This paper studies the pricing of volatility risk using the first-order conditions of a long-term equity investor who is content to hold the aggregate equity market rather than tilting towards value stocks and other equity portfolios that are attractive to short-term investors. We show that a...

We study the pricing of uncertainty shocks using a wide-ranging set of options that reveal premia for macroeconomic risks. Portfolios hedging macro uncertainty have historically earned zero or even significantly positive returns, while those exposed to the realization of large shocks have earned...

We document a form of excess volatility that is irreconcilable with standard models of prices, even after accounting for variation in discount rates. We compare prices of claims on the same cash flow stream but with different maturities. Standard models impose precise internal consistency...