At this point, it is an open question in the literature as to the degree to which market prices deviate from "true" value. Several recent papers, such as Lakonishok, Shleifer and Vishny (1994), and Haugen and Baker (1995), suggest that prices may not always be fair. Moreover, even if markets are semi-strong efficient, there is substantial evidence that insiders have superior information. In short, irrespective of questions over efficiency, the discretion that managers have as to whether or not to invest in their own firm by repurchasing shares is a source of value to long-term shareholders and may account for at least part of the favorable reaction to these programs observed in the marketplace.
If repurchase programs contain valuable options and are also relatively simple to establish, one might expect many companies to adopt them.(4) Recently, this has indeed been the case. Between 1994 and 1996, more than 3,000 US companies announced plans to repurchase up to $300 billion of stock on the open market.(5) Given that repurchase programs often have maturities of several years or more, it would appear that currently, firms representing a substantial fraction of the US stock market have in place the option to buy back their own shares. The fact that so many firms would choose to undertake these programs at one time might raise some doubt as to whether these firms were truly undervalued at the time of the announcement. Yet, such adoption rates are plausible when these programs are viewed as exchange options. Moreover, the fact that some programs go uncompleted is not surprising if these programs are viewed as options where managers have the ability to forego exercising.
Although open market repurchase programs have become popular in recent years, not all companies are adopting them. Considering that the value of the typical repurchase option is only on the order of the noise observed in daily stock prices, it should not be too surprising that some companies do not feel compelled to gain board authorization until they perceive that their stock is significantly undervalued. However, such a "wait-to-adopt" strategy will generally be interior to an early adoption strategy, indeed, if every firm were to follow such a wait-to-adopt strategy, open market program announcements would largely serve as information signals, in an efficient market, stock prices would rise substantially reflecting the degree of mispricing. Thus, although the market will have alleviated any temporary mispricing, firms will not be able to profit from this, conceivably eliminating a primary motivation for initiating the program. Thus, in contrast to the predictions of the signaling literature, companies such as Insteel Industries or Newbridge Network, who wish to establish repurchase programs without overly disturbing market prices, may be expected to adopt these programs in advance of any perceived mispricing.
The paper is organized as follows. In Section I, we develop the intuition behind the repurchase option and formalize this intuition employing Margrabe's (1978) model of exchange options. This is done under the presumption that management has no inside information at the time of the announcement. Thus, the theory is developed in the absence of signaling. Section II gives an overview of the repurchase sample we evaluate in this paper. Section III examines various empirical predictions of the model, and Section IV presents conclusions.
I. The Option to Repurchase Stock
In this section, we first illustrate the basic idea behind the repurchase option with a numerical example and then formalize our intuition.
We start with a simple numerical example. Assume a risk-neutral world with zero interest rates. At time [t.sub.0], a company with 100 shares outstanding announces that it may repurchase 20 shares via the open market "depending on market conditions" at time [t.sub.1]. The stock price at [t.sub.0] is $1 per share, reflecting the likelihood that at [t.sub.1] the value of the company's operating cash flows will be either $150 or $50 with equal probability. Assume that at [t.sub.0], both the market and the management are uninformed, and that at [t.sub.1] the management learns the true value of the firm but the market does not. If managers are interested in maximizing the wealth of the long-term stockholders, they will only buy back stock if the true stock price is $1.50. In that case, the post-repurchase stock price, in dollars, equals:
(1) 150 - (S)20 / 80 = 1.50 + 20 / 80 (1.50 - S)
where S is the market price at [t.sub.1]. Otherwise, the company will let the repurchase option expire, and not repurchase any shares, in which case the stock price falls to $0.50.
Equation (1) shows that, per share outstanding, the company has created a fraction (20/80) of an option to buy the true value of the operating cash flows per share at the market price. Hence, when the company announces a repurchase program, stock prices will increase to reflect the value of this option. In this case, the value of the option W, can be obtained by solving the following equation:
(2) W = 0.5 [20 / 80 (1.5 - (1 + W))]
which gives a value for W of $0.0556. Thus, at the announcement of the repurchase program, the market price per share should increase to $1.0556. Subsequently, if managers do indeed observe the true value of the operating cash flows per share to be $ 1,50, they will choose to repurchase 20 shares in the open market at the prevailing market price of $1.0556. The total gain generated by managers in this "insider" transaction is $8.889 (-- 20 (1.50 - 1.0556)). Given that 80 shares now exist subsequent to the repurchase and that the ex-ante probability of observing this gain is 50%, the expected total cash flow per share after the repurchase program has expired is $1.0556 (=0.5 ($0.50 + $1.50) + 0.5 (8.88/80)).
Note that the market price per share after the announcement of the repurchase program trades above simply the expected operating cash flows per share. Yet, as illustrated above, this does not imply a "freelunch" of sorts. On the contrary, if share prices subsequent to the repurchase announcement were to remain at $1, long-term investors who buy and hold the stock until the program expires would earn abnormal returns. The power to shift wealth from liquidity traders to long-term stockholders is the source of the option value, if these long-term stockholders set market prices (a condition for a market "without a free lunch"), then share prices should increase to reflect the value of the option, as the expected "long run" value per share is $ 1.0556.
The conclusion that the value of the firm is larger than the value of its expected operating cash flows is similar to the conclusions of the "real" options literature (see, for example, Dixit and Pindyck, 1994). Specifically, if a company has the option to defer investing in a project until more accurate information about the project's cash flows becomes available, the value of the project is larger than simply its net present value (i.e. the value of the project if the investment decision is made immediately). Similarly, if a company, acting in the interest of its long-term shareholders, can wait for better information before choosing to buy shares from liquidity traders, the value of such a repurchase program to long-term investors becomes larger than its (zero) net present value.
Note that liquidity traders who plan to sell prior to the expiration of the option are now in fact better off after the repurchase program announcement, even though there is some probability that they may be selling their shares to the company. Had the company not announced the repurchase program, these traders could only sell their stock for $1 per share. Hence, our model does not imply that these liquidity traders are "irrational" by selling their shares. In equilibrium, both long-term investors and short-term investors are expecting to earn $1.0556 per share. Note that we assume that liquidity traders cannot detect when the company is in the market. This assumption Is not unrealistic, considering that companies never specify an exact expiration dale for the repurchase option and various SEC regulations (discussed infra) prevent corporations from materially influencing prices or trading volume,
A final way to understand the intuition of the paper follows, Assume that a corporation has some excess cash which is invested in marketable securities, i.e. an investment with zero NPV. Assume that the company announces that from now on, it is going to use this cash to buy back its own shares when they are undervalued, if the market believes that the company at some time in the future may have superior information, the stock price will rise to reflect the expected (positive) net present value of these insider trading benefits. This occurs, even if the repurchase program has no effect on the firm's total assets. The intuition is that, after the expiration of the repurchase option, the stock price is determined by the cash flows per share, not by the total assets,
B. Market Microstructure Issues
The conclusion that share repurchase programs increase stock prices differs from that reached by Barclay and Smith (1988). They also assume that managers repurchasing shares will exploit their information advantage relative to outside shareholders. However, Barclay and Smith argue that repurchase programs lead to an increase in bid-ask spreads and a reduction in liquidity. If one considers the cost of capital as the sum of both the expected return for bearing risk and the expected loss faced by uninformed investors, repurchase programs have the effect of increasing the cost of capital and hence lowering the value of the firm.
If it is the case that bid-ask spreads increase following repurchase announcements, our analysis may overstate the value of the repurchase option. Specifically, the numerical example above assumed that the company can repurchase shares al $1.0556 without disturbing market prices. Suppose that this is not possible and that market makers are somehow able to sense when they may be trading against the firm. Traditional microstructure models suggest that market makers will respond to the firm's presence by raising ask prices. This, in essence, increases the exercise price of the option, hence decreasing the value of the option to less than $0.0556. Thus, depending on changes in microstructure, the option model provides an upper bound on the inherent value of open market programs.
The economic impact of market microstructure effects on stock prices is an empirical issue. Barclay and Smith, using a sample of 153 US programs announced between 1970 and 1978, find evidence that spreads increase following repurchase program announcements, However, more recent studies reach different conclusions, Wiggins (1994) examines market microstructure effects surrounding sleek buyback announcements utilizing transactions data for 195 programs announced between 1988 and 1990 and finds no evidence that spreads increase. Miller and McConnell (1995) report similar evidence using 248 repurchase programs from January 1984 through June 1988, And finally, Singh, Zaman, and Krishnamurti (1994), using a sample of 181 NASDAQ firms which made repurchase announcements between 1983 to 1990, also conclude that spreads do not increase following repurchase announcements. Thus, given the evidence. It is not immediately clear that market microstructure issues have a material impact on the option value inherent in open market programs, al least in more recent years.
Some might argue that evidence of no change in bid-ask spreads is contrary to the option model. Traditional microstructure models suggest that as informed traders (such as the firm) enter the market. spreads should rise. Thus, evidence which concludes that spreads do not change would appear to suggest that managers do not systematically use superior information to repurchase shares. However, the regulatory and institutional settings within which open market share repurchases occur is more complex than is typically acknowledged in the microstructure literature. The SEC, motivated by concerns of price manipulation, severely handicaps the trading activity of firms repurchasing their own shares in the open market through Rule 10b-18.(6) One facet of this rule, in particular, limits the price that firms may trade at to be no higher than the last independent trade or the prevailing bid, whichever is higher. This restriction may explain why spreads do not necessarily increase following repurchase announcements. For example, if market makers, sensing that the next buy order originated from the firm, were to respond by raising ask-prices, the firm can no longer trade. As this rule was only adopted in 1982, it may explain why more recent papers don't find the increase in bid-ask spread reported by Barclay and Smith (1988), Aside from price limits, Rule 10b-18 has volume limits as well, Thus, the anti-manipulation provisions of the rule also have the consequence (perhaps unintended) that the trading activity of the firm is obscured.(7) Thus, the traditional microstructure model (see Kyle, 1985) where a monopolistic insider trades against uninformed liquidity traders and market makers, and where the insider's private information is gradually incorporated into trading volume and prices, seems inappropriate in an open market share repurchase selling.
C. Market Response to Repurchase Announcements Without Signaling: Formalizing the Intuition
Our purpose is to model the flexibility that managers have in open market repurchase programs and to relate this to the market reaction to program announcements observed in practice. Formalizing the intuition helps us better assess the economic relevance and will also allow us to derive testable predictions of the theory.
In order to arrive at a market equilibrium, we make the following assumptions. First, we assume that after the announcement of the repurchase program, market prices are set by investors who recognize that these programs effectively create an option for the firm to buy shares from uninformed investors at some point in the future when management perceives market prices to be below their true value. Because of thin option, the value of the stock is greater than the present value of the expected operating cash flows per share. If market prices do not increase to reflect the value of the option. long-term investors will buy the stock and hold it until after expiration of the option. Competition between these investors guarantees that market prices reflect the option value. Second, we also assume that some liquidity- or noise-traders with short-term horizons exist and are willing to sell shares prior to the expiration of the option, even though there is some probability that they may be trading with the corporation. And finally, motivated by the regulatory constraints and recent empirical evidence, we also assume that specialists do not change bid-ask spreads subsequent to the repurchase program.
When a firm announces that it may buy back [n.sub.p] shores out of [n.sub.0] shares outstanding, it effectively creates, per share outstanding, a fraction [n.sub.p] / ([n.sub.0] - [n.sub.p]) of an option to exchange the market value of the stock for the true value of the stock. Margrabe (1978) derives a closed form solution fur such an exchange option. In the appendix, we extend this framework in the context of the firm's option to repurchase stock. To distinguish the repurchase option from the possible impact of information signals, we derive the model assuming that the company has no superior information regarding the true value of the firm when the program is announced. Under this scenario, the market reaction to the news of an open market program, x, is:
(3) x = F/1 - F [2N(d)-1)
where F is the fraction of shares outstanding the company may repurchase
(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Here, N([multiplied by]) is the standard normal cumulative distribution function: t is the time to expiration of the option: [[Sigma].sub.s], [[Sigma].sub.v], and [[Rho].sub.sv], represent long-term shareholders' assessments of the volatility of the stock return based on market prices, the true volatility of the stock return. and the correlation between the observed market rule of return on the stock and the true rule of return. respectively.
Margrabe's model is probably best viewed as a rough theoretical construct of the repurchase option. Some aspects of the model as applied in this context may not be entirely appealing. For example, the repurchase option is perhaps best characterized as an American option exercised sequentially over time. Margrabe's model describes a European option which generalizes to an American option if the share price and true value follow exogenous paths. If firms, in the course of repurchasing shares, affect market prices. one might question this assumption. On the other hand, the specific intent of the regulatory constraints firms face when repurchasing shares is to limit their ability to affect share prices. Given their existence, the assumption of independence seems reasonable.
The model specification assumes also that there is no tendency for the market price to converge to the true value: while price and value are correlated, the drift in the market price is independent of the difference between the market price and the true value. Hence, a more realistic model would probably incorporate some mean reversion in the difference between true value and market value. However, as the purpose of this paper is to present the basic idea behind the repurchase option, such extensions are left for future research.
D. Simulated Values
Table 1 reports simulated announcement returns when modeling repurchase programs as exchange options. Here we parametrize the model with a series of assumptions regarding [[Sigma].sub.s] the fraction of shares the firm authorizes for repurchase, the maturity of the option, and finally, the correlation between the true return and the observed market return on the stock. For convenience, we assume that [[Sigma].sub.s] equals [[Sigma].sub.v]; thus, [Sigma] in Equation (4) simplifies to [[Sigma].sub.s] [square root of 2(1-[[Rho].sub.sv]).(8) In the table, [[Sigma].sub.v] ranges from 20% to 60% per annum. The percentage of shares firms announce for repurchase varies in practice. We simulate announcement returns for three possible values: 5%, 10%, and 15%. Managers frequently do not explicitly report the maturity of these programs when they announce that they intend to repurchase shares. Moreover, even when managers do mention a specific date, they often extend the programs later. For a variety of reasons including SEC Rule 10b-18, then programs often span long periods of time. Hence, we simulate returns that assume program lengths of one and two years.
Table 1. Valuing the Exchange Option to Repurchase Shares on the Open Market
This table reports the market return tot he announcement of an open market share repurchase program (in percent) due only to the value of the exchange option, where "t" is the time to expiration of the option in years, [[Rho].sub.sv] measures the correlation between the "true" rate of return on the fundamental value of the firm and the market rate of return, and [[Sigma].sub.s] is the annual standard deviation of the market rate of return, which is assumed to equal [[Sigma].sub.v].
Fraction Purchased = 5% t = 1 Year t = 2 Years [[Rho].sub.sv] [Rho].sub.sv] 0.4 0.6 0.8 0.4 0.6 0.8 [[Sigma].sub.s] 0.2 0.46 0.36 0.26 0.63 0.52 0.38 0.3 0.68 0.56 0.40 0.98 0.79 0.53 0.4 0.89 0.74 0.52 1.26 1.05 0.73 0.5 1.10 0.93 0.65 1.57 1.26 0.92 0.6 1.33 1.10 0.79 1.88 1.56 1.12 Fraction Purchased = 10% t = 1 Year t = 2 Years [[Rho].sub.sv] [Rho].sub.sv] 0.4 0.6 0.8 0.4 0.6 0.8 [[Sigma].sub.s] 0.2 0.96 0.79 0.53 1.92 1.57 0.66 0.3 1.44 1.18 0.82 2.85 2.34 1.11 0.4 1.92 1.57 1.11 3.75 3.09 1.58 0.5 2.39 1.96 1.35 4.61 3.83 2.00 0.6 2.85 2.34 1.55 5.41 4.51 2.35 Fraction Purchased = 15% t = 1 Year t = 2 Years [[Rho].sub.sv] [Rho].sub.sv] 0.4 0.6 0.8 0.4 0.6 0.8 [[Sigma].sub.s] 0.2 1.52 1.25 0.71 3.05 2.49 1.23 0.3 2.30 1.88 1.41 4.53 3.72 1.87 0.4 3.05 2.49 1.76 5.96 4.91 2.47 0.5 3.79 3.11 2.11 7.32 6.07 3.17 0.6 4.53 3.72 2.64 8.61 7.18 3.67
The final parameter required by the model is [[Rho].sub.sv]. Making assumptions about the correlation between the market price of the stock and its true value reduces to an assumption regarding market efficiency. The debate regarding the degree to which market prices reflect fundamental value is not sallied.(9) Of course if [[Rho].sub.sv] equals 1.0. the option to repurchase stock is valueless. On the other hand, a substantial body of evidence suggests that the correlation is not perfect. Rather than take sides in this debate, we simply illustrate the value of the repurchase option using correlation coefficients that range between 0.40 and 0.80).
Table 1 shows that depending on how the model is parameterized, the market reaction arising only from the repurchase option varies between 0.26% and 8.61%. For example, if a company where both the opportunity for management to use its information advantage ([[Rho].sub.sv] = 0.40) and stock price volatility ([[Sigma].sub.sv] = 0.60) were high announced a two-year repurchase program for 10% or its outstanding shares, its stock price should increase by 5.41%. Of course, this might be a more extreme example. A more typical firm might be assumed to have an annual return volatility of 40% and [[Rho].sub.sv] = 0.60. Keeping all other features of the repurchase program the same, the price reaction inferred by the option model is 3.09%. This in similar in magnitude to the typical market reaction to buyback announcements of about 3.5% reported in the literature. Thus, if one accepts the notion that market prices can deviate significantly from their true value from time to time, it would appear that the option embedded in repurchase programs has the potential to explain a substantial portion of the observed market reaction.
To test some specific predictions of the model, we obtained the open market share repurchase announcement sample of Ikenberry, Lakonishok, and Vermaelen (1995). Their sample was formed from announcements reported in the Wall Street Journal from 1980 through 1990 stating that an NYSE, ASE, or NASDAQ firm intended to repurchase its common stock through open market transactions. To avoid excessive clustering, this sample excludes announcements made in the fourth quarter of 1987. Furthermore, we also exclude all repurchase programs seeking less than 2.5% of the shares outstanding. For very small repurchase programs, the value of the exchange option is negligible and would be difficult to empirically separate from noise.
One input in our analysis is [[Rho].sub.sv], which is of course unobservable. However, under certain assumptions, the [R.sup.2] of a regression of the market model provides a floor on the possible values of [[Rho].sub.sv]. Specifically assume that 1) both true and market returns are generated by the market model.(10) 2) the true beta. [[Beta].sub.v] is equal to the measured beta in the market. [[Beta].sub.s] and 3) [Sigma] equals [[Sigma].sub.v]. It follows that the correlation coefficient between the true return and the market return is equal to:
(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the variance of the rate of return on the market index, and coy([c.sub.v] [c.sub.s]) is the covariance between the true and market-based residual returns. Hence, the correlation coefficient decomposes into systematic and idiosyncratic components. The systematic component Is the fraction of the variance of the stock return explained by market-wide information or simply the R: from the market model, Given that one would not expect to find coy([c.sub.v] [c.sub.s]) negative, [R.sup.2] provides a floor of sorts on the possible values of [[Rho].sub.sv]. If the company-specific information incorporated in stock prices is independent of general market movements, then differences in [R.sup.2] will be associated with differences in [[Rho].sub.sv].
For each announcement, we obtain monthly returns beginning 36 months prior to the repurchase announcement. These returns are used to compute the standard deviation of returns and the R: obtained from a market model regression of stock returns on the CRSP equal-weighted index of NYSE and ASE firms. The standard deviation of the firm's monthly stock return is our estimate of [[Sigma].sub.s] and, by assumption, of [[Sigma].sub.s].
Table 2 provides an overview of the fraction of shares involved in our buyback sample, the market model [R.sup.2]. and the standard deviation (annualized) for our sample of 892 announcements. On average, companies in our sample announced repurchases for 8.0% of their shares (median: 6.15%). The average [R.sup.2] for our sample is 31.25% (median 31.0%). yet one-fourth of our sample has an [R.sup.2] greater than 43.0%. These values are greater than those reported by Roll (1988). Yet Roll also finds a significant relationship between [R.sup.2] and firm size, which would appear to explain, at least to some degree. our results. Our sample is drawn from repurchase announcements made in the Wall Street Journal where a bias favoring larger firms exists.
Table 2. Descriptive Statistics
The following table provides summary information for open market share repurchase programs announced in the Wall Street Journal between 1980 for ASE, NYSE and NASDAQ firms. Programs announced in the fourth quarter of 1987 or which were for less than 2.5% of outstanding shares are excluded. The number of announcements, the percentage of shares involved in the repurchase program, the [R.sup.2] from a regression of stock returns on the CSRP equal-weighted index of ASE and NYSE firms, and the annualized standard deviation of the stock returns are reported yearly and overall. The [R.sup.2] and standard deviation are calculated using returns from 36 months prior to the repurchase announcement.
Percent Repurchased Mean: 8:00% # of Announce- 2.5- 4.5- 6.25% Over Year ments 4.5% 6.25% 10% 10% 1990 53 11 21 15 6 1981 59 21 8 17 13 1982 88 25 24 24 15 1983 29 12 9 5 3 1984 140 54 33 31 22 1985 87 17 23 24 23 1986 96 24 19 23 30 1987 74 13 16 20 25 1988 90 15 23 27 25 1989 95 16 24 23 32 1990 81 15 23 23 20 1980-90 892 223 223 232 214 Annualized Standard [R.sup.2] Deviation Mean: 31.25% Mean: 37.58% 0- 20- 30- Over 27- 34- Year 20% 30% 43% 43% <27% 24% 45% >45% 1990 5 11 18 19 20 8 14 11 1981 8 17 14 20 9 14 12 24 1982 17 33 29 9 15 17 27 29 1983 16 5 7 1 11 3 7 8 1984 39 47 38 16 28 36 39 37 1985 42 18 20 7 25 25 21 16 1986 37 24 22 13 33 29 18 16 1987 18 20 20 16 3 25 8 18 1988 13 18 22 37 19 25 16 20 1989 14 14 13 54 16 21 37 21 1990 14 16 20 31 25 19 24 13 1980-90 223 223 223 223 224 222 223 223
Only two trends are of note in Table 2. First, the percentage of shares Involved in these repurchase programs gradually increased between 1980 and 1990. In 1980, the mean program was for 6.6% of the outstanding shares, By 1990, this percentage had risen to 8.7%, The highest value occurred in 1989 where the mean program was for 9.11% of the share base. A second trend evident in this table is the increase over time in the number of announcements made by firms whose stock returns were relatively highly correlated with the overall market.
III. Empirical Evidence
We evaluate the validity of viewing repurchase programs as exchange options by examining the empirical relationship between the market reaction to open market share repurchase programs and the theoretical determinants of the exchange option's value. To measure the average market reaction, we compute average risk-adjusted cumulative abnormal returns from two days before to two days following publication of the announcement in the Wall Street Journal. The mean market reaction to repurchase programs overall as well as by time period is reported at the top of Table 3. Below this, we report the mean reaction with respect to the fraction of shares involved in the program, the volatility of the stock, and [R.sup.2], our proxy for [[Rho].sub.sv].
Table 3. The Mean Market Reaction to Open Market Repurchase Announcements
This table reports the mean market reaction to the announcement of open market share repurchase programs by time period and by various factors affecting the value of the repurchase option: the fraction of shares the company plans to repurchase, the annualized standard deviation of the stock return, and the [R.sup.2] of the market model regression. Announcement period returns are calculated using market-model-adjusted abnormal returns summed from two days before to two days following the repurchase announcement. [R.sup.2] values are obtained from regressing monthly stock returns on the CRSP equal-weighted index of ASE and NYSE firms. [R.sup.2] and standard deviation are calculated using returns from 36 months prior to the repurchase announcement.
Average Abnormal Announcement Return Number (%) of Cases Overall 3.42 892 Time Period 1980 to 1983 4.57 229 1984 to 1986 3.21 397 1987 to 1990 2.63 266 Fraction Purchased 2.5 - 4.5% 2.63 223 4.5 - 6.15% 3.35 223 6.15- 10% 3.36 232 Over 10% 4.40 214 Annualized Standard 0 - 27 2.28 224 Deviation 27 - 34 2.99 222 34 - 45 3.43 223 Over 45 4.86 223 [R.sup.2] 0 - 20% 4.48 223 20 - 30% 3.40 223 30 - 43% 3.60 223 Over 43% 2.21 223
For all 892 repurchase programs in our sample, the mean market reaction is 3.42%. The average market reaction decreased during our sample period. During the early 1980s, the average market response was 4.57%. By the end of the decade, the average market response had fallen to 2.63%. This is consistent with the trend in [R.sup.2] we observed earlier whereby repurchase programs over time were increasingly made by firms with relatively large [R.sup.2] values. Other things the same, the repurchase option in such programs is less valuable than otherwise and thus provides us with our first piece of evidence consistent with viewing repurchase programs as exchange options. Yet other aspects of this table are consistent with the repurchase option hypothesis. Note that as repurchase programs increase in size from 2.5%-4.5% to above 10% of shares outstanding, the average market reaction increases from 2.63% to 4.40%. Moreover, as the volatility of stock returns increases, so does the market reaction, And finally, note that as [R.sup.2] increases, the market reaction generally declines. Each of these univariate properties is consistent with the option value embedded in open market repurchase programs.
In Table 4, we summarize the results from various cross-sectional regressions to further explore the relationship between the market reaction to program announcements and the fraction of shares involved in these programs (F), the volatility of the stock ([[Sigma].sub.s]), and the R-square of the stock with the market ([R.sup.2]). The first three models we report are univariate, the results of which are consistent with our earlier findings. Namely, bigger programs announced by firms with higher volatility and lower correlation with the market receive larger price reactions. Furthermore, these factors do not appear to subsume one another, since the coefficients change only slightly when included in a single regression.
Table 4. Cross-Sectional Regression of Announcement Returns
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] The dependent variable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the five-day (market model) abnormal return. F is the fraction of shares the firm announces that it intends to repurchase [[Sigma].sub.s] is the standard deviation of monthly returns estimated in the 36 months prior to the announcement, [R.sup.2] is estimated from the market model using 36 months of returns prior to the announcement, [[Sigma].sub.mkt] is the monthly standard deviation of the market return estimated over the same 36-month period as [R.sup.2] and [[Sigma].sub.s]. Reported below each regression coefficient is the associated t-statistic and p-value.
[[Beta].sub.1] [[Beta].sub.2] [[Beta].sub.3] 1 0.1107 t = 2.82 (0.0049) 2 0.3124 t = 6.39 (0.001) 3 -0.0516 t = 3.77 (0.0032) 4 0.0931 0.2850 -0.0405 t = 2.43 t = 5.80 t = 3.00 (0.0155) (0.0001) (0.0028) 5 0.0892 0.2964 -0.0326 t = 2.32 t = 5.98 t = -2.27 (0.0205) (0.0001) (0.0237) [[Beta].sub.4] 1 2 3 4 5 -0.4506 t = -1.61 (0.1068)
As a final check of whether the observed market reaction is indeed consistent with the repurchase option hypothesis, we include in the regressions reported in Table 4 overall market volatility prevailing at the time of the announcement, [[Sigma].sub.mkt]. The value of the repurchase option is sensitive to the underlying risk of the stock. However in our regression analysis, if volatility in the stock in simply proxying for overall market volatility, then one might expect [[Sigma].sub.mkt] to have a punitive coefficient and to subsume the relationship observed between [[Sigma].sub.s] and buyback announcement return. This would at least raise some suspicion with the repurchase option hypothesis, Yet, this does not occur. When market volatility is included, its coefficient estimate is negative, Coefficient estimates for [[Sigma].sub.s] remain positive and generally unaffected by the inclusion of [[Sigma].sub.mkt].
To gain further insight into the robustness of the evidence supporting the exchange option, we examine the market reaction to repurchase programs using a two-way sorting procedure, This is done using the three variables F, [[Sigma].sub.s], and [R.sup.2] in pair-wise combinations. We begin in Panel A of Table 5 by reporting the average market reaction using a two-way sort on the fraction to be repurchased and stock price volatility, We first sort firms into quartiles on the basin of the fraction of shares to be repurchased, Then within each of these quartiles, we further sort into quartiles on the basin of volatility, Average abnormal announcement returns are then computed for each of the 16 portfolios. Reported to the right of each row and the bottom of each column is the difference in the mean market reaction (and the associated t-statistic) between extreme quartiles, holding the relative ranking of one variable constant. For example, looking at the first row of Panel A, we see that even for relatively small programs, the market reaction rises from 1.68% for low-volatility stocks to 3,76% for high-volatility stocks, a pattern consistent with the option model. Moving down Panel A toward larger programs, we see that the highest announcement returns are observed in those portfolios having the greatest volatility. In three of the four comparisons. the difference is significant at least at the 0.05 level. To a large degree, the evidence in this panel is consistent with the implications of the exchange option model, For example, the second largest announcement return in Panel A (5.69%) is experienced by the portfolio with the largest volatility and the largest repurchase size. At the Name time, the second smallest announcement return (1.68%) is observed in firms with the smallest volatility announcing the smallest repurchase programs.
Table 5. Mean Repurchase Announcement Returns Using Two-Way Sorts
This table reports mean risk-adjusted returns (in percent) from two days following the repurchase announcements for portfolios formed using two-way sorts. Panel A reports portfolios formed by first sorting into quartiles on the basis of the fraction of shares announced for repurchase. Each of these quartiles is separately sorted into four portfolios on the basis of monthly standard deviation measured in the 36 months prior to the announcement. Panel B is formed similarly, on the second sort is done on the basis of R-square from a market model regression. Panel C forms portfolios first on the basis of monthly return standard deviation and secondly on the basis R-square, t-statistics (in parentheses) text whether the mean abnormal returns between extreme quartiles differ.
Panel A. Standard Deviation Fraction Repurchased Quartile 1 Quartile 2 Quartile 3 Quartile 1 1.68 1.41 3.68 Quartile 2 2.38 2.17 2.96 Quartile 3 3.00 3.47 3.11 Quartile 4 3.76 4.02 4.12 [Q.sub.1] - [Q.sub.2] 2.08 2.61 0.44 (t) (1.90) (3.04) (0.36) Panel A. Standard Deviation Differences [Q.sub.1] - Fraction [Q.sub.4] Repurchased Quartile 4 (t) Quartile 1 3.78 2.10 (3.79) Quartile 2 5.88 3.50 (4.13) Quartile 3 3.84 0.84 (1.31) Quartile 4 5.69 1.93 (2.00) [Q.sub.1] - [Q.sub.2] 1.91 (t) (1.12) Panel B. [R.sup.2] Fraction Repurchased Quartile 1 Quartile 2 Quartile 3 Quartile 1 2.84 3.61 2.46 Quartile 2 5.21 2.47 4.78 Quartile 3 4.01 3.21 3.70 Quartile 4 5.89 5.10 3.71 [Q.sub.1] - [Q.sub.2] 2.75 1.49 1.25 (t) (1.92) (1.03) (1.07) Panel B. [R.sup.2] Difference [Q.sub.1] - Fraction [Q.sub.4] Repurchased Quartile 4 (t) Quartile 1 1.62 -1.23 (2.80) Quartile 2 0.95 -4.26 (6.03) Quartile 3 2.50 -1.51 (2.44) Quartile 4 3.21 -2.37 (2.71) [Q.sub.1] - [Q.sub.2] 1.59 (t) (1.72) Panel C. [R.sup.2] Standard Deviation Quartile 1 Quartile 2 Quartile 3 Quartile 1 2.40 2.56 1.89 Quartile 2 3.94 2.67 2.94 Quartile 3 4.46 3.93 3.42 Quartile 4 7.13 4.63 5.60 [Q.sub.1] - [Q.sub.4] 4.73 2.07 3.71 (t) (3.32) (1.28) (2.95) Panel C. [R.sup.2] Differences [Q.sub.1] - Standard [Q.sub.2] Deviation Quartile 4 (t) Quartile 1 2.28 -0.12 (0.28) Quartile 2 2.95 -0.99 (1.51) Quartile 3 1.88 -2.58 (3.98) Quartile 4 2.10 -5.03 (5.06) [Q.sub.1] - [Q.sub.4] -0.18 (t) (0.12)
In Panel B, portfolios are formed by first ranking on the basis of the program size and then on the basis of [R.sup.2]. Holding the size of the program constant. announcement returns decrease as [R.sup.2] increases. Here. the highest abnormal return (5.89%) is observed in the firms with the lowest [R.sup.2] announcing the largest programs.
The last panel in thin table reports the mean market reaction to portfolios formed first on the basis of volatility and then on the basis of [R.sup.2]. Holding volatility constant, abnormal returns in the highest [R.sup.2] quartiles are consistently less than those in the smallest [R.sup.2] quartile. Holding [R.sup.2] constant, announcement returns tend to increase as price volatility increases. The exception to this generalization occurs in those portfolios having the highest [R.sup.2]. The option value in these programs is theoretically at a low point. Given the noise in security returns, measurement error in these subportfolios may be affecting our results. Nevertheless, the largest market reaction reported in this panel, 7.13%, occurs in the subsample having the highest volatility and the lowest [R.sup.2]. For this group, the average annualized standard deviation is 62%, while the average [R.sup.2] is 8.9%. These are stocks for which the option value embedded in repurchase programs would seemingly be greatest.
IV. Summary and Conclusions
Past research has identified a number of factors that may explain the positive announcement returns observed after buyback announcements: personal tax savings, wealth transfers from bondholders, improvements in capital structure, and signaling, in this paper, we add another explanation to this extensive list. This alternative explicitly recognizes that open market repurchase programs are not firm commitments. This attribute distinguishes this mechanism from other buyback mechanisms such as fixed-price offers, where the same tax savings, signaling, and other arguments pertain as well. Open market programs authorize managers to use their firm-specific knowledge to the benefit of long-term shareholders by quietly reacquiring shares at some point in the future when, in management's opinion, market prices may have deviated from "true" value. This discretion is valuable. We model this as an exchange option whereby the market price per share is exchanged for the true value of the firm. To the extent that prices are always fair, such options will be worthless. Yet if market prices are not always fair, open market share repurchase programs may be valuable, in this paper, we show that this can occur even if prices are fair at the time of the announcement and management has no superior information.
Using a large sample of announcements between 1980 and 1990, we show that the market reaction to open market repurchase programs is consistent with the predictions of the exchange option model. Announcement returns are directly related to the volatility of the stock and the fraction of shares to be purchased. The market reaction is negatively related with the correlation coefficient between stock returns and market returns. Viewing this correlation as a proxy for the relationship between the true value and market prices, firms announcing share repurchases with low correlations are cases in which the option to repurchase shares is most valuable.
Our analysis is in some ways similar to the "real" options literature, which shows that the option to wait for better information is valuable. Because repurchase programs are not firm commitments, managers have the option to wait for more information to arrive before actually deciding to repurchase shares. If stock prices do not increase above simply the expected operating cash flows of the firm to reflect the value of this option, a "free lunch" of sorts would exist for long-term investors as they would expect to earn positive abnormal returns by holding the stock until after the program expires.
Of course, the repurchase option hypothesis explored in this paper need not solely explain the market reaction to open market buyback announcements. Indeed, the evidence presented here is also consistent, at times, with other explanations, such as the signaling hypothesis. For example, one might argue that the signaling hypothesis also predicts that the information content may be greater in firms announcing larger buyback programs or in firms with high firm-specific risk. Indeed, on occasion, managers explicitly state when the programs are initialed that the buyback is motivated by perceived underevaluation. However, other aspects seem inconsistent with traditional signaling stories. Foremost of thane In that the inherent flexibility which gives rise to the exchange option by definition makes them less appealing as credible signals, particularly when other, more credible repurchase mechanisms exist. Moreover, it would appear difficult to explain using traditional signaling stories why thousands of firms have adopted these programs in recent years and also why many programs are not completed.
Although we estimate that currently more than 2,000 US firms have an option in place to buy back their own shares, one may ask why all companies do not adopt open market programs if they contain valuable options and are simple to enact. There are several answers to this question. First, the option value generated in the typical repurchase program where signaling is not involved is not much larger in scale than the noise observed in daily stock prices. Thus, adopting an open market repurchase program may not strike some managers as a pressing issue to immediately raise to their board, particularly when market prices may be fair. Second, the decision to exercise repurchase options requires company resources, in firms where resources are rationed, the firm's ability to exercise the options may be limited, thus reducing their value and making them unattractive, relative to other, real options (see Myers and Majluf, 1984). Share repurchase programs will be appealing to firms with excess debt capacity, excess cash, few growth opportunities, and, as the exchange model suggests, a potential for mispricing. Finally, the option to repurchase shares is only valuable to the extent that managers can detect valuation errors, if managers lack the ability to correctly detect deviations between market prices and "true" value, then the options will again be of little value, in these cases, managers may be as likely to buy overvalued shares to the detriment of long-term shareholders as they are to buy undervalued shares to the benefit of long-term shareholders. Of course, in cases where managers perceive that mispricing is extreme, even managers in firms with large agency costs or attractive growth opportunities may find it beneficial to authorize a repurchase program. These companies will follow a wait-to-adopt approach. Yet generally speaking, such an approach will not be optimal if companies are to capitalize on such temporary mispricings. Indeed, in contrast to the signaling literature, our model suggests that companies, if they are to benefit long-term shareholders, may wish to authorize open market programs in advance of any perceived mispricing.
(1) See, for example, Comment and Jarrell (1991); Dann (1981); Ikenberry, Lakonishok, and Vermaelen (1995); and Vermaelen (1981).
(2) See, for example, Dann (1981); Vermaelen (1981); Asquith and Mullins (1986); Ofer and Thakor (1987); Constantinides and Grundy (1989); and Haunch and Seward (1993).
(3) For example, Netter and Mitchell (1989) find evidence that many programs announced following the Crash of 1987 were not initiated. Although the crash was perhaps an unusual period of time, Wiggins (1994) finds similar results during the period from January 1988 to December 1990. He reports that fewer than 50% of the 193 NYSE and ASE companies that announced a repurchase program during this period, reported a decline of more than 0.5% in shares outstanding nine months following the announcement. Usem, Shulman, and Brown (1995) report that in 1994, S&P 500 companies bought back only 18% of the $46 billion in announced share repurchases. Stephens and Welsbach (1995) also report that a significant fraction of the firms in their sample never repurchased any shares in the three years after the announcement.
(4) In earlier years, this was not true. Prior to SEC Rule 10b-18 enacted in November 1982, ambiguity existed in the law as to whether firms repurchasing shares might be subject to prosecution for price manipulation. Subsequent to the adoption of Rule lob-18, this ambiguity was largely resolved. Since then, open market programs have become more prominent. Vermaelen (1981) finds 243 open market repurchase announcements between 1970 and ending 1978, approximately 27 programs per year. Between 1990 and 1995, more than 600 programs were announced each year on average.
(5) Securities Data Corporation, New York.
(6) Rule 10b.18 harbors firms from accusations of price manipulation while conducting open market transactions. The rule specifies 1) that trades are made through only one broker, 2) that none of the trades are made as the opening transaction or during the last half hour of trading on any given day, 3) that none of the trades may be completed at a price exceeding the highest current independent bid price or the last independent sale price, whichever is higher, and 4) that the total of such purchases in a day does not exceed 25% of the average daily trading volume for the preceding four weeks. Here, average daily volume excludes large block transactions.
(7) This would appear to explain why trading volume does not substantially increase after repurchase programs are established. In our sample overall, mean monthly trading volume in the year prior to open market program announcements was 6.4%, In the year following the announcement, it was 6.3%. This result holds even for large programs. For those programs for more than 10% of shares outstanding, mean monthly volume prior to the announcement was 7.9% and 7.4% afterward.
(8) This assumption leans in favor of efficiency. On the other hand, a lengthy debate exists as to whether market prices exhibit excess volatility. A few examples are Shiller (1981, 1990 and 1993): Flavia (1983); Pound and Shiller (1987): Bulkley and Tonks (1992): Kuplec (1992): Shiller, Kothari, and Shanken (1993): and Pontiff (1994).
(9) For Nome diverging views on this issue, see for example, Ball (1990); Black (1986): Fama (1991); Haugen and Baker (1995); Lakonishok, Schleifer, and Vishny (1994); and Roll (19##).
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Appendix. Valuing the Option to Repurchase Stock
Define V as the "true" fundamental value of the stock (known to management) and define S as the market price of a share. Assume that the rate of return on both values is given by
(A1) dS/S = [[Alpha].sub.s]dt + [[Sigma].sub.s][dz.sub.s]
(A2) dV/V = [[Alpha].sub.v]dt + [[Sigma].sub.v][dz.sub.v]
where [dz.sub.i] (i = V, S) is a Wiener process and [[Sigma].sub.i] is the standard deviation of the rate of return on asset i. By
employing the arbitrage argument that the position of an option buyer is similar to a dynamic trading strategy involving buying the true value of the share and shorting the stock traded in the market, Margrabe (1978) shows that the value of the option to exchange S for V is equal to
(A3) W(V,S,t) = VN([d.sub.1]) - SN([d.sub.2])
(A4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(A5) [d.sub.2] = [d.sub.1] - [Sigma][square root of t]
N([multiplied by]) is the cumulative standard normal density function, and t is the maturity of the option. The return variance on a portfolio involving a long position in the true value and a short Position in the market value of the stock, [[Sigma].sup.2], is equal to:
(A6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [[Rho].sub.sv] is the correlation coefficient between the observed market rate of return on the stock and the true rate of return. Note that the larger the correlation between the market rate of return and the true return, the lower the value of the option. This correlation can be viewed as a measure of efficiency. If the observable market price of the stock always equals the unobservable true value (i.e. S equals V at all times), then [[Rho].sub.sv] will be one and the value of the option will be zero as [[Sigma].sub.s] equals [[Sigma].sub.v].
In order to predict the market response to buyback programs, redefine V as the market value per share (assessed by long-term shareholders) after the repurchase announcement and S as the market price per share before the repurchase announcement. Note that V is smaller than the stock price after the announcement because the stock price will reflect the value of the option to take advantage of undervaluation in the future. Let us also redefine [[Sigma].sub.s], [[Sigma].sub.v], and [[Rho].sub.sv] as long-term shareholders' assessment of the volatility of the stock return based on market prices, the true volatility of the stock return, and the correlation between the true rate of return and the observed market rate of return on the stock, respectively. Note that as could be different from [[Sigma].sub.v]. For example, if long-term investors believe that stock markets are characterized by excess volatility, then [[Sigma].sub.s] [is greater than] [[Sigma].sub.v]. Hence, [[Sigma].sub.s], [[Sigma].sub.v]. and [[Rho].sub.sv] refer to the long-term investors' assessment of these parameters and may not equate to their actual values.
The announcement of a repurchase will have two effects according to Equation (A3). First, prices may increase if investors believe at the time of the announcement that insiders have superior information (i.e. that V is greater than S). This is akin to the classic argument that repurchases are information signals. Although this is, of course, clearly Possible, we focus exclusively on the second effect. Namely that even if prices are fair at the announcement and V equals S, the market reaction may still be positive as long as there exists some possibility in the future that management will recognize when market prices have diverged from true value. We refer to this as the option value of open market share repurchase programs, or more simply, the "repurchase option."
If the market perceives prices to be fair at the time of an open market share repurchase announcement, what is the value of the repurchase option? The answer to this question can be obtained by setting V equal to S in Equation (A3). In this case, the option value simplifies to:
(A7) W = S[2N([d.sub.1]) - 1]
(A8) [d.sub.1] = 1/2[Sigma][square root of t]
Note that this value derives from the ability to exchange the market price of one share for the true value of one share. As pointed out earlier, a repurchase program to buy [n.sub.p] shares out of [n.sub.o] shares outstanding creates, per share outstanding, a fraction [n.sub.p]/([n.sub.o] - [n.sub.p]) of this option value. Hence, the return at the announcement of a share repurchase due only to the option effect should be equal to:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where F is equal to [n.sub.p]/[n.sub.o]. The return is positively related to the fraction of shares the company plans to repurchase, the maturity of the option, the volatility of the true return, and the market return on the stock, it is negatively related to the correlation between the true return and the market return.
The authors are grateful to Pedro Santa Clara Gomes. Raghavendra Rau, Pat Armentor, and Chuck Burge for research assistance; and to Phelim Boyle, George Constantinides, Jeff Fleming, Paolo Fulghieri, Pekka Hietala, Josef Lakonishok George Kanatas, Steve Kaplan, Barb Ostdiek, Jesus Saa-Requejo, Richard Shockley, and an anonymous referee for helpful suggestions. We have also benefited from comments by seminar participants at the University of Chicago, INSEAD, ESSEC, and Erasmus University. This paper has been presented at the 1995 French Finance Association meetings tn Bordeaux. the 1995 European Finance Association meetings in Milan, and the 1996 American Finance Association meetings in San Francisco.
David L. Ikenberry is an Associate Professor of Finance at Rice University. Jones Graduate School. Theo Vermaelen is a Professor of Finance at the European Institute of Business Administration (INSEAD) and at the University of Limburg.
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|Title Annotation:||includes appendix|
|Author:||Ikenberry, David L.; Vermaelen, Theo|
|Date:||Dec 22, 1996|
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