Jump Mis-Specification and International Portfolio Selection

Abstract

In this paper we make a distinction between systemic co-jumps and independent idiosyncratic jumps, and examine the impact of their mis-specification on asset allocation. We discuss how jumps mis-specification may lead to jumps mis-estimation and to a suboptimal portfolio. Specifically, we develop a framework where security prices have three distinct parts: a diffusion component, a systemic co-jump component, and an independent idiosyncratic jump component. In our model, the intensity and the timing of systemic co-jumps is the same across all assets whilst the timing and intensity of the idiosyncratic jump is, obviously, asset specific. The recognition that stock market returns jump together as well as separately is crucial for cross-market asset allocation policy. Univariate jump diffusion is estimated through a Markov Chain Monte Carlo (MCMC) method for weekly MSCI index returns of eleven developed and emerging markets from 1988 to 2009. The MCMC procedure produces sample paths of the latent univariate jump processes which were used in estimating the systemic and idiosyncratic jumps between series. Our results suggest that in developed markets, the omission of (idiosyncratic) jumps has little impact on portfolio selection. Developed markets are more homogeneous and their stock returns tend to jump together. The covariance matrix absorbed a large part of the linear co-jump risks producing an optimised portfolio that is not too dissimilar to one produced by a diffusion model with only the possibility for co-jumping. However, we find that, for emerging markets that tend to have idiosyncratic jumps, the assumption of co-jumps produced biased jump estimates. Losses in portfolio certainty equivalence due to this wrong jump dependence assumption are economically significant.