Do CAPM results hold in a dynamic economy? A numerical analysis

Abstract

In this research we use the projection method (reported by Judd) to find numerical solutions to the Euler equations of a stochastic dynamic growth model. The mode1 that we solve is Brock's asset pricing model for a variety of parameterizations of the production functions. Using simulated data from the model, conjectures (which are not analytically tractable) can be verified. We show that the market portfolio is mean-variance efficient in this dynamic context. We also show a result that is not available from the static CAPM theory: the efficient frontier shifts up and down over the business cycle.

On the performance of West’s bubble test: A simulation approach

“…# Sign denotes the total number of samples in which a coefficient is significant at 5% level. (30). For 5% significance level the critical value is 43.77.…”

“…In order to analyze the properties of the solutions to the asset pricing model we must use numerical techniques instead. Akdeniz and Dechert [30] report the technical details of the numerical solution which we will not repeat here. In this study we use that solution and explore the parameter space for solutions to the model that, to a certain extent, fit some of the stylized facts of asset markets.…”

“…Our primary focus will be on the equity prices that come out of the Brock [2] asset pricing model. For the solution and the computational details please see Akdeniz and Dechert [30,31].…”

Risk and return in a dynamic general equilibrium model

“…We have chosen to use the projection method in Judd (1992). The details of the solution are in Akdeniz and Dechert (1997). …”

The equity premium in Brock's asset pricing model

“…Although they make no mention of the technical difficulties in solving Brock's model, it is likely that this was also a reason for their not having done so. Neither the algorithms nor the hardware used to produce the results in Akdeniz and Dechert (1997) were available then.…”