Don’t Put All Your Eggs in One Basket? Diversification and Specialization in Lending

Should lenders diversify, as suggested by the financial intermediation literature, or specialize, as suggested by the corporate finance literature? I model a financial institution's ("bank's") choice between these two strategies in a setting where bank failure is costly and loan monitoring adds value. All else equal, diversification across loan sectors helps most when loans have moderate exposure to sector downturns ("downside") and the bank's monitoring incentives are weak; when loans have low downside, diversification has little benefit, and when loans have sufficiently high downside, diversification may actually increase the bank's chance of failure. Also, it is likely that the bank's monitoring effectiveness is lower in new sectors; in this case, diversification lowers average returns on monitored loans, is less likely to improve monitoring incentives, and is more likely to increase the bank's chance of failure. Diversified banks may sometimes need more equity capital than specialized banks, and increased competition can make diversification either more or less attractive. These results motivate actual institutions' behavior and performance in a number of cases. Key implications for regulators are that an institution's credit risk depends on its monitoring incentives as much as on its diversification, and that diversification per se is no guarantee of reduced risk of failure.

Decoupling with random quantum circuits

Decoupling has become a central concept in quantum information theory with applications including proving coding theorems, randomness extraction and the study of conditions for reaching thermal equilibrium. However, our understanding of the dynamics that lead to decoupling is limited. In fact, the only families of transformations that are known to lead to decoupling are (approximate) unitary two-designs, i.e., measures over the unitary group which behave like the Haar measure as far as the first two moments are concerned. Such families include for example random quantum circuits with O(n^2) gates, where n is the number of qubits in the system under consideration. In fact, all known constructions of decoupling circuits use \Omega(n^2) gates. Here, we prove that random quantum circuits with O(n log^2 n) gates satisfy an essentially optimal decoupling theorem. In addition, these circuits can be implemented in depth O(log^3 n). This proves that decoupling can happen in a time that scales polylogarithmically in the number of particles in the system, provided all the particles are allowed to interact. Our proof does not proceed by showing that such circuits are approximate two-designs in the usual sense, but rather we directly analyze the decoupling property.Comment: 25 page

Short random circuits define good quantum error correcting codes

We study the encoding complexity for quantum error correcting codes with large rate and distance. We prove that random Clifford circuits with $O(n \log^2 n)$ gates can be used to encode $k$ qubits in $n$ qubits with a distance $d$ provided $\frac{k}{n} < 1 - \frac{d}{n} \log_2 3 - h(\frac{d}{n})$. In addition, we prove that such circuits typically have a depth of $O( \log^3 n)$.Comment: 5 page

Scrambling speed of random quantum circuits

Random transformations are typically good at "scrambling" information. Specifically, in the quantum setting, scrambling usually refers to the process of mapping most initial pure product states under a unitary transformation to states which are macroscopically entangled, in the sense of being close to completely mixed on most subsystems containing a fraction fn of all n particles for some constant f. While the term scrambling is used in the context of the black hole information paradox, scrambling is related to problems involving decoupling in general, and to the question of how large isolated many-body systems reach local thermal equilibrium under their own unitary dynamics. Here, we study the speed at which various notions of scrambling/decoupling occur in a simplified but natural model of random two-particle interactions: random quantum circuits. For a circuit representing the dynamics generated by a local Hamiltonian, the depth of the circuit corresponds to time. Thus, we consider the depth of these circuits and we are typically interested in what can be done in a depth that is sublinear or even logarithmic in the size of the system. We resolve an outstanding conjecture raised in the context of the black hole information paradox with respect to the depth at which a typical quantum circuit generates an entanglement assisted encoding against the erasure channel. In addition, we prove that typical quantum circuits of poly(log n) depth satisfy a stronger notion of scrambling and can be used to encode alpha n qubits into n qubits so that up to beta n errors can be corrected, for some constants alpha, beta > 0.Comment: 24 pages, 2 figures. Superseded by http://arxiv.org/abs/1307.063

Field trips, resource visitors, and persons for interview available to the public schools in the towns of Acton and Concord, Massachusetts.

Thesis (Ed.M.)--Boston Universit

Financial Intermediation

The savings/investment process in capitalist economies is organized around financial intermediation, making them a central institution of economic growth. Financial intermediaries are firms that borrow from consumer/savers and lend to companies that need resources for investment. In contrast, in capital markets investors contract directly with firms, creating marketable securities. The prices of these securities are observable, while financial intermediaries are opaque. Why do financial intermediaries exist? What are their roles? Are they inherently unstable? Must the government regulate them? Why is financial intermediation so pervasive? How is it changing? In this paper we survey the last fifteen years' of theoretical and empirical research on financial intermediation. We focus on the role of bank-like intermediaries in the savings-investment process. We also investigate the literature on bank instability and the role of the government.

Effective use of study-team review techniques in fifth and sixth grade social studies.

Thesis (Ed.M.)--Boston Universit