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Portfolio selection models using variance, Value-at-Risk (VaR) and expected shortfall measures of risk are analysed, assuming differing underlying return distributions. The expected shortfall approach provides advantages relative to the VaR approach in terms of lower portfolio downside risks. Furthermore, using the extreme value distribution provides more insights for the investor relative to the empirical distribution. Analysing portfolio selection using these differing risk measures around the recent sub-prime mortgage problem period provides topical insights into the asset allocation process for the investor.Journal of Asset Management (2008) 9, 121–137. doi:10.1057/jam.2008.15 [ABSTRACT FROM AUTHOR]

Hybrid dynamic systems include both continuous and discrete state variables. Properties of hybrid systems, which have an infinite state space, can often be verified using ordinary model checking together with a finite-state abstraction. Model checking can be inconclusive, however, in which case the abstraction must be refined. This paper presents a new procedure to perform this refinement operation for abstractions of hybrid systems. Following an approach originally developed for finite-state systems [11, 25], the refinement procedure constructs a new abstraction that eliminates a counterexample generated by the model checker. For hybrid systems, analysis of the counterexample requires the computation of sets of reachable states in the continuous state space. We show how such reachability computations with varying degrees of complexity can be used to refine hybrid system abstractions efficiently. Examples illustrate our counterexample-guided refinement procedure. Experimental results for a prototype implementation indicate significant advantages over existing methods. [ABSTRACT FROM AUTHOR]

This article presents a study which determined the market model and β factors for equity share data in Great Britain. The beta, or systematic risk, factor is a variable of considerable interest and importance in the field of financial economics. Essentially, the capital asset pricing model (CAPM) implies that, at equilibrium, investors will only be rewarded for the systematic risk that they are prepared to incur--unsystematic risk going unrewarded. The determination, or estimation, of the beta factor is, then, a matter of some interest to investors. Precision is of importance, since measurement errors in beta estimates will constitute unsystematic risk components. A considerable literature has developed in America concerned with various phenomena associated with the estimation of beta factors and this paper attempts to establish a number of the properties of the market model and the beta factor for British equities. A systematic pattern of negatively autocorrelated market model residuals was observed. The actual magnitude of the autocorrelation was small, as was the extent of heteroscedasticity. Both of these results are similar to findings using U.S. data. The market model parameters e.g. beta, R² and p1;, were found to be sensitive to the differencing interval over which returns were defined. Both beta and R² increased with increasing differencing interval, while p1; decreased. Cochrane-Orcutt and Bayesian techniques did not lead to very different results from ordinary least squares in terms of rankings for portfolio selection. However, Bayesian betas exhibited greater stationarity at both the individual security and portfolio level, and it would appear reasonable to presume that Bayesian estimates using more sophisticated priors would improve this stationarity Still further. Similarly, both Cochrane-Orcutt and Bayesian techniques led

This article presents a study on variable transactions costs, capital asset pricing model and corporate dividend decision. The study introduces variable transactions costs into the problem structure and investigates the implications for the corporate dividend decision. Introduction of fixed transactions costs into the analysis leads to considerable problems in deriving capital asset pricing models, since the resultant constrained optimization problem becomes a mixed integer programming problem. Variable transactions costs can be introduced into the problem structure and closed form capital asset pricing formulae can be derived. The type of costs falling within this set would be the variable transfer costs associated with buying and selling securities, which, throughout, will be assumed to be equal for buying and selling all securities. A single period capital asset pricing model incorporating variablem transactions costs is presented. The capital element, only, of terminal cash flows on risk assets was subject to transactions costs, with the result that the model (5), implied that the higher the dividend yield, the lower the required return at equilibrium. It was demonstrated that the model was consistent with empirical studies of the capital asset pricing model. The study analyzed the effects of transactions costs on the firm dividend decision and quantified the increase in stock prices on increasing dividend levels. In general, the stock price increase will be an increasing function of the level of transactions costs. Finally, a condition for dividend neutrality in a structure incorporating both transactions costs and homogeneous investor taxes was derived. To remove the dividend payout bias introduced by capital gains tax rates being less than income taxes, transactions costs on the capital element must equal the scaled difference between these tax rates.

This article discusses a study which analyzed intertemporal dividend models using the data on annual corporate earnings and, ordinary and preference dividends from Great Britain from 1964 to 1975. The most important result of the study has been its confirmation of the expected instability and disorientation introduced from 1973 onwards in the firm dividend decision by inflation, dividend restraint and introduction of Advanced Corporation Tax. The time-series work provided relatively strong insights into the intertemporal dividend behavior of firms for the period 1964 to 1974. This result is somewhat surprising in view of the structural changes present in the latter two periods of the sample. The structural changes could cause the disturbance term to have a non-zero expected value with the result that the parameter estimates would be biased, but there does not appear to be a clear cut reason why such well defined parameters, in terms of t-statistics, should have been obtained. The implications, then, are clear. The present economic climate in Great Britain precludes the development of intertemporal dividend models with predictive power until such time as sufficient data is available to reflect specifically the recent structural changes.

The article focuses on the impact of discrete changes in beta factors upon the estimators resulting from using all the data related to a particular company. Estimators can also utilize observations relating to the changed beta value. Estimates of beta factors are available from a number of institutions providing investment services. Betas may change in two different fashions. In the first case, betas might fluctuate randomly from period to period. In the second case, it may change suddenly from one value to another as a result of change in leverage policy. Various techniques for improving these estimates are continually being analyzed and investigated. One particular estimating problem has been the assumed inactivity of betas over the period of estimation and over the future periods for which investment decisions are made. To estimate beta, the researcher collects data over a past period of time and then runs an ordinary least squares regression. They assume that beta remains constant throughout this estimating period. The implicit assumption is reflected by the absence of a time subscript on the beta coefficient in equations.

The article presents a correction to the article "A Simple Measure of Price Adjustment Coefficients," by Aswath Damodaran, published in a 1993 issue.

Within the planetary boundary layer (PBL), surface forcing response, drag, turbulence, and vertical mixing are important processes and play a more critical role here than in the overlying "free atmosphere." The PBL height (PBLH) is an important parameter in climate models, weather forecasts, and air quality prediction. The NASA Goddard Earth Sciences Data and Information Services Center (GES DISC) provides data processing, archiving, and distribution services for numerous Earth science products. PBLH is a parameter in three products served by GES DISC, which are from the atmospheric infrared sounder (AIRS), the global positioning system (GPS) radio occultation (RO) experiment, and the NASA reanalysis product Modern‐Era Retrospective analysis for Research and Applications‐2 (MERRA‐2). These products have different spatial and temporal resolutions and coverages, and their PBLH definitions are also different. To better serve the PBL research community, we have summarized the specifications of these products. A 10‐year seasonal mean intercomparison is also conducted to provide further guidance to users. The intercomparison results show that MERRA‐2 has a much shallower PBL than AIRS and GPS RO. An experimental study indicates that the different PBLH definition in MERRA‐2 caused smaller values of PBLH. The improvement of the water vapor retrieval in AIRS version 7 over version 6 results in the version 7 PBLH agreeing better with GPS RO and MERRA‐2 than version 6, especially near the equator and low latitudes. Key Points: PBL height is available in atmospheric infrared sounder (AIRS), global positioning system radio occultation, and NASA reanalysis products served by Goddard Earth Sciences Data and Information Services CenterThe PBL height definition has immense impacts on the height values and global distributionsThe improved water vapor retrieval in AIRS version 7 makes the new version of PBL height agree better with other products [ABSTRACT FROM AUTHOR]