While it is now well understood that the equity premium is time-varying, this article deviates from the literature in its basic aim, which is to use theory to motivate a signal of expected returns that is based directly on asset prices. I go on to argue, more aggressively, that the lower bound appears empirically to be approximately tight, so that the SVIX index provides a direct measure of the equity premium. At horizons of less than a year, the equity premium fluctuates even more wildly: the lower bound on the monthly equity premium exceeded 4.5% (unannualized) in November 2008. The bound implies that the equity premium is extremely volatile, and that it rose above 21% at the height of the crisis in 2008. I call the associated volatility index SVIX and use the identity (coupled with a minimal assumption, the negative correlation condition, introduced in Section II) to derive a lower bound on the equity premium in terms of the SVIX index. Under the weak assumption of no arbitrage, the latter can be measured unambiguously from index option prices. The starting point of this article is an identity that relates the market's expected return to its risk-neutral variance.
Aside from its obvious intrinsic interest, the equity premium is a key determinant of the risk premium required for arbitrary assets in the capital asset pricing model (CAPM) and its descendants, and time variation in the equity premium lies at the heart of the literature on excess volatility. The expected excess return on the market, or equity premium, is one of the central quantities of finance and macroeconomics.
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