Referring to the above mentioned definition, the extent of the IPO-Underpricing could be measured as the (diskreet) difference between the first trading price and the issue price:
IRi = Pi,t - Ei
IRi means theinitial return(IR) of the share (i); Pi,t is the trading price (P) of the share (i) at its first trading day on the secondary market and Ei is the issue price (E) of the share (i).
Strictly speaking, it is necessary to take in fact the first trading price on the first exchange trading to analize the price effects of initial public offerings. But the empirical practice is often inaccurate.For instance, Saunders/Lim (1990) or Lee/Taylor/Walter (1996) use the closing price on the first trading day, Uhlir (1989) takes the "Kassakurs" (i.e.
the official market clearing price) and Carter/Manaster (1990) refer to the closing bid price two weeks after the offering.
To make the initial return of a share comparable to another one it is customary to quote the initial return in relation to the issue price of the share (and multiply with 100 to get a proportional return).
This measure considers the price difference only and allows no statement about the fact, it the issue was "too cheap" or "too expensive" - since there is no standard of comparison.
This would be an alternative investment, because an investor, sub-scribing to an IPO, has the possibilty of an alternative investment instead. In comparison to this alternative investment only it is possible to value the extent of underpricing - if the IPO was underpriced or overpriced.
This is the reason why the initial return of the share (IRi) is usually adjusted by the return of an alternative investment to measure the extent of underpricing.
UPi = IRi - M
This notion is themarket-adjusted underpricing because the initial return is adjusted by the return of "the market".
(M) means the price of the used market portfolio; (t) is the first trading price of the share (i) and (t,0) is the the price of the market portfolio on day "0".
For this day "0" it is customary to take the day before the first trading day; strictly speaking one has to take the price of the market portfolio at the end (or the conclusion) of the subscribing period of the share (i).
Regarding this formula it is evident, that the selection of the market portfolio is of high importance for the empirical determination of the extent of IPO-Underpricing.
Should the extent of the initial return be considered in comparison to a riskless investment or should the initial return be considered in comparison to an alternative investment which implies the same risk as the IPO? Aiming at the first, the underpricing is c.p.
higher as if aiming at the second (a positive initial return provided). If the market portfolio shoould be an alternative investment bearing nearly the same risks a wide share index could be use to quote the extent of a market adjusted underpricing.
Corporate Finance- IPO and Underpricing (XiaoPing Li)
This one is the customary approach. Using a market portfolio of the same risks of the IPO, the initial return would be risk-adjusted - but refering to Döhrmann (1989), the differences between the market-adjusted underpricing and the risk-adjusted underpricing are marginal only.
An alternative determination of the extent of IPO-Underpricing aiming not at the discreet difference of the first trading price and the issue price, but on a continual price adjustment between primary and secondary market.
For instance, Wasserfallen/Wittleder (1994) or Ljungqvist (1997) use the following logarithm:
Even if both formula could be use to determine the extent of undepricing empirically the different implications of the price adjustment should be considered.