The first chapter offers an explanation for the properties of the nominal term structure of interest rates and time- varying bond risk premia based on a model with rare consumption disaster risk. In the model, expected inflation follows a mean reverting process but is also subject to possible large (positive) shocks when consumption disasters occur. The possibility of jumps in inflation increases nominal yields and the yield spread, while time-variation in the inflation jump probability drives time-varying bond risk premia. Predictability regressions offer independent evidence for the model's ability to generate realistic implications for both the stock and bond markets. The second chapter studies the cross-section of stock returns. Why do value stocks have higher expected returns than growth stocks, in spite of having lower risk? Why do these stocks exhibit positive abnormal performance while growth stocks exhibit negative abnormal performance? This paper offers a rare-events based explanation, that can also account for facts about the aggregate market. Patterns in time-series predictability offer independent evidence for the model's conclusions. The third chapter studies an asset allocation problem. It shows that learning about the parameters of the return process induces a large negative hedging demand in an investor who is optimally rebalancing her portfolio, even after she has observed 83 years of market asset data. For example, an investor with a 5-year investment horizon decreases the percentage of wealth she allocates to the stock index by over 20 percent when she takes learning into account. Furthermore, I show that the initial estimation sample length needs to be at least 500 years in order for the effect of learning to vanish.