French-Schwert-Stambaugh (1987) Expected Stock Returns and Volatility

Summary

A foundational empirical study of the relation between the stock-market risk premium and its volatility. Using daily returns to build monthly volatility estimates (an early realized-volatility construction) and decomposing them into predictable and unpredictable components with univariate ARIMA models, the authors find that the expected risk premium is positively — but weakly — related to the predictable component of volatility. Far more strongly, unexpected returns are negatively related to unexpected changes in volatility. Because a rise in volatility raises the required return and thus lowers the current price, this negative contemporaneous relation is read as indirect evidence for a positive ex-ante risk-return tradeoff (the "volatility feedback" mechanism).

Key Claims

Positive (weak) ex-ante tradeoff. The expected market risk premium (portfolio return minus the Treasury-bill yield) is positively related to the predictable volatility of returns, consistent with the ICAPM/risk-return tradeoff, though the direct estimate is weak.
Strong negative return–volatility-innovation relation. Unexpected stock returns are strongly negatively correlated with unexpected changes in volatility — the empirical regularity later central to the "volatility feedback" and asymmetric-volatility literatures.
Volatility feedback, not just leverage. The negative relation is too large to be explained by financial leverage alone; it is interpreted as evidence that a positive shock to expected volatility raises expected returns and depresses current prices.
Two estimation strategies. (i) Daily-return-based monthly volatility + ARIMA predictable/unpredictable decomposition; (ii) a GARCH-in-mean specification estimating the risk premium jointly with conditional variance — both point the same way.
Predictable, persistent volatility. Monthly stock-market volatility is highly persistent and forecastable, a stylized fact underpinning the whole exercise.

Concepts Introduced or Extended

Risk-Return Tradeoff

Entities Mentioned

Quotes

"We find evidence that the expected market risk premium ... is positively related to the predictable volatility of stock returns. There is also evidence that unexpected stock market returns are negatively related to the unexpected change in the volatility of stock returns. This negative relation provides indirect evidence of a positive relation between expected risk premiums and volatility."

My Take

The paper that put the risk-return tradeoff and the asymmetric return–volatility relation on a firm empirical footing, and it did so with a strikingly modern toolkit: daily data aggregated to monthly "realized" volatility, ARIMA modelling of the predictable component, and GARCH-in-mean estimation side by side. Its lasting contribution is the decomposition — a weak positive relation between expected returns and predictable volatility, but a strong negative relation between return surprises and volatility surprises — which reframed the "negative GARCH-M coefficient" puzzle as a contemporaneous-innovation phenomenon rather than a refutation of the tradeoff. That reading is exactly what later structural work (Brandt-Kang, Bollerslev-Zhou) formalized. It sits naturally beside Engle-Lilien-Robins on the ARCH-M side and the GARCH and realized-volatility pages on the measurement side.