Basic Benchmark Measurement

A first step to build up a testable model is to choose a proper measurement benchmark. To measure the IPO under-pricing level, two approaches are adopted in previous literatures. Therefore, it is necessary to make a comparison between the two. The most widely accepted and used approach is to use the IPO raw initial return that is defined by the formula:

1 i r = 0 1 0 1 i i i i P D P P − + (1) where r is the ii1 th

IPO share’s daily return on the first trading day;

1

i

P is the closing price of the ith IPO share on the first trading day;

0

i

P is the offer price of the ith IPO share;

1

i

D is the dividend issued on the first trading day for the ith IPO share.

As a matter of fact, dividend in the first trading day is equal to zero. Therefore, the raw initial return (IPORETN) is defined by:

IPORETN = 0 0 1 P P P − (2)

as Ritter (1984).

On the other hand, some researchers such as Chi and Padgett (2005) also used market- adjusted abnormal initial return (MAAR) to measure the IPO under-pricing degree. The MAAR definition is:

1 i MAAR = 100 × ( 1 1 1 1 m i r r + + - 1) (3)

where r is the raw initial return; and i1 r is the same time market index return with m1

the definition: 1 m r = 0 0 1 m m m P P P − (4)

In the formula P is the closing market index on the first trading day and _m1 P is the _m0

closing market index on the offer day.

Chi and Padgett (2005) claimed that the market-adjusted initial return will give a more accurate picture. When MAAR is interpreted as an abnormal return, the i1

assumption is that the systematic risk of the IPO’s under consideration is the same as that of the index, i.e. the betas of the IPO's average to unity. Ibbotson (1975) and some other researchers have demonstrated that the average beta of newly listed firms is higher than one. Thus, the abnormal return MAAR calculated in above equation i1

provides a somewhat upwardly-biased estimate of the initial performance of the IPO relative to the market. On the other hand, the market-adjusted initial return provides a good measure of relative return. Since the under-pricing is measured against the average returns in the market, the market-adjusted return is more sensible measure according to the under-pricing definition. As a matter of fact, this thesis finds no

statistically significant difference between the two under-pricing measures of IPO raw initial return and the market-adjusted initial return. But for logic consistency, the thesis will present the statistics and regression results in terms of market-adjusted initial return.

A third measure of IPO under-pricing is the so-called odds (new share lottery winning ratio)-adjusted IPO initial return. As mentioned earlier, the IPO's in China are all oversubscribed and the oversubscription rates are normally very high which is reflected by a very low lottery winning ratio of new shares. It is suggested by some researchers to make adjustment of the possibility of being allocated the new shares to the IPO initial return. The logic is that if a high degree of under-pricing is achieved through a high degree of oversubscription which means a much higher demand than the supply then the initial return should be reduced accordingly to reflect the low probability of winning the new share. Such lottery winning odds-adjusted and market- adjusted IPO initial return has been used by researchers such as Liu (2003) in empirical studies. It is defined as follows:

1

i

OAMAR = MAAR_i1× WINNINGRATE_i1 (5)

where MAAR is the IPO market-adjusted initial return and WINNINGRATE is the i1

IPO new share lottery winning ratio. WINNIGRATE is defined by the following formula: WINNINGRATE = investors by the for applied shares Total firm issuing by the offered shares Total (6)

All quantities in formula 5 and 6 are calculated based on the data on the IPO listing date.

After appropriate proxy measure of the under-pricing magnitude has been chosen, the next step is to find the proper statistic model and identify other independent variables. As Stigler (1981) points out, the method of least square is the automobile of modern statistical analysis. This study is going to carry out the hypothesis test based on the so- called ordinary least square (OLS) regression model, particularly because the OLS regression is asymptotically efficient and is a best linear unbiased estimation (BLUE) model. The principle is to choose the estimated regression coefficients to fit in the regression model so that the sum of squares of prediction errors is minimized, given certain independent variables. In this sense, those independent variables that give the best fitting result will be the factors that have the biggest power in explaining the dependent variable. As decided, the IPO initial return will enter the left-hand side of the regression equation as the dependent variable while all other factors that may explain this initial return will enter the right-hand side of the regression equation as independent variables. The question then boils down to which factors ought to be included as the independent variables, because these independent variables are exactly the factors we are looking for. The hypothesis test will replace the independent variables in the regression with the proxy variables set up according to the hypotheses listed in the last chapter. If the proxy variable stands the statistical test, so does the hypothesis.

As a matter of fact, the original benchmark OLS regression model is usually adopted by previous researchers such as Dewenter and Malatesta (1997) and Su and Fleisher (1999). An illustrative example is given as follows:

i

MAAR = α0 + α1 × PRICE + i α2 × IPOSZ + i α3 × AGE + i α4 × MKECAP + i

5

α ×PROFSHA + i α6×GOVNT + i α7×TIMEIPO + i εi (7)

The meanings of every variable in above equation will be explained in more details later in the following sections, but the regression formulas for every individual sub- samples will be in a similar format as above. The MAARi on the left-hand side of the

regression equation stands for the dependent variable which in this instance is the ith IPO’s market-adjusted initial return, and all other independent variables are listed on the right-hand side of the equation with α’s standing for the regression coefficients of these independent variables. The above independent variables are just for demonstration purpose because they may not all be included in the same model for a specific hypothesis test. On the other hand, some other factors may be missing from above model, depending on which hypothesis is to be tested. For example, the turnover rate for speculation effect hypothesis test is not included in the model. The independent variables serving particular hypothesis will be set up according to the hypothesis later on. The definition of additional independent variables will be explained accordingly in the following sections.

After the model is chosen, the next issue under concern is the scaling of the measurement. There is a particular reason to scale the independent variables’ values so that the resulting numbers are not too large or too small and are similar in magnitudes to other variables. This is because large numbers cause overflow errors and small numbers cause round-off errors, especially when sums of squares are computed, which adversely affect the accuracy of results. If the scale of measurement of an independent variable is changed in a linear regression model, its regression

coefficient and the corresponding standard errors are affected by the same scale, but all other statistics are unchanged. Therefore the impact of changing the scale of measurement on the regression results is well justified. As can be seen later the units of measurement of the independent variables in this study range widely from tens to billions, it is necessary to scale the measurement units of these variables to a similar level. Scaling of every individual variable will be discussed in details in the following section when these independent variables are defined.