SEOs, Real Options, and Risk Dynamics: Empirical Evidence

Transcription

1 SEOs, Real Options, and Risk Dynamics: Empirical Evidence Murray Carlson, Adlai Fisher, and Ron Giammarino The University of British Columbia March 15, 2007 Abstract This paper investigates the dynamics of firm level beta and volatility around seasoned equity offerings. Beta increases prior to the SEO and decreases thereafter. This pattern is generally consistent with a real options explanation of SEO underperformance, but existing models predict a sharp risk drop, while we find a gradual decline. To reconcile this difference, we extend the theory to consider investment commitment and internal financing. In the cross-section, we show that firms with high prior return runups experience larger post-issuance underperformance, as well as more substantial post-issuance declines in beta. By contrast, large market-wide runups, which might be taken as a measure of sentiment, do not precede either postissuance underperformance or post-issuance beta declines. Finally, equity issues coincide with low points in both own firm and market-wide volatility, suggesting the possibility of volatility timing in corporate financing activities. Sauder School of Business, University of British Columbia, 2053 Main Mall, Vancouver, BC, V6T 1Z2. We thank for their helpful comments Felipe Aguerrevere, Michael Brandt, Alon Brav, Thierry Foucault, Francesco Franzoni, Cam Harvey, Ulrich Hege, Robbie Jones, Pete Kyle, Pierre Mella-Barral, Mark Ready, Andrew Roper, Eduardo Schwartz, Bob Whaley, Toni Whited, and seminar participants at Duke University, HEC Paris, Queen s University, the University of British Columbia, the University of Calgary, the University of Waterloo, the University of Wisconsin-Madison, the 2005 Bank of Canada Workshop in International Financial Markets, and the 2005 Northern Finance Association Meetings. Support for this project from the Social Sciences and Humanities Research Council of Canada (grant number ) and the UBC Bureau of Asset Management is gratefully acknowledged. Electronic copy of this paper is available at:

2 SEOs, Real Options, and Risk Dynamics: Empirical Evidence Abstract This paper investigates the dynamics of firm level beta and volatility around seasoned equity offerings. Beta increases prior to the SEO and decreases thereafter. This pattern is generally consistent with a real options explanation of SEO underperformance, but existing models predict a sharp risk drop, while we find a gradual decline. To reconcile this difference, we extend the theory to consider investment commitment and internal financing. In the cross-section, we show that firms with high prior return runups experience larger post-issuance underperformance, as well as more substantial post-issuance declines in beta. By contrast, large market-wide runups, which might be taken as a measure of sentiment, do not precede either post-issuance underperformance or post-issuance beta declines. Finally, equity issues coincide with low points in both own firm and market-wide volatility, suggesting the possibility of volatility timing in corporate financing activities. JEL Classification: G31, G32 Keywords: Seasoned Equity Offering, Real Options, Dynamic Risk, Dynamic Beta, Investment Commitment, Time-to-Build, Volatility Timing Electronic copy of this paper is available at:

3 1. Introduction The pattern of stock returns through seasoned equity offering (SEO) episodes has attracted a great deal of interest and research. Summarizing a large literature, 1 Ritter (2003) reports an average return of approximately 72% in the year prior to announcement, a two-day cumulative return of -2% around the announcement date, and underperformance of about 5% per year in the five years subsequent to issuance. Two views of these facts are emerging. Behavioral theories explain that pre-issuance run-up relates to overweighting of positive news; that managers (either deliberately or also through excessive enthusiasm) issue equity while stock prices are high; and that markets only partially react to the SEO announcement, permitting slow learning and long-run underperformance. 2 By contrast, real options theories explain that seasoned equity offerings are associated with real investment, optimally timed to occur after growth options move into the money and stock prices increase. Since the real options theory incorporates rational expectations, announcement of a seasoned offering impacts prices fully and immediately. Apparent long-run underperformance occurs because exercising (or deleveraging) a growth option causes an immediate reduction in asset risk. 3 The behavioral and real options theories explain the same set of average return facts, but have different implications for risk. In particular, current behavioral theory does not address how risk should evolve through the SEO episode. By contrast, a real options explanation suggests that risk loadings should increase prior to issuance, as optimally timed investment approaches and growth option leverage rises. Further, undertaking investment should cause risk to decline as growth option leverage falls. In this paper, we present new evidence on the dynamics of firm level risk throughout 1 Evidence on long-run performance is given by Brav, Geczy, and Gompers (2000), Clarke, Dunbar, and Kahle (2001), Eckbo, Masulis, and Norli (2000), Loughran and Ritter (1995), Lyandres, Sun, and Zhang (2005), Mitchell and Stafford (2000), and Spiess and Affleck-Graves (1995). Announcement effects are studied by Asquith and Mullins (1986), Masulis and Korwar (1986), Mikkelsen and Partch (1986), and others. Evidence of pre-seo stock price run-up is given by Korajczyk, Lucas, and McDonald (1990) and Loughran and Ritter (1995). Eckbo and Masulis (1995) survey the earlier literature. 2 Daniel, Hirshleifer, and Subrahmanyam develop a comprehensive behavioral theory of SEO episode returns. Loughran and Ritter (1995), Bayless and Chaplinsky (1996), and Baker and Wurgler (2002) give more informal discussions of windows of opportunity and market timing. Baker, Ruback, and Wurgler (2004) survey the behavioral corporate finance literature. 3 Carlson, Fisher, and Giammarino (2006) develop a comprehensive real options theory of SEO episode returns. This theory is broadly linked to contributions by Berk, Green, and Naik (1999), Brennan and Schwartz (1985), Carlson, Fisher, and Giammarino (2004), Cooper (2006), Gomes, Kogan, and Zhang (2003), Kogan (2004), Lucas and McDonald (1990), McDonald and Siegel (1985), Pastor and Veronesi (2005), and Zhang (2005a,b). 1

4 the SEO episode. Recent research, including Anderson and Garcia-Feijoo (2006) and Xing (2002), aims to test the real options theories of Berk, Green, and Naik (1999) and others by exploring whether investment explains the value premium. We instead directly test one of the primary predictions of real options theories, which is that risk loadings should change as real options move into or out of the money, and as they are exercised. Our principal empirical finding is that beta changes dramatically in the period around seasoned equity offerings. In particular, beta increases prior to the SEO announcement and decreases after issuance. We document this result using a sample of over 3,500 seasoned equity issuances over a twenty year period. Our base results use monthly betas calculated from daily data, following the high-frequency or realized beta approach used by Lewellen and Nagel (2005), Andersen, Bollerslev, Diebold, and Wu (2005), and Ghysels and Jacquier (2005). 4 We show that the basic results are robust to calculating beta over longer time periods, and to using leads and lags of the data to control for microstructure issues as in Dimson (1979). The pattern we find in beta is generally consistent with the predictions of the real options theory, but the existing stylized model predicts an immediate decline upon issuance, while we find a gradual decline over a period of three years. The model prediction derives from a strong assumption that when a growth option is undertaken, expansion takes place instantly and is entirely financed by an SEO that is registered and sold simultaneously. To reflect more realistic assumptions, we extend the basic real options model of SEO episode returns to include: 1) investment commitment or time-to-build, and 2) non- SEO equity financing through retained earnings and employee equity compensation. We assume that expansion requires a lumpy immediate investment, financed by an SEO, and further commits the firm to invest at a fixed rate over a fixed period of time. This additional commitment is financed by future operating cash flows, i.e., retained earnings. 5 Committing to future investment instantly raises the risk of the firm. Intuitively, investment commitment (time-to-build) engages the firm in a forward contract where 4 The term realized betas is used because of the analogy with realized volatility calculated from high frequency observations. The realized volatility approach is developed and used by Schwert (1989), Andersen and Bollerslev (1998), Andersen, Bollerslev, Diebold, and Ebens (2001), and many others. 5 If operating cash flows are not sufficient to cover the expansion commitment, we assume the firm can use stock compensation to employees, or stock sales to the company pension plan, to make up the difference. Our results do not change substantially if the company uses short-term debt financing to cover temporary cash flow shortfalls. 2

5 the cash flows to be received (future profits) have much higher risk than the cash outflow commitment (capital investment costs). 6 As the firm pays down the investment commitment over time, beta gradually drops. Thus, even without new equity issuances, risk gradually falls as the firm plows back operating cash flows to pay down expansion costs. The second major empirical issue we address is whether cross-sectional variations in SEO underperformance and post-seo beta change are consistent with the behavioral and real options theories. Both theories suggest that larger runups should lead to greater post-issuance underperformance, and we find support for this prediction in the data. An additional implication of the real options theory is that larger runups should lead to a larger post-seo decline in beta. We again find considerable support for this prediction in the data. The existing behavioral literature does not make any direct predictions about second moments in relation to SEOs. It is natural, however, to consider that sentiment waves might jointly drive both market runups and SEO issuance. 7 As sentiment becomes a more important part of valuations during a market runup, firms with high sentiment exposures will experience beta increases. After the bursting of a bubble, these same firms will then covary less with the market. In contradiction of this hypothesis, however, we find that large market runups predict less SEO firm underperformance and smaller post-issuance declines in SEO firm betas. The third major empirical issue we address is whether volatility dynamics around the SEO are consistent with real options theories. Since real option leverage applies equally to priced and unpriced risk, predictions about risk dynamics carry through to total volatility. We thus expect that total volatility should increase prior to SEO announcement and decrease after issuance. We calculate monthly realized volatilities using daily returns, following Schwert (1989), and find that these decrease prior to issuance and increase thereafter, over a period of several years. This finding is robust to accounting for microstructure issues by filtering out first-order autocorrelations as in Andersen, Bollerslev, Diebold, and Ebens (2001). Volatility dynamics thus contradict the basic real options model of seasoned offerings. 6 The effect of investment commitment on discount rates was first recognized in a capital budgeting context by Rice and Black (1995) in an unpublished working paper. Subsequent research has not used this insight. 7 Barberis, Shleifer, and Vishny (1998) provide a model of investor sentiment. Although not in the SEO context, Barberis, Shleifer, and Wurgler (2005) discuss comovement as a consequence of sentiment. 3

6 To better understand these volatility dynamics, we examine the volatilities of matched firms as well as market aggregates, and find that equity issues tend to occur during times of relatively low market volatility. This volatility timing phenomenon has at least two potential explanations. 8 First, issuers may prefer to come to market during times of relative stability, in order to face less uncertainty regarding the final pricing of the issue. An alternative is that the volatility of fundamentals is stochastic, rather than constant as in existing literature. In this case, managers have a rational motivation to endogenously time issuance at points of low volatility, since the option value of waiting is smaller when volatility declines. Our work relates to previous studies that examine whether risk changes discretely at the time of equity issuance due to financial leverage, as suggested by Hamada (1972). For instance, Healy and Palepu (1990) find that beta increases after an SEO, while Denis and Kadlec (1994) argue that after accounting for potential microstructure effects, risk falls slightly following an SEO. The focus of these papers is much different than ours, because financial leverage suggests a one-time change in risk. These studies thus examine only the change in beta from pre- to post-issuance over relatively short one-year windows. Our analysis uses a much larger sample, and analyzes dynamics throughout a variety of windows. We robustly find an increase in beta prior to the SEO and a decrease thereafter. Another related literature examines the link between real investment and expected returns. Authors including Anderson and Garcia-Feijoo (2006), Lamont (2000), Polk and Sapienza (2004), Titman, Wei, and Xie (2004), and Xing (2002) show that firms with higher investment rates tend to experience lower subsequent stock market returns. Many authors attribute these findings to inefficient investment caused by managerial empire-building or managerial overoptimism. Theories of optimal real investment (e.g., Carlson, Fisher, and Giammarino, 2006; Zhang, 2005b) have recently argued the ability to account for the same facts. Lyandres, Sun, and Zhang ( LSZ, 2005) add to the empirical evidence by showing that creating a long-short portfolio based on investment rates gives a priced factor that helps to reduce SEO underperformance. LSZ recognize that distinguishing between empire building and optimal real investment is difficult based on returns and investment rates alone. They therefore use corporate governance indices as a way to try to distinguish the two theories, and find partial support for the optimal real investment theory. Our approach is to instead directly examine the risk implications of the two theories. 8 Fleming, Kirby, and Ostdiek (2001) consider volatility timing in a dynamic asset allocation setting. Our results suggest that volatility timing may also be an important consideration for corporate managers. 4

7 Several recent studies complement our findings regarding risk dynamics. In particular, Campbell, Polk, and Vuoltenahu (2005) and Taliaferro (2005) show that beta is lower after periods of high corporate investment. Further, Brav, Michaely, Roberts, and Zarutskie (2005) find that bank loan spreads decrease following seasoned offerings. 9 These results are consistent with the real options theory that motivates our empirical work. The plan of our paper is as follows. Section 2 describes the primary behavioral and real options hypotheses in more detail. Section 3 describes the data and sample construction. Section 4 documents our main findings regarding dynamics in returns and beta, and explains how accounting for investment commitment and internal financing affects the real options theory. Section 5 examines the post-seo underperformance and beta dynamics in the cross-section. Section 6 examines volatility dynamics. Section 7 concludes. 2. The Behavioral and Real Options Theories This section discusses the basic behavioral and real options theories, and their implications for SEO firm risk and return. We begin with the behavioral theories, and then present a very simple theory of dynamic risk due to changing real option leverage Behavioral Theories The leading behavioral descriptions of SEO underperformance include Daniel, Hirshleifer, and Subrahmanyam ( DHS, 1998) and the windows of opportunity and market timing theories of Loughran and Ritter (1995) and Baker and Wurgler (2002). These models rely on cognitive biases and persistent mispricing to explain SEO return patterns. The intuition supporting behavioral models is compelling. Research in psychology establishes that individuals tend to be overconfident about their own abilities. Research also shows that individuals overweight evidence confirming their prior beliefs, and underweight contradictory evidence. This is called biased self-attribution. DHS present a rigorous and complete theory of mispricing based on these findings. Overconfidence is modelled as a belief that the precision of private signals is higher than it actually is. 9 Other authors have given some evidence of changes in risk around other types of securities issuance. For example, Lewis, Rogalski, and Seward (2002) find that asset risk tends to decrease after convertible debt issuances. Loughran and Ritter (1995) find that beta declines for three years subsequent to an IPO. 5

8 Biased self-attribution is introduced by assuming that overconfidence increases after an investor receives a public signal that is consistent with their private signal. As a result, prices overreact to private signals, and further overreaction occurs when confirmatory public information is released. DHS also derive implications for event studies. They allow an informed, rational manager to take advantage of overvalued shares through share issues. As with prior adverse selection models (e.g., Myers and Majluf, 1984), DHS assume that investors are aware of the motives of managers. The SEO episode as characterized by this theory thus consists of the following: SEOs are preceded by investors receiving positive private signals and confirmatory public signals that cause overreaction and inflated stock prices. Managers then sell shares, but because this is contradictory public information, investors underreact to it due to biased self-attribution. Prices thus remain higher than their fundamental value even after the public issuance decision, and investors then learn slowly about the overvaluation through subsequent private or public signals, which tends to drive prices back down to their fair value over time. For our purposes, the important fact about this behavioral explanation is that it relates return movements to factors other than priced risk. Thus, while the behavioral theory gives strong implications for returns, any evidence of dynamic risk would seem to be outside the scope of its predictions A Basic Real Options Theory of Dynamic SEO Returns In recent literature, theories of real options and real investment have been used to explain a number of financial anomalies. (See, e.g., Berk, Green, and Naik, 1999; Carlson, Fisher, and Giammarino, 2004; Cooper, 2005; Gomes, Kogan, and Zhang, 2003; Kogan, 2004; Lucas and McDonald, 1990; Pastor and Veronesi, 2005; Zhang, 2005a,b). In the context of seasoned equity offerings, Carlson, Fisher, and Giammarino ( CFG, 2006) develop of model of risk and return dynamics throughout the runup, announcement, and post-issuance period. We summarize here a simplified version of this model and its implications. A single all-equity firm begins at t = 0 with fixed output level q 0, and has one option to irreversibly expand output to q 1 >q 0 by paying an amount λ>0. The firm pays out all cash flows instantaneously as dividends, and all financing of new projects must be raised from investors through a seasoned equity offering. For t 0, and i {0, 1}, cash flows are given by X t q γ i 6

9 where X t is a state variable. Under the risk neutral measure, X t follows dynamics dx t =(r δ)x t dt + σx t dẑ t, where r is the risk-free rate, δ>0isaconstant, 10 σ is volatility, and ẑ t is a standard Brownian motion. For convenience, we assume that the cash flows of the firm have a beta of one; i.e., beta measures exposure to X risk. Under these assumptions, the firm optimally expands when the state variable X t hits the boundary x at stopping time τ. Prior to expansion, CFG show that firm value is given by V 0 (X t )= X tq γ 0 δ + ( ) ν Xt ε, (1) x where ν>1 is a constant related to the exogenous parameters of the model, and ε can be interpreted as the incremental value of the expansion when optimally undertaken. In this equation, the first term corresponds to the growing perpetuity value of assets in place. The second term, which we denote V0 G, corresponds to the value of growth options. The risk of the firm prior to expansion is β 0 =1+ V 0 G (ν 1). (2) V 0 The first term corresponds to the beta of assets in place, which was assumed equal to one. The second term captures the risk of the growth option, and is strictly greater than one, reflecting the leverage implicit in a real option. Prior to expansion, if demand X t grows towards x from below, the value of the growth option V0 G increases as a percentage of the total value of the firm. This implies that the beta of the firm increases as the option moves into the money, reaching its maximum just prior to exercise of the growth option. At the instant of expansion and issuance of seasoned equity, the beta of the firm changes by the amount β = V 0 G(x) (ν 1) < 0. V 0 (x) SEO issuance associated with investment thus leads to a drop in beta, by an amount proportional to the value of the growth option relative to the total value of the firm. 10 Under the objective probability measure, one can think of δ as the difference between the required return on X risk and the actual growth rate of X. 7

10 As opposed to previous theories of changes in risk at the time of equity issuance (e.g., Hamada, 1972), this theory does not rely on changes in financial leverage. The firm is entirely equity financed, and the investment associated with the SEO causes a more fundamental change in the total firm (or asset) beta. We also note that beta need not be market beta; it is a measure of exposure to any priced risk in the state variable X. The theory thus does not require any particular asset pricing model to hold. 3. SEO Data and Stated Use-of-Funds Our source for identifying seasoned equity issuers is the SDC New Issues database. Because we are motivated partly by the investment-based real options theory, we seek to specifically identify equity offerings used to finance new investment. To accomplish this, we categorize press releases at the time of the issuance into different stated-use-offunds categories. Since subjective categorization would be time consuming and open to potential biases, we seek a more objective classification method. Recent research (e.g., Antweiler and Frank, 2004) explores the use of natural language algorithms to provide new data sources in finance. 11 A straightforward approach, which we follow, is to define keywords associated with a category, and to search a relevant set of documents for these keywords. Our source for stated use-of-funds data is the Business News Wires ( news wires ) segment of the Lexis/Nexis database. To link this with the SDC New Issues database, we searched the news wires in a one year window centered around the issuance date for a combination of the company name and any of the keywords stock, equity, or issue. All returned documents were then manually scanned for information regarding 1) The first announcement date of the issuance, and 2) the stated use-of-funds. Any potentially useful portions of the news releases were recorded into a database. We first use this new data to refine the SDC announcement date of the issuance. Specifically, we redefine the announcement date as the earlier of a) the SEC filing date for the issuance given by SDC, and b) the earliest news wire mentioning the issuance. Second, we create a new data item for the stated use of funds. To generate this variable, we defined the following six categories and associated keywords (in italics): Capital Investment (INV): research, expan, propert, expenditure, construction, develop, build, equip; Acquisition Financing (ACQ): merge, acqui; 11 We thank Murray Frank for helpful discussions on devising the classification system. 8

11 Working Capital (WC): working, inventory, receivable; General Corporate Purposes (GC): general corporate purpose; Debt (D): debt, loan, credit, bank, repay, note, bond, borrow, debenture, redeem; No Information (NI): none of the above. We note that this classification is not mutually exclusive, so observations can belong to more than one category. We checked each classification to ensure that the keyword generating the match was being used in the sense intended by the classification. Our final sample begins in 1980, when large scale coverage of news wires on Lexis/Nexis becomes available, and ends in We exclude from our sample financial firms (SIC = 6XXX), utilities (SIC = 49XX), and pure secondary issues. We also restrict the sample to common shares traded on the NYSE, AMEX, or NASDAQ. The final sample includes 3,611 SEO firms. We also match each sample firm by size to a non-issuing firm from the CRSP database. Additional data on firm characteristics for sample firms and matches was obtained from SDC. 4. Mean Return and Risk Dynamics Around the SEO This section reports average return patterns and beta dynamics for our sample of SEO firms. The behavioral and real options theories match the average return patterns documented in previous literature and confirmed in our sample. They are thus indistinguishable in this regard. The theories can, however, be distinguished by their implications for risk. We document an increase in beta prior to the SEO, and a slow decrease thereafter. This seems inconsistent with the behavioral theory, and also does not match the simple real options theory in Section 2, which predicts an immediate decline in beta. We show that commitment to future investment, combined with financing from retained earnings to pay down this commitment, can explain a slow decline in risk for investing firms Average Return Dynamics We first document the average return pattern for our sample. Table 1 shows the runup, announcement effect, and buy-and-hold returns over intervals of six months, one, three, and five years after issuance for sample firms and matches. Results are reported for all sample firms and by use-of-funds subcategory. The data demonstrate the same general 9

12 patterns that have been reported previously in the literature: a substantial runup in the one year prior to issuance (100%), negative announcement effect in a three day window (-2.12%), and underperformance over long horizons relative to a matched sample (56% vs. 84% at five years). The average runup in our sample is large relative to previous studies, perhaps due to our inclusion of late 1990 s data. We also consider differences in runups across use-offunds subcategories: The lowest runups are for firms issuing to retire debt, which is not surprising since at least some of these firms are engaging in deleveraging recapitalizations as a response to financial distress. Given this motivation, the average runup in this category is surprisingly high (94%). Acquirers also have relatively low runups (94%), while firms investing in working capital have the largest runups (115%). Firms that are investing (108%), using funds for GCP (106%), and for which there is no information (106%) are in between. Announcement effects are most negative for firms issuing to retire debt (-2.4%), and least negative for firms with no information on the use of funds (-1.53%). The latter result appears surprising, but may be due to imprecise measurement of the announcement date when news wires of the announcement are not available. Five year post-issuance returns are lowest for firms with no information (41%) and retiring debt (52%), and highest for firms investing in working capital (72%) and for general corporate purposes (70%). The dynamics of the underperformance have not been emphasized in previous literature. In particular, for the first six months after the SEO, the sample firms outperform the matches by a substantial margin (8.1% to 5.3%), and this result is robust across subsamples. By the time one year has passed, the returns are closer with the SEO firms still outperforming (11.9% vs. 10.7%). This suggests that the matched sample makes up ground over the second six month period. We thus conclude that underperformance does not begin until six months after the equity offering takes place. Progressing to longer post-issuance horizons, the underperformance seems strongest three years after the issuance, when all categories underperform the matched sample by a significant amount. Investing firms have the lowest returns after three years (19%) as opposed to returns closer to 30% for the other categories. By five years after issuance, the underperformance has not increased substantially. Combining this set of facts, we conclude that most of the SEO underperformance takes place between six months and three years after the issuance date. 10

13 4.2. Average Beta Dynamics We now investigate whether movements in beta appear consistent with behavioral or real options theories. We would like to see how average SEO firm risk evolves through event time, and thus divide our sample period into twenty-one trading day periods ( months ) prior to the announcement and after issuance. We consider as a single period the interval between announcement and issuance, regardless of how long that interval is. Following the logic of realized or high-frequency betas, 12 in each month we regress log returns on a constant and the log return of the value-weighted CRSP index. As suggested by Scholes and Williams (1977), we aggregate returns across any days in which trading volume is zero, which helps to alleviate some of the problems associated with asynchronous trading. We apply this methodology to the base results described in this section, and in the following section we address additional robustness issues related to asynchronous trading. Our empirical approach has some similarities with Healy and Palepu (1990), and Denis and Kadlec (1994), who test for a discrete change in risk at the time of issuance. These studies also use daily data to estimate betas, but they confine their analysis to the one year period before issuance and the one year period after issuance. Their preissuance periods thus include the time between announcement and issuance. We view this period as fundamentally different, and treat it separately. Second, we calculate betas in a range of window sizes, including months and years. Third, we consider a much longer window of event time, and find interesting beta dynamics several years before announcement and after issuance. Finally, our sample size of over 3,500 firms over 20 years is considerably larger than either previous study. Figure 1a displays our average monthly beta estimates, across all sample firms, for the ten year period of event time centered on the SEO. In this graph, the value of zero on the horizontal axis corresponds to the time period between announcement and issuance; all positive numbers are months after issuance; and all negative numbers are months prior to announcement. We find that betas do not change substantially until two years before the SEO. A slight increases in beta for year -2 is followed by a larger increase in the year prior to the SEO. Beta continues to increase sharply until roughly two months after the SEO, when beta peaks, and then declines until approximately three years after issuance. At this point, beta is about the same as five years prior to the announcement. 12 See, for example, Andersen, Bollerslev, Diebold, and Wu (2005), Ghysels and Jacquier (2005), and Lewellen and Nagel (2005). 11

14 Risk thus changes considerably throughout the SEO episode, which seems outside the scope of the behavioral explanation of seasoned offerings. The general pattern of an increase in risk before announcement and a decline after issuance has similarities with the basic real options theory presented in Section 2. On the other hand, the real options theory implies an immediate reduction in risk after the firm instantaneously and simultaneously issues shares and expands, but we observe a gradual decline in beta empirically. We discuss in Section 4.5 how to account for gradually declining risk by allowing time-to-build and a gradual reduction in investment commitment as operating cash flows fund the continuing expansion. As a final characterization of the SEO episode, we present, in Figures 1b and 1c, beta dynamics by use-of-funds subsample. All categories show similar beta dynamics, increasing prior to issuance, peaking just after issuance, and gradually declining thereafter. Firms investing in real assets, working capital, acquisitions, and for general corporate purposes appear similar, with the acquirers having a slightly lower beta all around. Firms retiring debt appear to have a less pronounced increase and subsequent decrease in beta. The NI firms have a more sudden increase in beta on the SEO date. The risk patterns for the full sample and for most subsamples reject the hypothesis that risk does not change through an SEO episode Robustness of Average Beta Dynamics This section establishes that accounting for asynchronous trading effects does not significantly alter our view of beta dynamics. A common method of addressing potential illiquidity in SEO stocks is to calculate betas using the method of Dimson (1980). For example, Denis and Kadlec (1994) regress SEO returns on 2, 5, 10, and 15 leads and lags of market returns, in addition to the contemporaneous market return. The idea is that if a small stock trades several days after some original news affects market returns, the covariance may be better captured by one of the lagged coefficients. Summing the regression coefficients across all leads and lags gives the Dimson (1980) sum beta. We follow Denis and Kadlec in choosing lag structures of 0, 2, 5, 10, and 15 days. We similarly calculate annual betas, but we examine 5 annual periods after the issuance, and 5 years prior to issuance. Figure 2, Panel A shows our primary results. The sum betas increase with the number of lags, demonstrating that some asynchronous trading does exist. The general dynamic pattern in beta does not seem to be affected, however. To further demonstrate that beta dynamics are not substantially related to microstructure issues, Panel B plots the difference in beta relative to event time year 1. This demonstrates clearly that the 12

15 general pattern of an increase in beta prior to issuance, and a decrease thereafter, is robust to removing asynchronous trading effects The Post-SEO Beta Decline and the Case of Starbucks The real options theory in Section 2 predicts that risk will increase prior to an SEO and decrease immediately after. This reflects an assumption that the expansion takes place instantly and is entirely financed by a simultaneous SEO. The beta dynamics documented above reject this theory, since risk remains high for several months after the SEO and then declines gradually over a period of about three years. The nature of the rejection is informative, however, because it suggests that something in the post- SEO period may be more complex than the simple model s description. In order to obtain insights into what the missing elements might be, we examine in more detail a leading sample firm, Starbucks. Starbucks was a private company until 1992 when it undertook an IPO. At the end of 1992 Starbucks had 165 stores. In 1993, the company issued debentures and ended the year with 272 stores. On October 6, 1994 the firm announced plans to open at least 200 new stores in fiscal The announcement was quite specific about the company s plans, indicating that stores would open in Houston, Dallas, and Atlanta in the first quarter of 1995 and Las Vegas and Philadelphia in the second quarter. A month later, on November 8, 1994, Starbucks announced the public offering of 5.5 million shares. It ended that year with 425 stores. In 1995, the company completed a second convertible debenture issue and ended the year with 676 stores. In 1996, Starbucks converted the first debt issue into equity and ended the year with 1015 stores. Finally, in 1997 the company converted the remaining convertible debt into common shares and ended the year with 1412 stores. Since that time the company has not raised funds through an underwritten equity issue though it does continue to issue stock options and issue shares to employees. It has also repurchased shares on several occasions. At year end 2004 the company had over 8,500 stores, 20 times the number of stores that it had after completing the SEO that appears in our data. Figure 3, Panel A presents a time line of investment (change in net plant / plant size), new equity and debt issues, and cash over total assets. We also plot our estimate of Starbucks beta through this period. It certainly seems that Starbucks exercised a growth option, and that the firm s IPO and SEO were important parts of this option exercise. Panel B provides additional details on capital expenditures and their financing. Panel B shows clearly that the expansion was not confined to the year of the IPO or the SEO. Since Starbucks announced a timetable and a location for store openings, 13

16 we can infer that it planned an expansion that would last for at least the year following the SEO. While it may have been possible to stop or scale back these plans, significant non-sunk costs would likely be incurred. To some extent, then, in addition to exercising options to expand immediately, firms enter into commitments for further expansion. Rice and Black (1995) point out the increase in risk that results when a firm commits to expand. We can think of an expansion commitment as a forward contract, where the cash flows to be received (future profits) have much higher risk than the cash outflow commitment (capital investment costs). Panel B also shows that non-seo sources of equity such as employee stock savings plans and internally generated funds were important sources of financing. 13 After the SEO, the first wave of new stores provided cash flows for the ongoing expansion. In particular, Panel B shows that cash flows from operations became a significant contributor to the financing of growth starting in Moreover, Starbucks had an employee share ownership plan throughout this period, and as the number of employees grew, non-seo equity sales also increased. In fact, non-seo equity sales in 1999 were larger than the IPO that launched Starbucks as a public company seven years earlier. In terms of risk dynamics, commitment-to-build and financing-over-time through retained earnings and employee equity participation has important implications. The commitment-to-build is itself risky. On the other hand, increasing equity through non- SEO channels reduces the risk of this commitment. As employee equity participation and internal financing capabilities grow, the risk of the commitment falls. Hence, a growth option with a commitment keeps risk high until the commitment is met and financed with equity. The next section formalizes these ideas Risk Implications of Investment Commitment and Internal Financing: An Extended Real Options Model This section extends the simple model of section 2 to incorporate 1) time-to-build 14 and 2) financing through non-seo sources including operating cash flows and employee stock and option compensation. We consider a realistic form of two-part expansion in which a lumpy up front investment is financed by an SEO, and continuing costs of investing at a fixed rate for a fixed period of time ( the building time ) are funded from other sources (e.g., internally generated cashflows). The expansion is thus not completed in a single instant, but instead output jumps discretely at the SEO date 13 Fama and French (2004) document the importance of non-seo equity issues, including employee options, grants, and benefit plans. 14 See Dixit and Pindyck (1994) for a detailed discussion of time-to-build in real options models. 14

17 and then gradually increases to a new, higher, steady-state value. Correspondingly, Loughran and Ritter (1992) and Lyandres, Sun and Zhang (2005) document abnormally high post-seo investment that peaks around the time of issuance and declines slowly thereafter. An important assumption of our model is that the ongoing expenditures associated with expansion are committed to at the SEO date. We clarify that the qualitative nature of our results does not require an absolutely irreversible commitment. As long as significant frictions exist to make costly a reversal or scaling back of the initial investment decision, then qualitatively similar results will hold. We now characterize output for the firm with existing assets-in-place and a one-time opportunity to engage in the two-part expansion described above. Unlike the simple model where expansion occurs instantaneously at stopping time τ, the firm takes a finite interval of time of length T to fully expand. In particular, we specify q 0 if t<τ q t = q 1 e α(t τ) if τ t τ + T (3) if t>τ+ T q 2 where q 2 = q 1 e αt and α>0. Output from assets-in-place thus begins at a fixed amount q 0 and remains unchanged until the firm commits to expansion at the optimal stopping time τ, which we characterize below. On that date, the firm raises funds of λ through an SEO and instantly spends those funds on new capital. Output jumps to a new higher level q 1 >q 0 and then grows at a constant rate α throughout the building period. During this period, the firm finances the ongoing investment first from operating cash flows. If retained earnings are not sufficient at any instant, we assume the firm can obtain employee financing through stock or option based compensation, conversion of employee options, or contributions to the employee pension plan. 15 We assume that the investment rate required over the building period is constant, and denote this rate I. We also assume that any operating cash flows in excess of the required investment rate are paid out immediately as dividends to shareholders. Once the building period ends, new capacity in the amount q 2 remains forever in place and no further expenditures are required. 15 If the firm instead occasionally used short-term debt financing to cover expansion cost shortfalls, this would not dramatically alter the character of our results, although risk dynamics would become more complicated. In particular, use of short-term debt financing in response to temporary cash flow shortfalls would tend to make the level of risk more sensitive to economic conditions during the expansion period. 15

18 Valuation in this context is only slightly more complicated than in the simpler model with instantaneous expansion. We refer to a firm that has completed its expansion as mature, and its value is given by V 2t = X tq γ 2. (4) δ This equation corresponds to the perpetuity value of revenues, and can be recognized as the Gordon growth formula. The valuation formula for a firm undergoing an expansion (an adolescent firm) is slightly more complicated. In this case, discounting revenues and the committed costs gives: V 1t = X tq γ ( ) 1 δ eαγ(t τ ) 1 e δ (τ+t t) + X tq γ 2 δ I r δ(τ +T t) e ( 1 e r(τ+t t)), (5) where δ δ αγ. This equation is the continuous-time version of a two-stage growth model: Revenues grow quickly in the short-run, due to the growth in output at rate α and the corresponding growth in operating cash flows at rate αγ. In the second stage (the long-run), expected cash flow growth is identical to the drift of the state variable X t. The first term in the valuation equation thus corresponds to the fast growing annuity during the expansion phase; the second term gives the discounted perpetuity value of the mature firm; and the third term accounts for present value of the committed expansion costs. To aid further exposition, we observe V 1t = X t V A 1t V C 1t, (6) where V1t A qγ 1 δ e αγ(t τ) ( 1 e δ (τ +T t) ) + qγ 2 δ e δ(τ+t t) relates the value of future revenues generated by assets, and V1t C I ( r 1 e r(τ+t t) ) is the current value of the investment commitment, which declines at a constant rate. We now turn to the optimal investment policy and valuation for the juvenile firm that has not yet invested. Following Carlson, Fisher, and Giammarino (2006), it is straightforward to show: Proposition 1: The optimal investment strategy for a juvenile firm is x = ν λ + V1τ C ν 1 V1τ A qγ 0 /δ, and the firm value is q γ 0 V 0 (X t )=X t δ + ε Xν t x ν, 16

19 where ν = ( 1 2 r δ ) σ 2 + 2r σ 2 2 r δ σ 2 > 1 and ε = λ+v C 1τ (ν 1). This proposition shows that with time-to-build, the entire discounted value of current and future investment costs, λ + V1τ C, motivates the firm to wait to exercise its growth option. This affects the investment boundary x, but otherwise the valuation equation is similar to the case where there is no time-to-build. To obtain betas, recall that risk is fully characterized by the loading of an asset s return on X. As was the case without time-to-build, we normalize the mature firm s beta to one. It is then straightforward to show that the juvenile firm s beta is β 0t =1+ V 0 G (ν 1) (7) V 0 where the value of the growth option is V G 0 Xν t For the adolescent firm, investment commitment has an important effect on risk during the building period. The beta is characterized by β 1t =1+ V 1t C, (8) V 1t for τ<t T. This beta function is strictly decreasing in t, and falls to one at the end of the building period. We can now summarize beta dynamics throughout the entire SEO episode: Prior to the SEO, firm risk depends on the relative value of the growth option. This option has maximal value at the commitment date τ. Betas of SEO firms thus rise in the months preceding an SEO announcement. Our model then predicts a drop in beta on the SEO issue date that is proportional to the amount of proceeds λ. Risk then continues to fall throughout the building period as funds from operations and other sources extinguish the firm s expansion commitment. The relative magnitudes of these effects depends on the parameterization of the model. Figure 4 depicts the dynamics of β around an SEO under one possible parameterization of the model. 16 Prior to event time 0, beta increases as real option leverage rises, in an anticipation of the firm committing to its expansion plans. On the event date, real option leverage falls because of the injection of new funds of the amount λ. Unlike the simple model where the SEO proceeds completely unwind real option leverage, additional time-to-build remains, and beta continues to decline throughout the building period as the expansion commitment is paid down. The overall pattern described 16 The specific parameterization is: r f =0.04, δ =0.025, σ =0.2, α =0.5, γ =0.5, λ =1, I = 3, T =3, q 0 =1, and q 1 =1.5. ε x ν. 17

20 by the model is thus qualitatively consistent with the empirical patterns in SEO firm betas documented in Sections 4.2 and 4.3. This suggests that time-to-build may have important implications for firm risk. 5. SEO Underperformance in the Cross-Section This section examines in the cross-section how SEO firm run-ups and announcement effects relate to 1) underperformance and 2) post-issuance beta changes. We first develop hypotheses for the behavioral and real options theories. We then provide empirical results, and discuss how these relate to the predictions. Under a behavioral theory, it is natural to consider that some types of stocks may be more subject to the effects of overconfidence and biased self-attribution than others. For example, stocks with very stable and predictable cash flows should be less likely to become overvalued than difficult to analyze technology stocks. Thus, we predict that the larger the run-up, the more underperformance the firm should experience. Similar predictions for returns can be derived from a real options model with heterogeneity in investor anticipation of the expansion opportunity. Consider the extreme case where the market receives a signal of demand that is so noisy that it is completely uninformative. The market, therefore, is unable to recognize when demand grows. Consequently, prior to an SEO there is no price run-up and no increase in the risk of the traded equity. At the announcement date, however, the market realizes the existence of the growth option and that demand has grown by more than what was previously believed. In addition to seeing that a growth option exists, investors also recognize the adverse selection that accompanies issue decisions (e.g., Myers and Majluf, 1984). The net announcement effect may be positive or negative but will be larger (either larger positive or less negative), the less anticipated the growth option is. That is, the announcement effect provides-cross sectional information on how well anticipated the SEO announcement is. Since the difference between pre-seo and post-seo returns also reflects anticipation, underperformance relates to the price run-up and announcement effect. Thus, smaller runups and more positive announcement effects should be associated with 1) less underperformance; 2) smaller decrease in beta Post-Issuance Underperformance Regressions We first present evidence on the cross-section of return dynamics. Similar to Ritter (1991), we define relative performance as the log of the relative wealth ratio, e.g., 18