CONSISTENT ESTIMATION OF RESIDUAL VARIANCE IN REGULATORY EVENT STUDIES

This study presents new evidence on alternative methods used to test for abnormal returns in regulatory event studies where cross-sectional correlation in residuals is significant. Results contradict earlier studies that find no advantages to using joint generalized least squares (JGLS) methods over ordinary least squares (OLS). We find that in an actual regulatory event study cross-correlation is significant, and that failing to correct for this correlation results in substantially higher calculated F-statistics. In Monte Carlo simulations we find that OLS test statistics are not well specified when residuals exhibit cross-sectional correlation at levels that are reasonable to expect in daily return data, while JGLS test statistics are well specified. The study includes tests of the effective power of the OLS and JGLS statistics.     

Estimation of the underlying structure of systematic risk with the use of principal component analysis and factor analysis

We present an improved methodology to estimate the underlying structure of systematic risk in the Mexican Stock Exchange with the use of Principal Component Analysis and Factor Analysis. We consider the estimation of risk factors in an Arbitrage Pricing Theory (APT) framework under a statistical approach, where the systematic risk factors are extracted directly from the observed returns on equities, and there are two differentiated stages, namely, the risk extraction and the risk attribution processes. Our empirical study focuses only on the former; it includes the testing of our models in two versions: returns and returns in excess of the riskless interest rate for weekly and daily databases, and a two-stage methodology for the econometric contrast. First, we extract the underlying systematic risk factors by way of both, the standard linear version of the Principal Component Analysis and the Maximum Likelihood Factor Analysis estimation. Then, we estimate simultaneously, for all the system of equations, the sensitivities to the systematic risk factors (betas) by weighted least squares. Finally, we test the pricing model with the use of an average cross-section methodology via ordinary least squares, corrected by heteroskedasticity and autocorrelation consistent covariances estimation. Our results show that although APT is very sensitive to the extraction technique utilized and to the number of components or factors retained, the evidence found partially supports the APT according to the methodology presented and the sample studied.     

A LIKELIHOOD RATIO TEST OF THE ZERO-BETA CAPM IN AUSTRALIAN EQUITY RETURNS

This paper tests the zero-beta CAPM with Australian equity returns, using the multivariate approach developed by Gibbons (1982). For the period 1958 to 1987, based on its asymptotic distribution, the likelihood ratio test (LRT) statistic indicates a strong rejection of the model when an equally weighted market index is used. However, small sample adjustments to the test suggested by Jobson and Korkie (1982) and by Shanken (1985) place the validity of this conclusion in some doubt. When a value weighted market index is used for the period 1974 to 1987, the tests reveal at least moderate support for the zero-beta CAPM.     

Multivariate regression tests of the arbitrage pricing theory: The instrumental-variables approach

This article expands the theoretical basis upon which empirical testing of the arbitrage pricing theory (APT) rests. Specifically, it specifies linear restrictions for worlds in which the APT holds. These restrictions may, in principle, be tested. Since the regressors in the model are only “noisy” proxies for a specific linear transformation of the factors or mimicking portfolios, testing regressions suffer from an errors-in-variables problem. The standard econometric treatment for this problem is the instrumental-variables approach. A size-based example is employed to compare the test results derived from the instrumental-variables approach to those obtained via the ordinary least squares (OLS) method. The results from both methods cannot reject a two-factor APT for the size-sorted portfolio sample. The authors appreciate the helpful comments of Edwin Burmeister, Raymond Chiang, Steve Pruitt, participant at the 1989 Western Finance Association annual meetings, Indiana University, and University of Miami, and especially Shmuel Kandel.     

Trading frequency and event study test specification

We examine the effects of thin trading on the specification of event study tests. Simulations of upper and lower tail tests are reported with and without variance increases on the event date across levels of trading volume. The traditional standardized test is misspecified for thinly traded samples. If return variance is unlikely to increase, then Corrado's rank test provides the best specification and power. With variance increases, the rank test is misspecified. The Boehmer et al. standardized cross-sectional test (Event-study methodology under conditions of event-induced variance, Journal of Financial Economics 30, pp. 253–272) is properly specified, but not powerful, for upper-tailed tests. Lower-tailed alternative hypotheses can best be evaluated using the generalized sign test.     

Liquidity biases in asset pricing tests

Microstructure noise in security prices biases the results of empirical asset pricing specifications, particularly when security-level explanatory variables are cross-sectionally correlated with the amount of noise. We focus on tests of whether measures of illiquidity, which are likely to be correlated with the noise, are priced in the cross-section of stock returns, and show a significant upward bias in estimated return premiums for an array of illiquidity measures in Center for Research in Security Prices (CRSP) monthly return data. The upward bias is larger when illiquid securities are included in the sample, but persists even for NYSE/Amex stocks after decimalization. We introduce a methodological correction to eliminate the biases that simply involves weighted least squares (WLS) rather than ordinary least squares (OLS) estimation, and find evidence of smaller, but still significant, return premiums for illiquidity after implementing the correction.     

Nonparametric rank tests for event studies

Because stock prices are not normally distributed, the power of nonparametric rank tests dominate parametric tests in event study analyses of abnormal returns on a single day. However, problems arise in the application of nonparametric tests to multiple day analyses of cumulative abnormal returns (CARs) that have caused researchers to normally rely upon parametric tests. In an effort to overcome this shortfall, this paper proposes a generalized rank (GRANK) testing procedure that can be used on both single day and cumulative abnormal returns. Asymptotic distributions of the associated test statistics are derived, and their empirical properties are studied with simulations of CRSP returns. The results show that the proposed GRANK procedure outperforms previous rank tests of CARs and is robust to abnormal return serial correlation and event-induced volatility. Moreover, the GRANK procedure exhibits superior empirical power relative to popular parametric tests.     

The long-horizon returns behaviour of the Portuguese stock market1

In the last few years several research studies have challenged the traditional weak-form efficiency tests of the stock market. These studies suggested an alternative to the random walk model, containing temporary and permanent components. If stocks follow such a model then the traditional tests, using returns computed for short intervals would be unable to detect them. To investigate the evidence for such models in the Portuguese stock market ten stock indexes were created. This is a pioneer study of the Portuguese stock market, and uses nominal, real and excess returns, computed for longer horizons. Three methodologies were used: variance ratios, ordinary least squares regressions and weighted least squares regressions. The statistical significance of the results was studied using traditional parametric tests as well as non-parametric tests. The evidence is mixed, as the presence of tendencies towards mean aversion and mean reversion were detected. Results also show that the evidence is very sensitive to the methodology used and the signifcance tests performed. These results, however, do not necessarily reject the weak-form market efficiency hypothesis.     

On stability of operational risk estimates by LDA: From causes to approaches

The stability of estimates is critical when applying advanced measurement approaches (AMA) such as loss distribution approach (LDA) for operational risk capital modeling. Recent studies have identified issues associated with capital estimates by applying the maximum likelihood estimation (MLE) method for truncated distributions: significant upward mean-bias, considerable uncertainty about the estimates, and non-robustness to both small and large losses. Although alternative estimation approaches have been proposed, there has not been any comprehensive study of how alternative approaches perform compared to the MLE method. This paper is the first comprehensive study on the performance of various potentially promising alternative approaches (including minimum distance approach, quantile distance approach, scaling-based bias correction, upward scaling of lower quantiles, and right-truncated distributions) as compared to MLE with regards to accuracy, precision and robustness. More importantly, based on the properties of each estimator, we propose a right-truncation with probability weighted least squares method, by combining the right-truncated distribution and minimizing a probability weighted distance (i.e., the quadratic upper-tail Anderson–Darling distance), and we find it significantly reduces the bias and volatility of capital estimates and improves the robustness of capital estimates to small losses near the threshold or moving the threshold, demonstrated by both simulation results and real data application.     

THE EFFECT OF MARKET PROXY REBALANCING POLICIES ON DETECTING ABNORMAL PERFORMANCE

In this paper, effects on the measured abnormal performance of test portfolios are compared against market proxies having the same or different rebalancing policies. Results show that the common practice of comparing buy-and-hold test portfolios with equally weighted market proxies produces lower Jensen [ 7 ] alphas and lower alpha t-values. Comparing buy-and-hold test portfolios with value-weighted market proxies produces higher portfolio betas and alphas, but lower alpha t-values. Finally, comparing buy-and-hold test portfolios with buy-and-hold market proxies produces the most powerful tests of abnormal performance.     

Is the Short Rate Drift Actually Nonlinear?

Aït-Sahalia (1996) and Stanton (1997) use nonparametric estimators applied to short-term interest rate data to conclude that the drift function contains important nonlinearities. We study the finite-sample properties of their estimators by applying them to simulated sample paths of a square-root diffusion. Although the drift function is linear, both estimators suggest nonlinearities of the type and magnitude reported in Aït-Sahalia (1996) and Stanton (1997). Combined with the results of a weighted least squares estimator, this evidence implies that nonlinearity of the short rate drift is not a robust stylized fact.     

Return Distributions and Improved Tests of Asset Pricing Models

We compare and contrast some existing ordinary least squares(OLS)- and generalized method of moments (GMM)-based tests ofasset pricing models with a new more general test. This newtest is valid under the assumption that returns are ellipticallydistributed, a necessary and sufficient assumption of the linearcapital asset pricing model (CAPM). This new test fails to rejectthe CAPM on a dataset of stocks sorted by market valuations,whereas similar tests constructed from OLS and GMM estimationmethods reject the linear CAPM. We also find that outliers reducethe OLS-estimated mispricing of the linear CAPM on monthly returnssorted by previous performance, that is, momentum. Monte Carloevidence supports superior size and power properties of thenew test relative to OLS- and GMM-based tests.     

Methodological Considerations in the Statistical Modeling of Catastrophe Bond Prices

The problem of specifying and fitting a statistical model of the pricing of property catastrophe risk is addressed from a methodological perspective. Notable 21st century published efforts to do this are reviewed. The problem is framed in a business context and various strategic and tactical issues are investigated. A naïve application of ordinary least squares regression is seen to have undesirable consequences. Alternative approaches are offered, including weighted least squares with weights inversely proportional to capital requirements, and alternative functional forms. Recommendations are offered.     

STATISTICAL TESTS OF THE ACCURACY OF ALTERNATIVE FORECASTS: SOME RESULTS FOR U.S. UTILITY BETAS

The common approach for assessing the relative forecast accuracy of various predictors is simply to compare their simple ranks based on some measure(s) of forecast accuracy (such as the mean square errors). However, conventional methodologies for conducting a t-test or F-test of forecast accuracy are inappropriate and unreliable. A statistical methodology is proposed in this paper that rectifies most of the problems involved with conducting such conventional tests of statistical significance. Using this statistical methodology on the mean square errors of six beta predictors for five forecast horizons for fifty utilities, it was found that there are statistically significant differences between the forecast accuracies of the beta predictors for each and every forecast horizon, that the statistical rankings of the beta predictors were significantly different from and more congruent than the simple rankings as the forecast horizon lengthened, and that the ordinary least squares predictor was consistently ranked as one of the poorest beta predictors for all of the forecast horizons.     

PORTFOLIO FORMATION,MEASUREMENT ERRORS,AND BETA SHIFTS: A RANDOM SAMPLING APPROACH

This article demonstrates that the portfolio approach could suffer a serious problem when the sorting variables contain not only true values but also measurement errors. The grouped measurement errors will be embedded into the data used to test financial models and further bias the testing results. To correct for this measurement‐error problem, I develop a random sampling approach to form portfolios. Results from this new methodology are unbiased and robust. By applying this methodology to investigate beta shifts, I show that the previous results about beta shifts are driven by measurement errors. The actual beta shift pattern is more complicated than that predicted by previous studies. The risk shift hypothesis is unlikely to explain the mean‐reversion puzzle for stock returns. JEL classification: Gil, C43.     

Systematic risk estimation in the presence of large and many outliers

It is well recognized that the effect of extreme points on systematic risk estimates is not adequately captured through least squares estimation. This article uses the reweighted least median squares (RWLMS) approach, first proposed by Rousseeuw (1984), which accurately detects outlier presence. Using a large sample of 1350 NYSE/AMEX firms, the article demonstrates that least squares does indeed mask several potentially influential points, that this masking is very pervasive over the sample, and that it may persist even after conventional robust estimation techniques are applied. When these masked points are “unmasked” by RWLMS and zero weights assigned to such observations, the resulting RWLMS estimates of beta are on average 10%–15% smaller. However, a Bayesian treatment of such points (assigning a priori nonzero weights) is possible in both one and two factor market models.     

Perceptions of predictive testing for those at risk of developing a chronic inflammatory disease: a meta-synthesis of qualitative studies*

Background: The availability of tests to predict the risk of developing chronic diseases is increasing. The identification of individuals at high risk of disease can trigger early intervention to reduce the risk of disease and its severity. In order for predictive tests to be accepted and used by those at risk, there is a need to understand people’s perceptions of predictive testing. Method: A meta-synthesis of qualitative research that explored patient and public perceptions of predictive testing for chronic inflammatory diseases was conducted. Studies were coded by researchers and patient research partners, and then organised into common themes associated with the acceptability or use of predictive testing. Results: Perceived barriers to predictive testing were identified, including a concern about a lack of confidentiality around the use of risk information; a lack of motivation for change; poor communication of information; and a possible impact on emotional well-being. In order to reduce these barriers, the literature shows that a patient-centred approach is required at each stage of the testing process. This includes the consideration of individual needs, such as accessibility and building motivation for change; readily available and easy to understand pre and post-test information; support for patients on how to deal with the implications of their results; and the development of condition specific lifestyle intervention programmes to facilitate sustainable lifestyle changes. Conclusion: Patients and members of the public had some concerns about predictive testing; however, a number of strategies to reduce barriers and increase acceptability are available. Further research is required to inform the development of a resource that supports the individual to make an informed decision about whether to engage in a predictive test, what test results mean, and how to access post-test support.     

On the asymptotic distribution of weighted least squares estimators

Abstract

In the ELB (Empirical Linear Bayes)-approach to credibility, the unknown structural parameters are substituted by a set of parameter estimates. The weighted least squares estimators are known to be asymptotically normally distributed when the design variables are independent and identically distributed random variables. It is demonstrated that, with probability one, the conditional asymptotic distribution, given the design, is the same as the unconditional distribution. Estimation of the asymptotic covariance matrix will also be considered.     

Are Initial Returns and Underwriting Spreads in Equity Issues Complements or Substitutes?

The objective of this paper is to analyze the joint behavior of underwriting spreads and initial returns on equity issues for a large sample of issues over a 21-year period. Traditional empirical approaches to the determination of these direct and indirect issuing costs view them as independent. Using a three-stage least squares approach, we find these costs to be positively and significantly related. In the case of seasoned equity offerings, our results are robust to replacing initial returns with the offer price discount. We also find that low quality issuers are charged higher underwriting spreads and initial returns when compared to high quality issuers.     

The Market Valuation and Trading Volume Effects of the Creation of the Florida Hurricane Catastrophe Fund on Property-liability Insurers

The Florida Hurricane Catastrophe Fund was officially created in November, 1993. This study analyzes investor reactions during the creation of the Florida Hurricane Catastrophe Fund. We find significant share price reactions for four of six legislative events consistent with the predictions of the theory outlined. We use both a generalized least squares portfolio approach and Corrado's (1989) rank statistic, a nonparametric event study methodology, to arrive at our findings. Empirical analysis of trading volume corroborates the findings involving share price reactions. We also find that the market is able to discriminate between property-liability insurers on the basis of hurricane exposure and firm size.