George Chacko

Spectral GMM Estimation of Continuous-Time Processes

This paper derives a methodology for the exact estimation of continuous-time stochastic models based on the characteristic function. The estimation method does not require discretization of the process, and it is easy to apply. The method is essentially generalized method of moments on the complex plane. Hence it shares the optimality and distribution properties of GMM estimators. Moreover, we show that there are instruments that make the estimator asymptotically efficient. We illustrate the method with some applications to relevant estimation problems in continuous-time finance. We estimate a model of stochastic volatility, a jump-diffusion model with constant volatility and a model that nests both the stochastic volatility model and the jump-diffusion model. We find that negative jumps are important to explain skewness and asymmetry in excess kurtosis of the stock return distribution, while stochastic volatility is important to capture the overall level of this kurtosis. Positive jumps are not statistically significant once we allow for stochastic volatility in the model. We also estimate a non-affine model of stochastic volatility and we find that the power of the diffusion coefficient appears to be between one and two, rather than the value of one-half that leads to the standard affine stochatic volatility model. Finally, we offer an explanation for the observation that the estimate of persistence in stochatic volatility increases dramatically as the frequency of the observed data falls based on a multiple factor stochastic volatility model.

An Index-Based Measure of Liquidity

http://dx.doi.org/10.1016/j.jbankfin.2016.03.012 0378-4266/ 2016 Elsevier B.V. All rights reserved. ⇑ Corresponding author at: Santa Clara University, Lucas Hall, 500 El Camino Real, Santa Clara, CA 95053, United States. Tel.: +1 408 554 2776; fax: +1 408 554 5206. E-mail address: srdas@scu.edu (S. Das). 1 The Securities and Exchange Commission, as a matter of policy, disclaims responsibility for any private publication or statement by any of its employees. The views expressed herein are those of the author and do not necessarily reflect the views of the Commission or of the author’s colleagues upon the staff of the Commission. 2 One of the most widely used quotes during this time period was provided by the ‘‘sage of Omaha,” Warren Buffet, who said ‘‘You only find out who is swimming naked when the tide goes out” (Chairman’s Letter, 2001 Berkshire Hathaway Annual Report). One interpretation of this quote is that one can only tell how much and what types of risk a firm is really carrying in its balance sheet when the downside of that risk manifests itself. In hindsight, it appears that many financial institutions had substantial liquidity risk in their balance sheets and the crisis of ’07–’09 caused the ‘‘tide to go out” and make it clear which ones had the largest quantities of this risk. George Chacko , Sanjiv Das a,⇑, Rong Fan b

A theory of optimal timing and selectivity

Abstract We solve an extended optimal portfolio problem in continuous time for any horizon, where we allow the mean and variance of returns to be stochastic, introduce fund flows to and from the portfolio, permit differential investor preferences for dividend versus growth stocks, and allow the investor to buy costly information on the random mean and variance of the portfolio to improve his portfolio choice set. This model provides analytical results especially useful in understanding the expenditure on timing and selection information a mutual fund undertakes in attempting to improve performance relative to a benchmark. We examine this proposition for growth and income funds, long and short investment horizons, and also account for fund inflows and outflows. We also combine our model of costly learning with the traditional model of incomplete information to understand the interaction between costly and costless learning. The approach taken is a purely theoretical one, and in this regard the paper is normative in spirit. We anticipate that the propositions in this paper will provide two byproducts: (i) a framework for fund managers to think about how to allocate information expenses between timing and selection skills, and (ii) give academics, especially empirical researchers, a theoretical backdrop against which to examine the mutual fund industry.

Perturbation methods for dynamic portfolio allocation problems

Publisher Summary This chapter explores two perturbation methods for solving dynamic consumption/portfolio allocation problems under general preferences and a time-varying investment opportunity set. The restrictions that it imposes are that preferences can be represented by a general recursive utility formulation and that the investment opportunity set is affine. One important result for general recursive preferences is that the Sharpe ratio is sufficient to capture the time variation in the investment opportunity set. The first perturbation method is a perturbation around the exact solution when the elasticity of substitution is equal to the value of 1. It is built on the exact solution that exists for the unit elasticity case in order to show that an approximate solution exists to the general problem with arbitrary elasticity of substitution. The second perturbation method is a perturbation around the mean consumption-to wealth ratio of the solution. This perturbation reflects the difference between the realized consumption-wealth ratio and its unconditional mean and leads to an approximate analytic solution to the general consumption/portfolio allocation problem.