Alp Simsek

Belief Disagreements and Collateral Constraints

Belief disagreements have been suggested as a major contributing factor to the recent financial crisis. This paper theoretically evaluates this hypothesis. I assume that optimists have limited wealth and take on leverage in order to take positions in line with their beliefs. To have a significant effect on asset prices, they need to borrow from traders with pessimistic beliefs using loans collateralized by the asset itself. Since pessimists do not value the collateral as much as optimists do, they are reluctant to lend, which provides an endogenous constraint on optimists ability to borrow and to influence asset prices. I demonstrate that the tightness of this constraint depends on the nature of belief disagreements. Optimism concerning the probability of downside states has no or little effect on asset prices because these types of optimism are disciplined by this constraint. Instead, optimism concerning the relative probability of upside states could have significant effects on asset prices. This asymmetric disciplining effect is robust to allowing for short selling because pessimists that borrow the asset face a similar endogenous constraint. These results emphasize that what investors disagree about matters for asset prices, to a greater extent than the level of disagreements. When richer contracts are available, insurance contracts (similar to credit default swaps) endogenously emerge to facilitate betting. Richer contracts moderate the effect of belief disagreements on asset prices because the medium of betting shifts from buying (or shorting) the asset to trading alternative contracts.

Generalized Poincaré-Hopf Theorem for Compact Nonsmooth Regions

This paper presents an extension of the Poincare-Hopf theorem to generalized critical points of a function on a compact region with nonsmooth boundary, M, defined by a finite number of smooth inequality constraints. Given a function F: M → Rn, we define the generalized critical points of F over M, define the index for the critical point, and show that the sum of the indices of the critical points is equal to the Euler characteristic of M. We use the generalized Poincare-Hopf theorem to present sufficient (local) conditions for the uniqueness of solutions to finite-dimensional variational inequalities and the uniqueness of stationary points in nonconvex optimization problems.

Local Indices for Degenerate Variational Inequalities

We provide an index formula for solutions of variational inequality problems defined by a continuously differentiable function F over a convex set M represented by a finite number of inequality constraints. Our index formula can be applied when the solutions are nonsingular and possibly degenerate, as long as they also satisfy the injective normal map (INM) property, which is implied by strong stability. We show that when the INM property holds, the degeneracy in a solution can be removed by perturbing the function F slightly, i.e., the index of a degenerate solution is equal to the index of a nondegenerate solution of a slightly perturbed variational inequality problem. We further show that our definition of the index is equivalent to the topological index of the normal map at the zero corresponding to the solution. As an application of our index formula, we provide a global index theorem for variational inequalities which holds even when the solutions are degenerate.

Should Retail Investors' Leverage Be Limited?

This paper provides evidence that leverage constraints can improve investor welfare, reducing unprofitable speculation. In accordance with Dodd-Frank, the CFTC was given regulatory authority over the retail (household) market for foreign exchange and capped the maximum permissible leverage available to U.S. traders. By comparing U.S. traders on the same brokerages with their unregulated European counterparts, I show that the leverage constraint brought a reduction in average losses with no change in the volatility of their returns. Unable to use leverage to generate volatility, investors trade more frequently on days with high implied volatility, a form of risk shifting. Overconfident investors benefit most from the regulation. ∗Federal Reserve Bank of Cleveland. e-mail: rawley.heimer@researchfed.org. The views expressed in this article are those of the author and don’t necessarily reflect the position of the Federal Reserve Bank of Cleveland or the Federal Reserve System. Much of the work was done while I was a PhD candidate at Brandeis University. This research has benefited from conversations with Daniel B. Bergstresser, Alain P. Chaboud, Jens Hilscher, Blake LeBaron, Debarshi K. Nandy, Carol L. Osler, Lin Peng, David Sraer, and Egon Zakrajsek as well as seminar participants at CUNY Baruch, the University of Western Ontario, the University of Cincinatti, the Federal Reserve Bank of Cleveland, the Federal Reserve Bank of Philadelphia, the Board of Governors, and the SEC. I also thank the operators of the social network for providing me with the data, especially Alex Dusenbery for helping setup the database. All errors are my own.Does the provision of leverage to retail traders improve market quality or facilitate socially inefficient speculation that enriches financial intermediaries? We evaluate the effects of 2010 regulations that cap leverage in the U.S. retail foreign exchange market. Using three unique data sets and a difference-in-differences approach, we document that the leverage-constraint reduces trading volume by 23%, alleviates high-leverage traders’ losses by 40%, and reduces brokerages’ operating capital by 25%. Yet, the policy does not affect the relative bid-ask prices charged by the brokerages. These results suggest the policy improves belief-neutral social welfare without reducing market liquidity.