TY - JOUR
AU - Engel,Charles
TI - Some New Variance Bounds for Asset Prices
JF - National Bureau of Economic Research Working Paper Series
VL - No. 10981
PY - 2004
Y2 - December 2004
DO - 10.3386/w10981
UR - http://www.nber.org/papers/w10981
L1 - http://www.nber.org/papers/w10981.pdf
N1 - Author contact info:
Charles Engel
Department of Economics
University of Wisconsin
1180 Observatory Drive
Madison, WI 53706-1393
Tel: 608/262-3697
Fax: 608/262-2033
E-Mail: cengel@ssc.wisc.edu
AB - 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)).
ER -