The Consumption-Investment Decision of a Prospect Theory Household: A Two-Period Model

This study extends the literature on portfolio choice under prospect theory preferences by introducing a two-period life cycle model, where the household decides on optimal consumption and investment in a portfolio with one risk-free and one risky asset. The optimal solution depends primarily on the household’s choice of the present value of the consumption reference levels relative to the present value of its endowment income. If the present value of the consumption reference levels is set below the present value of endowment income, then the household behaves in such a way to avoid relative losses in consumption in any present or future state of nature (good or bad). As a result the degree of loss aversion does not directly affect optimal consumption and risk taking activity. However, it must be sufficiently high in order to rule out outcomes with relative losses. On the other hand, if the present value of the consumption reference levels is set exactly equal to the present value of the endowment income, i.e., the household sets its reference levels such that they are in balance with its income, then the household’s optimal consumption is the reference consumption in both periods and the household will not invest in the risky asset. Finally, if the present value of the household’s consumption reference levels is set above the present value of its endowment income, then the household cannot avoid experiencing a relative loss in consumption, either now or in the future. As a result, loss aversion directly affects consumption and risky investment. Reference levels play a significant role in consumption and risk taking activity. In most cases the household will “follow the Joneses” if the reference levels are set equal to the consumption levels of the Joneses. Independent of how consumption reference levels are set, being more ambitious, i.e., increasing one’s reference levels, will result in less happiness. The only case when this is not true is when reference levels increase with growing income (and the present value of reference levels is set below the present value of endowment income).