Shellability of noncrossing partition lattices

We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type $D_n$ and those of exceptional type and rank at least three.Comment: 10 page

The economic performance of small banks, 1985-2000

Several trends in the financial industry over the past decade and a half have potentially threatened the competitiveness of small banks. Among these developments are the numerous mergers that increased the size and scope of large banks and the increased competition from mutual funds and other nonbank financial institutions. This article examines the economic performance of small banks during the 1985-2000 period by focusing on their ability to attract and profitably intermediate insured and uninsured deposits. It finds that the expansion of deposits and assets at small banks, when adjusted to account for the effects of mergers on measured growth, has consistently exceeded the growth at large banks. Moreover, the profitability of small banks has risen to high levels over the period. These indications of strength among small banks as a whole also hold true for subgroups within the small bank sector. Aside from their success in attracting deposits, the key reasons for the generally good performance of small banks in recent years appear to be their ability to earn relatively high rates of return on their loans and an increase in the share of their portfolios devoted to loans.Bank mergers ; Bank size

Complexes of nonpositive curvature for extensions of F2 by Z

AbstractFor any extension G of F2 by Z, which is not virtually a direct product of the two factors, we construct a 2-complex of nonpositive curvature with fundamental group G. As a corollary we obtain a new proof of the fact that any such extension has an automatic structure

Over-Pessimism of Bank Stocks since the Great Recession of 2008

2nd Place 2020 Denman Business and SocietyIn September of 2008, the "Great Recession" began and wreaked havoc on the global financial system. This severe panic caused fear, volatility, and a rise in the perceived risk of securities. In this unique environment, banks were a deserved scapegoat of the recession and the future profitability of banks was in question. This research investigates whether this severely negative sentiment led to investors being over-pessimistic in their views regarding bank stocks. Did internal psychological biases play a role in investors' disdain towards bank stocks? If this hypothesized pessimistic behavior can be shown, this research can provide evidence that either investors are irrational actors who have routinely incorrect views towards future cash flow streams of securities or that human biases obscured the ability to see the opportunity for a recovery in these securities. For this work, earnings per share (EPS) announcements act as adjustments to the stock's intrinsic value as the market theoretically reacts accordingly, to either affirm past predictions or edit those previously false forecasts immediately after earnings are announced. In order to turn EPS metrics into earnings reactions, we measured the price reaction from the 3 day period before earnings announcements through the day after to gauge investor sentiment. From this, we were then able to find whether investors and analysts were over/under-optimistic or over/under- pessimistic towards a sample of 48 banks from 2008-2019. Through a detailed examination of earnings reactions and regression analyses, it can be determined that investors were significantly over-pessimistic towards financial stocks. For example, in Q2 2008, the sample had an average "positive surprise" of 11.34%, meaning that the stock prices increased 11.34% on average from the day before its earnings announcement to the day after's closing price, signifying that analysts and investors were too pessimistic before earnings revealed the new reality of bank conditions. This phenomenon is tested for many variables including testing over differing time periods, for banks of different sizes by market cap, among many other factors. Through these tests, we are able to determine that irrational behavior persisted in this time period, providing evidence towards incorrectly biased actors in the market, and thus evidence against the Efficient Markets Hypothesis (EMH).No embargoAcademic Major: Financ

h-vectors of generalized associahedra and non-crossing partitions

A case-free proof is given that the entries of the $h$-vector of the cluster complex $\Delta (\Phi)$, associated by S. Fomin and A. Zelevinsky to a finite root system $\Phi$, count elements of the lattice \nc of noncrossing partitions of corresponding type by rank. Similar interpretations for the $h$-vector of the positive part of $\Delta (\Phi)$ are provided. The proof utilizes the appearance of the complex $\Delta (\Phi)$ in the context of the lattice \nc, in recent work of two of the authors, as well as an explicit shelling of $\Delta (\Phi)$.Comment: 20 pages, 1 figur