What is the Expected Return on the Market?

This paper presents a new lower bound on the equity premium in terms of a volatility index, SVIX, that can be calculated from index option prices. This bound, which relies only on very weak assumptions, implies that the equity premium is extremely volatile, and that it rose above 20% at the height of the crisis in 2008. More aggressively, I argue that the lower bound---whose time-series average is about 5%---is approximately tight and that the high equity premia available at times of stress largely reflect high expected returns over the very short run. Under a stronger assumption, I show how to use option prices to measure the probability that the market goes up (or down) over some given horizon, and to compute the expected excess return on the market conditional on the market going up (or down).