July 2000 UPDATED VERSION
Joshua Rosenberg, Robert F. Engle
ABSTRACT
This paper investigates the empirical characteristics of investor risk aversion over equity return states by estimating
a daily semi-parametric pricing kernel. The two key features of this estimator are: (1) the functional form of
the pricing kernel is estimated semi-parametrically, instead of being prespecified and (2) the pricing kernel is
re-estimated on a daily basis, allowing measurement of time-variation in risk-aversion over equity return states.
Important empirical findings of the paper are as follows. Constant relative risk aversion over S&P500 return
states is rejected in favor of a model in which relative risk aversion is stochastic. Empirical relative risk aversion
over equity return states is found to be positively autocorrelated and positively correlated with the spread between
implied and objective volatilities. In addition, the constant relative risk aversion (power utility) pricing kernel
is found to underestimate the value of payoffs in large negative return states.
An option hedging methodology is developed as a test of the predictive information in the empirical pricing kernel
and its associated state probability model. The results of hedging performance tests for out-of-the-money S&P500
index put options indicate that time-varying risk aversion over equity return states is an important factor affecting
option prices.
Subject category: Investment/Derivatives, Investments/Econometrics, Hedging
Classification: Empirical, theoretical
Rosenberg: (212) 998-0311 jrosenb0@stern.nyu.edu
http://www.stern.nyu.edu/~jrosenb0
Engle: (619) 534-4553 rengel@weber.ucsd.edu
http://weber.ucsd.edu/~mbacci/engle.html
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