Asset Pricing with Observable Stochastic Discount Factors.

The stochastic discount factor model provides a general framework for pricing assets. By specifying the discount factor suitably it encompasses most of the theories currently in use, including CAPM and consumption CAPM. The SDF model has been based on the use of single and multiple factors, and on latent and observed factors. In most situations, and especially for the term structure, single factor models are inappropriate, whilst latent variables require the somewhat arbitrary specification of generating processes and are difficult to interpret. In this paper we survey the principal different implementations of the SDF model for FOREX, equity and bonds and we propose a new approach. This is based on the use of multiple factors that are observable and modelling the joint distribution of excess returns and the factors using a multi-variate GARCH-in-mean process. We argue that in general single equation and VAR models, although widely used in empirical finance, are inappropriate as they do not satisfy the no-arbitrage condition. Since risk premia arise from conditional covariation between returns and the factors, both a multi-variate context and having conditional covariances in the conditional mean process, is essential. We explain how apparent exceptions, such as the CIR and Vasicek models, in fact meet this requirement - but at a price. We explain our new approach, discuss how it might be implemented and present some empirical evidence, mainly from our own researches. Partly, to enable comparisons to be made, the survey also includes evidence from recent empirical work using more traditional approaches.Asset Pricing; Stochastic Discount Factors; Forex; Equity Term Structure; Affine Factor Models; Consumption CAPM; Financial Econometrics; GARCH

Macroeconmic Sources of FOREX Risk.

This paper considers the problem of measuring macroeconomic sources of financial risk. 1. It aims to provide a general theory of asset pricing suitable for taking account of macroeconomic sources of risk. Stochastic discount factor theory is used to provide the theoretical framework. This is capable of embracing most of the approaches in the literature, including general equilibrium theory. Market structure needs to be added to this. 2. It is shown that many of the models used in the empirical literature of asset pricing have a fundamental flaw: they admit unlimited arbitrage opportunities. High profile suites of computer programs just produced and sold world-wide suffer the same problem, and hence should not be used. 3. Modelling the exchange rate is key to much of monetary policy (eg the Bank of England's Monetary Policy Committee), and to testing FOREX market efficiency. The forward premium puzzle lies at the heart of the difficulty of doing this. The theoretical results of this paper are used to re-examine the distribution of exchange rate movements and to try to resolve this puzzle. Stochastic discount factor theory is used to derive expressions for the risk premia for domestic and foreign investors. It is shown that these are likely to be different. A combined theory of market risk when both types of investor are trading is then obtained. The cases of complete and incomplete markets are considered. It is shown how macroeconomic sources of risk can be introduced by modelling the stochastic discount factor using observable macroeconomic variables. Three SDF models are compared: a benchmark model which provides a reformulation of traditional tests of FOREX efficiency; inter-temporal consumption-based CAPM; and the monetary model of the exchange rate, a familiar macroeconomic model of FOREX which can be interpreted as arising from traditional hedging concerns. The joint distribution of the excess return to foreign exchange and the macro factors is specified in a way that satisfies the no-arbitrage assumption. It is assumed that the joint distribution has multivariate GARCH and it is shown that to eliminate arbitrage opportunities it is necessary for the conditional distribution of the excess return to exhibit GARCH-in-mean. The omission of the conditional covariance between the excess return and the sources of risk is the reason why nearly all financial statistical packages are not suitable for use in financial econometrics. The presence of this term implies that the analysis must be conducted in a multi-variate and not a uni-variate framework. The theory admits the possibility that domestic and foreign investors may have different attitudes to risk. This is incorporated into the model by introducing a switching formulation of the conditional covariance structure. Extreme changes in exchange rates suggest that the usual assumption of log-normality may fail to capture the excess kurtosis of excess returns. The model is therefore also estimated assuming a log t-distribution. It is notoriously difficult to achieve convergence in multi-variate GARCH models, and GARCH-in-mean effects increase the difficulty. This is a major limitation in the practicality of the whole approach. It is shown that assuming constant correlation greatly simplifies the estimation without sacrificing any essential elements. Tests are conducted to enable a comparison of different SDF models, different market structures, different attitudes to risk, and differences between the SDF model and the Fama approach. The empirical work is based on monthly data for the sterling-dollar exchange rate 1975-1997. Our main new finding is that the evidence is more consistent with the FOREX risk premium arising from traditional partial equilibrium models of currency risk that form the basis of hedging than with consumption-CAPM, a general equilibrium theory. In particular, US and UK output appear to be important sources of FOREX risk.FOREX, market efficiency, risk premium, stochastic discount factors, GARCH.

High Resolution Spectroscopy of Balmer-Dominated Shocks in the RCW 86, Kepler and SN 1006 Supernova Remnants

We report results from high resolution optical spectroscopy of three non-radiative galactic supernova remnants, RCW 86, Kepler's supernova remnant and SN 1006. We have measured the narrow component H-alpha line widths in Balmer-dominated filaments in RCW 86 and SN 1006, as well as the narrow component width in a Balmer-dominated knot in Kepler's SNR. The narrow component line widths measured in RCW 86 and Kepler's SNR show FWHM of 30-40 km/s, similar to what has been seen in other Balmer-dominated remnants. Of the remnants in our sample, SN 1006 is the fastest shock (~3000 km/s). The narrow component H-alpha and H-beta lines in this remnant have a FWHM of merely 21 km/s. Comparing the narrow component widths measured in our sample with those measured in other remnants shows that the width of the narrow component does not correlate in a simple way with the shock velocity. The implications for the pre-heating mechanism responsible for the observed line widths are discussed.Comment: Accepted by A&

Consumption, Size and Book-to-Market Ratio in Equity Returns

This study extends the standard consumption-based capital asset pricing model (C-CAPM) to include two additional factors related to firm size (SMB) and book-to-market value ratio (HML). The inclusion of HML improves mainly the fit of the low book-to-market portfolios, SMB, and HML that are not correctly priced in the standard C-CAPM. Consumption premium varies across size and coincides with the size effect. The effect of a HML premium is to reduce the amount of consumption premium, implying that low book-to-market ratio and, to a lesser degree, small portfolios are not as risky as consumption predicts. The HML premium across size is contradictory to the size effect as small firms have a larger negative HML premium.Risk Premium; Equity Return; Stochastic Discount Factor; Consumption

A Cross Section of Equity Returns: The No-Arbitrage Test

We propose a new test based on the no-arbitrage condition that compares cross-sectional variation in equity returns to the cross-sectional variation in their conditional covariance with the discount factors. Using the multivariate generalized heteroskedasticity in mean model (MGM) to estimate the 25 portfolios formed on size and book-to-market ratio, together with each with its own arbitrage condition, we find that the no-arbitrage test rejects the consumption-based capital asset pricing model (C-CAPM). Although the conditional covariances of returns with consumption exhibit negative variation across size, they do not vary across the book-to-market ratio. Thus, the C-CAPM can capture size effect, but not value effect. Allowing the coefficients on the consumption covariances to be different largely improves the fit of the C-CAPM, however. The value effect appears to be associated with book-to-market ratio as well as size. Book-to-market ratio separately does not generate information about average returns that cannot be explained by the C-CAPM.Risk Premium; Equity Return; Stochastic Discount Factor; No-arbitrage Condition

Composing Scalable Nonlinear Algebraic Solvers

Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for nonlinear algebraic systems, where nonlinear composition of different nonlinear solvers may significantly improve the time to solution. We describe the basic concepts of nonlinear composition and preconditioning and present a number of solvers applicable to nonlinear partial differential equations. We have developed a software framework in order to easily explore the possible combinations of solvers. We show that the performance gains from using composed solvers can be substantial compared with gains from standard Newton-Krylov methods.Comment: 29 pages, 14 figures, 13 table

Orbitofrontal epilepsy: Electroclinical analysis of surgical cases and literature review

Clinical and electrographic data were reviewed on 2 of our patients with orbitofrontal epilepsy who were seizure free at 5-year follow-up, and on 2 similar patients from the literature. One of our patients was lesional, and the other was nonlesional. Interictal EEG discharges were lateralized to the side of invasively recorded orbitofrontal seizures in the nonlesional case. In this case, no clinical manifestations occurred until the orbitofrontal discharge had spread to the opposite orbitofrontal and both mesial temporal areas. Unresponsiveness or arrest of activity were the initial manifestations of complex partial seizures in both cases. The 2 cases from the literature with long-term seizure-free follow-up had little impairment of awareness and displayed vigorous motor automatisms. Interictal epileptiform activity was bifrontally synchronous in 1 case. Ipsilateral frontotemporal discharges were seen in both. Invasive ictal epileptiform activity appeared maximal in the ipsilateral orbitofrontal region in both patients. No consistent electrographic or clinical pattern characterized these 4 cases. Seizures of orbitofrontal origin may be characterized by either unresponsiveness associated with oroalimentary automatisms or limited alteration of awareness and associated with vigorous motor automatisms. Invasive monitoring of the orbitofrontal cortex should be considered in nonlesional cases with complex partial seizures that show nonlocalizing ictal patterns and interictal frontal or frontotemporal epileptiform discharges. Copyright (C) 2004 S. Karger AG, Basel