Scandinavian Working Papers in Economics

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2015/11: Beyond the local mean-variance analysis in continuous time: The problem of non-normality

Knut K. Aase () and Jostein Lillestøl ()
Additional contact information
Knut K. Aase: Dept. of Business and Management Science, Norwegian School of Economics, Postal: NHH , Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
Jostein Lillestøl: Dept. of Business and Management Science, Norwegian School of Economics, Postal: NHH , Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway

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-di usion 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-codes: D50; G10; G12

22 pages, February 23, 2015

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