Elderly Asset Management

Abstract

In this paper we present a model of elderly asset management and results based on simulation analysis of the model. In our model elderly decide both how much to consume out of current income and wealth each period and the allocation of their remaining income and wealth between a risky asset and a riskless asset.

In our model an elderly person can be either in good health or poor health, and we specify a transition matrix for transitions from good to poor health, as well as for the probability of death next period; in addition, we include out-of-pocket health expenditures for those in poor health. By incorporating health we are able to study the relationship between health and health expenditure on the one hand and asset allocation decisions on the other; as far as we are aware this relationship has not previously been studied in a structural life-cycle model.

A specific novel aspect of our model is that we explore different possible shapes for the bequest function and the impact of the shape of this function on elderly asset management. Surprisingly, most previous models of bequests assume that the bequest function has the same shape as the utility function. Thus, it is tacitly assumed that the preferences elderly have regarding the wealth they will leave to their heirs are the same as their preferences over their own utility. As we discuss in the next section, there is no reason why this must be the case. Indeed we discuss why it is likely not to be the case, and discuss different shapes and their possible psychological basis. In our simulations we show that the shape of the bequest function impacts elderly asset management, especially at the very end of life, thus that this shape should be more prominent in discussions about the elderly and their management of their assets than it has been.

Several interesting qualitative features of elderly asset management emerge from our analysis. We find that when the bequest function is risk-neutral whereas the utility function exhibits risk aversion, individuals place a higher proportion of their assets in stock in middle and later periods of our model, thus in later old age. We call this result the risky shift. Although the elderly are often thought of as more risk averse, in late old age their investing behavior will be driven to a great extent by their bequest function, and if this function is in fact less concave than their utility function they may more invest heavily in risky investments like equity towards the end of life. We also find an interesting relationship between health status, bequest function, and asset management. In our model individuals in poor health place a slightly lower proportion of their assets in stock than individuals in good health.

Individuals in poor health face a greater risk of substantial future medical expenditures, which may lead towards more risk-averse investment behavior, as these expenditures tend to highlight the chances of a very low consumption state in the future, and since elderly are risk-averse regarding their own utility they wish to protect against this outcome.

Keywords: asset management

JEL Classification: D10, D91, J14