Research Papers

Runs on Money Market Mutual Funds

with Allan Timmermann and Russ Wermers

This paper studies daily investor flows to and from each money market mutual fund during the period surrounding and including the money fund crisis of September 2008. We focus on the determinants of flows in the prime money fund category to shed light on the covariates of money fund runs, since this category was, by far, the most heavily impacted by the money fund crisis. We find that outflows during the crisis period of September 17-19 are concentrated among a small fraction of funds having certain characteristics. Institutional investors focused their run-like behavior on large funds that were part of a complex having large amounts of institutional money funds (as a fraction of all money funds). In addition, such investors were more likely to run from funds with higher yields, lower expense ratios, and higher prior flow volatility, indicating that "hot money" chased yields, but selectively ran from higher-yield funds that were more vulnerable. Our analysis also suggests that prime retail money funds exhibited many of the same behaviors as institutional funds, although at a much slower and more drawn-out pace. Our paper provides a framework that is useful in understanding potential further regulatory responses to the crisis.

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An Empirical Test of Pricing Kernel Monotonicity

with Brendan Beare, Working Paper (NEW VERSION, UPDATED NOVEMBER 2012)

A large class of asset pricing models predict that securities which have high payoffs when market returns are low tend to be more valuable than those with high payoffs when market returns are high. More generally, we expect the pricing kernel to be a monotonically decreasing function of the market return. Numerous recent empirical studies appear to contradict this prediction. The nonmonotonicity of empirical pricing kernel estimates has become known as the pricing kernel puzzle. In this paper we propose and apply a formal statistical test of pricing kernel monotonicity. The test involves assessing the concavity of the ordinal dominance curve associated with the risk neutral and physical return distribution. We apply the test using thirteen years of data from the market for European put and call options written on the S&P 500 index. Statistically significant violations of pricing kernel monotonicity occur in a substantial proportion of months, suggesting that observed nonmonotonicities are real, and unlikely to be the product of statistical noise.

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Quantile Spacings: A Simple Method for the Joint Estimation of Multiple Quantiles

Walter P. Heller Memorial Award Winner for Best Third Year Paper

In a variety of economic applications, we would like learn about aspects of a conditional distribution which are not well described by conditional means and/or variances. One simple econometric approach is to model a representative number of conditional quantiles. However, many existing methods suffer from the well-known quantile crossing problem, namely that the estimated quantile functions do not satisfy a basic monotonicity requirement that every quantile function must satisfy. We propose a simple but flexible parametric model for conditional quantiles. These quantiles will satisfy the monotonicity requirement by construction, so they are not susceptible to the quantile crossing problem. Rather than directly modeling the level of each individual quantile, we begin with a single quantile (usually the median), and then add or subtract nonnegative functions (quantile spacings) obtain the other quantiles. We propose a simple interpolation method which generates a mapping from a finite number of quantiles to a probability density function. Two estimation methods are discussed in detail, and we characterize the limiting behavior of each. We identify a number of potential applications, and we highlight an application of the method by Schmidt, Timmermann, and Wermers (2013) to the study of a run on money market mutual funds in September 2008.

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Option Portfolio Selection Under Pricing Kernel Non-Monotonicity

with Brendan Beare, Working Paper (PAPER COMING SOON)

A recent literature in empirical finance documents the nonmonotone shape of pricing kernel estimates for several major market indices. In this paper we investigate the implications of pricing kernel nonmonotonicity for option portfolio choice. We propose a portfolio selection procedure that aims to deliver superior returns, relative to a direct market investment, by adapting to the shape of the pricing kernel. Numerical implementation of our procedure may be achieved using a multiobjective evolutionary algorithm. We investigate the out-of-sample performance of our portfolio selection procedure using twenty years of data from the market for European put and call options written on the S&P 500 index. Monthly portfolio returns outperform those of a direct market investment.

 

on The Dimensionality of Bounds Generated by the Shapley-Folkman Theorem

Journal of Mathematical Economics, January 2012

The Shapley-Folkman Theorem places a scalar upper bound on the distance between a sum of non-convex sets and its convex hull. We observe that some information is lost when a vector is converted to a scalar to generate this bound and propose a simple normalization of the underlying space which removes this loss of information. As an example, we apply this result to the Anderson (1978) core convergence theorem, and demonstrate how our normalization leads to an intuitive, unitless upper bound on the discrepancy between an arbitrary core allocation and the corresponding competitive equilibrium allocation.

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One Solution to the Option Pricing Overvaluation Problem: Using Down and Out Call Options

with Ronald Schmidt, Business Valuation Update, May 2011

Recent articles have pointed to concerns about the validity of using option pricing models (OPM) to determine the value of common stock in 409(a) valuations. At issue is the question of whether OPMs provide appropriate methodologies to establish the appropriate fair market value of common stock. Specifically, use of standard Black-Scholes algorithms will overstate the value of common stock by not properly modeling the impact of failure scenarios. We argue that claims to equity of early-stage companies may be more appropriately modeled as “down and out” call options, rather than traditional European call options (as required by the Black-Scholes formula). Like Black-Scholes, these options still have the benefit of a simple, closed-form solution, but they better account for the path dependence of enterprise value and allow for a higher probability of failure. We demonstrate that these alternative option pricing models can be used to either estimate enterprise value (back-solving) or to allocate value, and that their use can result in more reasonable estimates of common stock when compared with Black-Scholes.

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