Some New Variance Bounds for Asset Prices

14 Pages Posted: 21 Dec 2004 Last revised: 2 Jan 2023

See all articles by Charles M. Engel

Charles M. Engel

University of Wisconsin - Madison - Department of Economics; National Bureau of Economic Research (NBER); University of Washington - Department of Economics

Date Written: December 2004

Abstract

When equity prices are determined as the discounted sum of current and expected future dividends, Shiller (1981) and LeRoy and Porter (1981) derived a relationship between the variance of the price of equities, p(t), and the variance of the ex post realized discounted sum of current and future dividends: p*(t): Var(p*(t))>= Var(p(t)). The literature has long since recognized that this variance bound is valid only when dividends follow a stationary process. Others, notably West (1988), derive variance bounds that apply when dividends are nonstationary. West shows that the variance in innovations in p(t) must be less than the variance of innovations in a forecast of the discounted sum of current and future dividends constructed by the econometrician, p^(t). Here we derive a new variance bound when dividends are stationary or have a unit root, that sheds light on the discussion in the 1980s of the Shiller variance bound: Var(p(t)-p(t-1)) >= Var(p*(t)-p*(t-1))! We also derive a variance bound related to the West bound: Var(p^(t)-p^(t-1)) >= Var(p(t)-p(t-1)).

Suggested Citation

Engel, Charles M., Some New Variance Bounds for Asset Prices (December 2004). NBER Working Paper No. w10981, Available at SSRN: https://ssrn.com/abstract=633640

Charles M. Engel (Contact Author)

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