Aspiration Level and Asset Prices

Description

In our project, we will analyze a dynamic consumption-investment problem with aspiration-level-type utility. The agent derives utility not only from intermediate consumption, but also from achieving a predetermined consumption level, which we call her aspiration level. This aspiration level is time-varying and endogenously determined. Our preliminary analysis suggests that we can derive the optimality conditions in closed form. Then, we will extend our framework into a general equilibrium model. Such an extension will enable us to calibrate our model to market data, and to study the asset pricing implications of aspiration-level-type utility.Based on our preliminary analysis, our model can explain several asset pricing puzzles. Furthermore, it can provide an explanation to the formation and eventual burst of asset bubbles.First, in order to achieve her aspiration level, our agent, on average, tends to invest less of her wealth in the risky security. This will provide an explanation to the equity premium puzzle.Second, even though unconditionally the agent follows a more conservative investment policy, her willingness to take on more or less risk is time- and state-dependent. In some states, in order to ensure that she will have sufficient wealth in the next period to achieve her aspiration level, it will be optimal for her to “fly to safety” and invest less in the risky security. In other states, the only way for her to achieve her aspiration level is by investing more in the risky security. This variation in the optimal portfolio weights will lead to higher return volatility, and hence provide a resolution to the excess volatility puzzle.The time- and state dependency of the optimal investment policy not only increases return volatility, but it also leads to time-varying risk premia. This, in turn, will explain stock return predictability.Our model will not only provide a resolution to the above-mentioned asset pricing puzzles, but it will also exhibit periodical endogenous formation of asset bubbles and their eventual burst. Intuitively, as the agent increases her aspiration level, she will need to take on more and more risk. This will lead to higher and higher asset prices. After the agent cannot finance achieving her high aspiration level any more, she will suffer a one-time utility loss by investing most of her wealth in the money market account (“fly to safety”), which leads to a dramatic decrease in asset prices (the bubble bursts). Then, the process starts over.