Robust Estimation of Multiple Regression Model with asymmetric innovations and Its Applicability on Asset Pricing Model

In this paper, we first develop the modified maximum likelihood (MML) estimators for the multiple regression coefficients in linear model with the underlying distribution assumed to be symmetric, one of Student's t family. We obtain the closed form of the estimators and derive their asymptotic properties. In addition, we demonstrate that the MML estimators are more appropriate to estimate the parameters in the Capital Asset Pricing Model by comparing its performance with that of least squares estimators (LSE) on the monthly returns of US portfolios. Our empirical study reveals that the MML estimators are more efficient than the LSE in terms of relative efficiency of one-step-ahead forecast mean square error for small samples.Maximum likelihood estimators, Modified maximum likelihood estimators, Student’s t family, Capital Asset Pricing Model, Robustness

Robust Estimation of Multiple Regression Model with Non-normal Error: Symmetric Distribution

In this paper, we develop the modified maximum likelihood (MML) estimators for the multiple regression coefficients in linear model with the underlying distribution assumed to be symmetric, one of Student's t family. We obtain the closed form of the estimators and derive their asymptotic properties. In addition, we demonstrate that the MML estimators are more appropriate to estimate the parameters in the Capital Asset Pricing Model by comparing its performance with that of least squares estimators (LSE) on the monthly returns of US portfolios. Our empirical study reveals that the MML estimators are more efficient than the LSE in terms of relative efficiency of one-step-ahead forecast mean square error for small samples.Maximum likelihood estimators, Modified maximum likelihood estimators, Student's t family, Capital Asset Pricing Model, Robustness.

Preferences over Meyer’s Location-Scale Family

This paper extends Meyer’s (1987) location-scale family with general n random seed sources. Firstly, we clarify and generalize existing results to this multivariate setting. Some useful geometrical and topological properties of the location-scale expected utility functions are obtained. Secondly, we introduce and study some general non-expected utility functions defined over the location-scale (LS) family. Special care is made in characterizing the shape of the indifference curves induced by the LS expected utility functions and non-expected utility functions. Finally, efforts are also made to study several well-defined partial orders and dominance relations defined over the LS family. These include the first-, second- order stochastic dominance, the mean -variance rule, and a newly defined location-scale dominance.

Estimating Parameters in Autoregressive Models with Asymmetric Innovations

Tiku et al (1999) considered the estimation in a regression model with autocorrelated error in which the underlying distribution be a shift-scaled Student’s t distribution, developed the modified maximum likelihood (MML) estimators of the parameters and showed that the proposed estimators had closed forms and were remarkably efficient and robust. In this paper, we extend the results to the case, where the underlying distribution is a generalized logistic distribution. The generalized logistic distribution family represents very wide skew distributions ranging from highly right skewed to highly left skewed. Analogously, we develop the MML estimators since the ML (maximum likelihood) estimators are intractable for the generalized logistic data. We then study the asymptotic properties of the proposed estimators and conduct simulation to the study.

Prospect and Markowitz Stochastic Dominance

Levy and Levy (2002, 2004) develop the Prospect and Markowitz stochastic dominance theory with S-shaped and reverse S-shaped utility functions for investors. In this paper, we extend Levy and Levy's Prospect Stochastic Dominance theory (PSD) and Markowitz Stochastic Dominance theory (MSD) to the first three orders and link the corresponding S-shaped and reverse S-shaped utility functions to the first three orders. We also provide experiments to illustrate each case of the MSD and PSD to the first three orders and demonstrate that the higher order MSD and PSD cannot be replaced by the lower order MSD and PSD. Prospect theory has been regarded as a challenge to the expected utility paradigm. Levy and Levy (2002) prove that the second order PSD and MSD satisfy the expected utility paradigm. In our paper we take Levy and Levy's results one step further by showing that both PSD and MSD of any order are consistent with the expected utility paradigm. Furthermore, we formulate some other properties for the PSD and MSD including the hierarchy that exists in both PSD and MSD relationships; arbitrage opportunities that exist in the first orders of both PSD and MSD; and that for any two prospects under certain conditions, their third order MSD preference will be ???the opposite??? of or ???the same??? as their counterpart third order PSD preference. By extending Levy and Levy's work, we provide investors with more tools for empirical analysis, with which they can identify the first order PSD and MSD prospects and discern arbitrage opportunities that could increase his/her utility as well as wealth and set up a zero dollar portfolio to make huge profit. Our tools also enable investors to identify the third order PSD and MSD prospects and make better choices.Prospect stochastic dominance, Markowitz stochastic dominance, risk seeking, risk averse, S-shaped utility function, reverse S-shaped utility function

On the Estimation of Cost of Capital and its Reliability

Gordon and Shapiro (1956) first equated the price of a share with the present value of future dividends and derived the well-known relationship. Since then, there have been many improvements on the theory. For example, Thompson (1985, 1987) combined the "dividend yield plus growth" method with Box-Jenkins time series analysis of past dividend experience to estimate the cost of capital and its "reliability" for individual firms. Thompson and Wong (1991, 1996) proved the existence and uniqueness of the cost of capital and provided formula to estimate both the cost of capital and its reliability. However, their approaches cannot be used if the "reliability" does not exist or if there are multiple solutions for the "reliability". In this paper, we extend their theory by proving the existence and uniqueness of this reliability. In addition, we propose the estimators for the reliability and prove that the estimators converge to a true parameter. The estimation approach is further simplified, hence rendering computation easier. In addition, the properties of the cost of capital and its reliability will be analyzed with illustrations of several commonly used Box-Jenkins models.

Two-moment decision model for location-scale family with background asset

This paper studies the impact of background risk on the indifference curve. We first study the shape of the indifference curves for the investment with background risk for risk averters, risk seekers, and risk-neutral investors. Thereafter, we study the comparative statics of the change in the shapes of the indifference curves when the means and the standard deviations of the returns of the financial asset and/or the background asset change. In addition, we draw inference on risk vulnerability and investment decisions in financial crises and bull and bear markets

New Variance Ratio Tests to Identify Random Walk from the General Mean Reversion Model

We develop some properties on the autocorrelation of the k-period returns for the general mean reversion (GMR) process in which the stationary component is not restricted to the AR(l) process but take the form of a general ARMA process. We then derive some properties of the GMR process and three new non-parametric tests comparing the relative variability of returns over different horizons to validate the GMR process as an alternative to random walk. We further examine the asymptotic properties of these tests which can then be applied to identify random walk models from the GMR processes.mean reversion, variance ratio test, random walk, stock price, stock return

"A Trinomial Test for Paired Data When There are Many Ties"

This paper develops a new test, the trinomial test, for pairwise ordinal data samples to improve the power of the sign test by modifying its treatment of zero diRerences between observations, thereby increasing the use of sample information. Simulations demonstrate the power superiority of the proposed trinomial test statis- tic over the sign test in small samples in the presence of tie observations. We also show that the proposed trinomial test has substantially higher power than the sign test in large samples and also in the presence of tie observations, as the sign test ignores information from observations resulting in ties.

A Trinomial Test for Paired Data When There are Many Ties

This paper develops a new test, the trinomial test, for pairwise ordinal data samples to improve the power of the sign test by modifying its treatment of zero differences between observations, thereby increasing the use of sample information. Simulations demonstrate the power superiority of the proposed trinomial test statistic over the sign test in small samples in the presence of tie observations. We also show that the proposed trinomial test has substantially higher power than the sign test in large samples and also in the presence of tie observations, as the sign test ignores information from observations resulting in ties.Sign test; trinomial test; non-parametric test; ties; test statistics; hypothesis testing