Underpricing Skewed Assets : The Case of Initial IPO Returns

I bring together the issues of offering price accuracy and underpricing and point out that there is a trade-off between the two. If the underwriter intends to set an unbiased offering price, and thereby minimizing the mean absolute pricing error (MAPE), skewness might induce ex ante underpricing (i. e. an offering price below the expected secondary market price). In order to illustrate my rather statistical reasoning, I examine the simplest skewed price distribution one can think of: a discrete price distribution with just two possible prices. In order to come up with more general propositions, I allow for objective functions with differing costs of over- and underpricing including the case of equal costs as a special case. An equal cost of over- and underpricing induces the underwriter to minimize MAPE and thereby underprice on average positively skewed stocks. While skewness induces underpricing, I find that in a situation where underpricing is expected, an increased skewness is associated with less expected underpricing keeping standard deviation und expected value constant