What is the Expected Return on the Market?*
从指数期权价格中推导出一个波动率指数SVIX，并证明其可作为权益溢价的下界，该下界在2008年危机时超过20%，均值约5%，且未被数据拒绝，因此SVIX可作为权益溢价的代理变量。
Abstract I derive a lower bound on the equity premium in terms of a volatility index, SVIX, that can be calculated from index option prices. The bound implies that the equity premium is extremely volatile and that it rose above 20% at the height of the crisis in 2008. The time-series average of the lower bound is about 5%, suggesting that the bound may be approximately tight. I run predictive regressions and find that this hypothesis is not rejected by the data, so I use the SVIX index as a proxy for the equity premium and argue that the high equity premia available at times of stress largely reflect high expected returns over the very short run. I also provide a measure of the probability of a market crash, and introduce simple variance swaps, tradable contracts based on SVIX that are robust alternatives to variance swaps.