Expected Stock Returns and Volatility in a Production Economy: A Theory and Some Evidence

Padamja Singal and Stephen D. Smith
Federal Reserve Bank of Atlanta
Working Paper 99-8
July 1999

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The sign of the relationship between expected stock market returns and volatility appears to vary over time, a result that seems at odds with basic notions of risk and return. In this paper we construct an economy where production involves the use of both labor and capital as inputs. We show that when capital investment is "sticky," the sign of the relation between stock market risk and return varies in accordance with the supply of labor but requires no time variation in preferences. In particular, we show that for asset market equilibria where firms face an elastic supply of labor, the traditional positive risk-return relation obtains. Conversely, a negative relation obtains for asset market equilibria where there is positive probability that labor supply will be highly inelastic. A nice feature of our model is that, unlike earlier work, the sign of the stock market risk-return relation can be associated with observable features of the business cycle. Post–World War II macroeconomic and stock return data are used to test the predictions from the model. Using standard measures of stock market volatility, our results provide support for a stock market risk-return relation that is negative at the peaks of business cycles and positive at the troughs.

JEL classification: E23, E34, G12

Key words: stock markets, risk, return, production and business cycles

The authors thank Shomu Banerjee, Julie Hotchkiss, David Nachman, Tom Noe, and Michael Rebello for several useful comments and suggestions. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.

Please address questions regarding content to Padamja Singal, Department of Finance, College of Business Administration, Ohio University, Athens, Ohio 45701, 740/597-2901, 740/593-9539 (fax), singal@ohiou.edu; and Stephen D. Smith, Department of Finance, College of Business Administration, Georgia State University, Atlanta, Georgia 30303, and Research Department, Federal Reserve Bank of Atlanta, 404/651-1236, 404/651-2630 (fax), fncsds@langate.gsu.edu.