This paper defines asymptotic marginal expected shortfall (AMES) for banks within a financial system and provides corresponding estimation method based on multivariate extreme value theory. The estimation method does not assume a specific dependence structure among bank equity returns. Both theoretical AMES and the estimator possess additive property and thus can serve as a tool to allocate system-wide risk to individual institutions. We apply the AMES to 30 global systemically important financial institutions (G-SIFIs). We show that the AMES outperforms the MES in predicting extreme losses during extreme systemic events. By taking the AMES as the reference point for allocating systemic risk to individual institutions, we show that an allocation according to simple bank characteristics such as size and individual risk can be imperfect. The allocation unfairness of individual risk or size across all the G-SIFIs has increased since 2008.

We investigate whether Article 11 pro forma financial information assists investors in valuing IPOs. While the SEC expects it to be helpful in assisting investment decisions, Article 11 pro forma financial information is based on registrants' understanding and assumptions, and registrants can exercise their own judgment when preparing pro forma financial statements. It is therefore an empirical question whether the information contained in pro forma financial statements is useful to investors. We examine the association between pro forma adjustments of earnings and book value of equity and the IPO offer value and find asymmetric results. While positive pro forma adjustments of earnings and book value of equity are positively associated with the IPO offer value, negative pro forma adjustments of earnings and book value of equity are negatively associated with the IPO offer value, suggesting that negative pro forma adjustments are priced as growth opportunities. Additional analyses reveal that the association between pro forma adjustments of book value of equity and the IPO offer value varies across different time periods and industries and that pro forma adjustments of book value of equity are initially mispriced by investors. In contrast, we do not find similar results for pro forma adjustments of earnings. Further empirical tests show that the asymmetric results of mispricing of pro forma adjustments of earnings and book value of equity may be explained by the requirements of Article 11 of Regulation S‐X for pro forma adjustments dictating that adjustments to earnings reflect only recurring items while adjustments to book value reflect both recurring and nonrecurring items.