Frazzini and Pedersen (2014) document that a betting against beta strategy that takes long positions in low-beta stocks and short positions in high-beta stocks generates a large abnormal return of 6.6% per year and they attribute this phenomenon to funding liquidity risk. We find strong confirmation of their results on U.S. equity data, but provide evidence of an alternative explanation. Portfo...

The number T*(n, k) is the least positive integer such that every graph with n = (*:I) + t vertices (t > 0) and at least T*(n, k) edges contains k mutually vertex-disjoint complete subgraphs S, , S, ,..., Sk where S, has ivertices, I < i Q k. Obviously T*(n, k) > T(n, k), the Turan number of edges for a Ki . It is shown that if n > gkk” then equality holds and that there is c :0 such that for (...

In this paper we deduce a universal result about the asymptotic distribution of roots of random polynomials, which can be seen as a complement to an old and famous result of Erdős and Turan. More precisely, given a sequence of random polynomials, we show that, under some very general conditions, the roots tend to cluster near the unit circle, and their angles are uniformly distributed. The meth...

Extremal graph theory is, broadly speaking, the study of relations between various graph invariants, such as order, size, connectivity, minimum/maximum degree, chromatic number, etc., and the values of these invariants that ensure that the graph has certain properties. Since the first major result by Turan in 1941, numerous mathematicians have contributed to make this a vibrant and deep subject...

For every real p > 0 and simple graph G, set f (p,G) = ∑ u∈V (G) d (u) , and let φ (r, p, n) be the maximum of f (p,G) taken over all Kr+1-free graphs G of order n. We prove that, if 0 < p < r, then φ (r, p, n) = f (p, Tr (n)) , where Tr (n) is the r-partite Turan graph of order n. For every p ≥ r + ⌈√ 2r ⌉ and n large, we show that φ (p, n, r) > (1 + ε) f (p, Tr (n)) for some ε = ε (r) > 0. Ou...

In this paper, we develop machinery for proving sum of squares lower bounds on symmetric problems based on the intuition that sum of squares has difficulty capturing integrality arguments, i.e. arguments that an expression must be an integer. Using this machinery, we prove a tight sum of squares lower bound for the following Turan type problem: Minimize the number of triangles in a graph $G$ wi...

The problem of on-line bin packing restricted to instances with only two item sizes (known in advance) has a well-known lower bound of 4/3 for its asymptotic competitive ratio. We present an algorithm which shows that this lower bound is also an upper bound. Hence the asymptotic competitive ratio for this on-line problem is equal to 4/3. Our result extends the corresponding result of Faigle, Ke...

358 Ann Dermatol Received July 18, 2011, Revised August 9, 2011, Accepted for publication August 11, 2011 Corresponding author: Hakan Turan, M.D., Department of Dermatology, Duzce University Medical Faculty, Konuralp 81160 Duzce, Turkey. Tel: 90-380-542-13-90, Fax: 90-380-542-13-87, E-mail: drhakanturan@ gmail.com This is an Open Access article distributed under the terms of the Creative Common...