The Effect of Leveraged Investments on Life Cycle Investment Consumption Models

Emil Tanderup & Arne Weermann

Student thesis: Master thesis


The objective of this thesis is to investigate the optimal investment and consumption strategy for a model investor under several realistic conditions and constraints. More specifically, we identify the effects that leverage opportunities for housing and stock market investments have on the optimal strategy. The motivation for this thesis is to gain a better understanding of the well-established non-participation puzzle. This puzzle is caused by the fact that many people invest little or nothing in stock markets. We take a normative approach and calibrate a rich and encompassing life cycle investment and consumption model in order to determine the best course of action for investors and households when making decisions about consumption, asset allocation and savings over their life. Our model economy consists of the stock market, real estate market and a risk-free investment. Our problem features a decision maker who is habit-forming in housing consumption and receives a continuous labor income with unspanned risk throughout life. By imposing realistic constraints on the decision maker, the optimization problem turns from one with an extensive closed-form solution to one that requires a much more complex numerical optimization approach. We solve this problem by deploying the SAMS framework proposed by Kraft et al. (2018). This framework includus known closed-form solutions for life cycle problems in complete and unconstrained markets as well as Monte Carlo simulation and dynamic programming. The robustness and reach of our results are thoroughly examined with a sensitivity analysis, and we compare the optimal strategy of the model with an empirical dataset of the Danish population. Our results confirm the previous finding that housing investments dominate the optimal portfolio over the life cycle. In addition, they stress the fact that stock investments are optimal in most reasonable instances. Therefore our results does not support previous explanations of the non-participation puzzle from a normative stance. Furthermore, we find that risky investments should be partly financed by a short position in the risk-free asset. We conclude that the access to leveraged stock investments disproves several explanations of the non-participation puzzle, e.g. housing investments crowding out stock investments. The model, as calibrated, does not produce the commonly observed consumption hump but instead generates a strongly increasing consumption pattern over the life cycle which is hard to reconcile with empirical data.

EducationsMSc in Finance and Investments, (Graduate Programme) Final Thesis
Publication date2020
Number of pages121