Underpricing is commonly measured as the first day’s initial return on the IPO stock. Underpricing is thus measured as the difference between the offer price and the closing price at of the first trading day. A positive initial return implies that the offer price on the IPO stock was set too low, resulting in a price increase the first day of trading. An issue is overpriced if there is a negative initial return.
2.5.1 Simple initial return
The simple initial return is calculated using the following formula (Logue, 1973):
𝑅𝑅𝑖𝑖 = 𝑃𝑃𝑖𝑖,𝑡𝑡− 𝑃𝑃𝑖𝑖,𝑡𝑡−1
𝑃𝑃𝑖𝑖,𝑡𝑡−1
Ri= Simple initial return of stock i
Pi,t = Closing price of stock i at first day of trading Pi,t-1 = Offer price of stock i on last day of offer period
Alternatively to this calculation is using the price at opening of the trading day instead of closing price.
We argue that using the closing price is more correct; at closing, the market has stabilized as all investors interested in trading in the stock has had the time to do so. By using the opening price only
33
pre-opening bids have been registered and these bids are typically avoided by investors who want to see the public price before bidding.
Using this method all necessary information needed to decide the extent of the underpricing is reflected in the stock price at closing. Information regarding market movements during the period between the last offer day and the first day of trading is not. As there might be several days between the last offer day and the first day of trading, market movements will often affect the initial return. The longer the period between last offer day and first trading day, the more uncertainty there is regarding the effect of the market movements on the calculated initial return. It is therefore necessary to adjust for the market movement to see the net underpricing of the stock. Not adjusting the initial return might result in a bias in the estimates of underpricing. Several researchers do however choose not to adjust their estimates of initial return, arguing that it is of negligible importance for the results (Lowry and Schwert 2001; Derrien and Womack 2003; and Ljungqvist and Wilhelm 2003)
2.5.2 Market adjusted initial return
The market adjusted initial return is calculated using the following formula:
𝛼𝛼𝑖𝑖 = 𝑅𝑅𝑖𝑖 − 𝑅𝑅𝑚𝑚 =𝑃𝑃𝑖𝑖,𝑡𝑡− 𝑃𝑃𝑖𝑖,𝑡𝑡−1
𝑃𝑃𝑖𝑖,𝑡𝑡−1 −𝐼𝐼𝑖𝑖,𝑡𝑡− 𝐼𝐼𝑖𝑖,𝑡𝑡−1
𝐼𝐼𝑖𝑖,𝑡𝑡−1 αi = Market adjusted initial return of stock i
Ii,t = Index closing value on the first day of trading of stock i Ii,t-1 = Index value on the last day of the offer period of stock i
In this measure of underpricing a relevant index is used to capture the market movements. The return of the index in the relevant period is subtracted from the simple initial return of the new issue, a method first introduced by Logue (1973). Which market index one uses might impact the estimated underpricing and must therefore be chosen with care. Optimally the index should have the same risk profile as the new issue and thus act as an alternative investment. A general stock exchange index can be used as well as an industry specific one. As it is difficult to find an index that fully represent an
34
alternative investment, there might still be some effects of the market movement in the calculated underpricing, which could result in biased estimates.
To calculate underpricing adjusted for market return, we have chosen to use different indices for each exchange. All the exchanges in our sample are relatively small, so the industry specific indices are small, illiquid and highly dependent on a few companies. We therefore believe that the index containing the 20 – 60 most traded shares listed on the exchange give the more accurate picture of the actual market return in the period. As all the indices are based on the same principle, we further believe that they are comparable.
For Copenhagen Stock Exchange, the OMXC20 was chosen as the market portfolio. OMXC20 is a market capitalization weighted portfolio, meaning that the biggest companies on the exchange
constitute the biggest part of the portfolio. The index consists of the 20 most actively traded shares on the exchange and is adjusted twice a year; in the beginning of June and December. The index has developed from a base value of 100 from July 3, 1989 and gives a good indication of the development of the stock market as a whole during the year. From 2013 the index lost status as the leading index on the exchange to OMXC20 CAP. In OMXC20 CAP, no company can weigh more than 20% (Kjelland, 2013). Despite not being the leading index, we have chosen the OMXC20 as market index because OMXC20 CAP was not established until 2011. This means that data is not available for our entire sample period and we believe using the same index over the entire period gives the most consistent and comparable observations (Bloomberg, 2016).
For Oslo Stock Exchange, the OSEBX (Oslo Benchmark Index) was chosen. This is a portfolio that per December 31, 2015, consisted of 58 of the most traded shares listed on Oslo Stock Exchange. The index is tradable and adjusted every third Friday in June and December each year with respect to number of shares in the index and which companies are included. The index was chosen as we believe it to be a representative selection of all shares listed on OSE (Oslo Boers, 2016).
The OMXS30 was chosen as market portfolio for the Stockholm Stock Exchange. The index is equivalent to the OMXC20 only for the SSE and differs from the Danish index in that it contains 30 of the most
35
actively traded shares listed on the exchange. The index started at a base level of 125 as of September 30, 1986 and was subject to a 4-1 split in index value on April 27, 1998 (Bloomberg, 2016).
2.5.3 Offer size adjusted initial return
The offer size adjusted initial return is calculated to measure the underpricing relative to market value of the company. The following formula has been used (Neumann, 2003):
𝛾𝛾𝑖𝑖 = 𝛼𝛼𝑖𝑖∗ 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝑠𝑠ℎ𝑎𝑎𝑁𝑁𝑁𝑁𝑠𝑠 𝑜𝑜𝑜𝑜𝑜𝑜𝑁𝑁𝑁𝑁𝑁𝑁𝑜𝑜 𝑇𝑇𝑜𝑜𝑇𝑇𝑎𝑎𝑇𝑇 𝑠𝑠ℎ𝑎𝑎𝑁𝑁𝑁𝑁𝑠𝑠 𝑜𝑜𝑁𝑁𝑇𝑇𝑠𝑠𝑇𝑇𝑎𝑎𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 𝑝𝑝𝑜𝑜𝑠𝑠𝑇𝑇 𝐼𝐼𝑃𝑃𝐼𝐼 γi = Market adjusted underpricing adjusted for offer size
αi = Market adjusted underpricing
The offer size adjusted measure of underpricing reveals how much the underpricing would be if all shares were offered in the IPO. One may see this measure as the overall cost of getting a value of the company from the company’s point of view. As a company usually does not float all outstanding shares in an IPO, the offer size adjusted initial return is much smaller than the market adjusted return.