Expected returns vary when investors face time-varying investment opportunities. In theory, structural long-run risk models (Bansal and Yaron, 2004) and no-arbitrage affine models (Duffie, Pan, and Singleton, 2000) emphasize sources of risk that are not observable to the econometrician. We show...

We build a model for bond yields based on a small-scale representation of an economy with secular declines in inflation, the real rate and output growth. Long-run restrictions identify nominal shocks that influence long-run inflation but do not influence the long-run real rate or output growth....

We decompose the quadratic payoff on a stock into its loss and gain components and measure the premia associated with their fluctuations, called the loss and gain quadratic risk premium (QRP) respectively. The loss QRP interprets as the premium paid for downside risk hedging, while the gain QRP...

We decompose the quadratic payoff on a stock into its loss and gain components and measure the premia associated with their fluctuations, called the loss and gain quadratic risk premium (QRP) respectively. The loss QRP interprets as the premium paid for downside risk hedging, while the gain QRP...