Dynamic consumption and portfolio decisions with time varying asset returns

L. Grüne, W. Semmler, C. Öhrlein: Dynamic consumption and portfolio decisions with time varying asset returns
The Journal of Wealth Management 12 (2), 21 - 47, 2009

DOI: 10.3905/JWM.2009.12.2.021


Abstract:

Recently research in financial economics has studied consumption and portfolio decisions, where investment opportunities change over time. This type of work originates in Merton (1971, 1990) who has used the Bellman equation to solve the consumption as well as asset allocation decisions for one state and two choice variables. Campbell and Viceira (1999, 2002) study consumption and portfolio decisions in various models with time varying expected returns by assuming that new investment opportunities are not only arising from changing interest rates, but also from time varying risk premia. They have approximated such a dynamic decision model under the assumption that the consumption-wealth ratio should not vary too much. In this paper, we study dynamic consumption and portfolio decisions by using dynamic programming which allows to compute, with sufficient accuracy, the decision variables and the consumption-wealth ratio at any point of the state space. The dynamic decision problem is first analytically and numerically solved for a simple model with constant returns. Then we solve a model with dynamic consumption and portfolio decisions when time varying returns are calibrated from the low frequency components of US time series financial data. The implications of the change of investor's risk aversion, the change of returns and the time horizon are explored for the consumption decisions, the consumption-wealth ratio, the asset allocation and the path of wealth. The numerical results are based on C. Öhrleins Diploma thesis (24 MB, in German)

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