TY  - JOUR
AU  - Bekaert,Geert
AU  - Liu,Jun
TI  - Conditioning Information and Variance Bounds on Pricing Kernels
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 6880
PY  - 1999
Y2  - January 1999
UR  - http://www.nber.org/papers/w6880
L1  - http://www.nber.org/papers/w6880.pdf
N1  - Author contact info:
Geert Bekaert
Graduate School of Business
Columbia University
3022 Broadway, 411 Uris Hall
New York, NY 10027
Tel: 212/854-9156
Fax: 212/662-8474
E-Mail: gb241@columbia.edu

Jun Liu
Rady School of Management
UCSD
Pepper Canyon Hall Room 320
9500 Gilman Dr MC 0093
La Jolla CA 92093
Tel: 310/825-4083
E-Mail: junliu@ucsd.edu
AB  - We show how to use conditioning information optimally to construct a sharper unconditional  Hansen-Jagannathan (1991) bound.  The approach in this paper is different from that of Gallant, Hansen and Tauchen (1990), but both approaches yield the same bound when the conditional moments are known.  Unlike Gallant, Hansen and Tauchen, our approach is robust to misspecification of the first and second conditional moments.  Potential applications include testing dynamic asset pricing models, studying the predictability of asset returns, diagnosing the accuracy of competing models for the first and second conditional moments of asset returns, dynamic asset allocation and mutual fund performance measurement.  The illustration in this article starts with the familiar Hansen-Singleton (1983) setup of an autoregressive model for consumption growth and bond and stock returns.  Our innovation is to add time-varying volatility to the model.  Both an unconstrained version and a version with the restrictions of the standard consumption-based asset pricing model imposed serve as the data-generating processes to illustrate the behavior of the bounds. In the process, we discover and explore an interesting empirical phenomenon: asymmetric volatility in consumption growth.
ER  -