Shortfall Aversion

Shortfall aversion reflects the higher utility loss of a spending cut from a reference point than the utility gain from a similar spending increase, in the spirit of Prospect Theory's loss aversion. This paper posits a model of utility of spending scaled by a function of past peak spending, called target spending. The discontinuity of the marginal utility at the target spending corresponds to shortfall aversion. According to the closed-form solution of the associated spending-investment problem, (i) the spending rate is constant and equals the historical peak for relatively large values of wealth/target; and (ii) the spending rate increases (and the target with it) when that ratio reaches its model-determined upper bound. These features contrast with traditional Merton-style models which call for spending rates proportional to wealth. A simulation using the 1926-2012 realized returns suggests that spending of the very shortfall averse is typically increasing and very smooth.