This paper is concerned with the interaction of saving and portfolio decisions of a single consumer. Its building blocks are the classical theory of optimal allocation over time and Arrow's recent formulation of the theory of portfolio selection. The concept of a risk aversion function is extended to a two-period context and the implications of declining risk aversion are explored. Also discussed are the problems of the effect of changes in the rates of return and in the degree of risk, as well as the question of taxation and risk taking.