Long-Run Risk is the Worst-Case Scenario

We study an investor who is unsure of the dynamics of the economy. Not only are parameters unknown, but the investor does not even know what order model to estimate. She estimates her consumption process non-parametrically and prices assets using a pessimistic model that minimizes lifetime utility subject to a constraint on statistical plausibility. The equilibrium is exactly solvable and we show that the pricing model always includes long run risks. With a single free parameter determining risk preferences, the model generates high and volatile risk premia, excess volatility in stock returns, return predictability, interest rates that are uncorrelated with expected consumption growth, and investor expectations that are consistent with survey evidence. Risk aversion is equal to 4.8, there is no stochastic volatility or disasters, and the pricing model is statistically nearly indistinguishable from the true data-generating process. The analysis yields a general characterization of behavior under a very broad form of model uncertainty.