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Review of Quantitative Finance and Accounting

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01-01-2016 | Original Research

A theory of underwriters’ risk management in a firm-commitment initial public offering

Author: Edmund H. Mantell

Published in: Review of Quantitative Finance and Accounting | Issue 1/2016

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Abstract

A cynosure of the academic literature relating to initial public offerings (IPOs) is the question of why they are “mispriced” so frequently. The large and growing literature addressing this question is evidence as to its intractability. This paper develops a theory of underwriters’ behavior suggesting that they will exploit their private information to minimize the bilateral risks to themselves of firm-commitment IPOs. That minimization may cause them to knowingly underprice the issue. The main result in this paper is based, in part, on the premise that the random character of the investors’ demand for shares in the secondary market, given the spread, is governed by an estimable conditional probability distribution. The underwriters exploit their private knowledge of that probability distribution to influence the number of shares in the offering in such a way as to minimize their expected loss function.

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On December 8, 2011, the New York State Appellate Division, First Department, held in EBC I, Inc. v Goldman Sachs & Co. that Goldman Sachs & Co., the lead underwriter for the IPO of common stock by EBC I, Inc., formerly known as eToys, Inc., was not eToys’ fiduciary. NY Slip Op. 08839.

“A fiduciary relationship exists between two persons when one of them is under a duty to act for or give advice for the benefit of another upon matters within the scope of the relation.” Restatement [Second] of Torts § 874, Comment a.

The New York Court’s decision did nothing to change the law that underwriters can be held criminally and/or civilly liable if they engage in acts of fraud or if they make factual misrepresentations or if they conceal significant and relevant facts.

The court’s asymmetric reasoning regarding the underwriters’ risk and incentive(s) is mirrored by similar reasoning found in the finance literature. For example, Chen and Mohan (2002) stated: “We contend that underwriter spread may represent an explicit pricing of risk for an IPO issue and we find that it is significantly correlated with underpricing, which represents an implicit pricing of risk.” That statement recognizes only one source of underwriting risk. Similar opinions are expressed in other publications of the same or later vintage. See Jones and Yeoman (2011).

A special characteristic of H-shares is that they are shares of companies incorporated in China, but are also listed abroad.

The underwriters’ gross spread is usually expressed as a percentage discount of the offering price; e.g. P _i is 95 % of P _o.

This paper does not address underwriting of IPOs which are fully subscribed ab initio. In those kinds of IPOs all uncertainty is eliminated. Sherman (2005) states that those fully-subscribed IPOs have increased worldwide since the early 1990s.

There have been extensive studies of the effect of public and private information on the offer price. In addition to the study by Benveniste and Spindt (1989) cited in the text, see Bradley and Jordan (2002), Edelen and Kadlac (2005), Hanley (1993), Loughran and Ritter (2002) and Lowry and Schwert (2002).

The paper by Zhang (2012) makes the same assumption as to the endogeneity of the size of the IPO. That paper expressly assumes the absence of financial intermediation. Zhang’s assumption vitiates the verisimilitude of his theory.

The underwriters’ expected loss function expressed as Eq. (5) is similar to the so-called “boundary conditions” appearing as expression (2) in Bae and Levy (1990).

Adams et al. (2008) comments that the practitioners’ idiom describes the nominal loss as the “haircut” taken by the underwriters.

The mean of the Poisson distribution in the example is arbitrary.

Technically, the plaintiff was the Official Committee of Unsecured Creditors of eToys, Inc., a bankrupt internet start-up company that was incorporated in 1996. By order of the United States Bankruptcy Court for the District of Delaware, plaintiff was granted standing as a representative of eToys' bankruptcy estate and authorized to prosecute any litigation claim on behalf of eToys and the estate.

The general formula for the differentiation of an integral of a function with respect to a parameter, when the limits are also functions of the parameter, is stated below.

If \(\varphi \left( \alpha \right) = \mathop \int \limits_{a}^{b} g\left( {x, \alpha } \right)dx,\) where a and b are functions of \(\alpha\), and if some general restrictions are placed on \(g(x, \alpha )\) and \(\partial g(x, \alpha )/\partial \alpha\), then

\(\frac{d\varphi (\alpha )}{d\alpha } = \mathop \int \limits_{a}^{b} \frac{\partial }{\partial \alpha }\left[ {g(x, \alpha } \right]dx + g\left( {b,\alpha } \right)\frac{db}{d\alpha } - g(a, \alpha )\frac{da}{d\alpha }\)

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Title: A theory of underwriters’ risk management in a firm-commitment initial public offering
Author: Edmund H. Mantell
Publication date: 01-01-2016
Publisher: Springer US
Published in: Review of Quantitative Finance and Accounting / Issue 1/2016
Print ISSN: 0924-865X
Electronic ISSN: 1573-7179
DOI: https://doi.org/10.1007/s11156-014-0466-0

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