Jumps in Rank and Expected Returns:
Introducing Varying Cross-sectional Risk
 

Gloria González-Rivera
Department of Economics
University of California, Riverside
Tae-Hwy Lee
Department of Economics
University of California, Riverside
Santosh Mishra
Department of Economics
Oregon State University
 

Abstract
We propose an extension of the meaning of volatility by introducing a measure, namely the
Varying Cross-sectional Risk (VCR), that is based on a ranking of returns. VCR is defined
as the conditional probability of a sharp jump in the position of an asset return within the
cross-sectional return distribution of the assets that constitute the market, which is represented
by the Standard and Poor’s 500 Index (SP500). We model the joint dynamics of the crosssectional
position and the asset return by analyzing (1) the marginal probability distribution of
a sharp jump in the cross-sectional position within the context of a duration model, and (2) the
probability distribution of the asset return conditional on a jump, for which we specify different
dynamics in returns depending upon whether or not a jump has taken place. As a result, the
marginal probability distribution of returns is a mixture of distributions. The performance of
our model is assessed in an out-of-sample exercise. We design a set of trading rules that are
evaluated according to their profitability and riskiness. A trading rule based on our VCR model
is dominant providing superior mean trading returns and accurate Value-at-Risk forecasts.
 

Key words: Cross-sectional position, Duration, Leptokurtosis, Momentum, Mixture of normals,
Nonlinearity, Risk, Trading rule, VaR, VCR.
 

JEL Classification: C3, C5, G0.