IPO pricing: a case of short-sale restrictions and divergent expectations

Abstract

Prior research shows that short-sale restrictions during an IPO lead to higher aftermarket prices. Using this and heterogeneous expectations on the factor pricing coefficient, our model sheds additional light on the impact of the short-selling constraint. Like prior research, short-sale restrictions in the IPO market lead to higher aftermarket prices. Importantly, our model predicts that this constraint leads to a different factor pricing coefficient than the analog under complete markets. Our empirical tests over an extended period of time support the model's predictions.

Keywords:

• Applied finance
• Applied investment analysis
• Behavioral finance
• Investments management
• Short selling
• IPO
• Inefficiencies

Acknowledgements

Nayar is grateful for financial support from the Hans Julius Bär Endowed Chair. We are also grateful to Ajai K. Singh at Case Western for providing data on IPOs used in the empirical part of the paper.

Notes

†This presumes the absence of asymmetric information and that the investment banker sets the IPO offer price with full knowledge of the supply and demand schedules for the IPO shares.

‡The current settlement of trades follows the T + 3 convention, where T refers to the transaction date. However, in earlier times it was T + 5.

† An exception is the empirical examination of Ofek and Richardson (2003) which investigates internet stocks during the dot-com boom. While this is a key study, their results may not be generalizable to the entire IPO market.

‡This is because short selling is profitable only when new issues decline at a rate sufficient to cover the opportunity costs, which the short seller owes to the lender of the stock. These opportunity costs consist of the dividends on the borrowed stocks and the market interest rate at the time of the borrowing, since the brokerage will hold the proceeds from a short sale in escrow, pay no interest, and any subsequent price rise requires additional deposits to cover the loss. Therefore, an ex-ante proxy for the expected returns from the new issues should be this interest cost. These findings are supported by Figlewski (1981).

†As mentioned earlier, estimation risk/parameter uncertainty and attendant pricing effects are exacerbated when there is no prior history of trading data (Brown 1979, Coles and Loewenstein 1988, Coles et al. 1995).

‡For instance, see Almazan et al. (2000), Liu and Longstaff (2000), and Mitchell et al. (2002). It is also pointed out by Daouk et al. (2006) that security laws are an important factor in performance.

§As part of the research undertaken by Geczy et al. (2002), the authors document several facts related to shorting within the IPO market such as investors with good access can short most IPOs at first, but investors without access to specials cannot. After about a month, at least a quarter of IPOs are available to investors without access to specials.

¶See www.eseclending.com for an overview of the lending market and process.

†Assumptions: (1) there are no transaction costs; (2) shares of stock are infinitely divisible; (3) security returns are multivariate normal; (4) the risk-free interest rate is constant; (5) investors can borrow and lend freely at the risk-free rate; and (6) all investors have identical beliefs about the available securities other than the IPO shares, in which investors have a divergence of opinion.

‡The negative exponential utility function has also been justified by Grossman (1976) and Grossman and Stiglitz (1980).

§We assume in the model that the short-sale restriction is strictly imposed. This assumption is stronger than reality. For example, Geczy et al. (2002) report that it is not impossible to short sell the IPO stock the first day itself. Nonetheless, we assert that short selling during the initial life of an IPO stock is not very easy.

¶Multifactors certainly could be assumed. However, as is discussed later, our focus here is on the impact of short-sale restrictions and different opinions on the IPO's relation with the market randomness. Therefore, some abstraction here by assuming a combined component that represents all other random sources would serve our purpose better.

⊥We acknowledge that our modeling follows Daniel et al. (2001) in spirit.

†In the model that follows, investors’ difference of opinion about the IPO stock, J, involves their estimate of the factor loading, . Specifically, some investors may believe that the factor loading is large, whereas others may believe it is low. Without loss of generality, each asset composite term can be assumed to have zero mean since any non-zero mean can be transferred to the constant term, , in the model. As is generally assumed with factor models, the asset composite terms have non-zero variances and are not correlated with the systematic factor, i.e. E() > 0 and for j = 1,…,J. However, the composite terms may be correlated with each other, i.e. for k and j = 1, … , J. Denote the covariance matrix of composite terms as .

‡We assume away the possibility of different opinions on the IPO's composite term in order to focus on our hypothesis that investors have different opinions on the IPO's correlation with the systematic factor.

†As mentioned earlier, a difference of opinion about the IPO stock involves the estimate of the factor loading, , with some investors believing it to be large whereas others may believe it to be small.

‡We use the term beta to denote the factor loading.

§We acknowledge that several researchers have tried to directly collect data, such as lending rates, etc., and presented them as the evidence of short-sale restriction related to IPOs. Direct data collection is not easy, and there could be some difficulties with it. Presumably, the rates also vary by broker. For example, the lending rates are not unique at each time, based on interest rate changes, and are not universally available for all IPOs over a broad period of history of the financial markets. Thus, empirical tests that do not rely on lending rates are needed to verify the effect of short sales on stock prices in the IPO aftermarket.

†We use these periods of [+1, +30] and [+91, +120] relative to the offer date (day 0) to examine the change in beta because we believe that short-sale restrictions should be strongest in the first 30 days after the offer date and should be less restrictive in the latter period. This is because, in the later period, investor clienteles have possibly been identified and trading patterns have stabilized in the IPO stock. Further, the first 25 days is the ‘quiet period’ of the IPO and may be the time that price stabilization activities by the underwriter of the offering is the strongest. At the suggestion of an anonymous referee, we also examined the robustness of our results for alternate event–time windows where short sales may not have been restrained (i.e. instead of the [+91, +120] window). These periods included [+31, +60], [+31, +90], and [+31, +120], and the results are qualitatively the same as those reported in the paper. These results are available upon request.

‡We discuss the relationship between γ_j and other variables later. Note that we are not analysing the effect of divergence of opinion on long-term performance as in Gao et al. (2006).

§When we aggregated the data for all firms and ran a single time-series cross-sectional regression as denoted in equation (9), the value of the beta change parameter, γ, was –0.156, significant at the 0.0001 level with an adjusted R ² value of 6.31%. This indicates that, on average, the beta of IPO firms falls over the two time intervals mentioned earlier, consistent with the view that short-sales constraints are present in the initial IPO aftermarket.

¶For example, see Hanley-Weiss et al. (1993), Benveniste et al. (1996), Prabhala and Puri (1999), Aggarwal (2000), and Fishe (2001).

⊥Higher reputation investment bankers have a higher value for the IBRANK_j variable.

†We also employed the natural logarithm of IPO size as a proxy variable for divergence of opinion. The logic behind using this variable is that larger IPOs are supposedly more researched and thus have more information available about them. As such, with this increased information availability, larger IPOs should be associated with less divergence of opinion. However, this variable was not as significant as the High Tech variable in our tests. Nonetheless, we note that other proxies for divergence of opinion are also possible. We acknowledge the input of an anonymous reviewer in encouraging us to pursue this possibility.

‡This High Tech variable is based on the classification from the SDC database of IPOs. The use of this variable can be seen in Lowry and Schwert (2001), Bradley and Jordan (2002), and Ljungqvist and Wilhelm (2003), who employ it in a similar vein.

§We thank Professor Ajai K. Singh at Case Western University for providing us with an expanded version of the sample of IPOs used by Bradley et al. (2004).