What Is the Expected Return on the Market?

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. JEL Codes: E44, G1.

(Almost) Model‐Free Recovery

“…The choice yields a different lower bound on the equity premium, given by the second forward moment of returns. Martin () justifies the latter bound theoretically under various economic conditions . The broader family of covariance conditions in Definition allows us to embed existing equity premium lower bounds and more flexibly constrain the moments of returns, in a way that can be made more consistent with both the empirical evidence and mild economic assumptions.…”

“…Similar to Martin (), sufficient conditions for bound in benchmark economies can be provided . For instance, it is easy to see that in such economies, our extended conditions hold for relative risk aversion parameters larger than p .…”

“…All of these bounds depend on unobservable pricing kernel dispersion properties. Martin () motivates a negative covariance condition (NCC) on returns and unobservable pricing kernels, which yields an observable lower bound for expected returns. We contribute to this literature with a broader set of NCCs that correspond to a wider and more flexible family of observable lower bounds on the moments of returns.…”

Capital Share Risk in U.S. Asset Pricing

“…An alternative reason for focusing on longer‐horizon betas is that the simple SDF is likely to be misspecified because it misses some additional risk factors. A growing body of evidence using equity options data suggests the existence of a volatile but highly transitory component in equity market risk premia that is at odds with a range of consumption‐based models, even those that generate a time‐varying market risk premium (e.g., see the evidence in Bollerslev, Tauchen, and Zhou (), Andersen, Fusari, and Todorov (), and Martin ()). The time‐variation in market risk premia generated by standard consumption‐based models is much less volatile and much more persistent than that suggested by options data.…”

The Quanto Theory of Exchange Rates

“…(To streamline the discussion, this description is an oversimplification and strengthening of the condition we actually need to hold for our approach to work, which is based on a general identity presented in Result 1.) This approach has been shown by Martin (2017) and Martin and Wagner (2018) to be successful in forecasting returns on the stock market and on individual stocks, respectively.…”