A STOCHASTIC SIMULATION OF THE PERSONAL INVESTMENT DECISION

THE ACCUMULATION of personal wealth is a process that involves two decision elements: choice of the amount to be saved (investment scale) and choice of assets in which savings are to be held (investment mix). Although each of these has received considerable attention in the literature, they are typically treated separately and statically. Portfolio-selection models, for example, normally assume that the amount to be invested is given; time-preference models, at the same time, usually specify a given and certain investment-opportunity schedule. This implies independence of the distributions of scale and mix outcomes over time. It also suggests that personal utility functions should be described separately with respect to time and risk preferences. Separate treatment of relevant determinants provides a limited description of the wealth-accumulation process. This study attempts to conceptualize and construct an integrated decision model, one which accommodates the scale and mix decisions simultaneously and dynamically. The general model proposed consists of a set of algebraic statements describing the financial and personal environment facing an individual investor. Functional relationships to be specified include consumption preference and expected values of salary, rate of return on investment, taxes and the initial wealth position. Any of these can be defined as randomly distributed. The Monte Carlo method is then employed to trace interim and terminal wealth positions over the life cycle of the investor. Successive iteration generates a distribution of wealth positions for each scale-mix combination at each desired observation point over the life cycle. The generalized model described above is flexible, and it can be applied to a number of relevant questions facing individual investors. To cite one example, the wealth effect of alternative life-insurance programs can be evaluated. Timing considerations can also be accommodated; the minimum level of expenditure required to educate one's children may be used to constrain acceptable interim wealth positions. The estimation of return on human investment is another promising area for experimentation, since the costs and benefits of educational and professional activity can be defined as part of the structure of any particular model. For purposes of this study, a hypothetical investor was defined, and a computer program was designed and operated to test the feasibility of the model. Since the assumed environment is not considered to be excessively unrealistic, model outcomes were also subjected to a sensitivity analysis in an attempt to assess the relative significance of each of the decision variables. Salary patterns and consumption propensities were allowed to vary, and the investor was viewed as attempting to maximize wealth within the living standard imposed by his budget constraint. A two-parameter portfolio set was assumed, and parameters were estimated empirically by employing the Sharpe diagonal model. Federal taxes were computed on the basis of existing regulations. The experimental outcomes have relevance, properly speaking, only for the model's hypothetical investor. Nevertheless, some findings have implications of more general in-