Stephen E. Satchell

Modelling Emerging Market Risk Premia Using Higher Moments

The purpose of this paper is to assess the incremental value of higher moments in modelling capital asset pricing models (CAPMs) of emerging markets. Whilst it is recognized that emerging markets are unlikely to yield sensible results in a mean-variance world, the high skewness and kurtosis present in emerging markets returns make our assessment potentially interesting. Generalized method of moments (GMM) is used for the estimation. We also present new versions of higher-moment market models of the data-generating process of the individual emerging markets and use these to identify model parameters. We find some evidence that emerging markets are better explained with additional systematic risks, such as co-skewness and co-kurtosis, than the conventional mean-variance CAPM. Copyright @ 1999 by John Wiley & Sons, Ltd. All rights reserved.

THE BERNSTEIN COPULA AND ITS APPLICATIONS TO MODELING AND APPROXIMATIONS OF MULTIVARIATE DISTRIBUTIONS

We define the Bernstein copula and study its statistical properties in terms of both distributions and densities. We also develop a theory of approximation for multivariate distributions in terms of Bernstein copulas. Rates of consistency when the Bernstein copula density is estimated empirically are given. In order of magnitude, this estimator has variance equal to the square root of the variance of common nonparametric estimators, e.g., kernel smoothers, but it is biased as a histogram estimator.We would thank Mark Salmon for interesting us in the copula function and Peter Phillips, an associate editor, and the referees for many valuable comments. All remaining errors are our sole responsibility.

On the foundation of performance measures under asymmetric returns

Abstract We examine two performance measures advocated for asymmetric return distributions: the Sortino ratio—originally introduced by Sortino and Price (Sortino F and Price L 1994 J. Investing 59–65)—and a measure based on power utility introduced in Leland (Leland H 1999 Financial Analysts J. 27–36). In particular, we investigate the role of the maximum principle in this context, and assess the conditions under which the measures satisfy it. Our results add further motivation for the use of a modified Sortino ratio, by placing it on a sound theoretical foundation. In this light, we discuss its relative merits compared with alternative approaches.

Interactions Between Property and Equity Markets: An Investigation of Linkages in the United Kingdom 1972–1992

Two strands of real estate research—that concerned with the relationships between securitized real estate and the underlying market and that dealing with the role of property in the wider economy—rarely are considered together. The paper utilizes the U.K. equity market and property company share data to explore the relationships between real estate and the rest of the economy, using a two-sector analytic model. Causality analysis suggests that the wider economy leads the real estate market in the short term but that, with a longer lag structure, positive real estate returns may point to negative future returns in the rest of the economy. This provides weak confirmatory evidence for theories of capital switching between sectors.

Estimating the volatility of stock prices: a comparison of methods that use high and low prices

The volatility of stock prices has played an important role in the financial literature. Different methods of estimating the volatility are suggested and applied to British financial assets. Since we cannot observe the real volatility, we investigate the efficiency of the methods through simulation. The question of which estimator to use rather depends on the distributional assumption of returns. If it is log-normal, methods based on high/low prices are preferred. Furthermore, if there is drift in the data, then one may wish to use a procedure devised by Rogers and Satchell. If the drift is varying with time, the Rogers and Satchells method is clearly superior.

The Hazards of Doing a PhD: An Analysis of Completion and Withdrawal Rates of British PhDs in the 1980s

The paper examines UK PhD completion and withdrawal rates, in a competing risks framework, using the 1986 National Survey of 1980 Graduates. The statistical problem of thresholding of completion data is also addressed. We argue that our results suggest that there are problems with the use of PhD completion rates as performance indicators for academic departments. The principal results of the analysis are as follows. First, research council funding significantly increases only the male completion rate. Second, male and female completion rates are highest where the subject area of research is in the sciences or engineering. Third, ability increases the completion rate for men, but for women increases both the withdrawal and completion rates. Finally, a significant maternal role model effect is observed for female completions.

Market risk and the concept of fundamental volatility : measuring volatility across asset and derivative markets and testing for the impact of derivatives markets on financial markets

This paper proposes the unobserved fundamental component of volatility as a measure of risk. This concept of fundamental volatility may be more meaningful than observed volatility for market regulators. Fundamental volatility may be obtained using a stochastic volatility model. The authors decompose four FTSE100 stock index related volatilities into transitory noise and unobserved fundamental volatility. The question as to whether derivative markets destabilise asset markets is addressed. The analysis shows that introducing European options reduces fun-damental volatility, while transitory noise in the underlying and futures markets does not show significant change. It is concluded that, for the FTSE100 index, introducing an options market has stabilised underlying and derivative markets.

Correlated ARCH (CorrARCH): Modelling the time-varying conditional correlation between financial asset returns

Abstract Although the time variation of the conditional correlations of asset returns is a well established stylized fact (and of crucial importance for efficient financial decisions) there is no explicit general model available for its estimation and forecasting. In this paper, we propose a bivariate GARCH covariance structure in which conditional variances can follow any GARCH-type process, while conditional correlation is generated by an explicit discrete-time stochastic process, the CorrARCH process. A high order CorrARCH can parsimoniously be represented by a CorGARCH process. The model successfully generates the reported stylized facts, establishes an autocorrelation structure for correlations and thus provides an explicit framework for out-of-sample forecasting. We provide empirical evidence from the G7 Stock Market Indexes.

An Extended Family of Financial-Risk Measures

Recalling the class of risk measures introduced by Stone [1973], the authors survey measures from different academic disciplines—including psychology, operations research, management science, economics, and finance—that have been introduced since 1973. We introduce a general class of risk measures that extends Stones class to include these new measures. Finally, we give four axioms that describe necessary attributes of a good financial risk measure and show which of the measures surveyed satisfy these. We demonstrate that all measures that satisfy our axioms, as well as those that do not but are commonly used in finance, belong to our new generalized class.

Diversification When It Hurts? The Joint Distributions of Real Estate and Equity Markets

This article examines claims about the diversification benefits of real estate. In particular, does real estate investment in a mixed asset portfolio provide protection when other asset classes are performing badly? Conventional portfolio strategy models utilising covariance statistics may result in a misallocation of capital if correlation structures between assets differ across the distribution of returns. Models of asymmetric dependence using the copula function, drawn from the recent finance literature are used to examine the relationships between real estate and equity at different points in their joint return distributions. For both UK and Global markets, real estate securities and common equities are shown to exhibit strong tail dependence – particularly in the negative tail. This suggests that real estate securities offer, at best, limited diversification protection when it is needed most – when other asset markets are falling. This has implications for allocation strategies in mixed asset portfolios. 1. Paper originally presented to the European Real Estate Society Annual Conference, Dublin, June 2005.