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Table 1 Comparison of IPO pricing and underpricing under fixed-price and bookbuilding issuing. The table shows the issuing pricing、Equilibrium price of secondary market、IPO intentional underpricing and unintentional underpricing under Fixed-price issuing and Bookbuilding issuing. The results come from the IPO underpricing model (3) and model (6). The table are shown as follows:

From: Heterogeneous expectations, IPO Underpricing and issuing mechanism

Issuing way Issuing price Equilibrium price of secondary market IPO underpricing Intentional underpricing Unintentional underpricing (non-homogenous expectation)
Fixed-price issuing \( \overline{E}(U)-\frac{1}{2}\rho {\sigma_1}^2 \) Ē(U) + V 2 − V \( \frac{\rho {\sigma_1}^2+2\left({V}_2-{V}_1\right)}{2\overline{E}(U)-\rho {\sigma_1}^2} \) \( \frac{\rho {\sigma_1}^2}{2\overline{E}(U)-\rho {\sigma_1}^2} \) \( \frac{2\left({V}_2-{V}_1\right)}{2\overline{E}(U)-\rho {\sigma_1}^2} \)
Book building issuing \( \frac{n{\sigma_2}^2\overline{E}(U)+{\sigma_1}^2{\displaystyle {\sum}_{i=1}^n{s}_i-\rho k}}{n\left({\sigma_1}^2+{\sigma_2}^2\right)} \) \( \frac{{\sigma_2}^2\overline{E}(U)+{\sigma_1}^2V-n{\sigma_1}^2{\displaystyle {\sum}_{i=1}^n{s}_i}}{\left(n+1\right){\sigma_1}^2+{\sigma_2}^2}+{V}_2-{V}_1 \) \( \frac{k\rho {\sigma_1}^2{\sigma_2}^2+n\left({\sigma_1}^2+{\sigma_2}^2\right)\left({V}_2-{V}_1\right)}{n\overline{E}(U)\left({\sigma_1}^2+{\sigma_2}^2\right)-k\rho {\sigma_1}^2{\sigma_2}^2} \) \( \frac{k\rho {\sigma_1}^2{\sigma_2}^2}{n\overline{E}(U)\left({\sigma_1}^2+{\sigma_2}^2\right)-k\rho {\sigma_1}^2{\sigma_2}^2} \) \( \frac{n\left({\sigma_1}^2+{\sigma_2}^2\right)\left({V}_2-{V}_1\right)}{n\overline{E}(U)\left({\sigma_1}^2+{\sigma_2}^2\right)-k\rho {\sigma_1}^2{\sigma_2}^2} \)