Optimal Consumption and Portfolio Choice with Loss Aversion

Abstract

In their seminal paper, Kahneman and Tversky (1979) suggest that investors are more sensitive to losses than gains and that they tend to be risk seeking after losses and risk averse after gains, rather than purely risk-averse as postulated by the classical portfolio theory. Since then many researcher have incorporated loss aversion into the theory of portfolio and studied its implications for the choice of risky assets. This literature typically applies the idea of loss aversion to the return of risky assets or to fluctuations of financial wealth, around a certain reference point. However in their seminal paper, Kahneman and Tversky argue that loss aversion is a general mental framework that can be applied to any kind of choice whose outcomes can be coded in terms of gains and losses, and not only to stock returns. Motivated by this observation, I analyse the portfolio problem of an investor who is loss averse over consumption relative to a time-varying reference level. At any point in time the investor decides how to allocate wealth between consumption, risk-free and risky assets. In addition, the reference level of consumption evolves over time and is given by a weighted average of past and current consumption.I show that loss aversion changes the traditional consumption smoothing behavior. The loss averse agent smooths consumption only in good time (i.e., when the consumption good is cheap) and reduces consumption to the subsistence level in bad times (i.e., when the consumption good is expensive). The particular nature of the optimal consumption strategy implies that the investor's optimal portfolio has two components: a standard mean variance component and a gambling portfolio consisting of aggressive investments in stocks. The weight assigned to these two portfolios is time varying. In good times, the loss averse investor wishes to maximize the probability that his/her consumption stays above the reference level and the weight assigned to the mean variance portfolio increases. In bad times, the consumption smoothing strategy is abandoned and the investor opts for a gambling for resurrection strategy, thus rebalancing his/her portfolio toward risky assets.This consumption-investment strategy differs from what suggested by the traditional portfolio theory and is consistent with several recent stylized facts about investors' behaviour, such as the pro-cyclical behavior of consumption smoothing, or the tendency of many individual investors to increase their equity position during the recent financial crisis. Optimal Consumption and Portfolio Choice with Loss AversionGiuliano Curatola * Goethe Universität Frankfurt March 16, 2016Abstract This paper analyses the consumption-investment problem of a loss averse investor equipped with s-shaped utility over consumption relative to a time-varying reference level. Optimal consumption exceeds the reference level in good times and descend to the subsistence level in bad times. Accordingly, the optimal portfolio is dominated by a mean-variance component in good times and...