Gopal K. Basak

A Direct Test For The Mean Variance Efficiency Of A Portfolio

We develop a direct test for examining the mean-variance efficiency of a given benchmark asset return. Unlike traditional tests for mean-variance efficiency, this test allows for the possibility that short positions in the primitive assets may not be possible. Using this test, we can not reject the hypothesis that the value weighted return on exchange traded stocks is mean-variance efficient with reference to the mean-variance frontier generated by the 25 stock portfolios constructed by Fama and French (1993), when short selling is not allowed.

Assessing the Risk in Sample Minimum Risk Portfolios

We show that the in-sample estimate of the variance of a global minimum risk portfolio constructed using an estimated covariance matrix of returns will on average be strictly smaller than its true variance. Scaling the in-sample estimate upward by a standard degrees-of-freedom related factor or using the Bayes covariance matrix estimator can be inadequate; the correction is likely to be twice as large as the standard correction when returns are i.i.d. multivariate Normal. We develop a Jackknife-type estimator of the optimal portfolios variance that is valid when returns are i.i.d.; and a variation that may be better when returns exhibit volatility persistence. We empirically demonstrate the need to correct for in-sample optimism by considering an optimal portfolio of 200 stocks that has the lowest tracking error when the SP our correction, 1.24 percent; and the weighted Jackknife, 1.36 percent.

Stabilization of dynamical systems by adding a colored noise

Stabilization of dynamics of a system has been of great concern to researchers and practitioners over the years. It is observed that the system is more viscous if one adds a noise in the system. In the present situation, the system is perturbed by a (multiplicative) noise and the stable/unstable behavior is examined. It is then observed that, one can stabilize or destabilize a large class of systems of ordinary differential equations (ODE) and stochastic differential equations (SDE) if a noise is carefully added.

A functional central limit theorem for a class of urn models

We construct an independent increments Gaussian process associated to a class of multicolor urn models. The construction uses random variables from the urn model which are different from the random variables for which central limit theorems are available in the two color case.

Order selection of continuous time models: Applications to estimation of risk premiums

This paper develops an order selection criterion for a continuous autoregressive (CAR) time series. Based on the quadratic variation consideration of a CAR(p) process, a new order selection criterion, the quadratic variation criterion (QVC) is proposed. It is shown that this new order selection criterion is consistent and provides an effective means to estimate the order of a CAR(p) model. Simulation studies suggest that the proposed method is efficient and outperforms other order selection criteria. The QVC is applied to select the order of the cumulative excess return process and the effect of the risk premium of a GARCH-M model when changing variance is taken into account.

A Test of Mean-Variance Efficiency When Short Selling is Prohibited

We develop a statistical test for examining whether a given portfolio is mean-variance efficient with reference to the mean-variance frontier generated using a set of primitive assets. The set of primitive assets may include the given portfolio.We allow for short-sale restrictions while generating the mean-variance frontier using the primitive assets. Our measure of inefficiency is the difference between the variance of the given portfolio and the variance of the mean-variance efficient portfolio that has the same mean as the given portfolio. We derive the asymptotic distribution of the estimated measure of mean-variance inefficiency.