ante expected degree of underpricing as Ut =
t t t m i d µ µ ˆ ˆ −
, where midt serves as a estimate of the expected
issue price and is defined to be the market capitalization computed from the midpoint of the announced
p r i c e r a n g e a n d t h e a n n o u n c e d s h a r e q u a n t i t i e s 3 0 a n d t µ ˆ i s t h e e x a n t e m a r k e t f o r e c a s t o f t h e p o s t - I P O
market value estimated from equation (3). We correlate this withσˆt , the ex ante market uncertainty
estimated from equation (3). From the date that the first initial price ranges and share quantities were
announced (with Amendment 4 on 7/26/04) through the IPO date (8/18/04), the correlation coefficient
was -0.62 (t = -2.56, p-value = 0.018). While this result is not strictly counter to Rock’s (1986)
prediction,31 it is indicative of a relationship between underpricing and uncertainty that would go in the
opposite direction of his model.
4. Evidence on Theories that Involve Discretionary Allocations of Shares or Pre-
commitment to IPO Prices
Further evidence on theory comes from Google’s unique auction mechanism. Benveniste and
Spindt (1989) and other models (e.g., Loughran and Ritter, 2002) rely on discretionary allocations of
shares by the investment banker. Some models rely on pre-commitment to underprice (e.g., Benveniste
and Spindt, 1989). Others rely on pre-commitment to a price, after which investors gather information
(e.g., Chemmanur, 1993). Because the auction mechanism severely restricted discretion in allocating
shares and determined the allowable maximum IPO price after bids were submitted, underpricing here is
evidence against models that rely on such factors. If these factors alone explained underpricing, we
should not have observed it in Google’s case.
30 Whether we use the midpoint, the upper end or the lower end makes no substantive difference to the results that follow. 31Again, his model would predict a positive cross-sectional correlation between ex ante uncertainty and average levels of ex post under pricing. Here, we show a positive time series correlation between ex ante uncertainty and ex ante forecasts of underpricing.