> For the complete documentation index, see [llms.txt](https://laurence-wilse-samson.gitbook.io/textbooks/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://laurence-wilse-samson.gitbook.io/textbooks/financial-economics-claims-prices-holders/part-iii-asset-markets/chapter_12_equity_issuance.md).

# Chapter 12: Equity Issuance and the Life of the Public Firm

*Part III: Asset Markets — Financial Economics: Claims, Prices, and Holders*

***

## Opening Episode: The Auction Nobody Copied

On 29 April 2004, Google filed a registration statement that opened with a letter from its founders. "Google is not a conventional company," it said. "We do not intend to become one." Most of the letter was about corporate governance — the dual-class structure that would leave the founders with ten votes a share — but one paragraph was about market design. The company intended to sell its shares by auction.

The reasoning was stated plainly and was, in substance, an argument from this book's Chapter 7. In a conventional initial public offering, the price is set by the underwriters after a period of private consultation with institutional investors, and the shares are then allocated at the underwriters' discretion. Google proposed instead to collect sealed bids from anyone with a brokerage account and a bidder identification number, rank them, and clear the market at a price that would sell the offered shares. The founders wrote that they wanted a share price that reflected an efficient market valuation, and they wanted it available to individual investors on the same terms as to institutions.

What happened next is the reason the episode is worth a chapter opening.

The auction was run by Morgan Stanley and Credit Suisse First Boston, who did not want to run an auction, and by a syndicate of banks that had less to sell and less discretion over who got it than in any comparable deal. The registration process went badly on its own terms: an interview with the founders appeared in a magazine during the quiet period, unregistered employee share grants had to be disclosed and remedied, and the road to the offering was interrupted twice by the Securities and Exchange Commission. The initial price talk, filed in August, was a range of roughly 108 to 135 dollars a share. Nine days later the company cut the range to 85 to 95 dollars and cut the size of the offering by roughly a quarter, from about 25.7 million shares to about 19.6 million.

Google priced at eighty-five dollars on 18 August 2004 and began trading the next morning. It opened just above a hundred dollars and closed its first day at 100.34, up about 18 percent on the offer price. The company raised roughly 1.7 billion dollars in total, with a bit under 1.2 billion of that going to the company rather than to selling shareholders, at a valuation of roughly 23 billion dollars at the offer price and closer to 27 billion at the close.

Two facts about that first day organize this chapter.

The first is that the auction still left money on the table. Multiply the first-day gain of 15.34 a share by the shares sold and the number is roughly 300 million dollars — the amount that the buyers of the offering, rather than the company and its selling shareholders, took home on day one. It is a smaller fraction than a typical deal of the era produced, and Google's founders plainly thought the auction had worked. But the mechanism designed to eliminate the first-day pop did not eliminate it.

The second is that almost nobody followed. The auction had just been used by one of the most closely watched companies of the decade; it had raised the money; the founders had said publicly why they preferred it. Over the following decade, US auction offerings can be counted on two hands — Morningstar in 2005, Interactive Brokers in 2007, Rackspace in 2008, a handful of small deals run through WR Hambrecht's OpenIPO, the boutique that had championed the format — and then the method effectively disappeared. Bookbuilding, the process Google set out to bypass, is today more dominant than it was in 2004.

This is the chapter's question. The standard machinery for selling equity to the public transfers, on average, a large and measurable sum from issuers to a set of investors chosen by the underwriter. Issuers know this. A well-understood alternative exists, has been tried by a company with every reason and every resource to make it work, and was abandoned. Something about that machinery is doing work that the arithmetic of the first day does not show. The rest of the chapter is about what.

***

## 12.1 What Going Public Buys, and What It Costs

An initial public offering does four things, and a firm rarely wants all four equally.

**It raises capital.** New shares are sold, and the proceeds go to the company. This is the textbook reason and, empirically, often the smallest one. In many offerings a substantial share of the stock sold is *secondary* — existing shares sold by founders, employees, and venture investors — and the company receives none of that money.

**It creates liquidity for insiders.** A private company's equity can be sold only in a negotiated transaction, at a discount, and usually with the board's consent. Listing converts that claim into one that trades continuously, which is worth something in itself: Chapter 11's argument that liquidity is a priced characteristic applies with full force to the founder deciding whether to list. The lockup — typically 180 days, during which insiders may not sell — is the price of an orderly transition, and lockup expiry is one of the cleanest predictable supply shocks in equity markets.

**It creates an acquisition currency.** A listed share has an observable price, which makes it usable as consideration in a merger. Chapter 22 §22.5 treats what that does to acquisition behavior, including the awkward finding that stock-financed acquirers do worse.

**It certifies.** Audited accounts, quarterly reporting, analyst coverage, and a market price are, collectively, an information-production technology. Customers, suppliers, and lenders can all read the price. This is Chapter 7's efficiency argument applied to a single firm.

Against these sit the costs, and they have grown.

The direct costs are visible and roughly stable: an underwriting spread that has been remarkably sticky at 7 percent of gross proceeds for mid-sized US deals for three decades, plus legal, accounting, and listing fees. The sticky spread is itself a puzzle, and the standard reading is that it is not a competitive price but a focal point sustained by the fact that issuers select underwriters on reputation and placement power rather than on fee.

The indirect costs are larger and are the reason §12.7 exists. A public company files quarterly, discloses executive compensation, maintains internal-control attestations, faces securities litigation, and answers to a shareholder base it did not choose. It also reveals to competitors things a private firm need not reveal. Chapter 24 treats the governance side of this bargain — the rights the public shareholder gets in exchange for the money, and what those rights are worth. Here the point is only that the bargain has a price, that the price is paid every quarter for as long as the listing lasts, and that a firm with access to private capital can decline to pay it.

***

## 12.2 The Machinery: Bookbuilding, the Roadshow, and Allocation

The dominant method of selling equity to the public in the United States, and now nearly everywhere, is **bookbuilding**. Its three stages are worth separating, because the explanations of underpricing in §12.3 attach to different ones.

**Filing and valuation.** The company files a registration statement and the underwriters propose an indicative price range. The range is a negotiating position, not an estimate: the empirical regularity is that final pricing above the range predicts a *larger* first-day return, not a smaller one, which is the first hint that the range is being set to elicit something rather than to forecast.

**The roadshow and the book.** Over one to two weeks the management team presents to institutional investors, and the underwriters record **indications of interest** — how many shares at what price each account would take. These are not binding orders. The book is private and stays private; the issuer sees a summary.

**Pricing and allocation.** The underwriters set a single price for everyone and then decide who gets shares. This second discretion is the important one and has no analogue in an auction. In a bookbuilt deal the underwriter chooses the shareholder base: which institutions, in what size, and — this matters for §12.3 — which of them will be asked to take shares in the next deal that is harder to sell.

Add two mechanical features. The **greenshoe**, or over-allotment option, lets the syndicate sell up to 15 percent more shares than the base deal and cover the resulting short position either by exercising the option (if the stock trades up) or by buying in the aftermarket (if it trades down), which is a legal price-stabilization mechanism. And the **lockup** restricts insider sales for a set period after the offering.

One institutional caveat sits underneath all three stages. The firms that ran them in 2007 — standalone investment banks, most of them partnerships within living memory — no longer exist in that form, and the survivors do this work inside bank holding companies that are capitalized and supervised as such, which is the population Chapter 19 §19.3 describes. Whether an underwriter's allocation discretion is exercised the same way from inside a regulated balance sheet is a question §12.3's agency account has not been re-asked since the change.

An auction, by construction, discards the second and third stages. It sets the price by the bids and allocates by the rule. That is exactly the point of Google's design, and it is also exactly what the underwriting industry lost by it — which is the first candidate explanation for why the format did not spread.

***

## 12.3 Underpricing

The central empirical fact of this literature is easy to state and hard to explain away. On average, shares sold in an initial public offering close their first day of trading well above the price at which they were sold.

**Table 12.1: Average first-day returns on US initial public offerings, by period**

| Period                  | Number of offerings | Average first-day return |
| ----------------------- | ------------------- | ------------------------ |
| 1980-1989               | 2,047               | 7.2%                     |
| 1990-1998               | 3,616               | 14.8%                    |
| 1999-2000               | 856                 | 64.6%                    |
| 2001-2025               | 2,824               | 19.1%                    |
| Full period (1980-2025) | 9,343               | 19.0%                    |

*Source: Jay R. Ritter, "Initial Public Offerings: Underpricing", Table 1 (University of Florida, free online), updated December 24, 2025; sample 1980-2025, retrieved 25 August 2026. Period means are equal-weighted across offerings. Ritter's screens: an offer price of at least $5.00, excluding ADRs, unit offers, SPACs, closed-end funds, REITs, natural-resource limited partnerships, small best-efforts offers, banks and savings-and-loans, and stocks not on CRSP, which covers the NYSE, NYSE American and Nasdaq; proceeds exclude overallotment options. The whole-sample figures recomputed from the yearly rows — 9,343 offerings at 19.0 percent — reproduce the summary line Ritter prints. Money left on the table was $67 billion in 1999 and 2000 together and $250 billion over 1980-2025.*

Three features of the table deserve emphasis before any explanation is offered. The average is positive in every period, so this is not a bubble artifact. The average is enormously variable across periods, so whatever generates it is not a constant institutional fee. And the 1999-2000 column is not a rounding error: in those two years alone the sums transferred from issuers to first-day buyers ran to tens of billions of dollars, and the cumulative figure since 1980 is a number in the hundreds of billions.

Figure 12.1 puts the table's four periods back into the years they average over.

![Figure 12.1: IPO underpricing](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-f5b05b0d609f54a9941a1788e9aabc3b2c6ad1e6%2Ffig_12_01_ipo_underpricing.png?alt=media)

**Figure 12.1: IPO underpricing.** Average first-day return by year since 1980, with the number of offerings on the right axis. Table 12.1's periods are blocks of these bars, and reading the bars rather than the blocks changes the impression in two ways. The variability is not between periods but within them: the 1990s contain years at six percent and years at fifty, and no period average describes any particular year. And 1999 and 2000 are not the top of a distribution — they are off it, at 64.6 percent across 856 offerings, with sixty-seven billion dollars left on the table in two years against two hundred and fifty over the whole forty-six. The line is the number of deals, and it carries the fact that the average alone cannot. The primary market does not clear by repricing when conditions turn; it closes. Deal counts fall by an order of magnitude in bad years while first-day returns move by far less, which is the quantity response of a market in which the issuer can wait and the intermediary's certification cannot be manufactured on demand. *Source: Jay R. Ritter, "Initial Public Offerings: Underpricing", Table 1 (University of Florida, free online), updated December 24, 2025; author's calculations. Ritter's screens are those printed under Table 12.1.*

The natural way to measure the transfer at the level of a single deal is the **money left on the table**:

$$
\text{money left on the table} = (p\_1 - p\_0) \times Q\_{\text{sold}},
$$

where $$p\_0$$ is the offer price, $$p\_1$$ the first-day closing price, and $$Q\_{\text{sold}}$$ the number of shares sold in the offering. Problem 2 works an example in which this quantity is nearly seven times the underwriting fee on the same deal — which is the standard reason for saying that the fee is not where the interesting money is.

Four families of explanation compete. They are not mutually exclusive, and the honest position is that all four are probably operating.

### Winner's curse

Rock's (1986) model is the canonical statement and is the one that survives best. Suppose some investors are informed about the value of the offering and others are not. The informed bid only for the good deals. The uninformed bid for everything — and therefore receive their full order in the deals nobody else wants and a rationed fraction of the deals everyone wants. Their allocation is systematically worse than the average deal. An uninformed investor who computes the average first-day return across offerings and expects to earn it is making the winner's-curse error.

The consequence is a pricing constraint rather than a pricing preference. If the market needs uninformed capital — and it does, because informed capital alone is not deep enough to absorb the deals — then the offer price must be low enough that the uninformed break even *after* rationing. Problem 1 computes that price with clean numbers and produces the model's signature result: an equal-weighted average first-day return of over eleven percent coexisting with a zero expected return to the uninformed investor who actually receives the allocations.

That prediction has been tested directly, and it holds. Studies that weight IPO returns by the allocations investors actually receive rather than by deal find far smaller returns than the headline average, which is the sharpest available evidence that the headline average is not free money.

### Information revelation

Benveniste and Spindt (1989) turn the underwriter's discretion into the mechanism rather than the problem. An institutional investor who tells the underwriter honestly that the deal is worth more than the range has just argued itself into a higher price. It will do so only if compensated. Underpricing plus preferential allocation is that compensation, and the discretion the auction discards is precisely what makes the payment enforceable — the underwriter can reward truthful bidders across repeated deals in a way an anonymous auction cannot.

This theory explains the partial-adjustment fact directly: deals priced above the range are the ones where investors revealed favorable information, so they are the ones where the promised compensation must be paid, and they show the largest first-day returns. It also supplies the sharpest argument against auctions. If bookbuilding buys information, an auction that eliminates it is not a free improvement; it is a trade of one cost for another.

### Agency and allocation favors

The third family takes the underwriter's discretion seriously in a less flattering way. If the underwriter allocates underpriced shares, it is distributing something valuable, and it can be paid for the distribution in currencies other than the fee: in commission business directed to its trading desk, in future underwriting mandates, or — the version that produced regulatory settlements after 2000 — in **spinning**, the allocation of hot IPO shares to the personal accounts of executives whose companies were prospective clients. On this reading, underpricing is not a cost the issuer pays to the market; it is a cost the issuer pays to the underwriter's other relationships, and the issuer's agency problem is with its own bank.

### Issuer behavior

The last family asks why issuers tolerate any of it. Loughran and Ritter's answer is behavioral: the founder who sees the stock double on the first day has simultaneously learned that the retained stake — usually far larger than the shares sold — is worth much more than expected. Framed as a single mental account, a large gain net of a smaller foregone gain is still a large gain, and the loss goes unmourned. Chapter 15's treatment of reference dependence and mental accounting supplies the machinery.

### What Google tested, and what it did not

Return to the opening episode with these four in hand. The auction removed allocation discretion, so it should have removed the agency channel and the information-revelation payment. It could not remove the winner's curse, since an auction's bidders still face adverse selection, and Google's clearing price still had to be low enough to attract uninformed bids. And the eighteen percent first-day return says that something survived.

What the episode establishes cleanly is narrower and more useful: an auction can raise a large sum for a large company, so the format is feasible. What it does not establish is that the format is cheaper once the information-production and distribution services bundled into bookbuilding are priced. Google is one observation, and the industry's response — no adoption — is evidence, though evidence contaminated by the fact that the industry choosing whether to adopt is the industry that would lose the discretion.

> **Box 12.1 — The bank that ran the auction**
>
> The chapter opens with Google's 2004 auction and the fact that almost nobody copied it. Part of the reason is in §12.3's agency channel, and the case that made the channel visible has names and dates.
>
> In the years around 2000 the allocation of hot initial public offerings became a subject of regulatory action. The pattern alleged was straightforward: an underwriter with discretion over who receives shares in an underpriced offering is handing out something of value, and the value can be recovered from the recipient in another currency. Two forms of recovery were pursued. In the first, institutional clients paid inflated commissions on unrelated trades in exchange for allocations; Credit Suisse First Boston settled with the SEC and the NASD over this practice in January 2002, paying penalties and disgorgement without admitting or denying the findings. In the second — "spinning" — allocations went to the personal accounts of executives at companies whose future banking business the underwriter wanted, a practice that produced its own settlements and, later, a prohibition.
>
> The rulemaking that followed is what makes this an institutional box rather than a scandal. NASD Rule 2790, adopted in 2003 and now FINRA Rule 5130, prohibits allocating a new issue to "restricted persons" — broker-dealers, their personnel, and their immediate families — and requires the underwriter to obtain representations before allocating. A separate rule addressed spinning to executives directly. The regulatory response, in other words, was not to reduce underpricing. It was to restrict who may receive it.
>
> The coda is the part §12.3 wants. Credit Suisse First Boston, having settled over allocation practices in 2002, was one of the two lead banks on Google's auction in 2004. The auction removed exactly the discretion the settlements had been about. It was not copied, and §12.3 gives the reasons; but the sequence is a fair statement of where the resistance sits. The mechanism that generates the money on the table is also the mechanism that lets the underwriter decide who picks it up.

***

## 12.4 What Happens Next: Long-Run Performance and Its Caveats

Ritter (1991) and Loughran and Ritter (1995) reported a second regularity that is harder to interpret than the first: over the three to five years following the offering, IPO firms underperformed comparable seasoned firms substantially. The same held for firms conducting seasoned offerings, which is why the two findings were labeled together as the new-issues puzzle.

The caveats are not decoration; they are most of the debate.

The finding is a statement about *abnormal* returns, and an abnormal return is defined relative to a model. Adjust IPO returns for size and book-to-market rather than against the market alone, as Chapter 6's factor machinery prescribes, and the underperformance shrinks sharply and concentrates in small, low-book-to-market firms — a corner of the cross-section where many strategies look bad. Long-horizon buy-and-hold returns are also skewed and cross-correlated, since offerings cluster in time and in industry, so the standard errors that make three-year underperformance look decisive are usually too small. Weighting matters: equally weighted portfolios of new issues underperform far more than value-weighted ones, which is another way of saying the effect lives among small firms.

The defensible summary is this. New issues, especially small ones sold into hot markets, have earned low subsequent returns. Whether that constitutes an anomaly or a correctly priced exposure to characteristics that Chapter 6 already knows about is exactly the bad-model problem, and it has not been settled. What the finding does support, robustly, is the market-timing reading of §12.5: firms issue when their equity is expensive, and expensive equity subsequently earns less.

***

## 12.5 Seasoned Offerings and the Issuance Decision

A **seasoned equity offering** is a sale of additional shares by a company that is already public. The market's reaction is the fact to explain: announcement returns for US industrial firms average roughly minus two to minus three percent, concentrated in the first day or two. Selling equity is bad news.

The standard explanation is adverse selection, and it takes two sentences. A manager who knows the firm's true value issues equity when the market's valuation exceeds it and declines to issue when it does not; a rational market, knowing this, marks the price down on the announcement, and the markdown is large enough that some managers with genuinely good projects decline to issue at all. That is Myers and Majluf's argument, and it delivers the pecking order — internal funds first, then debt, then equity — as a consequence rather than an assumption. Chapter 23 §23.3 develops it properly, alongside the trade-off theory of §23.2 and the evidence on what actually explains leverage in §23.6.

A **rights issue** offers the new shares to existing shareholders first, pro rata, usually at a discount to the market price. It sidesteps the adverse-selection markdown in principle, because a shareholder who subscribes proportionally cannot be diluted by an underpriced issue: the discount is a transfer from the shareholder's old shares to the shareholder's new ones, and Problem 3 verifies that a subscribing holder's wealth is unchanged no matter how deep the discount goes. Rights are the dominant form in the United Kingdom, much of Europe, and much of Asia, and are rare in the United States, where firm-commitment underwritten offerings and, increasingly, overnight accelerated bookbuilds dominate. That the cheaper mechanism lost is a long-standing puzzle in this literature, and the usual answers — underwriter certification, the cost of a shareholder base that will not exercise, and the speed of an accelerated deal — are the same answers offered for the survival of bookbuilding in §12.3.

The last regularity is the one that matters most for this book's framing. Equity issuance is not smooth. It clusters: aggregate offering volume rises sharply when market valuations are high and collapses when they are low, and the firms issuing at the peaks are disproportionately the ones whose subsequent returns are poor. Baker and Wurgler build a theory of capital structure on this pattern — that observed leverage is largely the cumulative residue of past attempts to time the equity market — and Chapter 23 §23.4 assigns it. Here it is enough to record the direction of causation the pattern suggests: the quantity of equity issued responds to its price, and its price is set by whoever is currently willing to hold it. Section 12.9 closes on that point.

***

## 12.6 Buybacks and the Negative Sign

The most surprising number in this chapter is a sign.

Aggregate **net equity issuance** by US nonfinancial corporations — gross issuance, including employee compensation shares, minus repurchases and minus equity retired for cash in mergers — has been persistently *negative* since the mid-1980s. The Financial Accounts of the United States report it directly, and outside a few crisis years in which firms recapitalized, the series sits below zero year after year, commonly by several hundred billion dollars annually in the recent period. The stock market, taken as a whole, is not a place where American corporations raise money. It is a place where they return it.

![Figure 12.3: Payout has replaced issuance](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-773d54ad72dfc6c62dfb32bdac0c8ec56a3ac51c%2Ffig_12_03_payout_has_replaced_issuance.png?alt=media)

**Figure 12.3: Payout has replaced issuance.** Net issues of corporate equities by US nonfinancial corporate business, annual, from 1950. The sign is the finding. Through the 1950s, 1960s and 1970s the series is small and positive — the corporate sector raising modest sums in the public market, which is what a reader who has been taught that the stock market allocates capital to firms would expect. It turns in 1984 and, apart from 1991 to 1993 when firms recapitalized after that recession, it does not turn back: thirty-eight of the forty-one years since 1985 are negative, and the recent magnitudes run to several hundred billion dollars a year, reaching 635 billion in 2022 alone. Two readings follow. The first is about this chapter: whatever an initial public offering is for, financing the aggregate corporate sector is not it, and §12.1's underpricing cost is a cost on a flow that is dwarfed by the flow running the other way. The second is about Part IV: if the corporate sector retires more equity than it issues, the quantity of public equity is shrinking, and the price at which the remaining float clears must do its adjusting against demand rather than against new supply. That is Chapter 20 §20.3's supply side, and Figure 12.3 is the reason its elasticity is set near zero. *Source: Financial Accounts of the United States (Z.1), table F.223, net issues of corporate equities by nonfinancial corporate business, seasonally adjusted annual rate, via the FRED mirror; author's calculations.*

Two mechanics produce the number.

A **share repurchase** is a purchase by the firm of its own shares, most often through an open-market program announced as an authorization rather than a commitment, sometimes through an accelerated repurchase executed with a dealer, and occasionally through a tender offer at a premium. Gross repurchases by the largest US listed firms have exceeded 900 billion dollars in a single year. The second mechanic is cash-financed acquisition: when one public company buys another for cash, the target's shares are extinguished and the cash goes to its former shareholders. That is equity retirement even though no one calls it a buyback, and in some years it is comparable in size.

Set against these, gross issuance is modest. Initial and seasoned offerings together raise a small fraction of the sums returned; the largest gross issuance item for many mature firms is shares delivered under employee compensation plans, a substantial part of which is promptly repurchased.

Why firms choose repurchases over dividends, and what payout policy signals about a firm, is Chapter 23 §23.5's subject and is not developed here. One issuance-side fact belongs in this chapter. Repurchases and dividends are close substitutes in what they do to the aggregate float but not in what they do to the composition of holders. A dividend pays every holder in proportion and forces the tax event on all of them; a repurchase pays only the shareholders who sell, leaves the others with a larger proportional stake and no tax event, and is discretionary in a way a dividend is not — firms cut repurchases in downturns freely and cut dividends only under duress. The shift in the payout mix toward repurchases since the 1980s therefore changed not only how much cash left the corporate sector but which holders received it and when.

The consequence for this book's framing is direct. If the corporate sector is a net supplier of cash rather than a net issuer of shares, then the aggregate quantity of public equity is shrinking rather than growing, and the price at which the remaining float clears is doing most of its adjusting against demand rather than against new supply. Chapter 20's inelastic-markets arithmetic is the machinery; §12.9 is the single cleanest piece of evidence for it.

***

## 12.7 The Listing Decline and Its Private Substitutes

**Table 12.2: Listed domestic companies, United States**

| Year        | Listed domestic companies |
| ----------- | ------------------------- |
| 1975        | 4,775                     |
| 1996 (peak) | 8,025                     |
| 2012        | 4,102                     |
| 2025        | 3,908                     |

*Source: 1975, 1996 and 2012 from Doidge, Karolyi and Stulz, "The U.S. Listing Gap" (NBER working paper 21181, the free version of their 2017 paper), which counts from CRSP through 1988 and from the World Bank and the World Federation of Exchanges thereafter; the 2025 figure from the World Bank's World Development Indicators, listed domestic companies for the United States (CM.MKT.LDOM.NO), indicator updated 2026-07-13, retrieved 25 August 2026. The two sources agree exactly for 2012 (4,102) and differ by 65 firms for 1996, where the World Bank has 8,090. They cannot be mixed before 1980: the World Bank series records 2,401 firms in 1979 and 5,164 in 1980, a coverage break rather than an event, which is why the 1975 baseline is the CRSP-based one. Jay Ritter's free posting of CRSP counts, on a narrower domestic-operating-company definition that excludes REITs, closed-end funds and ETFs, puts the peak at 7,451 at the end of 1997:Q2 and the count at 3,657 at the end of 2025. Screens differ across all three; magnitudes, not exact counts, are what the table is for.*

The United States has roughly half as many listed companies as it had in the late 1990s. Doidge, Karolyi and Stulz make the fact precise and add the comparison that gives it force: relative to what a country of its size, wealth, and legal quality would be predicted to have — and relative to what the United States itself had in 1975 — the shortfall runs to thousands of firms. They call it the **listing gap**. The decomposition matters as much as the level. The gap comes from both ends: an unusually high rate of firms leaving, overwhelmingly through acquisition rather than through failure, and an unusually low rate of firms entering.

![Figure 12.2: The listing decline](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-2b2648416a90097e158055741c9ec462e719ea5d%2Ffig_12_02_the_listing_decline.png?alt=media)

**Figure 12.2: The listing decline.** Listed domestic companies in the United States, with Table 12.2's four counts marked on it. The series is drawn from 1980 only: the World Bank records 2,401 firms in 1979 and 5,164 in 1980, which is a change in coverage rather than in the world, and plotting through it would draw a tripling of the American stock market in one year. The 1975 count therefore comes from Doidge, Karolyi and Stulz counting from CRSP, and it is marked separately for that reason. Three things are visible that the table's four rows are not. The decline is not a single event: the fall from the 1996 peak runs in two distinct legs, one through the dot-com bust and one through the 2000s, with a long flat stretch between them and a partial recovery in 2021 that did not hold. The current level is below the 1975 level, which is the comparison that gives the listing gap its force — this is not a market that grew more slowly than the economy, it is one that has fewer firms in absolute terms than it had half a century and roughly five times the real GDP ago. And the shape is robust to the definitional disputes: Ritter's narrower count of domestic operating companies runs about six hundred firms lower throughout and traces the same path. *Source: World Bank World Development Indicators, listed domestic companies for the United States (CM.MKT.LDOM.NO); Doidge, Karolyi and Stulz, "The U.S. Listing Gap" (NBER working paper 21181) for 1975; Jay Ritter's listed-firms deck for the narrower count.*

Three candidate causes are usually offered, and they are not exclusive.

**Regulation.** Sarbanes-Oxley in 2002 raised the fixed cost of being listed, and fixed costs bite hardest on small firms, which is where the entry shortfall is concentrated. The timing is suggestive but the decline began before 2002, and other countries with different regulatory histories show related patterns, so this cannot be the whole story.

**Scale economies.** If the returns to scale in a modern firm's technology and distribution have risen, the efficient number of firms in an industry falls, and the efficient path for a promising small firm is to be bought by a large one rather than to grow into a competitor. This reading treats the delisting-by-acquisition channel as the phenomenon rather than as a symptom.

**Private capital.** A firm stays private only if it can be financed privately. Over the same period, the pools available to do that grew enormously: venture funds, growth equity, buyout funds, sovereign wealth funds, crossover mutual funds investing in late-stage private rounds, and the committed-but-uncalled capital Chapter 18 §18.3 calls dry powder. Regulatory changes worked the same direction, by raising the shareholder threshold that forces registration and by widening the exemptions under which private placements can be sold.

The result is that firms **stay private longer**. The median age and, more importantly, the median valuation of a company at its initial public offering are far higher than a generation ago. A firm that would once have listed at a valuation in the low hundreds of millions and grown in public view now lists in the billions.

This is where the chapter's framing earns its keep, because staying private longer is not a neutral change in timing. It reallocates who is permitted to hold the growth. The returns earned between a private valuation of two hundred million and a public valuation of twenty billion accrue to the holders of Chapter 18 — venture and growth funds and their limited partners, which are endowments, sovereign funds, and pension plans — and not to the holders of Chapter 14, the households whose retirement accounts buy the shares at listing. Whether that is a distributional problem, an efficient assignment of risk to the investors best able to bear illiquidity, or both, is a real question rather than a rhetorical one; Discussion Question 2 poses it. What is not in doubt is that the public equity market now sees a later and more mature slice of the corporate life cycle than it once did.

Two institutional variations belong here.

A **direct listing** registers existing shares for trading without selling new ones and without underwriters allocating anything: the shares begin trading in an opening auction with a reference price, and supply comes from existing holders who choose to sell. Spotify used it in April 2018, Slack in 2019, Coinbase in 2021. It suits a company that needs liquidity for its holders but not capital — precisely the profile of a firm that stayed private long enough to be well funded. It removes underwriter allocation discretion, and it therefore removes the same things the Google auction removed, which is why its adoption has also been narrow.

A **special purpose acquisition company** inverts the sequence: a shell raises money in a conventional IPO at a standard unit price, holds it in trust, and then finds a private company to merge with, at which point the private company becomes public without a traditional offering. The sponsor's compensation is the **promote** — founder shares typically amounting to about twenty percent of the post-IPO equity, acquired for a nominal sum. The arithmetic that follows is the reason the structure is contested: because the promote and the warrants issued to IPO investors dilute the trust, and because a large fraction of IPO investors redeem their shares for cash rather than staying through the merger, the cash actually delivered per surviving share has been documented, in the 2019-2020 merger cohort studied by Klausner, Ohlrogge and Ruan, at well below the headline trust value per share. Those estimates are cohort-specific and have been disputed on sample and measurement grounds, and the terms have since been renegotiated in many deals; the durable point is structural rather than numerical. The dilution is borne by the shareholders who do not redeem, and the sponsor's incentive is to complete a merger rather than to complete a good one.

> **Box 12.2 — How a company stays private**
>
> Section 12.7 records that firms now stay private for longer and in larger numbers. The reason is not a mood. It is a set of exemptions that make private capital raising cheap and a threshold that no longer forces registration.
>
> **The exemption.** Regulation D is the safe harbour under which most private capital is raised. Its principal rule permits an unlimited amount to be sold to accredited investors, without registration, provided the issuer does not generally solicit — or, under the rule the JOBS Act added, permits general solicitation provided every purchaser is verified as accredited. The filing an issuer makes is a Form D, a short notice filed after the first sale rather than a registration statement reviewed before it. The Commission publishes the Form D filings, which is why the private market is countable at all.
>
> **The threshold that used to force the issue.** Section 12(g) of the Exchange Act requires registration when a company exceeds an asset test and a holder-of-record count. That count is what took companies public against their preference in earlier decades: grow, distribute equity to employees, cross the line, register. The JOBS Act of 2012 raised the threshold from 500 holders of record to 2,000 (or 500 non-accredited), and excluded holders who received their shares under employee compensation plans. A firm can now have thousands of employee shareholders and remain private.
>
> **What the two rules do together.** They make it possible to raise a billion dollars from a few dozen institutions without a registration statement, an exchange listing, or a quarterly earnings call, and to keep doing it. The consequence for this book is a question of ownership rather than of corporate policy. The returns to a company's growth years now accrue to the holders of Chapter 18 — venture funds, growth funds, and their limited partners — rather than to the dispersed public shareholders of Chapter 14, because the public is not admitted until later and sometimes not at all.
>
> The Rule 144A market, which does the same job for debt, belongs to Chapter 25 §25.1.

***

## 12.8 Ownership: Where It Lives in This Book

Who holds US public equity — households directly, funds, insurers and pensions, and the rest of the world, in what proportions and with what fifty-year trend — is answered by Chapter 2's master holdings table (Table 2.5) and its §2.4, and the behavior of each holder class is the subject of Part IV. Cross-border holdings of US equity, cross-listing, depositary receipts, and the global equity market's structure are treated in depth in *International Finance*, Chapter 14, and are not rebuilt here.

The only ownership fact this chapter needs is the one §12.9 uses: a large and known fraction of the float of any index-member stock is held by investors whose demand for it is fixed by a mandate rather than by a view.

***

## 12.9 Who Holds This Claim, and What Their Constraints Do to Its Price

Everything in this chapter has been about the supply of equity. This section is about the fact that supply meets a demand curve, and about the one experiment that shows the curve is not flat.

### The logic

Textbook asset pricing gives an individual stock a nearly horizontal residual demand curve: a share is a bundle of exposures, close substitutes for the bundle exist in other shares and in derivatives, and arbitrage should absorb any quantity at a price set by the bundle's value. If that is right, an issuer's decisions about *quantity* — how many shares to sell, how many to buy back, whether to list at all — have no first-order effect on price, and most of this chapter is about frictions of secondary importance.

Index inclusion tests it, because it changes who must hold a stock without changing what the stock will pay. Providers state as policy that inclusion is not a judgment about prospects; yet it obliges every fund tracking the index to buy, in a known amount, by a known date, at whatever price clears. It is a demand shock with the information content removed by construction — which is why Chapter 20 opens on Shleifer's 1986 use of it, and why this section reviews the evidence rather than re-narrating that episode.

Problem 5 makes the size of the shock concrete and produces an identity worth stating in words: the shares the trackers must buy, as a fraction of a stock's float, equal the share of the index's float-adjusted capitalization that is tracked. When a seventh of the index is held passively, addition to the index is a purchase order for a seventh of the stock's float. That is not a rounding error in anyone's arithmetic.

### The evidence, and its decline

Early studies found large effects — abnormal returns around additions in a range usually quoted as three to seven percent, growing over time in step with indexed assets, and disputed from the beginning over whether the move persisted or reversed within weeks. Modern estimates of the S\&P 500 addition effect are near zero.

The decline is the interesting part, and it has three competing readings, developed in Chapter 17 §17.4 and compressed to a clause each here: more arbitrage capital standing ready to supply the shares, better anticipation moving the price response outside the event window, and smaller incremental shocks because most additions are now promotions from indices that already held the stock. The first two leave the demand curve sloped and say only that someone is being paid to slide along it; the third says the experiment has lost its power, not that the world has changed. A reader who takes "the inclusion effect went away" as evidence that demand curves are flat has drawn a conclusion the evidence does not support.

What survives is the class of cases where the shock overwhelms available arbitrage capacity — Chapter 17's opening episode, an addition at a weight near 1.5 percent requiring tens of billions of dollars of mechanical purchases in one closing auction, is a demonstration of the mechanism rather than an exception to it.

### What this does to issuers

If index membership changes the demand curve a firm's shares face, then index membership becomes a corporate objective, and the chapter's supply side and this section's demand side meet.

The mechanisms are visible in the eligibility rules. S\&P's US indices apply a profitability screen — positive earnings in the most recent quarter and over the trailing four — which is a boundary a firm can sit near and manage its way across. Providers have also written share-class rules that issuers respond to: the 2017 decision to exclude new multiple-share-class companies from the S\&P's main indices, since reversed, changed the calculus for founders designing a capital structure before an offering. And firms choosing where to place a primary listing weigh which national and global indices that choice makes them eligible for, and therefore how much mandated demand comes with it.

State the claim at the strength the evidence supports. The criteria are known, binding, and gameable at the margin, and issuers and their advisers plainly attend to them; whether the attention produces material real distortion — earnings managed across the profitability line, listings relocated, share structures abandoned — is a live empirical question with suggestive rather than settled answers. The direction is not in question: index construction, a private product decision by a few firms (Chapter 17 §17.7), has entered the corporate issuer's problem.

### The bridge

Which is the point the chapter has been circling. Issuance is not an autonomous corporate decision that the market then prices; it is a response to who is willing to hold the claim and on what terms. Firms sell equity when valuations are high, buy it back when it is cheap and when their holders want cash instead, stay private when private holders will fund them better, and shape themselves to qualify for the mandates of the market's largest holders.

Chapter 23 §23.7 states the strong form of this on the debt side, as **gap-filling**: firms supply the securities investors are short of, and the composition of corporate issuance moves to fill what the market is otherwise not supplied. This chapter is the equity-side version of the same claim, and it compresses to one sentence. The corporate sector does not merely issue claims into a market; it issues the claims the market's holders are constrained to want.

In Chapter 1 §1.2's terms, an index-inclusion move is the flow reading in the purest form the evidence offers: the information content is removed by the provider's own policy, leaving only money that must arrive by a known date at whatever price clears.

***

## Elsewhere in the Series

* **Global equity markets, cross-listing and depositary receipts, cross-border equity holdings, and the mechanics of index funds and ETFs in an international setting** — *International Finance*, Chapter 14, which owns all of it. Section 12.8 points there rather than duplicating; Chapter 17 §17.5 keeps only the compact creation and redemption mechanism this book's readers need.
* **This book**: the master holdings table for US equity and its fifty-year reallocation — Chapter 2 §§2.3-2.4. Factor adjustment of long-horizon abnormal returns, and the bad-model problem — Chapter 6. Event-study evidence and information production by listed firms — Chapter 7, with the mechanics in Appendix A. Liquidity as a priced characteristic — Chapter 11. Households as the ultimate holders of listed equity — Chapter 14. Reference dependence and mental accounting, behind §12.3's issuer-behavior explanation — Chapter 15. Index construction, inclusion effects in full, and index-provider power — Chapter 17 §§17.4 and 17.7. Private funds, dry powder, and the returns that accrue before an offering — Chapter 18. Demand elasticities, price multipliers, and the inelastic-markets estimate — Chapter 20, whose opening episode is the 1986 index-inclusion paper this chapter's §12.9 builds on. Acquisitions, stock as consideration, and acquirer returns — Chapter 22 §22.5. Capital structure, the pecking order, payout policy, market timing, and gap-filling — Chapter 23 §§23.3-23.5, 23.7. The governance bargain a listing entails, and what it costs — Chapter 24 §§24.3-24.4.

***

## Summary

1. **Google's 2004 auction is the chapter's test case and its puzzle.** A large, sophisticated issuer bypassed the allocation discretion at the heart of bookbuilding, priced at eighty-five dollars against initial talk of 108 to 135, and still saw an 18 percent first-day rise and roughly 300 million dollars left on the table. Almost no one copied the format, and bookbuilding is more dominant now than it was then.
2. **An offering does four things**: raises capital, creates liquidity for insiders, creates an acquisition currency, and certifies through disclosure. The costs are a sticky 7 percent underwriting spread on mid-sized US deals plus the recurring burden of being public, which is what §12.7's listing decline is a response to.
3. **Bookbuilding has three stages and one discretionary act.** Filing and range-setting, the roadshow and the book of indications, then pricing and — the part that has no counterpart in an auction — allocation. The greenshoe and the lockup are the two mechanical add-ons.
4. **Underpricing is large, universal, and enormously time-varying** (Table 12.1): roughly 7 percent in the 1980s, roughly 15 percent through the 1990s, roughly 65 percent in 1999-2000, and roughly 18 percent since. Money left on the table is the deal-level measure, and it commonly dwarfs the underwriting fee.
5. **Four explanations, all probably operating.** Rock's winner's curse makes underpricing the price of keeping uninformed capital in the market, and predicts — correctly — that allocation-weighted returns are far below equal-weighted ones. Benveniste-Spindt makes it the payment for information revealed during bookbuilding, and explains why deals priced above the range pop most. The agency account makes it a currency the underwriter distributes for its own account. The behavioral account explains why issuers do not object.
6. **Long-run IPO underperformance is real but fragile.** It shrinks sharply under size and book-to-market adjustment, is concentrated in small growth firms, and rests on long-horizon tests with cross-correlated, skewed returns. It survives best as evidence for market timing rather than as an anomaly in its own right.
7. **Seasoned offerings announce badly** — roughly minus two to minus three percent — for the adverse-selection reason Myers and Majluf give and Chapter 23 §23.3 develops. Rights issues avoid the dilution objection arithmetically (Problem 3) and dominate outside the United States, and their absence in the United States is the same puzzle as bookbuilding's survival.
8. **Net equity issuance by US nonfinancial corporations has been negative for four decades.** Repurchases and cash-financed acquisitions retire far more equity than offerings create. The public equity market is where the American corporate sector returns money, not where it raises it, and the aggregate float is shrinking against demand.
9. **US listings roughly halved from the late-1990s peak** (Table 12.2), through both high exit by acquisition and low entry, and the shortfall against a size-and-development benchmark is the listing gap. Regulation, scale economies, and abundant private capital all contribute; firms stay private longer, and the returns earned before listing accrue to Chapter 18's holders rather than to Chapter 14's.
10. **Index inclusion is the cleanest quasi-experiment in holder-driven pricing.** It changes who must hold a stock without changing its cash flows, and the required purchase equals the passively tracked share of the float. Early effects of several percent have declined toward zero for reasons that are unresolved (Chapter 17 §17.4) and that matter, because two of the three readings leave the demand curve sloped.
11. **Eligibility becomes a corporate objective.** Profitability screens, share-class rules, and primary-listing choices all enter the issuer's problem once index membership carries mandated demand with it — stated as documented mechanism rather than as identified effect.
12. **The chapter's thesis in one line.** Issuance responds to holder demand: firms supply the claims that constrained holders are obliged to want, which is the equity-side statement of the gap-filling argument Chapter 23 §23.7 makes on the debt side.

***

## Key Terms

* **Initial public offering (IPO)**: The first sale of a company's shares to public investors, combining primary shares sold by the company with secondary shares sold by existing holders, and conferring a listing with its recurring disclosure and governance obligations
* **Bookbuilding**: The dominant method of selling new equity, in which underwriters collect non-binding indications of interest from institutions during a roadshow, set a single price, and then allocate the shares at their own discretion
* **Underpricing**: The gap between the offer price and the first trading price, measured as the first-day return; the deal-level dollar measure is the money left on the table, $$(p\_1 - p\_0)$$ times shares sold
* **Winner's curse**: Rock's mechanism, in which uninformed investors receive full allocations of the deals informed investors avoid and rationed allocations of the deals they want, so the offer price must be set low enough for the uninformed to break even after rationing
* **Greenshoe (over-allotment option)**: The syndicate's right to sell up to 15 percent more shares than the base offering and to cover the resulting short either by exercising the option or by buying in the aftermarket, which is the legal form of price stabilization
* **Lockup**: The contractual restriction, typically 180 days, on insider sales after an offering; its expiry is a predictable supply shock
* **Seasoned equity offering (SEO)**: A sale of additional shares by an already-listed company, announced at an average share-price reaction of roughly minus two to minus three percent
* **Rights issue**: An offering of new shares to existing shareholders pro rata, usually at a discount; the theoretical ex-rights price and the value of a right follow arithmetically, and a subscribing holder's wealth is unaffected by the size of the discount
* **Share repurchase (buyback)**: A firm's purchase of its own shares, most often through an announced open-market authorization; a discretionary substitute for dividends that pays only the holders who sell
* **Net equity issuance**: Gross equity issued less equity retired through repurchases and cash-financed mergers; persistently negative for US nonfinancial corporations since the mid-1980s
* **Listing gap**: Doidge, Karolyi and Stulz's measure of the shortfall between the number of US listed firms and the number predicted by the country's size, wealth, and institutional quality
* **Special purpose acquisition company (SPAC)**: A shell that raises money in a conventional offering, holds it in trust, and merges with a private company; the sponsor's promote is founder equity of roughly a fifth of the post-offering shares, acquired for a nominal sum
* **Direct listing**: Registration of existing shares for trading with no new shares sold and no underwriter allocation, with supply set by existing holders in an opening auction
* **Inclusion effect**: The abnormal return around a stock's addition to an index, interpreted as a measurement of the slope of the demand curve for that stock because the index provider's decision carries no cash-flow information

***

## Readings

### Required

* Ritter, J. R. and I. Welch (2002). "A Review of IPO Activity, Pricing, and Allocations." *Journal of Finance* 57(4): 1795-1828. *The survey to read first. It states the three facts — underpricing, cycles in volume, and long-run underperformance — and grades the competing explanations of each. The verdict that asymmetric-information theories cannot carry the whole load, and that allocation and agency channels must be part of the answer, is the frame of §12.3.*
* Rock, K. (1986). "Why New Issues Are Underpriced." *Journal of Financial Economics* 15(1-2): 187-212. *The winner's-curse model, short and worth reading in the original. The result to extract is that underpricing is the price of retaining uninformed capital, and that its magnitude therefore depends on how much informed capital is competing for the same allocations. Problem 1 is this paper in numbers.*

### Recommended

* Ritter, J. R. (2003). "Investment Banking and Securities Issuance." In G. M. Constantinides, M. Harris and R. M. Stulz (eds.), *Handbook of the Economics of Finance*, Volume 1A, Chapter 5. North-Holland. *The long-form companion to the required Ritter-Welch survey, by the same author at roughly four times the length. Its taxonomy of competing underpricing explanations maps onto §12.3 subsection by subsection, its treatment of alternative pricing and allocation mechanisms is the auction-versus-bookbuilding comparison the opening episode needs, and its sections on announcement effects and long-run performance of seasoned offerings are the source for §12.5, which otherwise has no reading of its own.*
* Doidge, C., G. A. Karolyi and R. M. Stulz (2017). "The U.S. Listing Gap." *Journal of Financial Economics* 123(3): 464-487. *The measurement behind §12.7. Read it for the decomposition — the gap comes from too few new listings and too many disappearances by merger — and for the benchmarking exercise that makes "gap" a claim rather than an observation.*
* Benveniste, L. M. and P. A. Spindt (1989). "How Investment Bankers Determine the Offer Price and Allocation of New Issues." *Journal of Financial Economics* 24(2): 343-361. *The theory that turns the underwriter's discretion into the mechanism rather than the abuse. It is also the strongest available argument against auctions, and should be read against the Google episode.*
* Morrison, A. D. and W. J. Wilhelm (2008). "The Demise of Investment Banking Partnerships: Theory and Evidence." *Journal of Finance* 63(1): 311-350. *Why underwriting was organized as a partnership for a century and why it stopped being one. Read it for §12.2's caveat: the discretion that Benveniste-Spindt makes efficient was exercised by a firm whose partners' own capital stood behind the reputation, and that firm no longer exists.*
* Financial Conduct Authority (2016). "Investment and Corporate Banking Market Study: Interim Report." MS15/1.2. *A regulator's evidence on how mandates are actually won, how league tables function as a marketing instrument, and how allocations are actually made — from outside the United States, and gathered with powers no academic has. The institutional counterpart to §12.2 and §12.3.*
* Loughran, T. and J. R. Ritter (2002). "Why Don't Issuers Get Upset About Leaving Money on the Table in IPOs?" *Review of Financial Studies* 15(2): 413-443. *The behavioral answer to §12.3's last question, and the paper that made mental accounting a standard part of this literature. Read alongside Chapter 15.*
* Dorn, D. (2009). "Does Sentiment Drive the Retail Demand for IPOs?" *Journal of Financial and Quantitative Analysis* 44(1): 85-108. *Retail demand for new issues measured directly, at the account level. The population Rock's model calls uninformed turns out to overpay in the aftermarket rather than in the allocation, which is a sharper version of §12.3's winner's-curse story than the model states.*
* Swedberg, R. (2005). "Conflicts of Interests in the U.S. Brokerage Industry." *§12.3's agency channel stated institutionally rather than as a model parameter: how research, underwriting, and distribution came to sit inside one firm, and what the settlements of the early 2000s did and did not change.*
* Ritter, J. R. IPO statistics tables and working papers, University of Florida (free online, updated annually). *Not a paper but the field's shared dataset: first-day returns by year, by size, by venture backing and by industry, with money left on the table and long-run performance tabulated. The chapter's data exercise runs on it.*
* Klausner, M., M. Ohlrogge and E. Ruan (2022). "A Sober Look at SPACs." *Yale Journal on Regulation* 39(1): 228-303. *The dilution arithmetic behind §12.7's two hedged sentences, worked through for a specific cohort. Read the objections to it as well; the structure is more durable than the point estimates.*
* Financial Economists Roundtable (2002). "Statement on the Structure of Securities Markets." *What a group of senior financial economists collectively thought public-market structure should be, dated just before the listing decline of §12.7 set in. Useful as a period document: read what they worried about against what actually happened.*

***

## Discussion Questions

1. **Why did the auction not win?** Google demonstrated that an auction can raise nearly two billion dollars for a large company, and it removed the allocation discretion that §12.3's agency explanation identifies as the abuse. Yet the format effectively disappeared. Construct the three strongest arguments for why bookbuilding survived: one in which it survives because it is genuinely more efficient, one in which it survives because the party choosing the method is not the party bearing the cost, and one in which it survives because of coordination — no issuer wants to be the one experimenting with its own offering. What evidence would distinguish them? Direct listings removed the same discretion and also stayed rare; does that observation favor one of your three arguments over the others, and if so which?
2. **Is the listing decline a problem or a substitution?** The United States has roughly half the listed companies it had in 1996, while the aggregate value of listed equity is far larger and private capital pools have grown enormously. Argue first that nothing is wrong: firms are being financed, capital is being allocated, and listing is one financing technology among several with no special claim. Then argue that something is wrong, using at least one argument about price discovery, one about who is permitted to hold growth-stage returns, and one about the information that public disclosure produces for parties other than shareholders. Which of your six arguments would change your mind if it were shown to be false?
3. **Allocation as compensation.** Under Benveniste and Spindt, the underwriter's discretion to allocate underpriced shares is what buys truthful information from institutional investors. Under the agency account, that same discretion is what lets the underwriter sell allocations for its own benefit. The two accounts predict the same institution and the same underpricing. Specify at least three observable implications on which they differ — think about which investors receive allocations, what happens to their subsequent trading, how allocations respond to the information a given investor supplied, and what happens after a regulatory ban on one particular use of discretion. Which of these has actually been tested?
4. **The negative sign.** Net equity issuance by US nonfinancial corporations has been negative for four decades. A commentator concludes that the stock market no longer performs its function of financing corporate investment. State two ways in which the inference is wrong or incomplete, using the composition of the flows in §12.6 and the private markets of §12.7. Then state the strongest version of the commentator's claim that survives your objections, and say what evidence would test it.
5. **Does the machinery travel?** Outside the United States, regulators who have examined underwriting with subpoena powers report that mandates are won partly on the strength of the bank's existing lending relationship with the issuer, that league-table position is itself a marketing instrument, and that allocations favor investors who supply other business to the bank. Sort §12.3's explanations into those that describe a universal information problem and those that describe one industry's organization. Which of them would you expect to survive in a market with a third as many underwriters, a more concentrated institutional investor base, and a bank-centered corporate finance system — and what observable would tell you? (The comparative structure of underwriting across countries belongs to *International Finance*, Chapter 14; answer here from the mechanisms of §12.3.)
6. **When the experiment stops working.** The measured price effect of S\&P 500 addition has fallen to near zero. Explain why this is consistent with each of Chapter 17 §17.4's three readings, and design the sharpest test you can that separates "the demand curve flattened" from "the demand shock shrank." Use cross-sectional variation — additions of firms already held by broad-market trackers versus firms not held; additions to indices with different amounts of tracking capital; markets with less arbitrage capital than the United States. What data would you need, and which part of your design is the weakest?

***

## Problems

**Problem 1 — Rock's winner's curse with clean numbers.** An offering of 100 shares will be worth either 13 (with probability one half) or 7 (with probability one half) once trading begins. Informed investors learn the value before bidding and, collectively, bid for 100 shares when the value is 13 and for nothing when it is 7. Uninformed investors bid for 100 shares in either case. Shares are allocated pro rata among all bidders.

(a) Compute the number of shares uninformed investors receive in the good offering and in the bad offering.

(b) At an offer price of 10 — the unconditional expected value — compute the uninformed investors' expected profit. Should they participate?

(c) Find the offer price at which uninformed investors break even.

(d) At that price, compute the first-day return in the good state, in the bad state, and the equal-weighted average across the two offerings. Then compute the return the uninformed investor actually earns on the dollars invested. Explain in two sentences why the two numbers differ and what that implies for a study that measures underpricing by averaging across deals.

(e) Suppose informed capital triples, so that informed investors bid for 300 shares in the good offering. Recompute the break-even price and the equal-weighted average first-day return. Does more informed capital make offerings more or less underpriced, and why?

**Problem 2 — Money left on the table.** A company sells 12 million shares at an offer price of 18. The underwriting gross spread is 7 percent. The stock closes its first day at 26.50. The company had 48 million shares outstanding before the offering, all of them retained by existing holders.

(a) Compute gross proceeds, the underwriting fee, and net proceeds to the company.

(b) Compute the first-day return and the money left on the table.

(c) Express the money left on the table as a multiple of the underwriting fee.

(d) Show that the money left on the table equals the value of the additional shares the company had to sell in order to raise the same gross proceeds at the offer price rather than at the closing price. (Compute the number of shares that would have been needed at the closing price, and value the difference.)

(e) Express the money left on the table per pre-offering share. A founder holding 5 million pre-offering shares sees a paper gain on that stake of 8.50 a share at the close. Using §12.3's behavioral explanation, explain why this founder may not experience the result in (e) as a loss, and state what the founder would have to believe about the counterfactual for that reaction to be rational rather than a framing effect.

**Problem 3 — Rights issue arithmetic.** A company has 40 million shares outstanding trading at 25 cum-rights. It announces a one-for-four rights issue — one new share for every four held — at a subscription price of 15.

(a) Compute the number of new shares, the gross proceeds, and the theoretical ex-rights price, using

$$
\mathrm{TERP} = \frac{N\_{\text{old}}p\_{\text{cum}} + N\_{\text{new}}p\_{\text{sub}}}{N\_{\text{old}} + N\_{\text{new}}}.
$$

(b) Compute the value of a right attached to one existing share, in two ways: as the drop from the cum-rights price to the theoretical ex-rights price, and as one quarter of the gain available on subscribing. Confirm that the two agree.

(c) A shareholder owns 4,000 shares. Compute her total wealth under three courses of action: subscribe in full, sell the rights and keep the shares, or do nothing. Which one loses money, how much, and why is that loss not a dilution effect in the economic sense?

(d) The board instead sets the subscription price at 10. Recompute the theoretical ex-rights price and the value of a right, and recompute the wealth of a shareholder who subscribes in full. State in one sentence what the depth of the discount does and does not affect.

(e) Explain, using (d), why a rights issue does not carry the adverse-selection markdown that §12.5 attributes to a seasoned public offering — and then state the condition on the shareholder base under which that argument fails.

**Problem 4 — Reading net issuance.** Table 12.3 gives figures for the US nonfinancial corporate sector in a single year, in billions of dollars. They are illustrative but of realistic magnitude.

**Table 12.3: Equity and debt flows for one year, US nonfinancial corporate business (billions of dollars)**

| Item                                                        | Amount |
| ----------------------------------------------------------- | ------ |
| Gross public equity issued (initial and seasoned offerings) | 180    |
| Shares issued under employee compensation plans             | 120    |
| Share repurchases                                           | 900    |
| Equity retired in cash-financed mergers                     | 210    |
| Net debt issuance                                           | 400    |

*Source: Illustrative; constructed to match the structure of the Financial Accounts of the United States corporate equity table. Magnitudes are realistic but the figures are not those of any single reported year.*

(a) Compute net equity issuance for the sector.

(b) The aggregate market value of the sector's equity is 50 trillion. Express net equity issuance as a percentage of that value.

(c) Compute net external finance raised by the sector (equity plus debt) and state in one sentence what the corporate sector did with its balance sheet that year.

(d) A newspaper reports that "American companies raised 180 billion in the stock market this year." State precisely what is wrong with the sentence and write a one-sentence replacement that is accurate.

(e) A student applies Chapter 20's price multiplier — roughly five dollars of market value per dollar of flow — to your answer in (a) and concludes that the negative net issuance should have raised the market's value by several trillion dollars that year. Give two distinct reasons the calculation is wrong.

**Problem 5 — Index inclusion as a demand shock.** A company has 400 million shares outstanding at a price of 50, of which 80 percent is free float. It is added to an index whose total float-adjusted market capitalization is 40 trillion. Funds tracking that index hold 6 trillion of assets. The stock's average daily trading volume is 4 million shares.

(a) Compute the company's float-adjusted market capitalization and its index weight in basis points.

(b) Compute the dollar amount and the number of shares that index trackers must buy, and express the share count as a percentage of the free float. Then show that this percentage equals the ratio of tracked assets to the index's float-adjusted capitalization, and explain in one sentence why that identity holds for every stock in the index.

(c) Express the required purchase in days of average trading volume.

(d) Suppose the aggregate demand elasticity for this stock is $$\zeta$$, in the sense of Chapter 20 §20.2: a one percent rise in price reduces the quantity demanded by $$\zeta$$ percent, with characteristics held fixed. Compute the price change that clears the market for $$\zeta = 0.5$$, $$\zeta = 1$$, and $$\zeta = 5$$.

(e) The measured abnormal return around modern index additions is near zero. Using Chapter 17 §17.4's three explanations, state for each one what it implies about the numbers you computed in (b) and (d) — which input is wrong, and in which direction.

***

## Selected Solutions

*Solutions to Problems 1 and 5 follow. Solutions to the remainder are in the instructor materials.*

**Problem 1.**

(a) In the good offering, total demand is 200 shares for 100 available, so every bidder receives half. Uninformed investors receive **50 shares**. In the bad offering the informed do not bid, total demand is 100 for 100, and the uninformed receive **100 shares**.

(b) At an offer price of 10 the uninformed earn $$50\times(13-10) = 150$$ in the good state and $$100\times(7-10) = -300$$ in the bad state, so expected profit is $$\tfrac12(150) + \tfrac12(-300) = -75$$. It is negative, so they should not participate — and if they do not, the offering cannot be sold, since informed capital covers only half the deals.

(c) Set $$\tfrac12\cdot 50(13-p\_0) + \tfrac12\cdot 100(7-p\_0) = 0$$. Expanding, $$325 - 25p\_0 + 350 - 50p\_0 = 0$$, so $$75p\_0 = 675$$ and $$p\_0 = 9$$.

(d) At an offer price of 9 the first-day return is $$(13-9)/9 = 44.4$$ percent in the good state and $$(7-9)/9 = -22.2$$ percent in the bad, for an equal-weighted average across the two offerings of **11.1 percent**. The uninformed investor's own return is zero by construction: he invests $$50\times 9 = 450$$ in the good offering and $$100\times 9 = 900$$ in the bad, a total of 1,350, and receives $$50\times 13 + 100\times 7 = 1{,}350$$. The two numbers differ because the deal-weighted average gives equal weight to an offering in which the uninformed investor holds 50 shares and one in which he holds 100. A study that averages first-day returns across deals therefore measures a quantity no investor earns; it overstates the return to the marginal supplier of capital by exactly the rationing.

(e) With informed demand of 300, the good offering has total demand of 400 for 100 shares, so the uninformed receive 25. Break-even now requires $$\tfrac12\cdot 25(13-p\_0) + \tfrac12\cdot 100(7-p\_0) = 0$$, giving $$62.5p\_0 = 512.5$$ and $$p\_0 = 8.20$$. The equal-weighted average first-day return rises to $$(10-8.20)/8.20 = 22.0$$ percent. More informed capital makes offerings **more** underpriced, not less: the uninformed are rationed harder in exactly the deals worth having, so the compensation required to keep them bidding rises. This is the model's most useful comparative static, and it is what makes underpricing a function of the market's information structure rather than of the underwriter's generosity.

**Problem 5.**

(a) Float-adjusted capitalization is $$400\text{m}\times 0.80\times 50 = 16$$ billion. Against an index capitalization of 40 trillion the weight is $$16/40{,}000 = 0.0004$$, or **4 basis points**.

(b) Trackers holding 6 trillion must buy $$6{,}000\text{bn}\times 0.0004 = 2.4$$ billion of stock, which at a price of 50 is **48 million shares**. Free float is $$400\text{m}\times 0.80 = 320$$ million shares, so the purchase is $$48/320 = 15$$ percent of the float. Tracked assets are $$6/40 = 15$$ percent of index capitalization — the same number. The identity holds because both the required purchase and the float are proportional to the same float-adjusted capitalization: trackers must hold each stock in its index weight, so collectively they hold the tracked fraction of every member's float, and an addition is the order that takes them there.

(c) At 4 million shares a day, 48 million shares is **12 days** of average volume, which must be executed against a known deadline that every other participant also knows.

(d) A demand shock of 15 percent of float, cleared against elasticity $$\zeta$$, moves the price by $$15/\zeta$$ percent: **30 percent** at $$\zeta = 0.5$$, **15 percent** at $$\zeta = 1$$, and **3 percent** at $$\zeta = 5$$. The first two are the range Chapter 20 §20.2 reports for institutional demand estimates; the third is closer to what a frictionless substitution argument would predict. Note that none of the three is zero.

(e) Under the **arbitrage-capacity** reading, $$\zeta$$ in part (d) is the wrong input: the effective elasticity facing the trackers is much higher than the holders' own elasticity, because arbitrage capital stands ready to sell into the announced order, so the price impact falls without the underlying demand curve changing slope. Under the **anticipation** reading, both inputs are right but the timing is wrong: the price change in (d) still happens, spread over the weeks before the event window in which it is measured. Under the **migration** reading, part (b) is the wrong input: if broad-market and mid-cap trackers already hold the stock, the *incremental* purchase is a fraction of 48 million shares, and the shock rather than the elasticity is small. The first two leave demand curves sloped; only the third says the experiment has lost its power. Distinguishing them is Discussion Question 5.

***

## Data Exercise: Underpricing, the Listing Count, and the Negative Sign

Parts A through C run entirely on free data. Part D is the licensed extension.

**Part A — Underpricing from the canonical source (free).** Jay Ritter's IPO data pages at the University of Florida post, in spreadsheet form, average first-day returns by year, counts of offerings, money left on the table, and breakdowns by offer size, venture backing, and industry. Download the current files.

1. Plot the average first-day return by year from 1980 to the present, with the number of offerings on a second axis. Mark 1999-2000 and the 2020-2021 window. Describe the relationship between the two series: does underpricing lead, lag, or move with volume? State what that relationship implies for the market-timing reading in §12.5.
2. Rebuild Table 12.1 exactly from the file, and report how your figures differ from the chapter's rounded ones. Read the notes tab and list the screens applied — minimum offer price, exchange listing, exclusion of unit offers and depositary receipts. Recompute the full-period average with one screen relaxed and report how much the answer moves.
3. Using the money-left-on-the-table series, compute the cumulative total since 1980 and the share of it accounted for by 1999-2000. Compare the annual total in each year with the aggregate underwriting fees implied by a 7 percent spread on gross proceeds. In how many years was money left on the table larger than total fees?
4. Split the sample by venture backing and by offer size. Which cut produces the larger difference in average underpricing, and does the ranking support Rock's winner's curse, Benveniste-Spindt, or neither?

**Part B — The listing count (free).** The World Bank's World Development Indicators publish listed domestic companies by country and year; the World Federation of Exchanges publishes member-exchange listing counts.

5. Plot the US count from the earliest available year to the present and mark the peak. Compute the peak-to-trough decline in percentage terms and compare it with Table 12.2.
6. Add three comparison countries with different institutional histories — the United Kingdom, Japan, and one emerging market of your choice — indexed to their own 1996 values. Is the decline a US phenomenon? Where the pattern differs, offer an institutional explanation and say what would falsify it.
7. Scale the US count by real GDP and by population, which is the form of the Doidge-Karolyi-Stulz benchmark. Does the gap look larger or smaller than the raw count suggests, and why?

**Part C — The negative sign (free, FRED and Z.1).** The Financial Accounts of the United States report corporate equity issuance and retirement for the nonfinancial corporate sector; the series are available through FRED and in the Z.1 release tables directly.

8. Plot net equity issuance by nonfinancial corporate business, annually, from 1950 to the present. Identify the decade in which the series turns durably negative and the years in which it is positive. What was happening in each positive year?
9. Overlay net debt issuance for the same sector. In which periods do the two move together, and in which do they offset? Relate the pattern to §12.5's market-timing evidence and to Chapter 23 §§23.2-23.4's capital-structure theories.
10. Deflate the net issuance series by the market value of corporate equity outstanding, so that it becomes a rate rather than a level, and plot it against a valuation measure such as the aggregate market-to-book or the cyclically adjusted earnings yield. State what the correlation is and, carefully, what it cannot establish about causation.

**Part D ★ — Deal-level evidence (WRDS).** With access to SDC Platinum (or Refinitiv's successor product) for new issues and CRSP for prices:

11. Build a deal-level file of US initial public offerings for a twenty-year window: offer date, offer price, filing range, shares offered, primary versus secondary split, underwriter, and the first-day closing price from CRSP. Reproduce the partial-adjustment result — regress the first-day return on the revision from the midpoint of the filing range to the offer price — and report the coefficient with an interpretation.
12. Construct calendar-time portfolios of firms in the three years after their offering, and compute alphas against the market model, the three-factor model, and the five-factor model. Report all three. Then repeat with equal and value weighting. Write one paragraph on how much of §12.4's long-run underperformance survives your most demanding specification, and state which of your six numbers you would print if you had to print one.
13. Using CRSP and the index provider's published addition announcements, construct an event study of S\&P 500 additions by decade, with the machinery in Appendix A. Report cumulative abnormal returns over the announcement-to-effective window and over the following sixty trading days. Split the modern sample by whether the added firm was already a member of a broad total-market index, and report the difference. This is the test Discussion Question 5 asks you to design.