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.
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Paper provided by Department of Economics, University of York in its series Discussion Papers with number
01/13.
Length: Date of creation: Date of revision: Handle: RePEc:yor:yorken:01/13
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