Beyond the Local Mean-Variance Analysis in Continuous Time: The Problem of Non-Normality

23 Pages Posted: 26 Feb 2015

See all articles by Knut K. Aase

Knut K. Aase

Norwegian School of Economics (NHH) - Department of Business and Management Science

Jostein Lillestol

Norwegian School of Economics (NHH) - Department of Business and Management Science

Date Written: February 23, 2015

Abstract

The paper investigates the effects of deviations from normality on the estimates of risk premiums and the real equilibrium, short-term interest rate in the conventional rational expectations equilibrium model of Lucas (1978). We consider a time-continuous approach, where both the aggregate consumption process as well as cumulative dividends from risky assets are assumed to be jump-diffusion processes. This approach allows for random jumps in the fundamental underlying processes at random time points. Preferences are time separable and additive. We derive testable expressions for these quantities, and confront these with 20. century sample estimates. Since there are non-linear components in the formulas for the risk premiums and the interest rate, we can readily explore what effect deviation from normality has on these quantities. Our results test the boundaries of the conventional model.

Keywords: Mean-variance analysis, Consumption based CAPM, Equilibrium real interest rate, The equity premium puzzle, jump-diffusions, Bi-variate Normal Inverse Gaussian distribution

JEL Classification: D50, G10, G12

Suggested Citation

Aase, Knut K. and Lillestol, Jostein, Beyond the Local Mean-Variance Analysis in Continuous Time: The Problem of Non-Normality (February 23, 2015). NHH Dept. of Business and Management Science Discussion Paper No. 2015/11. Available at SSRN: https://ssrn.com/abstract=2569610 or http://dx.doi.org/10.2139/ssrn.2569610

Knut K. Aase (Contact Author)

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway

Jostein Lillestol

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway

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